<caption>**Table 5**
Numerical Models of super-Eddington black hole accretion.</caption>

Source: Adapted from Kitaki et al. (2021).

<table><thead><tr><th>Paper</th><th>Method</th><th>Compton [Yes/No]</th><th>R<sub>out</sub> [R<sub>g</sub>]</th><th>R<sub>K</sub> [R<sub>g</sub>]</th><th>R<sub>qqs</sub> [R<sub>g</sub>]</th><th>R<sub>trap</sub> [R<sub>g</sub>]</th><th>M&#x0307;<sub>BH</sub> [m&#x0307;]</th><th>M&#x0307;<sub>outflow</sub> [m&#x0307;]</th></tr></thead><tbody><tr><td>Kitaki+ 21</td><td>2D-RHD</td><td>Yes</td><td>6000</td><td>4860</td><td>~1200</td><td>~540</td><td>~18</td><td>~2.4</td></tr><tr><td>Ohsuga+ 05</td><td>2D-RHD</td><td>No</td><td>1000</td><td>200</td><td>~60</td><td>~400</td><td>~260</td><td></td></tr><tr><td>Ohsuga+ 11</td><td>2D-RMHD</td><td>No</td><td>105</td><td>40</td><td>~10</td><td>~150</td><td>~100</td><td></td></tr><tr><td>Jiang+ 14</td><td>3D-RMHD</td><td>No</td><td>100</td><td>50</td><td>~40</td><td>~660</td><td>~22</td><td>~40</td></tr><tr><td>Sądowski+ 15</td><td>2D-GR-RMHD</td><td>Yes</td><td>5000</td><td>42</td><td>~70</td><td>~1280</td><td>~42</td><td>~700</td></tr><tr><td>Sądowski+ 16</td><td>3D-GR-RMHD</td><td>Yes</td><td>1000</td><td>40</td><td>~20</td><td>~520</td><td>~18</td><td>~52</td></tr><tr><td>Hashizume+ 15</td><td>2D-RHD</td><td>No</td><td>10000</td><td>200</td><td>~200</td><td>~460</td><td>~15</td><td>~50</td></tr><tr><td>Takahashi+ 16</td><td>3D-GR-RMHD</td><td>No</td><td>250</td><td>34</td><td>~20</td><td>~600</td><td>~20</td><td></td></tr><tr><td>Kitaki+ 18</td><td>2D-RHD</td><td>Yes</td><td>6000</td><td>600</td><td>~400</td><td>~840</td><td>~28</td><td>~30</td></tr><tr><td>Jiang+19<sup>a</sup></td><td>3D-RMHD</td><td>Yes</td><td>1600</td><td>80</td><td>~30</td><td>~760</td><td>~25</td><td></td></tr></tbody></table>

$R_{\text{out}}$ – radius at the outer boundary, $R_K$ – initial Keplerian radius (“circularization radius”), $R_{\text{qqs}}$ – radius, inside which a quasi-steady state is established, $R_{\text{trap}}$ – photon-trapping radius derived based on Eq. (34) (with right hand side multiplied by ~1.5), $M_{\text{BH}}$ is the accretion rate onto the black hole, $M_{\text{outflow}}$ is the outflow rate at around $R_{\text{out}}$. It is indicated whether the Compton scattering effect is taken into account or not.

<figure><img src="image_18.png" /><figcaption>**Fig. 16.** Schematic view of the structure of the super-Eddington accretion flow and associated outflow based on our numerical results. The black arrows indicate the gas motion. Kitaki et al. (2021).</figcaption></figure>

method or the M1 closure. This might explain differences between the radiative energy distribution and radiation collimation observed between the two sets of simulations. On the other hand, in Jiang et al. (2014) the inner edge of the simulation box is located outside the horizon which, as showed by McKinney and Gammie (2002) can lead to reflection of energy that would have normally been advected into the black hole.

However, as pointed out and discussed in some detail by Kitaki et al. (2021), all the simulations above suffer from one serious drawback that puts into question their relevance to direct modelling of ULXs: their circularization radii, as well as the outer radii of the quasi-steady disc region are always inside the trapping and spherization radii (see Table 5). Therefore although all numerical models predict wind plus advection dominated flow configurations it remains to be seen where such features occur, and what their properties are in real systems with, say, $R_{\text{out}} > 10^4 R_g$ and $R_{\text{sph}} > 750 R_g$ (corresponding to $R_{\text{out}} > 3 \times 10^{10}$ cm for a $10 M_{\odot}$ black hole and $\dot{m} > 10$, respectively) (see Fig. 17).

Kitaki et al. (2021) have made a substantial contribution towards reaching this objective (see first line of Table 5). They performed simulations with an outer radius of $6000 R_g$ and circularization radius $4860 R_g$. Their calculations achieved a quasi-stationary state inside $R_{\text{qqs}} \approx 1200 R_g$, a radius 3 to 120 times larger than in previous simulations of super-Eddington accretion flows. Kitaki et al. (2021) used a 2D R-RH code, with a viscosity parameter $\alpha = 0.1$. The black hole mass is $10 M_{\odot}$ and a Paczyński-Wiita “potential” is used to describe massive-particle motions. Matter is continuously added at $R_{\text{out}}$ at a rate $\dot{m} = 70$, with specific angular momentum $3.12 \times 10^{18} \text{ cm}^2 \text{ s}^{-1}$. All matter arriving at $R_{\text{in}} = 4 R_g$ is absorbed.

The structure obtained by Kitaki et al. (2021) is schematically shown in Fig. 16. The accretion rate onto the black hole is $\dot{m}_{\text{BH}} = 18$. The flow forms a well-delimited disc structure with a surface defined as the loci at which the radiation force balances the gravity in the radial direction. Near the black hole and up to $R \sim R_{\text{trap}}$ the disc height $H$ is proportional to $H (H/R \sim 1)$, above this radius it is constant

<footnote>aIn these simulations the black-hole mass is $5 \times 10^8 M_{\odot}$.</footnote>
<figure><img src="image_19.png" /><figcaption>Fig. 17. Stream lines around a (1.4 M⊙) neutron star (left) and a (10 M⊙) black hole (right). Red (blue) lines indicate that the radial velocity is in the positive (negative) direction.</figcaption></figure>

Source: From Takahashi et al. (2018).

$H \sim 22-34 \dot{m}_{BH} R_g$. The trapping radius $R_{trap} \sim 50 \dot{m}_{BH} R_g$. This means, as expected from simple models (Section 3.2), that for $R \lesssim R_{trap}$ the flow is advection dominated, while at larger radii it behaves like a radiation-pressure dominated, Shakura-Sunyaev-type accretion disc. Such discs should be thermally unstable, but this does not seem to occur in Kitaki et al. (2021) simulations despite the calculation time amply allowing the instability to develop. The reasons for this remain unclear (see, however, Jiang et al., 2013) but are worth investigating.

Closer to the black hole, at $R_{lau} \sim 26 \dot{m}_{BH} R_g$, an outflow is produced, but the expelled gas is not able to reach infinity and falls back on to the disc. Only at $R_{lau}^\infty \sim 15 \dot{m}_{BH} R_g$ is a real outflow (wind) blown out. The formula for $R_{lau}^\infty$ has the same form as that for $R_{sph}$ (Eq. (30)) but with $\dot{m}_{BH}$ instead of $\dot{m}$ which in Eq. (30) corresponds to the rate at which matter is fed to the outer radius (in the simulations under discussion, $\dot{m} = 70$, while $\dot{m}_{BH} = 18$). We discuss this difference later in this section. Finally, in the regions closest to the black hole, below $R_{inflow} \sim 4.4 \dot{m}_{BH} R_g$, most of the gas flows in at a rate $\dot{m} = 18$, with some weak outflow $\dot{m}_{outf} \sim 1.3$.

The Kitaki et al. (2021) solution is fully consistent with what one expects from an accretion–launched wind. The wind speed is $v \sim 0.1c$, and $L_{mech} \approx 0.05-0.08 L_{rad}$, with $L_{rad} = L_X \approx 2-3 L_{Edd}$, so $L_{mech} \approx 0.1-0.24 L_{Edd}$. The launch radius of the wind is $R_{lau} \sim 100 R_g$, in agreement with the wind speed $v \sim (2GM/R_{lau})^{1/2}$. This gives a wind momentum rate $\dot{M}_{out} v = (2/v) L_{mech} \sim 20 L_{mech}/c \sim L_{rad}/c$ as one would expect when the mass supply is not hyper-Eddington (here it is $\sim \dot{m} = 18$). These values are similar to analytic estimates (King and Pounds, 2003) for momentum-driven winds.

This solution suggests that for black-hole accretors, below $R \sim 1000 R_g$, most of the mildly ($\dot{m} \sim \text{few} \times 10$) super-Eddington mass accretion is simply swallowed, as predicted by slim-disc models. The outflow to accretion ratio $\dot{m}_{outflow}/\dot{m}_{BH} - 0.14$ is much lower than in previous simulations which Kitaki et al. (2021) attribute to the sizes of the simulated flows, theirs being much larger than in the preceding calculations, thus avoiding having the whole simulated domain in the region where the flow is puffed-up from the start. But we note that although $R_{qss} \sim 1200 R_g$ is 20 to 30 times larger than the corresponding radius in R-GR-MHD calculations, it is still “only” $1.8 \times 10^9 \text{cm}$, well

inside the circularization radius. The net accretion flow for $R \lesssim R_{qss}$ is roughly constant ($\dot{m} \sim 18$) while the mass inflow rate decreases from $\dot{m} \sim 30$ at $R \approx R_{qss}$ to $\dot{m} = 18$ for $R \sim 40 R_g$ ($\dot{m} \sim R^{-0.2}$), but it is not clear what happens above $1200 R_g$, where the simulated configuration is not relaxed.

For example, for $R > 1202 R_g$, the gas pressure dominates over radiation pressure and the disc should be geometrically thin (see Eq. (25) with $\dot{m} = 70$). This should reduce the outflows, thus making the whole configuration potentially inconsistent. It seems that we are still some distance from having a complete description of the whole picture of super-Eddington accretion onto black holes.

Indeed, recently, Hu et al. (2022) simulated super-Eddington accretion onto a $10^3 M_\odot$ black hole. The physical outer radius of their simulation domain is $R = 1500 R_g$, four times shorter then in Kitaki et al. (2021). In their case, however, the steady-state radius $R_{qss} = 1500 R_g$, slightly longer than in Kitaki et al. (2018). The flows they study settle down to a quasi-steady state in millions of the orbital timescale, which in their case corresponds to the viscous time at $\sim 1000 R_g$ (they take $\alpha = 0.01$). In their case $M_{in} \propto r^p$ with $p \sim 0.5-0.7$ and contrary to the Kitaki et al. (2021) only a small fraction of the inflowing matter feeds the central black hole. Indeed, their solutions can be represented as

$$ 
\begin{aligned}
\dot{M}_{BH} &= 17.1 \dot{M}_{Edd} \left( \frac{\dot{m}_0}{300} \right)^{0.5} \\
\dot{P}_{out} &= 0.51c \dot{M}_{Edd} \left( \frac{\dot{m}_0}{300} \right)^{0.5} \\
\beta &= 17.5 \left( \frac{\dot{m}_0}{300} \right)^{0.5} - 1
\end{aligned}
\qquad (92) $$

and the wind velocity is

$$ \langle v_{wind} \rangle = 1.7 \times 10^{-3} c \left( \frac{\dot{m}_0}{300} \right)^{-0.5}, \qquad (93) $$

where $\beta = \dot{M}_{out}/\dot{M}_{in}$ is the wind loading fraction. It is only $\sim 0.13$ in Kitaki et al. (2021) but $\sim 20$ in the model of Hu et al. (2022), so that even in the case of a black hole, advection does not play a significant role when accretion rate are very strongly super-Eddington. Therefore the main difference between the two numerical models is that in Kitaki et al. (2021) most of the outflowing gas fails to escape from the outer boundary and falls back onto the disc, while in Hu et al. (2022) most matter is lost in the wind. Hu et al. (2022) attribute the large differences between the two approaches to several factors, numerical and physical. First, Kitaki et al. (2021) impose in their computational domain equatorial mirror-symmetry of the accretion flow across the equatorial plane. It seems that this imposed symmetry tends to suppress global convective motion that crosses the equator and is known to produce outflows coherently through the equator rather than the polar regions (see Li et al., 2013). The second reason would be that Kitaki et al. (2021) assume a viscous parameter of $\alpha = 0.1$ (Hu et al., 2022, assume $\alpha = 0.01$) which is apparently known to cease convective/turbulent motion of advection dominated flows and thus to reduce the outflow rate (see, e.g. Inayoshi et al., 2018). These differences do not necessarily favour the model with stronger outflows. For example, it seems that high values of the viscosity parameter $\alpha > 0.1$ are appropriate to the description of high-accretion rate flows (Tetarenko et al., 2018). Only a self-consistent calculation with a MRI-determined (anomal) viscosity could decide if numerical models can reproduce the mechanical power observed in some ULXs. In the most recent paper of the Ohsuga group (Yoshioka et al., 2022) it is concluded that the fraction of the failed outflow decreases with the decrease of $\dot{M}_{in}$. They leave the comparison with the Hu et al. (2022) simulation for a future paper. What's more important, their simulations confirm the effect of radiation beaming at high accretion rates since they found that “the higher $\dot{M}_{in}$ is, the more vertically inflated becomes the disk surface, which makes radiation fields more confined in the region around the rotation axis”.
An interesting result of most numerical simulations is that they do not see any evidence of the photon bubbles proposed as a solution of the super-Eddington luminosity problem by Begelman (2002). When such bubbles do appear, they play no significant role in super-Eddington accretion flows (see, e.g., Jiang et al., 2014).

We are even further away from understanding supercritical accretion through numerical simulation when the accretor is a rotating, magnetized neutron star, as discussed in the next section.

### 3.8.2. Numerical simulations relevant to PULXs

The difficulty of simulating super-Eddington accretion on to rotating, magnetized neutron stars is probably best illustrated by the fact that until now only four papers have dealt with the problem: Takahashi and Ohsuga (2017), Takahashi et al. (2018), Abarca et al. (2018, 2021). The maximum dipole field strength considered is ~ $10^{10}$ G (in two cases $B=0$ G), and none of the simulations describes a rotating accretor with a hard surface.

All attempts to describe super-Eddington accretion on to neutron stars use GRRMHD codes, similar to, or inspired by, the codes used in the description of black-hole accretion, described above. There are, however, two further difficulties that must be overcome when such codes are applied to magnetized neutron stars. First, it is not easy to describe in the same code both magnetically-dominated flows with a force-free character and the “normal” properties expected from the (GRR)MHD equations. This difficulty has been partially removed by Parfrey and Tchekhovskoy (2017).

The second difficulty is in fixing the inner boundary conditions, i.e. the physical properties of the accreting matter at the neutron star surface. In contrast to black holes, whose surface is always fully absorbing independently of what – and how much – is falling on to it, the properties of matter arriving at the neutron-star surface depend on the magnetic field strength and the accretion rate (see Abarca et al., 2021, and references therein). As in most black-hole simulations, limits on the available computational time restrict the range of radii for which the solutions relax to quasi-stationarity; in all simulations $R_{QSS} \lesssim 50R_g$, while the spherization radius is $R_{sph} \lesssim 500R_g$ and the computational domain extends up to $1000R_g$.

Takahashi et al. (2018) and Abarca et al. (2018) consider the case of super-Eddington ($\dot{m} \sim 10$) accretion onto a non-magnetic and non-rotating neutron star with a reflective surface, and compare it with the case of accretion on to a black hole. They both observe more powerful outflows in the neutron-star case and Takahashi et al. (2018) find that for a neutron-star accretor, the accretion flow inside $R \lesssim 10R_g$ (in their case $R_{QSS} \sim 10R_g$) corresponds to the SS73 windy solution (Section 3.3), whereas in the black-hole case the flow is advection dominated.<fnref n="13" /> The strong wind blown out from the vicinity of a super-Eddington accreting neutron star is very optically thick to electron scattering “which would lead to the obscuring of any NS pulsations observed in corresponding ultraluminous X-ray sources” (Abarca et al., 2018). Since the model of a non-rotating and unmagnetized neutron star would produce no pulses in any case, this is not a big drawback, but stresses that the presence of optically-thick outflows from super-Eddington accreting neutron stars cannot be neglected when describing their X-ray emission.

Abarca et al. (2021) performed a 2D axisymmetric radiative GRMHD simulation of accretion onto a neutron star with a $2 \times 10^{10}$ G dipolar magnetic field. The combination of the hard surface and confinement of the gas into an accretion column near the star, allows the flow to release radiative energy at a rate of several times the Eddington limit. They compared their results to the KLK17 model and found a larger beaming

intensity, but they believe that post-processing would show a less intensely beamed distribution of radiation at infinity. They also note that they do not model the same system as considered in KLK17 (e.g. they have super-Eddington accretion rates in the accretion column). In their case the distance between the Alfvén radius and spherization radius is large, and their star is non-rotating. This paper reveals the difficulties current numerical simulations still face in modelling real PULXs.

In all simulations, the estimated minimum values of the inverse of the beaming parameter $b$ (maximum beaming) obtained from various models range from $1/b = 1/30-1/20 \approx 0.033-0.05$, which compares quite well with the range of values $b = 0.009-0.6$ from Table 3 in Section 3.7.1. i.e. with the results of the KLK17 model.

The simulations of super-Eddington accretion on to neutron stars thus provide strong support for the assumptions of the KLK17 PULX model, i.e. that the accretion flow inside the spherization radius is well described by the SS73 windy model, and that the X-ray luminosity is beamed. Although the simulations assume weakly magnetized and non-rotating neutron stars, their basic results – weak advection unlike in the black-hole case, requiring strong optically thick outflows, probably hold for stronger fields and faster rotation of the accretor.

### 3.8.3. Numerical simulations of PULX accretion columns

Numerical models of super-Eddington accretion on to a strongly magnetized neutron star are given by Kawashima et al. (2016, hereafter K16) and Kawashima and Ohsuga (2020, hereafter K20). The simulations describe the last part of the accretion flow, where the infalling plasma forms a column above the neutron star surface. In both papers, the accretion column is represented by a truncated cone with a base (“polecap”) occupying a fraction 0.07 of the stellar surface. Since the method used is radiation hydrodynamics, the value of the magnetic field does not appear explicitly, but in K16 it is estimated to be ~ $10^{10}$ G, while in K20 the magnetic field strength is $\gtrsim 10^{12}$ G. In the first case, the plasma is allowed to move transversely, in the second, the motion of matter is restricted to the radial directions. In K16 the initial uniform density in the column gives a time-averaged accretion rate of $\dot{m} = 50$; K20 uses the same initial set-up but also a lower-density model, giving $\dot{m} = 3$. In both types of model, a radiative shock forms above the neutron-star surface (fixed at 10 km) at a height ~ 3 km for the “weak magnetic field” and at ~ 10 km in the case where the accreting matter motion is restricted to the radial direction. In the “weak-field” simulations, practically all the radiation is released below the shock and radiated sideways. The apparent luminosity is highly anisotropic; it can reach ~ 50 $L_{Edd}$ sideways, but is close to Eddington vertically along the accretion column. In contrast to the “weak-field” case, where the radiation field below the shock is homogenized by circular motions of radiation bubbles, the “strong-field” simulations show that matter is accreted along the side walls of hollow cones while matter inside the cones is blown away by radiation. For $\dot{m} = 3$, only one hollow cone forms, while for very high accretion rates ($\dot{m} = 50$), the column contains three such structures. Also in this case the apparent luminosity is highly anisotropic, radiation still managing to get out mainly sideways, but radiated from a larger surface than in the “weak-field” case. The sideways luminosity can reach $30 L_{Edd}$.

Using the K16 model, Inoue et al. (2020) calculated the light-curves produced by such an accretion column, taking into account general-relativistic effects on light propagation near the neutron-star surface. The pulses they obtain are quasi-sinusoidal. They obtain a high pulsed fraction of the emitted light, from 5% up to 50%, depending on the magnetic and observational inclination angles. However, a narrow magnetic column for a highly super-Eddington accretion rate, and field of ~ $10^{10}$ G does not seem to give the best representation of a real PULX since high accretion rates and low magnetic fields should instead favour wide accretion columns.

The papers K16 and K20 are important contributions to the understanding of supercritical accretion in strong magnetic fields, but it is unlikely that they correspond to the accretion structure of real PULXs.

<footnote n="13">¹³ This clear physical difference between accretion flows on to compact objects which have, or do not have, surfaces, makes the advection-dominated solutions of Chashkina et al. (2019) rather unrealistic.</footnote>
<figure><img src="image_20.png" /><figcaption>Fig. 18. Schematic picture explaining energy flow from gas (potential energy) to outgoing radiation within a supercritical accretion column. The blue arrows represent the energy flow carried by gas: their length and width are drawn in proportion to the kinetic energy flux and the mass accretion rates, respectively, whereas the red arrows represent energy flow carried by radiation and their widths are drawn in proportion to the radiation energy flux (Kawashima et al., 2016).</figcaption></figure>

The accretion flow in these systems probably does not form a column extending to $2 \times 10^8$ cm (~200 neutron-star radii) above the neutron star surface. Since PULXs are binary systems, matter transferred from the neutron-star's companion forms a disc extending down to a magnetosphere where the pressure of the accreting matter is comparable to the magnetic pressure. The size of the magnetosphere will determine the angular size of the column, which will vary with magnetic-field intensity, differing by two orders of magnitude. For the parameters of K16, the magnetospheric radius is close to the neutron star surface at ~$3 \times 10^6$ cm (see Eq. (64)) and for the K20 set-up $R_M < 10^8$ cm. What is most important, however, is that accretion within the magnetosphere is most likely highly dissipative, since the flow along fieldlines requires a highly supersonic flow to bend and shock, while in K16 and K20, the first shock occurs very near the neutron-star surface, because in the simulations (different from the schematic view of Fig. 18) the fieldlines are straight. By necessity, the K16 and K20 simulate only the last part of the PULX accretion flow and they assume that it arrives at the magnetosphere at a super-Eddington rate, which is rather unlikely in reality (Takahashi et al., 2018).

### 3.9. PULXs as magnetars in binary systems

The discovery that ULX M82 X-2, with an apparent luminosity $L \approx 1.8 \times 10^{40}$ erg s$^{-1}$, is a pulsar with a coherent periodicity $P = 1.37$ s (Bachetti et al., 2014), raised the possibility that its apparent super-Eddington luminosity might be intrinsic (cf Tong, 2015; Ekşi et al., 2015; Dall'Osso et al., 2015; Mushtukov et al., 2015a). If the strength of its magnetic field is magnetar-like ($B \sim 10^{14}$ G), the reduction in electron scattering opacity for some directions and polarizations can be quite substantial.

At first sight, this idea is similar to the one motivating Paczynski (1992) to explain the luminosity $L \sim 10^4 L_{Edd}$ observed in the soft-gamma repeater (SGR), GB 790305 ("the 5 March event"), by the presence of a magnetic field $B \approx 3 \times 10^{14}$ G. In a very strong magnetic field, the Thomson and Compton scattering cross-sections are strongly reduced for photons with energies $E_\gamma$ much lower than the energy corresponding to cyclotron frequency $E_{cyc} = 11.6 B_{12}$ keV, where $B_{12}10^{12}$ G = B (Canuto et al., 1971). From Herold (1979) one has

$$ \frac{\sigma_1}{\sigma_T} \approx \sin^2 \theta + \left( \frac{E_\gamma}{E_{cyc}} \right)^2 \cos^2 \theta \quad (94) $$

$$ \frac{\sigma_2}{\sigma_T} \approx \left( \frac{E_\gamma}{E_{cyc}} \right)^2, \quad \text{for} \quad \frac{E_\gamma}{E_{cyc}} \ll 1, \qquad (95) $$

where indices 1 and 2 correspond to the two linear photon polarisations, and $\theta$ is the angle between the directions of the magnetic field and light propagation. Paczynski (1992) gives an approximate relation between the “new” critical luminosity and the Eddington luminosity, defined through the Rosseland mean opacity:

$$ \frac{L_{\text{crit}}}{L_{\text{Edd}}} \approx 2B_{12}^{4/3} \left( \frac{g}{2 \times 10^{14} \text{ cm s}^{-2}} \right)^{-1/3}, \qquad (96) $$

where $g = GM/R^2$, when $L_{\text{crit}} \gg L_{\text{Edd}}$. This critical luminosity is of course only approximate because it is not properly integrated over angles, but estimates of the Rosseland mean opacities vary with angle only by a factor two (Paczynski, 1992).

From Eq. (96), for a $1.4 M_\odot$ neutron star, a sub-critical luminosity $L \lesssim 0.1 L_{\text{crit}}$ implies

$$ L \lesssim 2 \times 10^{40} \left( \frac{B}{10^{14} \text{ G}} \right)^{4/3} \text{ erg s}^{-1}, \qquad (97) $$

so that explaining PULXs with $L > 10^{40}$ erg s$^{-1}$ assuming isotropic radiation, requires magnetic field strengths that would be considered extreme, even among magnetars.

In PULX models by Tong (2015), Dall'Osso et al. (2015), Ekşi et al. (2015), Chashkina et al. (2017), the fields are in the range ~$3 \times 10^{13}-6 \times 10^{16}$ G (the last value considered by the authors to be “rather unphysical”), so that the critical luminosities corresponding to the first three PULXs discovered put them safely into the sub-critical luminosity regime, even with a magnetic moment derived by magnetic torque considerations.

But there is a fundamental difference between SGRs and PULXs: SGRs are powered by magnetic energy (Duncan and Thompson, 1992), while the luminosity of PULXs comes from accretion. For SGRs the magnetic field allowing $L \approx 10^4 L_{Edd}$ is consistent with pulsar slowdown and the required magnetic energy. There is no known alternative to magnetar-strength fields in SGRs and anomalous X-ray pulsars, and there is so far no observational evidence against the presence of fields with these strengths.

This is not true of the magnetar hypothesis for PULXs. First, no magnetar is observed to be a member of a binary system. All ~30 known magnetars (or “candidate” magnetars) are isolated neutron stars (Olausen and Kaspi, 2014). Conversely, all neutron stars in X-ray binaries are observed to have magnetic field strengths < $10^{13}$ G, below the magnetar range (see, e.g., Revnivtsev and Mereghetti, 2016).

The superstrong magnetic field in magnetars is thought to be formed in a process which destroys (or merges) the binary, of which its progenitor was a member (Popov, 2016). This would explain their apparent absence from binary systems. Magnetars are supposed to form through neutron-star mergers (e.g., Giacomazzo and Perna, 2013; Piro et al., 2017) or in type Ibc supernova outbursts in massive binaries. The first mechanism obviously produces a single object. In the second, the superluminous supernovae disrupt the binary and produce an isolated magnetar, as demonstrated by the magnetar CXOU J1647-45 in the young massive cluster Westerlund 1 (Clark et al., 2014).

We note that “most of theoretical considerations do not favour even existence, not speaking about active decay, of magnetar-scale fields in neutron stars older than $10^6$ yrs” (Popov, 2022).

These considerations make the presence of rapidly rotating, strongly accreting magnetars in binary systems highly unlikely. Their presence in ULXs would evidently require a cosmic conspiracy.

### 3.10. ULX populations

The beaming formula (55) allows one to study the populations of disc-wind beamed ULXs in galaxies. If the host galaxies have space density $n_g$ Mpc$^{-3}$, and each host contains N ULXs with randomly
oriented beams, one would need to search through ~ 1/Nb galaxies, occupying a space volume ~ 1/n_g Nb, to be sure of being in the beam of one ULX. Then the nearest ULX must be at a distance

$$D_{\min} \sim \left( \frac{3}{4\pi n_g N b} \right)^{1/3} \sim 0.7(n_g N)^{-1/3} \dot{m}_1^{2/3} \text{ Mpc} \quad (98)$$

where $\dot{m}_1 = \dot{m}/10$, and has apparent (isotropic) luminosity

$$L = 2.2 \times 10^{39} m_* \dot{m}_1^2 \text{ erg s}^{-1} \quad (99)$$

where $m_* = m/(10 M_\odot)$. The scalings $m_*, \dot{m}_1$ are appropriate for black holes of mass ~ 10 M_\odot, so by the argument following Eq. (58) the luminosity normalization here would be $2.2 \times 10^{40} \text{ erg s}^{-1}$ for neutron-star ULXs. These relations can be used to show that the ULX luminosity function of the Local Group is consistent with the idea that beamed ULXs are the evolutionary stage following the standard high-mass X-ray binary phase (cf Mainieri et al., 2010).

### 3.10.1. Pseudoblazars?

The beaming described by (55) potentially allows one to see suitably-oriented ULXs out to very large distances. The extreme object SS433 has $\dot{m} \sim 300-10^4$ (King et al., 2000; Begelman et al., 2006, see Section 3.14.1). With $\dot{m} = 10^4 \dot{m}_4$, the nearest object of this kind which we would observe within the beam is at a distance

$$D_{\min} \sim \left( \frac{3}{4\pi n_g N b} \right)^{1/3} \sim 660 N^{-1/3} \dot{m}_4^{2/3} \text{ Mpc} \quad (100)$$

where we have taken $n_g \sim 0.02 \text{ Mpc}^{-3}$ as appropriate for $L^*$ galaxies. The apparent isotropic luminosity of such an object would be

$$L_{\text{sph}} = 2.2 \times 10^{45} m_* \dot{m}_4^2 \text{ erg s}^{-1}. \quad (101)$$

This distance and apparent luminosity are typical for active galactic nuclei (AGN), so without further information one could not easily pick out a bright ULX like this from a sample of observed AGN. But unlike a genuine AGN, there is no reason to suppose that a given ULX lies in the nucleus of its host galaxy. There are possible candidates for such systems: the BL Lac system PKS 1413+135 (Perlman et al., 2002) has distance $D \simeq 1$ Gpc and isotropic luminosity ~ $10^{44} \text{ erg s}^{-1}$, but lies at $13 \pm 4$ mas from the centre of the host galaxy, and HXL-1 could be a system of this type (cf Section 2.7). Of course it is difficult to exclude the possibility that this system may lie at the nucleus of a fainter line-of-sight galaxy.

### 3.11. ULXs and binary stellar evolution

Sections 3.6-3.8 above have shown how the phenomena characterizing ULXs arise, in many cases, from strongly super-Eddington mass transfer in binaries containing compact objects (white dwarfs, neutron stars or black holes) which have reached the end of their stellar evolution. We should now ask what causes these very high mass transfer rates. To do this we need to consider the evolution of binary systems where one of the stars is compact (a black hole, neutron star, or white dwarf) and the companion star transfers mass to it, powering accretion. The rate of mass transfer is determined by the evolution, both of the companion star, and of the binary orbit, as mass transfer in general changes this. Dissipation in the mass transfer process generally makes the binary orbit circularize.

Kepler's laws give the orbital angular momentum of a circular binary system consisting of stars of mass $M_1, M_2$ as

$$J = M_1 M_2 \left( \frac{Ga}{M} \right)^{1/2}, \quad (102)$$

where $M = M_1 + M_2$ is the total binary mass, and $a$ is the orbital separation. We take star 1 as the compact object, and star 2 as an extended star. In a high-mass X-ray binary (HMXB, star 2 is hot, and loses mass in a wind. The X-rays result when some of this wind is captured by the compact star (a neutron star or black hole). But as the

extended star 2 approaches the end of core hydrogen-burning it begins to expand. Eventually its radius $R_2$ fills its Roche lobe

$$R_L = f(q)a \quad (103)$$

(where $q = M_2/M_1$ is the binary mass ratio, and $f(q) < 1$ is a slowly-varying function of $q$). The star begins to transfer mass through the inner Lagrange point, the saddle point of the combined gravitational-centrifugal, Roche pseudopotential between the two stars. It is generally a good approximation to assume that all the mass lost by star 2 is accreted by the compact star 1, and that the orbital angular momentum $J$ is conserved in this process. Then $J = 0, \dot{M}_1 + \dot{M}_2 = \dot{M} = 0$, and logarithmic differentiation of Eq. (102) gives

$$\frac{\dot{a}}{a} = 2 \left( \frac{-\dot{M}_2}{M_2} \right) \left( 1 - \frac{M_2}{M_1} \right) \quad (104)$$

Since $-\dot{M}_2 > 0$, we see that if the extended, mass-losing star is more massive than the compact star, the effect of mass transfer is to shrink the binary separation ($\dot{a} < 0$). As $f(q)$ varies only weakly with mass ratio $q$, $R_L$ also shrinks, tending to increase the rate of mass transfer. The result is that mass transfer from the more massive to the less massive star is self-sustaining, at least for a time.

But there is a limit to this process. The outermost stellar gas – above the saddle point of the Roche potential – is lost on a dynamical timescale, and gas from below flows towards the saddle point on the same timescale, trying to refill the Roche lobe. But this gas is not now in thermal equilibrium because its rapid rise means that it retains the same specific entropy it had when deeper in the star. In stars with a radiative envelope (typically, blue stars with effective temperatures $T_{\text{eff}} \gtrsim 10^4$ K), the equilibrium entropy increases outwards, so the new gas has too little entropy for its new position. This means that it is denser and cooler than the gas it replaces, making the radius of this part of the star smaller, and reducing the mass transfer rate. To reach thermal equilibrium, this gas must absorb some heat from the stellar radiation field, on a thermal timescale. In doing so it expands, returning this part of the star to the equilibrium radius for its new (slightly smaller) mass.<fnref n="14" />

The argument above shows that mass transfer from a more massive radiative companion cannot happen on a timescale shorter than the star's thermal timescale, $t_{\text{th}} \sim GM_2^2/R_2L_2$ (where $R_2, L_2$ are the star's radius and luminosity respectively). But this is usually much shorter than the nuclear timescale in stars of mass a few $M_\odot$, and we find values $-\dot{M}_2 \sim M_2/t_{\text{th}}$ as large as ~ $10^{-7}-10^{-4} M_\odot \text{ yr}^{-1}$, depending on the stellar mass $M_2$.

Rates like this are far higher than the value $\dot{M}_{\text{Edd}}$ defined above, which would give the Eddington luminosity if it could be accreted, and so it is very likely that the super-Eddington excess is expelled.

As we mentioned in the Introduction and Section 3.6, the neutron star in the long-period ($P = 9.84$ d) low-mass X-ray binary Cyg X-2, appears to have expelled most of the mass transferred to it in this way. The distinctive feature of this system is the unusual state of the companion star. Combining spectroscopic information, photometry of the ellipsoidal variation of the companion, and the geometry of the Roche potential, King and Ritter (1999) showed that this star had a low mass $M_2 \approx 0.5-0.7 M_\odot$, and yet a large radius ($R_2 \approx 7 R_\odot$) and very high luminosity ($L_2 \approx 150 L_\odot$). This is just what one expects at the end of an episode of thermal-timescale mass loss: the hot central region of what was initially a much more massive star has been exposed, and has had no time to cool. The evolution followed by Cyg X-2 is called early massive Case B, in the terminology of Kippenhahn and Weigert (1967).

<footnote n="14">¹⁴ If the star instead has a convective envelope, and so constant specific entropy, mass transfer can reach very high (near-dynamical) values, and the system develops a deep common envelope. This may lead to a merger of the two stars. King and Begelman (1999) show that this is very unlikely to happen with a radiative envelope, even for transfer rates as high as ~ $10^{-4} M_\odot \text{ yr}^{-1}$.</footnote>
The most important feature of this evolution is that the neutron star accretor has evidently gained almost none of the ~3 M☉ transferred to it by the companion: its current mass is only $1.78 \pm 0.3$ M☉. This expulsion cannot have come from common-envelope evolution – the orbital binding energy released in shrinking the binary to the separation given by the current period of almost 10 days is far too small to expel any matter. This leaves only accretion energy – the accretion disc around the neutron star must have expelled most of the transferred mass. This is just the process discussed by Shakura and Sunyaev (1973), and summarized in Section 3.3. As we discuss in Sections 3.8 and 3.14, it leads to the production of a quasi-spherical wind with typical outflow velocity $v \sim 0.1c$, with open funnels along the disc axes which collimate a large fraction of the accretion energy released as radiation. In this picture, ULXs are the evolutionary stage following the wind-fed HMXB phase, once the massive companion star fills its Roche lobe. This seems particularly likely for the pulsing PULXs, which contain neutron stars very similar to those in HMXBs.

Although thermal-timescale mass transfer is very probably the cause of ULX behaviour in many cases, it is not the only way to make a ULX. Evidently any process that produces a significantly super-Eddington mass transfer rate can do this. We have already mentioned that some Be X-ray binary systems become ULXs from time to time, because of dynamical effects on the Be-star disc. Three other possible ways involve mass transfer on the nuclear timescale of a massive donor (Rappaport et al., 2005), transient outbursts involving the thermal-viscous disc instability (King, 2002; Hameury and Lasota, 2020, see Section 3.16), and gravitational-wave driven mass transfer from a white dwarf onto a neutron star (King, 2011) – a so-called ultra-compact binary (UCB). UCBs are often found in globular clusters (see Dage et al., 2021, and references therein), where they are formed by dynamical capture, so these sources offer a possible explanation for ULXs sometimes claimed in elliptical galaxies. We will discuss other evolutionary paths, especially for weak ($L_X \approx 3 \times 10^{39}$ erg s⁻¹) ULXs in Section 3.13.

### 3.12. 'Super-Eddington Accretion'

These possibilities illustrate that ULXs are likely to be binaries containing a compact accretor in an epoch of strongly super-Eddington mass transfer. It is worth emphasizing that the commonly used phrase 'super-Eddington accretion' is highly ambiguous, and a frequent cause of confusion. As the example of Cyg X-2 shows, the accretors in ULXs do not gain mass at significantly super-Eddington rates: it is the mass *supply rate* which is super-Eddington, not the accretion. Accordingly, the phrase 'super-Eddington mass supply' is strongly preferable.

### 3.13. Population syntheses

Population synthesis of ULXs was first performed by Rappaport et al. (2005) who showed that the population of ULXs in spiral galaxies can be explained by short phases of high mass transfer (with nuclear or thermal timescales) in black-hole plus evolved-star binaries. However, they neglected the pre-supernova evolution phase in their calculations and did not take into account other types of binaries, such as systems containing neutron-star accretors, or evolved donors. Their study was expanded by Madhusudhan et al. (2008) who completed it by predicting the observational properties of the ULX population. Linden et al. (2010) used the StarTrack population synthesis code (Belczynski et al., 2002, 2008) to show that the bulk of ULXs can be interpreted as the high-luminosity tail of high-mass X-ray binaries. Neutron-star accretors were included in population studies of ULXs only after the discovery of PULXs.

Wiktorowicz et al. (2015) performed a proof-of-concept study where they showed that any ULX, including the most luminous ones, and neutron-star systems, can be a short-lived phase in the life of a binary star. The detection of double compact object mergers (Abbott

et al., 2016) triggered investigations of the connection between binary compact objects and ULXs (e.g., Finke and Razzaque, 2017; Marchant et al., 2017; Klencki et al., 2018).

A problem encountered when performing ULX population synthesis is the unfortunate choice of the threshold ULX luminosity at $10^{39}$ erg s⁻¹, because it fails to separate “standard” X-ray binaries (XRBs) from “generic” ULXs. At least five transient Galactic XRBs reach luminosities $> 10^{39}$ erg s⁻¹ (Tetarenko et al., 2016). Middleton et al. (2015a) suggested that one should take $3 \times 10^{39}$ erg s⁻¹ as the minimum luminosity defining ULXs whose nature is “contentious”. The idea was to ensure that if the accretor was a black hole (BH), the apparent luminosity would be super-Eddington. But we now know that stellar evolution can produce black holes with masses $\gtrsim 30$ M☉ (Belczynski et al., 2010; Abbott et al., 2016), up to $50$ M☉ under favourable conditions (see e.g. Belczynski 2020; the fact that the maximum value of black-hole masses observed in X-ray binaries is $\sim 20$ M☉ follows from the limited range of metallicities scanned by X-ray observations (Olejak et al., 2020)). So only sources with luminosities $\gtrsim 6 \times 10^{39}$ erg s⁻¹ qualify as (apparently) super-Eddington for a BH resulting from stellar evolution. BH.<fnref n="15" /> The current outdated but default definition of ULXs as $L \gtrsim 10^{39}$ erg s⁻¹ tends to coerce population syntheses to use it, at the cost of producing “excesses” of sources with luminosities which in most cases are actually sub-Eddington.

Existing population syntheses do not include Be-X systems, and until recently they considered only Roche-lobe overflowing (RLOF) companions of the compact accretor, so excluding wind-fed systems. The second omission was corrected by Wiktorowicz et al. (2021), and wind-accreting ULXs will be discussed below, but there is not much hope that the difficulties inherent in the first (Be-X) will be overcome any time soon. Although current models of Be stars allow simple modelling of their discs at radii far from the stellar surface, they also contain hidden assumptions that are not physically plausible (Nixon and Pringle, 2020). If the model for Be-star discs proposed by the latter authors (the disc material originating from small-scale magnetic flaring events on the stellar surface) is correct, it will be problematic to incorporate it in a population-synthesis code.

Wiktorowicz et al. (2017, 2019) performed comprehensive simulations of ULX populations by using the StarTrack population synthesis code (Belczynski et al., 2002, 2008) with significant updates described in Dominik et al. (2012), Wiktorowicz et al. (2014). They simulate the evolution of $2 \times 10^7$ binary systems for every model and scale the results to a Milky-Way equivalent galaxy ($M_{MWEG} = 6 \times 10^{10}$ M☉; Licquia and Newman, 2015). Two star formation cases are considered: a constant rate of $6.0$ M☉ yr⁻¹ for 10 Gyr, and $600$ M☉ yr⁻¹ in bursts of star-formation lasting 100 Myr). They consider three metallicity prescriptions: solar ($Z_{\odot}$), 10% of solar ($Z_{\odot}/10$), and 1% of solar ($Z_{\odot}/100$). The fiducial accretion model for ULX evolution in this study assumes the SS73 windy solution and beaming described by Eq. (55), with a saturation limit at $\dot{m} = 150$. For higher mass accretion rates, the beaming is assumed to be constant and equal to $b \approx 3.2 \times 10^{-3}$ ($\theta \approx 9^\circ$). For comparison, seven other models with different accretion and/or beaming configurations are considered. In general, the results do not depend strongly on the assumptions about the accretion mode or the beaming model, except for the case where beaming is assumed to be constant ($b = 0.1$) which, by lowering the ULX luminosity threshold, results in neutron-star ULX always dominating the population at late times.

It is known from observations, that ULXs are often associated with low metallicity environments (e.g. Pakull and Mirioni, 2002; Soria et al., 2005; Luangtip et al., 2015; Mapelli et al., 2010) Massive black holes apparently form more easily in low-metallicity environments (e.g., Zampieri and Roberts, 2009; Mapelli et al., 2009; Belczynski et al.,

<footnote n="15">¹⁵ The limit can be even higher for He-rich accretion, and for the most massive BHs (e.g. Belczynski, 2020).</footnote>
<caption>**Table 6**
Number of ULXs per MWEG 100 Myr after the start of stellar formation.</caption>

*Source:* Adapted from Wiktorowicz et al. (2017).

<table><thead><tr><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td rowspan="3">Z<sub>☉</sub></td><td>#ULX</td><td>407</td><td>65</td><td>14</td><td>0.5</td></tr><tr><td>#BHULX</td><td>372</td><td>40</td><td>4.7</td><td>0.38</td></tr><tr><td>#NSULX</td><td>35</td><td>25</td><td>9.4</td><td>0.13</td></tr><tr><td rowspan="3">Z<sub>☉</sub>/10</td><td>#ULX</td><td>7281</td><td>1940</td><td>200</td><td>12</td></tr><tr><td>#BHULX</td><td>7200</td><td>1900</td><td>180</td><td>11</td></tr><tr><td>#NSULX</td><td>81</td><td>40</td><td>12</td><td>0.43</td></tr><tr><td rowspan="3">Z<sub>☉</sub>/100</td><td>#ULX</td><td>5000</td><td>2400</td><td>390</td><td>15</td></tr><tr><td>#BHULX</td><td>4900</td><td>2400</td><td>380</td><td>15</td></tr><tr><td>#NSULX</td><td>16</td><td>12</td><td>9.0</td><td>0.075</td></tr></tbody></table>

'MWEG' = 'Milky Way Equivalent Galaxy'.

2010), and RLOF onto a compact object is therefore more frequent than in high metallicity cases (Linden et al., 2010).

Wiktorowicz et al. (2017) found that metallicity has a strong impact on the number of ULXs, but only in star-forming regions. They show that the number of black-hole ULXs increases significantly for $Z_{\odot}/10$ in comparison with $Z_{\odot}$. But the number of neutron-star ULXs is virtually unaffected by metallicity. Interestingly, for models with the lowest investigated metallicity ($Z_{\odot}/100$) they find fewer ULXs than for $Z = Z_{\odot}/10$. This suggests that the relation between the number of ULXs and metallicity is not monotonic (see Prestwich et al., 2013). The reasons for this are currently not understood.

The general conclusions of the ULX population synthesis by Wiktorowicz et al. (2017) are:

* ULX with NS accretors dominate the post-burst ULX populations, and those with constant stellar formation (duration > 1 Gyr) in high-Z environments, consistent with current understanding of binary evolution. Neutron-star ULXs are present in significant numbers (≥ 10%) also during the star-formation bursts and in lower-Z ULX populations.

* ULXs appear in a very specific sequence after the start of the star formation ($t$ denotes the time since the beginning of star formation):

1. $t \approx 4-40$ Myr BH-MS (5.6-11 M<sub>☉</sub>),

2. $t \approx 6-800$ Myr NS-MS (0.9-1.5 M<sub>☉</sub>),

3. $t \approx 430-1100$ Myr NS-HG (0.6-1.0 M<sub>☉</sub>),

4. $t \approx 540-4400$ Myr NS-RG (~ 1.0 M<sub>☉</sub>);

(BH-black hole, NS - neutron star, MS - main sequence, HG - H-rich Hertzsprung gap, RG - red giant.)

* Neutron-star ULXs may reach luminosities as high as those of black-hole ULXs ($L_{X,\max} > 10^{41}$ erg s<sup>-1</sup>).

* The most luminous ULXs ($L_X \gtrsim 10^{41}$ erg s<sup>-1</sup>) contain HG donors (black-hole ULXs; $M_2 \approx 1.2-3.7$ M<sub>☉</sub>) or evolved helium stars (neutron-star ULXs; $M_2 \approx 1.7-2.6$ M<sub>☉</sub>), which overfill their Roche lobe and transfer mass on a thermal timescale. They form typically within 15-75 Myr after the ZAMS.

Finally, as seen in Table 6, the ULX population is in all cases strongly dominated by sources with $L_X < 3 \times 10^{39}$ erg s<sup>-1</sup>.

The results of Wiktorowicz et al. (2017) describe the evolution of the intrinsic ULX population, but since at least these sources are supposed to be beamed, the observed ULX population is different. Wiktorowicz et al. (2019) use the results of the population synthesis described above to derive the properties of the observed ULX population. They use the fiducial model defined in Wiktorowicz et al. (2017) but remove the beaming saturation condition because extremely beamed sources are not only hard to observe, but also extremely rare and shortlived, so have no influence on the final results.

Mondal et al. (2020) discuss the full range of possible ways of making a ULX. This paper also estimates that at low redshift, about 50 per cent of merging BH-BH progenitor binaries evolved through a ULX phase. They find that observed ULXs with black-hole accretors typically emit isotropically ($b = 1$) and undergo nuclear-timescale mass transfer, whereas those with neutron-star accretors are predominantly beamed (typically $b = 0.7-0.2$) and in most cases the mass transfer occurs on a thermal timescale. They also show that beaming depends on the stellar environment; very young (burst) populations (age < 10 Myr), dominated by black-hole ULXs, are significantly beamed, while black-hole ULXs in older stellar populations are usually isotropic emitters. In contrast, the majority of neutron-star ULXs are always beamed, irrespective of the stellar environment. The ratio of neutron-star ULXs to black-hole ULXs is higher in the total sample than in the observed sample. For continuous star formation, black-hole ULXs typically outnumber the NS ULXs in the observed sample. Black-hole ULXs also outnumber neutron-star ULXs in the observed sample for burst stellar formation at early times, but after the star formation burst, neutron star ULXs tend to dominate the observed population. Here the observed neutron-star ULXs represent only 20% of the total neutron-star ULX population, and many are expected to be obscured (in the absence of precession, which may act to bring some into view, see, Dauser et al., 2017; Middleton et al., 2018).

Heida et al. (2019b) pointed out that the growing number of ULXs with (tentatively identified) red supergiant donors (for which RLOF is dynamically unstable) motivates the study of wind-driven mass-transfer, previously neglected in the context of ULXs. Including wind accreting X-ray binary models into StarTrack, Wiktorowicz et al. (2021) showed that wind-fed ULXs can constitute a significant fraction of all ULXs, and in some environments may even be the majority. Bondi-Hoyle-Lyttleton accretion is a standard form of accretion in StarTrack (Belczynski et al., 2008, 2020) and they additionally adapt a wind RLOF (WRLOF) scheme from Mohamed and Podsiadlowski (2007), already used by Ilkiewicz et al. (2019), to analyse the relation between SNIa and wide symbiotic binaries. With somewhat optimistic assumptions for wind-accretion efficiency, they suggest that wind-fed ULXs should not be neglected. The wind-fed ULX sample they found contains a significant fraction of RSG companions, supporting the suggestion that the apparent superposition of some ULXs and RSGs results from coexistence as a binary. Although some of these systems will evolve into double compact objects, none of the ULX systems with a RSG donor is a viable progenitor of double compact object mergers with $t_{merge} < 10$Gyr, because they have large orbital separations.

It is important to note that models of wind accretion and emission suffer from serious uncertainties. This problem cannot be solved by extensive numerical simulations alone, but also requires systematic quantitative observational data. Wiktorowicz et al. (2017, 2019, 2021) do not consider the origin or evolution of neutron-star magnetic fields, considering that this problem contains too many unknowns to be worth including in population synthesis.

Kuranov et al. (2020) do not share this view, and perform population synthesis of binaries containing magnetized neutron stars only. They assume solar abundances and neglect magnetic field evolution. They consider two accretion-flow models: the standard Shakura and Sunyaev (1973) model adapted to magnetized accretors by Chashkina et al. (2017) and for the supercritical accretion they use the Chashkina et al. (2019) “advective” model (for the suitability of advection models to describe accretion onto neutron stars see Section 3.8.2). The results are presented as a $P_s - L_x$ figure on which the observed values of 10 PULXs are superposed. Although Be-X stars are not present in the modelled population, the authors use four Be-ULX data points. When the data points fall into the regions where the calculations predict the existence of PULXs, they consider this as a success of their model. Which is the case for both of the accretion models considered, only NGC 5097 ULX-1 shows, as usual, some resistance. They conclude that that standard evolution of close binary systems and accretion on
to magnetized neutron stars can quantitatively explain the observed properties of PULX i.e. their X-ray luminosities, spin periods, orbital periods and masses of visual components, without assuming beamed X-ray emission. In a model galaxy with star formation rate 3 − 5 M⊙ yr$^{-1}$ “there can exist” several PULXs. If PULXs are not beamed, it is not clear why they are invisible in the Milky Way. (The single PULX observed in the Galaxy is in a Be-X binary – because of their uncertain evolutionary status, such systems are not taken into account in population syntheses.) Kuranov et al. (2020) assert that discovery of powerful winds from PULXs with $L_X \sim 10^{41}$ erg s$^{-1}$ may be a signature of super-Eddington accretion onto magnetised neutron stars. If so, this raises two questions.

(i) In the absence of beaming why would such sources not be observable as bright X-ray sources?

(ii) with such powerful outflows, how one can avoid beaming?

Finally, although these authors assert that, in their models, the PULXs represent “a subset of neutron stars at the stage of disc accretion in close binary systems with luminosity $L_X > 10^{39}$ erg s$^{-1}$”, they take no account of the other distinctive parameter that singles out the PULXs: their extremely high spin frequency derivatives $\dot{v}$ (see Fig. 13).

### 3.14. Winds and feedback from ULXs

We have seen (in Section 3.6) that the characteristic feature of the disc–wind beaming picture of ULXs is that their accretion discs eject the super-Eddington part of the mass transferred to them. If $\dot{M} \gg \dot{M}_{Edd}$ this is of course most of the transferred mass. In all cases we expect a quasispherical accretion disc wind, with most of the emitted radiation escaping through open funnels along the disc axis. The dynamics of the wind are controlled by radiation pressure, and therefore by the electron–scattering optical depth distribution of the outflow. For modest Eddington factors $\dot{m} = \dot{M}/\dot{M}_{Edd} \gtrsim 1$ we expect that the photons produced by the conversion of accretion energy will find the open funnels around the rotational axis of the disc and so escape after only a small number of scatterings. The front–back symmetry of non–relativistic electron scattering means that, on average, a photon gives up all of its momentum (but not energy) in each scattering event. Then we expect that the accretion disc wind should have an outgoing momentum of order that in the original radiation field, i.e. just the Eddington momentum

$$Mv \approx \frac{L_{Edd}}{c}, \qquad (105)$$

so that the outflow velocity is

$$v \approx \frac{\eta}{\dot{m}} c \sim 0.1c, \qquad (106)$$

where $\eta = L_{Edd}/\dot{M}_{Edd}c^2 \approx 0.1$ is the radiative efficiency of accretion (King and Pounds, 2003). Winds with the properties ((105), (106)) are seen in many AGN (see King and Pounds, 2015, for a review), where the Eddington factor is unlikely to be large.

But in ULXs, the condition $\dot{m} \gg 1$ is a distinct possibility, and here we expect considerably more scatterings before a photon finds the open funnels around the disc axis and escapes. Instead we expect that the radiation field may put a significant fraction of its energy into the wind, i.e.

$$\frac{1}{2} \dot{M} v'^2 \approx l' L_{Edd}, \qquad (107)$$

with $l' \sim 1$. This now leads to an outflow velocity

$$v' \approx \left( \frac{2l'\eta}{\dot{m}} \right)^{1/2} c, \qquad (108)$$

(King and Muldrew, 2016). Despite the different physics involved, the two types of winds have surprisingly similar velocities, i.e.

$$v, v' \approx 0.05c-0.2c \qquad (109)$$

for values $10 < \dot{m} < 100$. Observations show the presence of winds with velocities of this order in most (~70%) ULXs (Section 2.2.1).

An observer not located very close to the central accretion disc axis (i.e. not in the narrow beam defining the ULX) would observe the photosphere of the quasi–spherical wind. King and Muldrew (2016) show that this has radius

$$R_{ph} \approx 1 \times 10^4 l'^{-1/2} \dot{M}_{w10}^{3/2} \eta_{0.1}^{-3/2} M_{10} \text{ km} \qquad (110)$$

and effective temperature

$$T_{\text{eff}} = 1 \times 10^6 l'^{1/4} \dot{M}_{w10}^{-3/4} \eta_{0.1}^{3/4} M_{10}^{-1/4} \text{ K} \qquad (111)$$

where $\dot{M}_{w10}$ is the wind mass outflow rate in units of $10\dot{m}$, $\eta_{0.1}$ is the accretor efficiency in units of 0.1, and $M_{10}$ is the accretor mass in units of $10 M_{\odot}$.

Objects almost precisely like this – with blackbody emission at temperature ~100 eV, from photospheres of order (110) are observed, in the form of the ultraluminous supersoft sources (ULSS, Kong and Di Stefano, 2003). Evidently these are ULXs viewed ‘from the side’. The well–know extreme Galactic source SS433 is probably a member of this class, as we discuss below.

ULX/ULS winds are quasispherical, and hypersonic with respect to the interstellar medium (ISM) surrounding the ULX, and so must be slowed in a strong reverse shock against it. A weaker forward shock propagates into the surrounding ISM ahead of the contact discontinuity between the ULX wind and the ISM, sweeping this gas outwards in a shell. As in the similar problem for supermassive black holes (see King and Pounds, 2015, for a review) the nature of ULX feedback on the interstellar gas depends on whether the shock slowing the ULX wind is cooled by radiation losses within a flow timescale or not. In the first case, where the shock is efficiently cooled, most of the energy of the wind is lost to radiation, and the wind transmits only its momentum to the ISM. If instead shock cooling is inefficient, the outflow gives all of its energy adiabatically to this gas. These two cases are often called momentum–driven and energy–driven respectively.<fnref n="16" />

For ULXs, we will see that feedback is in practice always energy–driven, which in turn means that ULXs generally have a significant effect on their surroundings. The temperature of the reverse shock slowing the ULX wind is $T_s \sim m_H u^2/k \sim 10^{10}-10^{11}$ K, where $u \sim v, v'$, and $k$ is Boltzmann's constant. Since this is far higher than the $T \lesssim 10^8$ K radiation field of the ULX, inverse Compton scattering off the ULX radiation field is the main cooling mechanism, as in the SMBH case. (The thermal bremsstrahlung timescale is far longer.) King (2003) shows that the ratio of Compton cooling time and flow timescale $R/v$ is

$$\frac{t_c}{t_{\text{flow}}} \approx \frac{2}{3} \left( \frac{m_e}{m_p} \right)^2 \frac{R}{R_g} \frac{c}{v} \qquad (112)$$

at distance $R$ from the ULX. From (109) this defines a cooling radius

$$R_c = 5 \times 10^5 R_g \sim 5 \times 10^{10} \text{ cm}, \qquad (113)$$

which is generally smaller than the ULX binary’s orbit. Shock cooling is never important for ULX outflows, and all ULX feedback is energy–driven.

We can easily see the effect of this feedback. If the interstellar gas has uniform density $\rho$ and the shock exerts pressure $P$ on it, momentum conservation at the radius $R$ of the interface between the ULX wind and the ISM gives

$$4\pi R^2 P = \frac{d}{dt} \left( \frac{4\pi}{3} R^3 \rho R \right) \qquad (114)$$

<footnote n="16">¹⁶ In SMBH accretion, feedback switches from momentum– to energy–driven once the SMBH mass reaches the $M-\sigma$ value $M \propto \sigma^4$. This fixes the limit to SMBH mass growth, since the ISM gas ultimately fuelling its growth is expelled at this point, in a galaxy–wide high–speed outflow. See King and Pounds (2015).</footnote>
so that

$$ \frac{P}{\rho} = \frac{1}{3} R \ddot{R} + \dot{R}^2. \qquad (115) $$

Since energy is transmitted adiabatically from the wind we have

$$ \frac{d}{dt} [2\pi R^3 P] = L_{Edd} - P \frac{d}{dt} \left( \frac{4\pi R^3}{3} \right) $$

Eliminating P gives the equation of motion for the shock as

$$ \frac{L_{Edd}}{2\pi\rho} = \frac{1}{3} R^4 \ddot{R} + \frac{8}{3} R^3 \dot{R} + 5R^2 \dot{R}^3 \qquad (116) $$

All solutions of this equation tend to the attractor

$$ R = \left( \frac{125 L_{Edd}}{101 \pi \rho} \right)^{1/5} t^{3/5}, \qquad (117) $$

(cf Eq. (18)) or numerically

$$ R \approx 50 \left( \frac{L_{39}}{\rho_{-25}} \right)^{1/5} t_{5}^{3/5} \text{ pc}, \qquad (118) $$

where $L_{39} = L_{Edd}/10^{39} \text{ erg s}^{-1}$, $t_5 = t/10^5 \text{ yr}$, and $\rho_{-25} = \rho/10^{-25} \text{ g cm}^{-3}$. The conditions correspond to a ULX with a lifetime of order the thermal timescale of a massive companion star, driving a wind into an ISM of number density ~ 0.1 cm⁻³ H atoms per cm³. The shell of swept-up ISM gas expands at a speed

$$ \dot{R} = 300 \left( \frac{L_{39}}{\rho_{-25}} \right)^{1/5} t_{5}^{-2/5} \text{ km s}^{-1}, \qquad (119) $$

so the forward shock into the ISM is much weaker than the reverse shock slowing the ULX wind (cf Eq. (109)). For longer thermal timescales or more powerful wind mechanical luminosities, $L_{39} \sim 10$, and the predicted nebulae can have sizes ~ 500 pc. Observations (Section 2.6) show that many ULXs are associated with wind-blown nebulae of order 50 - 500 pc in size. These are significantly larger than supernova remnants (~3 pc).

### 3.14.1. SS433

The well-known extreme Galactic binary system SS433 fits closely into this picture. King et al. (2000) show that it probably has a mass transfer rate implying $\dot{m}_{w10} \sim 10^3$, and $t_5 \sim 1$. The mechanical luminosity is then. ~ $10^{39} \text{ erg s}^{-1}$. For a 10 M$_{\odot}$ black hole accretor, Eq. (119) implies a spherical nebula (excluding the ‘ears’ formed by the precessing jets) comparable with the observed ~ 30 pc size. King and Muldrew (2016) note that this implies a quasispherical wind speed close to the observed velocity width ~ 1500 km s⁻¹ of the so-called stationary H alpha line. Despite its very high mass transfer rate, SS433 is a remarkably weak X-ray source – Watson et al. (1986) estimate $L_X \approx 10^{36} \text{ erg s}^{-1}$ and a mechanical luminosity $\approx 10^{39} \text{ erg s}^{-1}$, and it is likely that the softer (<10 keV) X-rays come only from the prominent jets the system produces (the harder X-ray emission may originate from scattering inside the wind-cone, Middleton et al. 2021b). In a detailed study, Begelman et al. (2006) show that SS433 has a viewing angle appropriate to a ULS, but is not observable as one: from (111) we have $kT_{\text{eff}} \sim 10 \approx 5 \text{ eV}$, which is too soft to be detectable as this system is heavily reddened ($A_V \approx 7$). SS433 is distinctive because of the huge periodic redshift and blueshifts of the H-alpha lines emitted by its precessing jets. These evidently result from its extreme Eddington factor, and precess (and are baryon-loaded and slowed to 0.26c) probably because they are deflected by a thick precessing central disc. As a mark of this, the precession rate of the jets does show power at the binary orbital period (Begelman et al., 2006).

### 3.15. Be-star ULXs

The luminosity of ULXs is generally variable, but two classes of ultraluminous X-ray sources are transient. One of these consists of systems appearing in the transient X-ray sky only as ultraluminous sources. We discuss these in the next section.

The other class is a small set of systems which normally appear as high-mass X-ray binaries, but occasionally become ULXs. This class has only recently been recognised, but actually includes A0538-66, the first system observed to have an apparently super-Eddington X-ray luminosity (White and Carpenter, 1978), and also the Milky Way’s only known ULX, Swift J0243.6+6124, first detected on 3 October 2017 during a giant X-ray outburst (Kennea et al., 2017, see Table 2). In all these systems, a neutron star, often with a noticeable magnetic field, accretes from a much more massive Be (or Oe) star in a wide eccentric orbit.

Be stars are unusual in having a large disc of material surrounding their rotational equator. The origin of the disc is unclear, but is evidently related to the star’s rotation, and possibly mediated by small-scale surface magnetic fields (Nixon and Pringle, 2020, for a recent discussion). Be X-ray binaries generally produce most of their X-ray emission when the neutron star is near pericentre and interacts with the circumstellar disc. The X-rays therefore generally indicate the orbital period.

But it is now known that, on a much longer timescale, this interaction is much stronger, and the system becomes a ULX. The origin of this behaviour is probably von Zeipel – Lidov – Kozai (ZLK) oscillations of the Be star disc (Martin et al., 2014). Highly misaligned test particle orbits around one component of a binary cyclically exchange inclination for eccentricity (von Zeipel, 1910; Kozai, 1962; Lidov, 1962). This process conserves the component of the angular momentum orthogonal to the binary orbital plane, i.e.

$$ (1 - e_p^2)^{1/2} \cos i_p = \text{constant.} \qquad (120) $$

Here $i_p$ is the inclination of the particle orbit to the binary orbit and $e_p$ is the test-particle eccentricity. A test particle initially on a circular strongly misaligned orbit oscillates to closer alignment. Then $|\cos i_p|$ increases, requiring larger $e_p$. The oscillations occur only if the initial inclination $i_{p0}$ inclination satisfies

$$ \cos^2 i_{p0} < \frac{3}{5}, \qquad (121) $$

so $39^\circ < i_{p0} < 141^\circ$, and the maximum eccentricity that an initially circular test orbit can reach is

$$ e_{\text{max}} = \left(1 - \frac{5}{3} \cos^2 i_{p0}\right)^{1/2}. \qquad (122) $$

Martin et al. (2014) show that this test-particle behaviour extends to full hydrodynamical discs, which undergo global ZLK cycles of the disc inclination and eccentricity. The spins of Be stars are known in general to be strongly misaligned from the orbits of their neutron star companions in Be–X-ray binaries, probably as a result of the asymmetric supernova explosion producing the neutron star. At maximum disc eccentricity, it is likely that the neutron star accretes much more gas from the Be-star disc, and this may turn it into a ULX. Global ZLK cycles typically have periods an order of magnitude longer than the binary orbit, so the transition to the ULX state is relatively infrequent.

### 3.16. Modelling transient ULXs

Accretion discs in low-mass X-ray binaries are subject to a thermal-viscous instability when the mass transfer rate from the companion falls below a critical value depending mainly on the size of the disc (orbital period; Coriat et al., 2009). The instability is similar to that in cataclysmic variables leading to dwarf nova outbursts (Lasota, 2001; Hameury, 2020), but X-ray self-irradiation of the disc plays a crucial role both in the instability criterion (van Paradijs, 1996) and the outburst development (King and Ritter, 1998; Dubus et al., 1999, 2001).

The thermal-viscous disc instability is naturally associated with low mass transfer rates, but since the critical accretion rate increases strongly with the disc size, for large enough binary systems, even super-Eddington mass transfer can correspond to an unstable disc (Lasota
et al., 2015; Hameury and Lasota, 2020). So for sufficiently large orbital periods, accreting systems have large unstable discs and can produce outbursts bright enough to explain some ULXs (King et al., 2000). Although as discussed in Section 2.5.2 it is very difficult to determine the binary parameters of these distant systems, it is clear that many of them have giant or supergiant companion stars (Section 2.5.1) and have orbital periods longer than 2 days. Several ULXs are classified as transient (see e.g. Brightman et al. 2020a). Usually their light curves are only sparsely covered, but the recent well sampled observations of a transient ULX source in the galaxy M 51 by Brightman et al. (2020a) provides a light curve that can be compared with model predictions. Some long-period, sub-Eddington X-ray transients show long-lasting outbursts (tens of years), so some apparently steady ULXs could actually be transients observed during long outbursts.

The critical rate below which a disc is unstable is well approximated by:

$$ \dot{M}_{\text{crit}}^{+} \approx 2.4 \times 10^{19} M_{1}^{-0.4} f_{\text{irr}}^{-0.5} \left( \frac{R_{\text{out}}}{10^{12} \text{ cm}} \right)^{2.1} \text{ g s}^{-1}, \quad (123) $$

where $R_{\text{out}}$ is the outer disc radius and $f_{\text{irr}} = \eta_t C/(5 \times 10^{-4})$ and C is defined through

$$ \sigma T_{\text{irr}}^{4} = C \frac{\eta_{d} \dot{M} c^{2}}{4\pi r^{2}}. \quad (124) $$

C contains all the physics of the irradiation process, and $\eta_t$. Dubus et al. (2001) found that the light curves of low-mass X-ray transients are reasonably well reproduced, and Coriat et al. (2012) found that the corresponding stability criterion provides the observed division of sources into steady and outbursting, if one uses a constant $\eta_t C$ of order $10^{-3}$. The radiative accretion efficiency $\eta_t$ is defined as the ratio of the true luminosity (without the beaming factor) to $c^2$, and is therefore:

$$ \begin{aligned} \eta_t &= 0.1 & \text{if } \dot{m} < 1, \\ &= 0.1(1 + \ln \dot{m})/\dot{m} & \text{if } \dot{m} \ge 1. \end{aligned} \quad (125) $$

From Eq. (123) it follows that neutron-star ULXs may be unstable for super-Eddington mass transfer rates at orbital periods $\gtrsim 10$ days (slightly shorter for black-hole ULXs). But if the front fails to reach the outer disc edge, the peak outburst luminosity is given by Eq. (123) with $R_{\text{out}}$ replaced by $R_{\text{tr,max}} \le R_{\text{out}}$, where $R_{\text{tr,max}}$ is the maximum radius reached by the instability-triggering heating front. In this case, the peak luminosity can be up to 50 times larger (Hameury and Lasota, 2020). This means that wide binaries in which the mass transfer is sub-Eddington might become transient ULXs at, and close to, the maximum outburst luminosity if their discs are unstable.

Hameury and Lasota (2020) derived analytical formulae describing typical X-ray transient light curves with great accuracy. They apply also to transient ULXs. When the heating front brings the whole disc to a hot state ($R_{\text{tr,max}} \approx R_{\text{out}}$), the $\dot{M}(t)$ relation during the decay from outburst maximum is very well described by Ritter and King (2001)<fnref n="17" />

$$ \dot{M} = \dot{M}_{\text{max}} \left[ 1 + \frac{t}{t_0} \right]^{-10/3}, \quad (126) $$

where the integration constant $t_0$ is given by:

$$ t_0 = 3.19 \alpha_{0.2}^{-4/5} M_1^{1/4} R_{12}^{5/4} \dot{M}_{\text{max},19}^{-3/10} \text{ yr}, \quad (127) $$

with $\dot{M}_{\text{max},19} = \dot{M}_{\text{max}}/10^{19} \text{ g s}^{-1}$. Here $t_0$ is not the characteristic timescale of disc evolution, which is instead

$$ \tau = \frac{M_d}{\dot{M}} = 0.81 \psi f^{-0.3} M_1^{0.37} f_{\text{irr}}^{0.15} R_{12}^{0.62} \alpha_{0.2}^{-0.8} \text{ yr}, \quad (128) $$

where $M_d$ is the disc mass and $f = \dot{M}_{\text{max}}/\dot{M}_{\text{crit}}^+(r_{\text{out}}) > 1$ (for the derivation see Hameury and Lasota, 2020). One can then relate the maximum outburst accretion rate to the characteristic decay time.

$$ \dot{M}_{\text{max}} = 2.0 \times 10^{19} \alpha_{0.2}^{2.71} f^{2.02} M_1^{-1.65} \left( \frac{\tau}{1 \text{ yr}} \right)^{3.39} f_{\text{irr}}^{-1.01} \text{ g s}^{-1}, \quad (129) $$

Then when both $\dot{M}_{\text{max}}$ and $\tau$ are known from observations, this relation determines $f$, and hence $\dot{M}_{\text{crit}}^+$ and the size of the accretion disc.

This phase of the outburst corresponds to a viscous decay, during which X-ray irradiation prevents the formation and propagation of a cooling front. This ends when the decreasing accretion rate falls to the critical value $\dot{M}_{\text{crit}}^+$ and the front starts propagating into the disc.

If the heating front is unable to reach the outer regions – which happens quite often in large discs – the viscous decay phase is missing and, from the start, the decay–from–maximum $\dot{M}(t)$ relation corresponds to the cooling–front propagation, and has the form

$$ \dot{M} = 1.31 \times 10^{17} \alpha_{0.2}^{2.71} M_1^{-1.65} f_{\text{irr}}^{-1} \left[ \frac{\xi}{\xi_0} \left( \frac{t_0' - t}{1 \text{ yr}} \right) \right]^{3.39} \text{ g s}^{-1}, \quad (130) $$

where $t_0'$ is a constant that is determined by the condition that, when the cooling front starts, $\dot{M}$ is equal to $\dot{M}_{\text{crit}}^+$ at the maximum transition radius. Then $t_0'$ can be written as:

$$ t_0' = 4.64 \xi^{-1} M_1^{0.37} f_{\text{irr}}^{0.15} \alpha_{0.2}^{-0.8} r_{12}^{0.62} \text{ yr}, \quad (131) $$

and $\xi$ is a constant to be calibrated by numerical simulations; it is found to be in the range $2.47 < \xi \le 8.0$. Here $t_0'$ is equal to the duration of this phase of the outburst, and can be directly compared to observations. As before, there exists a relation between $\dot{M}_{\text{max}}$ and $t_0'$:

$$ \dot{M}_{\text{max}} = 3.1 \times 10^{19} \alpha_{0.2}^{2.71} M_1^{-1.65} \left( \frac{\xi}{5} \frac{t_0'}{1 \text{ yr}} \right)^{3.39} f_{\text{irr}}^{-1.01} \text{ g s}^{-1}, \quad (132) $$

which is essentially the same as in Eq. (129), with $f=1$.

It is important to realise that, for super-Eddington accretion rates, $\dot{M}(t)$ does not directly represent the observed $L_X(t)$ light curve, as the relation between the luminosity and accretion rate is no longer linear. Then when considering an outburst whose apparent luminosity is larger than $L_{\text{Edd}}$ Hameury and Lasota (2020) use the following relations

$$ \begin{aligned} L_X &= (1 + \ln \dot{m}) \left[ 1 + \frac{\dot{m}^2}{\bar{b}} \right] L_{\text{Edd}} & \text{if } \dot{m} \ge 1 \\ &= \dot{m} L_{\text{Edd}} & \text{if } \dot{m} < 1, \end{aligned} \quad (133) $$

where $b = (1 + \dot{m}^2/\bar{b})^{-1}$ is a beaming term; the larger the beaming parameter $\bar{b}$, the larger $b$ and hence the smaller the beaming effect. Eq. (55) corresponds to $b = \bar{b}/\dot{m}^2$ with $\bar{b} = 73$. Since the beaming factor $\bar{b}/\dot{m}^2$ applies only for $\dot{m} > \sqrt{\bar{b}}$, in time-dependent calculations, one replaces it by $(1 + \dot{m}^2/\bar{b})^{-1}$ in order to get a smooth transition with the case where beaming is negligible.

Further, when $\dot{m} \gg 1$ so that the apparent luminosity scales approximately as $\dot{m}^2$, the decay time of the luminosity $\tau_L$ is one half of the decay time of the accretion rate, and Eq. (129) has to be written as:

$$ \dot{m}_{\text{max}} = 132 \alpha_{0.2}^{2.71} f^{2.02} M_1^{-2.65} \left( \frac{\tau_L}{1 \text{ yr}} \right)^{3.39} f_{\text{irr}}^{-1.01}. \quad (134) $$

If not all of the disc reaches the hot state, the total outburst duration is related to the maximum mass accretion rate via Eq. (132), and we must have:

$$ \dot{m}_{\text{max}} = 24.0 \alpha_{0.2}^{2.71} M_1^{-2.65} \left( \frac{\xi}{5} \frac{t_0'}{1 \text{ yr}} \right)^{3.39} f_{\text{irr}}^{-1.01}, \quad (135) $$

where $t_0'$ now refers to the outburst duration.

### 3.16.1. M51 XT-1

M51 XT-1 is currently the only ULX transient source whose light curve is suitable for comparison with the prediction of the disc-instability model. Fig. 19 shows how observational data of M51 XT-1 (Brightman et al., 2020a) compare with the predictions of the disc-instability model when the light curve comes from Eqs. (126) and (130), combined with Eq. (133) with the beaming parameter $\bar{b} = 73$. Two cases are shown. A 1.4 M$_\odot$ accreting neutron star with a disc size $4.8 \times 10^{11}$ cm; and a 10 M$_\odot$ accreting black hole, with a disc extending

<footnote n="17">¹⁷ The corresponding formula in the original publication contains a misprint.</footnote>
<figure><img src="image_21.png" /><figcaption>**Fig. 19.** Observed flux from M51 XT-1 as compared with model predictions for a 1.4 M☉ neutron star (red curve) and a 10 M☉ black hole (green curve). Black points correspond to SWIFT data and blue points to Chandra or XMM-Newton observations. Source: Courtesy M. Brightman, see also Brightman et al. (2020a).</figcaption></figure>

to 4.9 × 10¹¹ cm. As can be seen, the agreement is reasonably good, and as acceptable as the original fit with a power law with index -5/3 (Brightman et al., 2020a). These data can also be fitted with a 10 M☉ accreting black hole, with a disc extending to 4.9 × 10¹¹ cm.

In the neutron star case, the maximum accretion rate is 6×10¹⁹ g s⁻¹, while in the black hole case it is 1.5 × 10²⁰ g s⁻¹. Hence the emission from a black-hole system would not be beamed, but for a neutron-star accretor the beaming factor would be *b* = 0.06, as expected for *ṁ* = 33. The mass transfer rate can be very roughly estimated to be of order 1%–2% of the maximum accretion rate, i.e. 1–3 × 10¹⁸ g s⁻¹.

Hameury and Lasota (2020) showed that taking $\bar{b}$ = 200 instead of $\tilde{b}$ = 73 in Eq. (133) also provides an acceptable fit, but $\tilde{b}$ = 20 is excluded by the Chandra and XMM-Newton points, thus suggesting only moderate beaming.

### 3.16.2. HLX-1 in ESO 243-49

HLX-1 in the galaxy ESO 243-49 (Farrell et al., 2009) attracted a lot of attention as the best IMBH candidate among ULXs. It is the brightest ULX candidate known; its luminosity is variable and can exceed 10⁴² erg s⁻¹ at maximum. Its association with the galaxy ESO 243-49 at a distance of 95 Mpc is fairly well established (Wiersema et al., 2010; Soria, 2013) so there is little doubt about its luminosity (see, however, Lasota et al., 2015). Greene et al. (2020) conclude that a self-consistent scenario is that HLX-1 is a central massive black hole on the low-mass end of the mass distribution of nucleated 10⁹ – 10¹⁰ M☉ galaxies. Its small host galaxy was accreted and tidally stripped by ESO 243-49, leaving only the bare nuclear star cluster near the black hole (e.g., Mapelli et al. 2013). Star formation, perhaps encouraged by the merger, could have increased the capture rate for the hole to acquire a companion star on which it is currently feeding. Then by the definition adopted in this review HLX-1 is not an IMBH candidate, but was the central MBH of a small galaxy, which (unusually) has been accreted and disrupted by a larger one.

In line with this picture, HLX-1's historical light curve (see e.g. Godet et al. 2014) initially showed a promising series of almost annual outbursts, only to lose this quasi-periodicity later on. Subsequent to its discovery, a number of so-called QPE ('quasiperiodic eruption') sources have recently been found from the centres of small galaxies (e.g. Miniutti et al. 2019, 2020, Arcodia et al. 2021). These can be modelled as tidal disruption near-misses (King, 2020): instead of being fully disrupted by filling its tidal radius near the MBH (a tidal disruption event or TDE) an infalling star fills its tidal lobe only at the

pericentre of a very eccentric orbit about the MBH. In the small galaxy GSN 069 the star is probably a low-mass white dwarf (King, 2020), and the predicted CNO anomaly was later found (Sheng et al., 2021). It appears that this model works well for all the currently recognised QPE systems (King, 2022). These systems all have very short lifetimes as the orbits shrink under gravitational radiation, which is what drives the mass transfer.

Modelling HLX-1 instead as a transient IMBH source undergoing disc outbursts shows that the outburst timescales are incompatible with a central mass of $\ge 10^4$ M☉, as would be required to explain the peak luminosity of $10^{41}$ erg s⁻¹ (Hameury and Lasota 2020 and references therein).

### 3.17. Beaming or not?

The arguments in favour of luminosity beaming in PULXs presented above are simple and fundamental. The main one is that the observed X-ray luminosities of magnetic ULXs lie between 6 and 500 $L_{Edd}$, with the classic (non Be/X) systems having $L_X > 20L_{Edd}$. Even if mass is supplied at a super-Eddington rate, the luminosity is only $L \approx L_{Edd}(1+\ln \dot{m})$, so even $\dot{m} \approx 1000 (> 10^{-5} M_{\odot} \text{yr}^{-1})$ produces only $\sim 8 L_{Edd}$.

Explaining these huge excess luminosities by appealing to superstrong magnetic fields appears unpromising. We have argued above that the presence of magnetars in PULXs is extremely unlikely. Among other problems, it requires a cosmic conspiracy confining magnetars to just these binary systems. Be-PULXs spend most of the time as standard pulsed X-ray sources, and clearly do not have magnetar-strength fields. Assertions that the “apparent luminosity [of PULXs] is close to the actual one” (Mushtukov et al., 2020) are rather surprising, especially when it is not explained how this is supposed to be achieved.

Mushtukov et al. (2020) refer to a table in King and Lasota (2020) to claim that these authors require $a = 1/b \sim 20$ for M82 ULX-2, NGC 7793 P13 and NGC 300 ULX1 and $\sim 100$ for NGC 5. But Table 3 shows that the values of $1/b$ for the first three sources are respectively 17, 6, 6, to which one can add 10 for ULX-7 in M51.

### 3.18. Measuring mass transfer via the orbital period derivative?

The most important parameter in understanding ULXs, as in any accreting system, is the instantaneous mass transfer rate $-\dot{M}_2$ in the host binary system. Unfortunately, precisely because we do not yet have a clear picture of how exactly the mass transfer rate specifies the luminosity of ULXs, it is difficult to measure $-\dot{M}_2$ directly from observation. But if we assume conservative mass transfer (i.e. conserving both total mass and angular momentum) we see from Section 3.11 that all quantities such as the companion mass $M_2$, the binary separation $a$, and by Kepler's law, the binary period $P \propto a^{3/2}$, evolve on the mass transfer timescale $M_2/(-\dot{M}_2)$ – see Eq. (104). This makes it tempting to use the much more easily measured orbital period derivative $\dot{P}$ to estimate $-\dot{M}_2$. The recent papers by Bachetti et al. (2021a,b) try to use this method for the ULX M82 X-2.

As we noted above, the problem of measuring $-\dot{M}_2$ is common to all interacting binary systems, not simply ULXs. There is a long history of efforts to find $-\dot{M}_2$ by using $\dot{P}$ and assuming conservative evolution, going back at least to early studies of cataclysmic variables (where a low-mass main-sequence star transfers mass to a white dwarf in a very circular orbit). But all these attempts give uniformly disappointing results – not least because even the sign of $\dot{P}$ often flatly contradicts that expected from conservative evolution. The underlying reason for these difficulties is that relations like (104) hold only if the quantities $\dot{P}$, $-\dot{M}_2$ are averages over a timescale long compared with the time $t_H$ for the Roche lobe to move one scaleheight within the donor star. This requirement arises because stars have smooth density distributions rather than sharp edges. On timescales shorter than $t_H$ the instantaneous value of $\dot{P}$ is always in practice dominated by large but short-term effects, with varying signs often in conflict with the long-term rate. This point has
<table><caption>**Table 7**
Models of ULXs.</caption><thead><tr><th>Model</th><th>blackbody L ∝ T<sup>-4</sup></th><th>winds & nebulae</th><th>evolution</th><th>luminosity fn</th><th>L > 3 × 10<sup>40</sup> erg s<sup>-1</sup></th><th>pulsing</th><th>BeX</th><th>BH & NS</th></tr></thead><tbody><tr><td>disc-wind beaming</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>magnetic beaming</td><td>No</td><td>?</td><td>Yes</td><td>?</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>IMBH</td><td>needs M > 3 × 10<sup>4</sup>M<sub>☉</sub></td><td>?</td><td>?</td><td>?</td><td>Yes</td><td>No</td><td>No</td><td>No</td></tr><tr><td>magnetars</td><td>No</td><td>No</td><td>fieldstrength?</td><td>No</td><td>No</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>photon bubble</td><td>No</td><td>No</td><td>?</td><td>?</td><td>No</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>oriented jets</td><td>?</td><td>?</td><td>?</td><td>?</td><td>No</td><td>?</td><td>No</td><td>?</td></tr></tbody></table>

been made repeatedly in the literature, going back at least to Pringle (1975); see also e.g. Ritter (1988) and Frank et al. 2002 (Section 4.4). Pringle (1975) concluded that “... an accurate estimate of the rate of mass transfer cannot be deduced from a change of binary period”.

In response to Bachetti et al. (2021a), King and Lasota (2021) estimated $t_H \sim 1000$ yr for M82 X-2. Then observations of $\dot{P}$ over humanly accessible timescales cannot give information about $-\dot{M}_2$. King and Lasota (2021) further pointed out that direct application of the method of Bachetti et al. (2021a) to three well-studied X-ray transients with known values of $\dot{P}$ (Nova Muscae 1991, XTE J1118+480, A0620-00, see González Hernández et al. 2017 and references therein) was possible, but not encouraging. These Roche-lobe filling systems are all currently in the faint quiescent state. Under the assumption of conservative evolution, their values of $\dot{P}$ would instead predict that all three of them should currently have high mass transfer rates. Their accretion discs should therefore be steady rather than transient, putting them stably in bright states – indeed Nova Muscae 1991 would actually be a ULX. The subsequent publication (Bachetti et al., 2021b) does not answer these points.

## 4. Conclusions

Table 7 summarises how various models of ULX behaviour compare with observations. The case for disc-wind beaming appears fairly strong, and is so far compatible with a large body of data. Given that the photon-bubble model does not appear promising, this is the only model which can straightforwardly apply to both black-hole and neutron-star accretors.

Other models come into consideration if we allow for the idea that ULXs might not be a single homogenous population, but instead consist of various different types of systems (as in the example of long and short gamma-ray bursts). IMBH clearly cannot account for PULXs or Be-star ULXs, and have not been widely tested in other aspects. Unless their masses are $> 3 \times 10^4 M_☉$ they cannot account for the striking universal $L_{soft} \propto T^{-4}$ behaviour of ULX soft X-ray components with luminosities $> 3 \times 10^{39}$ erg s$^{-1}$.

Observations of Be-X-ray binaries pose a particular problem for models invoking magnetic beaming, as they make regular transitions between normal Be X-ray binary states to PULXs, and back again, when their mass supply rates are increased or decreased by von Zeipel-Lidov-Kozai cycles. None of the Be-star ULXs is observationally distinct from other Be X-ray systems when it is in its usual Be X-ray binary state, and in the ULX state these systems have all the same properties as other PULXs, including a markedly more rapid spin up rate (cf Fig. 13). None of the Be X-ray binaries appears to have a very strong magnetic field. This makes it inescapable that very strong dipole magnetic fields are not required for making a PULX. Highly-magnetic PULXs might then at most constitute some fraction of the PULX population, but there is so far no clinching demonstration that any PULX contains a neutron star with this kind of field. Even then there remains the difficulty that this model requires us to believe that strong-field neutron stars in binaries are unobservable unless the companion star supplies them with mass at a super-Eddington rate.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

No data was used for the research described in the article.

## Acknowledgments

JPL was supported by a grant from the French Space Agency CNES. MM thanks G. Israel, S. Carpano, M. Bachetti, F. Fuerst, S. Tsygankov, R. Sathyaprakash and G. Rodriguez for providing the data for Fig. 7.

## Appendix. “Standard” X-ray pulsars

To illustrate the fact that PULXs differ from standard X-ray pulsars not only in luminosity $> 10^{39}$ erg s$^{-1}$, but also in their very large spin-up rates $\dot{v} > 10^{-10}$ s$^{-2}$, we used the XRP sample with known luminosities and spin-up rates (Table A.8) as compiled by Ziolkowski (1985).

<table><caption>**Table A.8**
Observed properties of ‘classical’ X-ray pulsars.</caption><thead><tr><th>Name</th><th>L<sub>x</sub> (max) [erg s<sup>-1</sup>]</th><th>P<sub>x</sub> [s]</th><th>ν [s<sup>-2</sup>]</th></tr></thead><tbody><tr><td>SMC X-1</td><td>5.0 × 10<sup>38</sup></td><td>0.71</td><td>2.6 × 10<sup>-11</sup></td></tr><tr><td>Cen X-3</td><td>5.0 × 10<sup>37</sup></td><td>4.84</td><td>1.9 × 10<sup>-12</sup></td></tr><tr><td>GX 1+4</td><td>4.0 × 10<sup>37</sup></td><td>122</td><td>5.2 × 10<sup>-12</sup></td></tr><tr><td>4U 0115+63</td><td>3.4 × 10<sup>37</sup></td><td>3.61</td><td>2.2 × 10<sup>-12</sup></td></tr><tr><td>A 0535+26</td><td>1.0 × 10<sup>37</sup></td><td>104</td><td>3.0 × 10<sup>-12</sup></td></tr><tr><td>Her X-1</td><td>1.0 × 10<sup>37</sup></td><td>1.24</td><td>8.5 × 10<sup>-14</sup></td></tr><tr><td>Vela X-1</td><td>1.5 × 10<sup>36</sup></td><td>283</td><td>5.6 × 10<sup>-13</sup></td></tr><tr><td>GX 301-2</td><td>1.0 × 10<sup>36</sup></td><td>696</td><td>3.8 × 10<sup>-13</sup></td></tr><tr><td>X-Per</td><td>3.9 × 10<sup>33</sup></td><td>835</td><td>6.4 × 10<sup>-15</sup></td></tr></tbody></table>

## References

* Abarca, D., Kluźniak, W., Sądowski, A., 2018. Radiative GRMHD simulations of accretion and outflow in non-magnetized neutron stars and ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 479, 3936–3951. http://dx.doi.org/10.1093/mnras/sty1602, arXiv:1712.08295.

* Abarca, D., Parfrey, K., Kluźniak, W., 2021. Beamed emission from a neutron-star ULX in a GRRMHD simulation. arXiv e-prints, arXiv:2107.01149.

* Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.X., et al., 2016. Astrophysical implications of the binary black-hole merger GW150914. Astrophys. J. Lett. 818, L22. http://dx.doi.org/10.3847/2041-8205/818/2/L22, arXiv:1602.03846.

* Abbott, R., Abbott, T.D., Abraham, S., Acernese, F., Ackley, K., Adams, e., 2020. GWTC-2: Compact binary coalescences observed by LIGO and virgo during the first half of the third observing run. arXiv e-prints, arXiv:2010.14527.

* Abolmasov, P., Fabrika, S., Sholukhova, O., Afanasiev, V., 2007a. Spectroscopy of optical counterparts of ultraluminous X-ray sources. Astrophys. Bull. 62 (1), 36–51. http://dx.doi.org/10.1134/S199034130701004X, arXiv:astro-ph/0612765.

* Abolmasov, P., Fabrika, S., Sholukhova, O., Kotani, T., 2008. Optical spectroscopy of the ULX-associated nebula MF16. arXiv e-prints, arXiv:0809.0409.

* Abolmasov, P.K., Swartz, D.A., Fabrika, S., Ghosh, K.K., Sholukhova, O., Tennant, A.F., 2007b. Optical spectroscopy of the environment of a ULX in NGC 7331. Astrophys. J. 668 (1), 124–129. http://dx.doi.org/10.1086/520828, arXiv:0707.2099.

* Abramowicz, M.A., Czerny, B., Lasota, J.P., Szuszkiewicz, E., 1988. Slim accretion disks. Astrophys. J. 332, 646–658. http://dx.doi.org/10.1086/166683.

* Abramowicz, M., Jaroszynski, M., Sikora, M., 1978. Relativistic, accreting disks. Astron. Astrophys. 63, 221–224.

* Agrawal, V.K., Nandi, A., 2015. Discovery of a quasi-periodic oscillation in the ultraluminous X-ray source IC 342 X-1: XMM-Newton results. Mon. Not. R. Astron. Soc. 446 (4), 3926–3931. http://dx.doi.org/10.1093/mnras/stu2291, arXiv:1411.4135.
Alston, W.N., Pinto, C., Barret, D., D'Aì, A., Del Santo, M., Earnshaw, H., Fabian, A.C., Fuerst, F., Kara, E., Kosec, P., Middleton, M.J., Parker, M.L., Pintore, F., Robba, A., Roberts, T.P., Sathyaprakash, R., Walton, D., Ambrosi, E., 2021. Quasi-periodic dipping in the ultraluminous X-ray source, NGC 247 ULX-1. Mon. Not. R. Astron. Soc. 505 (3), 3722–3729. http://dx.doi.org/10.1093/mnras/stab1473, arXiv:2104.11163.

Andersen, B.C., Ransom, S.M., 2018. A Fourier domain “jerk” search for binary pulsars. Astrophys. J. Lett. 863 (1), L13. http://dx.doi.org/10.3847/2041-8213/aad59f, arXiv:1807.07900.

Anderson, P.W., Itoh, N., 1975. Pulsar glitches and restlessness as a hard superfluidity phenomenon. Nature 256 (5512), 25–27. http://dx.doi.org/10.1038/256025a0.

Archibald, R.F., Kaspi, V.M., Tendulkar, S.P., Schlöp, P., 2016. A magnetar-like outburst from a high-B radio pulsar. Astrophys. J. Lett. 829 (1), L21. http://dx.doi.org/10.3847/2041-8205/829/1/L21, arXiv:1608.01007.

Arcodia, R., Merloni, A., Nandra, K., Buchner, J., Salvato, M., Pasham, D., Remillard, R., Comparat, J., Lamer, G., Ponti, G., Malyali, A., Wolf, J., Arzoumanian, Z., Bogensberger, D., Buckley, D.A.H., Gendreau, K., Gromadzki, M., Kara, E., Krumpe, M., Markwardt, C., Ramos-Ceja, M.E., Rau, A., Schramm, M., Schwope, A., 2021. X-ray quasi-periodic eruptions from two previously quiescent galaxies. Nature 592 (7856), 704–707. http://dx.doi.org/10.1038/s41586-021-03394-6, arXiv:2104.13388.

Árévaló, P., Uttyler, P., 2006. Investigating a fluctuating-accretion model for the spectral-timing properties of accreting black hole systems. Mon. Not. R. Astron. Soc. 367 (2), 801–814. http://dx.doi.org/10.1111/j.1365-2966.2006.09989.x, arXiv:astro-ph/0512394.

Arnaud, K., Dorman, B., Gordon, C., 1999. XSPEC: An X-ray spectral fitting package. arXiv:9910.005.

Asvarov, A.I., 2014. Size distribution of supernova remnants and the interstellar medium: the case of M 33. Astron. Astrophys. 561, A70. http://dx.doi.org/10.1051/0004-6361/201322774, arXiv:1311.5166.

Atapin, K., Fabrika, S., Caballero-García, M.D., 2019. Ultraluminous X-ray sources with flat-topped noise and QPO. Mon. Not. R. Astron. Soc. 486 (2), 2766–2779. http://dx.doi.org/10.1093/mnras/stz1027, arXiv:1904.04905.

Bachetti, M., Harrison, F.A., Walton, D.J., Grefenstette, B.W., Chakrabarty, D., Fürst, F., Barret, D., Beloborodov, A., Boggs, S.E., Christensen, F.E., Craig, W.W., Fabian, A.C., Hailey, C.J., Hornschemeier, A., Kaspi, V., Kulkarni, S.R., Mac-carone, T., Miller, J.M., Rana, V., Stern, D., Tendulkar, S.P., Tomsick, J., Webb, N.A., Zhang, W.W., 2014. An ultraluminous X-ray source powered by an accreting neutron star. Nature 514, 202–204. http://dx.doi.org/10.1038/nature13791, arXiv:1410.3590.

Bachetti, M., Heida, M., Maccarone, T., Huppenkothen, D., Israel, G.L., Barret, D., Brightman, M., Brumback, M., Earnshaw, H.P., Forster, K., Fürst, F., Grefenstette, B.W., Harrison, F.A., Jaodand, A.D., Madsen, K.K., Middleton, M., Pike, S.N., Pilia, M., Poutanen, J., Stern, D., Tomsick, J.A., Walton, D.J., Webb, N., Wilms, J., 2021a. Orbital decay in M82 X-2. arXiv e-prints, arXiv:2112.00339v1.

Bachetti, M., Heida, M., Maccarone, T., Huppenkothen, D., Israel, G.L., Barret, D., Brightman, M., Brumback, M., Earnshaw, H.P., Forster, K., Fürst, F., Grefenstette, B.W., Harrison, F.A., Jaodand, A.D., Madsen, K.K., Middleton, M., Pike, S.N., Pilia, M., Poutanen, J., Stern, D., Tomsick, J.A., Walton, D.J., Webb, N., Wilms, J., 2021b. Orbital decay in M82 X-2. arXiv e-prints, arXiv:2112.00339v2.

Bachetti, M., Maccarone, T.J., Brightman, M., Brumback, M.C., Fürst, F., Harrison, F.A., Heida, M., Israel, G.L., Middleton, M.J., Tomsick, J.A., Webb, N.A., Walton, D.J., 2020. All at once: Transient pulsations, spin-down, and a glitch from the pulsating ultraluminous X-Ray source M82 X-2. Astrophys. J. 891 (1), 44. http://dx.doi.org/10.3847/1538-4357/ab6d00, arXiv:1905.06423.

Bachetti, M., Rana, V., Walton, D.J., Barret, D., Harrison, F.A., Boggs, S.E., Christensen, F.E., Craig, W.W., Fabian, A.C., Fürst, F., Grefenstette, B.W., Hailey, C.J., Hornschemeier, A., Madsen, K.K., Miller, J.M., Ptak, A.F., Stern, D., Webb, N.A., Zhang, W.W., 2013. The ultraluminous X-Ray sources NGC 1313 X-1 and X-2: A broadband study with NuSTAR and XMM-Newton. Astrophys. J. 778 (2), 163. http://dx.doi.org/10.1088/0004-637X/778/2/163, arXiv:1310.0745.

Baldassare, V.F., Dickey, C., Geha, M., Reines, A.E., 2020. Populating the low-mass end of the M<sub>BBH</sub>–σ relation. Astrophys. J. Lett. 898 (1), L3. http://dx.doi.org/10.3847/2041-8213/aba0c1, arXiv:2006.15150.

Basko, M.M., Sunyaev, R.A., 1976. The limiting luminosity of accreting neutron stars with magnetic fields. Mon. Not. R. Astron. Soc. 175, 395–417. http://dx.doi.org/10.1093/mnras/175.2.395.

Begelman, M.C., 2002. Super-eddington fluxes from thin accretion disks? Astrophys. J. Lett. 568, L97–L100. http://dx.doi.org/10.1086/340457, arXiv:astro-ph/0203030.

Begelman, M.C., King, A.R., Pringle, J.E., 2006. The nature of SS433 and the ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 370, 399–404. http://dx.doi.org/10.1111/j.1365-2966.2006.10469.x, arXiv:astro-ph/0604497.

Belczynski, K., 2020. The most ordinary formation of the most unusual double black hole merger. Astrophys. J. Lett. 905 (2), L15. http://dx.doi.org/10.3847/2041-8213/abcbf1, arXiv:2009.13526.

Belczynski, K., Bulik, T., Fryer, C.L., Ruiter, A., Valsecchi, F., Vink, J.S., Hurley, J.R., 2010. On the maximum mass of stellar black holes. Astrophys. J. 714, 1217–1226. http://dx.doi.org/10.1088/0004-637X/714/2/1217, arXiv:0904.2784.

Belczynski, K., Kalogera, V., Bulik, T., 2002. A comprehensive study of binary compact objects as gravitational wave sources: Evolutionary channels, rates, and physical properties. Astrophys. J. 572, 407–431. http://dx.doi.org/10.1086/340304, arXiv:astro-ph/0111452.

Belczynski, K., Kalogera, V., Rasio, F.A., Taam, R.E., Zezas, A., Bulik, T., Mac-carone, T.J., Ivanova, N., 2008. Compact object modeling with the StarTrack population synthesis code. ApJ 174, 223–260. http://dx.doi.org/10.1086/521026, arXiv:arXiv:astro-ph/0511811.

Belczynski, K., Klencki, J., Fields, C.E., Olejak, A., Berti, E., Meynet, G., Fryer, C.L., Holz, D.E., O'Shaughnessy, R., Brown, D.A., Bulik, T., Leung, S.C., Nomoto, K., Madau, P., Hirschi, R., Kaiser, E., Jones, S., Mondal, S., Chruslinska, M., Drozda, P., Gerosa, D., Doctor, Z., Giersz, M., Ekstrom, S., Georgy, C., Askar, A., Baibhav, V., Wysocki, D., Natan, T., Farr, W.M., Wiktorowicz, G., Coleman Miller, M., Farr, B., Lasota, J.P., 2020. Evolutionary roads leading to low effective spins, high black hole masses, and O1/O2 rates for LIGO/Virgo binary black holes. Astron. Astrophys. 636, A104. http://dx.doi.org/10.1051/0004-6361/201936528, arXiv:1706.07053.

Belloni, T.M., Altamirano, D., 2013. High-frequency quasi-periodic oscillations from GRS 1915+105. Mon. Not. R. Astron. Soc. 432 (1), 10–18. http://dx.doi.org/10.1093/mnras/stt500, arXiv:1303.4551.

Berghea, C.T., Dudik, R.P., 2012. Spitzer observations of MF 16 nebula and the associated ultraluminous X-Ray source. Astrophys. J. 751 (2), 104. http://dx.doi.org/10.1088/0004-637X/751/2/104, arXiv:1203.4276.

Berghea, C.T., Dudik, R.P., Weaver, K.A., Kallman, T.R., 2010a. The first detection of [O IV] from an ultraluminous X-Ray source with spitzer. I. Observational results for Holmberg II ULX. Astrophys. J. 708 (1), 354–363. http://dx.doi.org/10.1088/0004-637X/708/1/354, arXiv:0904.1837.

Berghea, C.T., Dudik, R.P., Weaver, K.A., Kallman, T.R., 2010b. The first detection of [O IV] from an ultraluminous X-ray source with spitzer. II. Evidence for high luminosity in Holmberg II ULX. Astrophys. J. 708 (1), 364–374. http://dx.doi.org/10.1088/0004-637X/708/1/364, arXiv:0909.5225.

Bhattacharya, D., van den Heuvel, E.P.J., 1991. Formation and evolution of binary and millisecond radio pulsars. Phys. Rep. 203 (1–2), 1–124. http://dx.doi.org/10.1016/0370-1573(91)90064-S.

Binder, B., Levesque, E.M., Dorn-Wallenstein, T., 2018. No strong geometric beaming in the ultraluminous neutron star binary NGC 300 ULX-1 (SN 2010da) from swift and gemini. Astrophys. J. 863 (2), 141. http://dx.doi.org/10.3847/1538-4357/aad3bd, arXiv:1807.05309.

Bonnet-Bidaud, J.M., van der Klis, M., 1981. Long term X-ray observations of SMC X-1 including a turn-on. Astron. Astrophys. 97, 134–138.

Brice, N., Zane, S., Turolla, R., Wu, K., 2021. Super-eddington emission from accreting, highly magnetized neutron stars with a multipolar magnetic field. Mon. Not. R. Astron. Soc. 504 (1), 701–715. http://dx.doi.org/10.1093/mnras/stab915, arXiv:2104.06138.

Brightman, M., Earnshaw, H., Fürst, F., Harrison, F.A., Heida, M., Israel, G., Pike, S., Stern, D., Walton, D.J., 2020a. Swift monitoring of M51: A 38 day superorbital period for the pulsar ULX7 and a new transient ultraluminous X-Ray source. Astrophys. J. 895 (2), 127. http://dx.doi.org/10.3847/1538-4357/ab7e2a, arXiv:1912.04431.

Brightman, M., Harrison, F.A., Bachetti, M., Xu, Y., Fürst, F., Walton, D.J., Ptak, A., Yukita, M., Zezas, A., 2019. A ~60 day super-orbital period originating from the ultraluminous X-Ray pulsar in M82. Astrophys. J. 873 (2), 115. http://dx.doi.org/10.3847/1538-4357/ab0215, arXiv:1901.10491.

Brightman, M., Harrison, F.A., Fürst, F., Middleton, M.J., Walton, D.J., Stern, D., Fabian, A.C., Heida, M., Barret, D., Bachetti, M., 2018. Magnetic field strength of a neutron-star-powered ultraluminous X-ray source. Nat. Astron. 2, 312–316. http://dx.doi.org/10.1038/s41550-018-0391-6, arXiv:1803.02376.

Brightman, M., Harrison, F., Walton, D.J., Fuerst, F., Hornschemeier, A., Zezas, A., Bachetti, M., Grefenstette, B., Ptak, A., Tendulkar, S., Yukita, M., 2016. Spectral and temporal properties of the ultraluminous X-Ray pulsar in M82 from 15 years of chandra observations and analysis of the pulsed emission using NuSTAR. Astrophys. J. 816 (2), 60. http://dx.doi.org/10.3847/0004-637X/816/2/60, arXiv:1507.06014.

Brightman, M., Walton, D.J., Xu, Y., Earnshaw, H.P., Harrison, F.A., Stern, D., Barret, D., 2020b. Spectral evolution of the ultraluminous X-Ray sources M82 X-1 and X-2. Astrophys. J. 889 (1), 71. http://dx.doi.org/10.3847/1538-4357/ab629a, arXiv:2001.07285.

Brorby, M., Kaaret, P., Prestwich, A., 2014. X-ray binary formation in low-metallicity blue compact dwarf galaxies. Mon. Not. R. Astron. Soc. 441 (3), 2346–2353. http://dx.doi.org/10.1093/mnras/stu736, arXiv:1404.3132.

Bykov, S.D., Gilfanov, M.R., Tsygankov, S.S., Filippova, E.V., 2022. ULX pulsar Swift J0243.6+6124 observations with NuSTAR: dominance of reflected emission in the super-Eddington state. Mon. Not. R. Astron. Soc. 516 (2), 1601–1611. http://dx.doi.org/10.1093/mnras/stac2239, arXiv:2208.03126.

Campana, S., Stella, L., Kennea, J.A., 2008. Swift observations of SAX J1808.4-3658: Monitoring the return to quiescence. Astrophys. J. Lett. 684 (2), L99. http://dx.doi.org/10.1086/592002, arXiv:0807.4444.

Canuto, V., Lodenquai, J., Ruderman, M., 1971. Thomson scattering in a strong magnetic field. Phys. Rev. D 3 (10), 2303–2308. http://dx.doi.org/10.1103/PhysRevD.3.2303.
Cappelluti, N., Predehl, P., Böhringer, H., Brunner, H., Brusa, M., Burwitz, V., Churazov, E., Dennerl, K., Finoguenov, A., Freyberg, M., Friedrich, P., Hasinger, G., Kenziorra, E., Kreykenbohm, I., Lamer, G., Meidinger, N., Mühlegger, M., Pavlinsky, M., Robrade, J., Santangelo, M., Schmitt, J., Schwope, A., Steinmitz, M., Strüder, L., Sunyaev, R., Tenzer, C., 2011. eROSITA on SRG. A X-ray all-sky survey mission. Memorie Della Societa Astronomica Italiana Supplementi 17, 159, arXiv:1004.5219.

Carpano, S., Haberl, F., Maitra, C., Vasilopoulos, G., 2018. Discovery of pulsations from NGC 300 ULX1 and its fast period evolution. Mon. Not. R. Astron. Soc. 476, L45-L49. http://dx.doi.org/10.1093/mnrasl/sly030, arXiv:1802.10341.

Castro-Tirado, A.J., Brandt, S., Lund, N., 1992. GRS 1915+105. IAU Circ 5590, 2.

Chandra, A.D., Roy, J., Agrawal, P.C., Choudhury, M., 2020. Study of recent outburst in the Be/X-ray binary RX J0209.6-7427 with AstroSat: a new ultraluminous X-ray pulsar in the Magellanic Bridge? Mon. Not. R. Astron. Soc. 495 (3), 2664-2672. http://dx.doi.org/10.1093/mnras/staa1041, arXiv:2004.04930.

Chashkina, A., Abolmasov, P., Poutanen, J., 2017. Super-Eddington accretion on to a magnetized neutron star. Mon. Not. R. Astron. Soc. 470 (3), 2799-2813. http://dx.doi.org/10.1093/mnras/stx1372, arXiv:1703.07005.

Chashkina, A., Lipunova, G., Abolmasov, P., Poutanen, J., 2019. Super-Eddington accretion discs with advection and outflows around magnetized neutron stars. Astron. Astrophys. 626, A18. http://dx.doi.org/10.1051/0004-6361/20183441, arXiv:1902.04609.

Christodoulou, D.M., Laycock, S.G.T., Kazanas, D., 2019. Meta-analysis of electron cyclotron resonance absorption features detected in high-mass X-ray binaries. Res. Astron. Astrophys. 19 (10), 146. http://dx.doi.org/10.1088/1674-4527/19/10/146, arXiv:1905.05363.

Churazov, E., Gilfanov, M., Revnivtsev, M., 2001. Soft state of Cygnus X-1: stable disc and unstable corona. Mon. Not. R. Astron. Soc. 321 (4), 759-766. http://dx.doi.org/10.1046/j.1365-8711.2001.04056.x, arXiv:astro-ph/0006227.

Clark, J.S., Ritchie, B.W., Najjarro, F., Langer, N., Negueruela, I., 2014. A VLT/FLAMES survey for massive binaries in Westerlund 1. IV. Wd1-5 binary product and a pre-supernova companion for the magnetar CXOU J1647-45? Astron. Astrophys. 565, A90. http://dx.doi.org/10.1051/0004-6361/201321771, arXiv:1405.3109.

Colbert, E.J.M., Mushotzky, R.F., 1999. The nature of accreting black holes in nearby galaxy nuclei. Astrophys. J. 519, 89-107. http://dx.doi.org/10.1086/307356, arXiv:astro-ph/9901023.

Copperwheat, C., Cropper, M., Soria, R., Wu, K., 2007. Irradiation models for ULXs and fits to optical data. Mon. Not. R. Astron. Soc. 376 (3), 1407-1423. http://dx.doi.org/10.1111/j.1365-2966.2007.11551.x, arXiv:astro-ph/0701764.

Corbet, R.H.D., Laycock, S., Coe, M.J., Marshall, F.E., Markwardt, C.B., 2004. Monitoring and discovering X-ray pulsars in the small magellanic cloud. In: Kaaret, P., Lamb, F.K., Swank, J.H. (Eds.), X-Ray Timing 2003: Rossi and beyond. In: American Institute of Physics Conference Series, Vol. 714, pp. 337-341. http://dx.doi.org/10.1063/1.1781051, arXiv:astro-ph/0402053.

Coriat, M., Corbel, S., Buxton, M.M., Bailyn, C.D., Tomsick, J.A., Körding, E., Lemczi, E., 2009. The infrared/X-ray correlation of GX 339-4: probing hard X-ray emission in accreting black holes. Mon. Not. R. Astron. Soc. 400, 123-133. http://dx.doi.org/10.1111/j.1365-2966.2009.15461.x, arXiv:0909.3283.

Coriat, M., Fender, R.P., Dubus, G., 2012. Revisiting a fundamental test of the disc instability model for X-ray binaries. Mon. Not. R. Astron. Soc. 424, 1991-2001. http://dx.doi.org/10.1111/j.1365-2966.2012.21339.x, arXiv:1205.5038.

Cseh, D., Corbel, S., Kaaret, P., Lang, C., Grisé, F., Paragi, Z., Tzioumis, A., Tudose, V., Feng, H., 2012. Black hole powered nebulae and a case study of the ultraluminous X-ray source IC 342 X-1. Astrophys. J. 749 (1), 17. http://dx.doi.org/10.1088/0004-637X/749/1/17, arXiv:1201.4473.

Cseh, D., Grisé, F., Kaaret, P., Corbel, S., Scaringi, S., Groot, P., Falcke, H., Körding, E., 2013. Towards a dynamical mass of the ultraluminous X-ray source NGC 5408 X-1. Mon. Not. R. Astron. Soc. 435 (4), 2896-2902. http://dx.doi.org/10.1093/mnras/stt1484, arXiv:1308.1251.

Cseh, D., Kaaret, P., Corbel, S., Grise, F., Lang, C., Kording, E., Falcke, H., Jonker, P.G., Miller-Jones, J.C.A., Farrell, S., Yang, Y.J., Paragi, Z., Frey, S., 2014. Unveiling recurrent jets of the ULX Holmberg II X-1: evidence for a massive stellar-mass black hole? Mon. Not. R. Astron. Soc. 439, L1-L5. http://dx.doi.org/10.1093/mnrasl/slt166, arXiv:1311.4867.

Cseh, D., Miller-Jones, J.C.A., Jonker, P.G., Grisé, F., Paragi, Z., Corbel, S., Falcke, H., Frey, S., Kaaret, P., Körding, E., 2015. The evolution of a jet ejection of the ultraluminous X-ray source Holmberg II X-1. Mon. Not. R. Astron. Soc. 452 (1), 24-31. http://dx.doi.org/10.1093/mnras/stv1308, arXiv:1506.02988.

Cui, W., 1997. Evidence for “propeller” effects in X-Ray pulsars GX 1+4 and GRO J1744-28. Astrophys. J. Lett. 482 (2), L163-L166. http://dx.doi.org/10.1086/310712, arXiv:astro-ph/9704084.

Dage, K.C., Kundu, A., Thygesen, E., Bahramian, A., Haggard, D., Irwin, J.A., Maccarone, T.J., Nair, S., Peacock, M.B., Strader, J., Zepf, S.E., 2021. Three ultraluminous X-ray sources hosted by globular clusters in NGC 1316. arXiv e-prints, arXiv:2103.16576.

Dage, K.C., Zepf, S.E., Peacock, M.B., Bahramian, A., Noroozi, O., Kundu, A., Maccarone, T.J., 2019. X-ray spectral variability of ultraluminous X-ray sources in extragalactic globular clusters. Mon. Not. R. Astron. Soc. 485 (2), 1694-1707. http://dx.doi.org/10.1093/mnras/stz479, arXiv:1902.05073.

Dage, K.C., Zepf, S.E., Thygesen, E., Bahramian, A., Kundu, A., Maccarone, T.J., Peacock, M.B., Strader, J., 2020. X-ray spectroscopy of newly identified ULXs associated with M87's globular cluster population. Mon. Not. R. Astron. Soc. 497 (1), 596-608. http://dx.doi.org/10.1093/mnras/staa1963, arXiv:2007.00671.

Dai, H.L., Li, X.D., 2006. Accretion torque on magnetized neutron stars. Astron. Astrophys. 451 (2), 581-585. http://dx.doi.org/10.1051/0004-6361:20053907, arXiv:astro-ph/0601211.

Dall'Ossó, S., Perna, R., Papitto, A., Bozzo, E., Stella, L., 2015. The accretion regimes of a highly magnetised NS: the unique case of NuSTAR J095551+6940.8. arXiv e-prints, arXiv:1512.01532.

Dauser, T., Middleton, M., Wilms, J., 2017. Modelling the light curves of ultraluminous X-ray sources as precession. Mon. Not. R. Astron. Soc. 466, 2236-2241. http://dx.doi.org/10.1093/mnras/stw3304, arXiv:1612.05035.

Davis, S.W., Narayan, R., Zhu, Y., Barret, D., Farrell, S.A., Godet, O., Servillat, M., Webb, N.A., 2011. The cool accretion disk in ESO 243-49 HLX-1: Further evidence of an intermediate-mass black hole. Astrophys. J. 734 (2), 111. http://dx.doi.org/10.1088/0004-637X/734/2/111, arXiv:1104.2614.

De Marco, B., Ponti, G., Miniutti, G., Belloni, T., Cappi, M., Dadina, M., Muñoz-Darias, T., 2013. Time lags in the ultraluminous X-ray source NGC 5408 X-1: implications for the black hole mass. Mon. Not. R. Astron. Soc. 436 (4), 3782-3791. http://dx.doi.org/10.1093/mnras/stt1853, arXiv:1310.0042.

Dewangan, G.C., Griffiths, R.E., Rao, A.R., 2006. Quasi-periodic oscillations and strongly comptonized X-Ray emission from Holmberg IX X-1. Astrophys. J. Lett. 641 (2), L125-L128. http://dx.doi.org/10.1086/504258, arXiv:astro-ph/0602472.

Dib, R., Kaspi, V.M., 2014. 16 Yr of RXTE monitoring of five anomalous X-Ray pulsars. Astrophys. J. 784 (1), 37. http://dx.doi.org/10.1088/0004-637X/784/1/37, arXiv:1401.3085.

Dib, R., Kaspi, V.M., Gavriil, F.P., 2009. Rossi X-Ray timing explorer monitoring of the anomalous X-ray pulsar 1E 1048.1 - 5937: Long-term variability and the 2007 march event. Astrophys. J. 702 (1), 614-630. http://dx.doi.org/10.1088/0004-637X/702/1/614, arXiv:0811.2659.

Dolan, J.F., Boyd, P.T., Fabrika, S., Tapia, S., Bychkov, V., Panferov, A.A., Nelson, M.J., Percival, J.W., van Citters, G.W., Taylor, D.C., Taylor, M.J., 1997. SS 433 in the ultraviolet. Astron. Astrophys. 327, 648-655.

Dominik, M., Belczynski, K., Fryer, C., Holz, D.E., Berti, E., Bulik, T., Mandel, I., O'Shaughnessy, R., 2012. Double compact objects. I. The significance of the common envelope on merger rates. Astrophys. J. 759, 52. http://dx.doi.org/10.1088/0004-637X/759/1/52, arXiv:1202.4901.

Done, C., Gierliński, M., Kubota, A., 2007. Modelling the behaviour of accretion flows in X-ray binaries. Everything you always wanted to know about accretion but were afraid to ask. A&Ar 15 (1), 1-66. http://dx.doi.org/10.1007/s00159-007-0006-1, arXiv:0708.0148.

Dopita, M.A., Payne, J.L., Filipović, M.D., Pannuti, T.G., 2012. The physical parameters of the microquasar S26 in the Sculptor Group galaxy NGC 7793. Mon. Not. R. Astron. Soc. 427 (2), 956-967. http://dx.doi.org/10.1111/j.1365-2966.2012.21947.x, arXiv:1208.3500.

Doroshenko, V., Santangelo, A., Ducci, L., 2015. Searching for coherent pulsations in ultraluminous X-ray sources. Astron. Astrophys. 579, A22. http://dx.doi.org/10.1051/0004-6361/201425225, arXiv:1410.7264.

Doroshenko, V., Tsygankov, S., Santangelo, A., 2018. Orbit and intrinsic spin-up of the newly discovered transient X-ray pulsar Swift J0243.6+6124. Astron. Astrophys. 613, A19. http://dx.doi.org/10.1051/0004-6361:201732208, arXiv:1710.10912.

Dubus, G., Hameury, J.-M., Lasota, J.-P., 2001. The disc instability model for X-ray transients: Evidence for truncation and irradiation. Astron. Astrophys. 373, 251-271. http://dx.doi.org/10.1051/0004-6361:20010632, arXiv:astro-ph/0102237.

Dubus, G., Lasota, J.-P., Hameury, J.-M., Charles, P., 1999. X-ray irradiation in low-mass binary systems. Mon. Not. R. Astron. Soc. 303, 139-147. http://dx.doi.org/10.1046/j.1365-8711.1999.02212.x, arXiv:astro-ph/9809036.

Dudik, R.P., Berghea, C.T., Roberts, T.P., Grisé, F., Singh, A., Pagano, R., Winter, L.M., 2016. Spitzer IRAC observations of IR excess in Holmberg IX X-1: A circumbinary disk or a variable jet? Astrophys. J. 831 (1), 88. http://dx.doi.org/10.3847/0004-637X/831/1/88, arXiv:1608.05348.

Duncan, R.C., Thompson, C., 1992. Formation of very strongly magnetized neutron stars: Implications for Gamma-ray bursts. Astrophys. J. Lett. 392, L9. http://dx.doi.org/10.1086/186413.

Earnshaw, H.P., Heida, M., Brightman, M., Fürst, F., Harrison, F.A., Jaodand, A., Middleton, M.J., Roberts, T.P., Sathyaprakash, R., Stern, D., Walton, D.J., 2020. The (re)appearance of NGC 925 ULX-3, a new transient ULX. Astrophys. J. 891 (2), 153. http://dx.doi.org/10.3847/1538-4357/ab77b8, arXiv:2001.00642.

Earnshaw, H.P., Roberts, T.P., Middleton, M.J., Walton, D.J., Mateos, S., 2019. A new, clean catalogue of extragalactic non-nuclear X-ray sources in nearby galaxies. Mon. Not. R. Astron. Soc. 483 (4), 5554-5573. http://dx.doi.org/10.1093/mnras/sty3403, arXiv:1812.04684.

Earnshaw, H.P., Roberts, T.P., Sathyaprakash, R., 2018. Searching for propeller-phase ULXs in the XMM-Newton serendipitous source catalogue. Mon. Not. R. Astron. Soc. 476 (3), 4272-4277. http://dx.doi.org/10.1093/mnras/sty501, arXiv:1802.07753.
Edge, W.R.T., Coe, M.J., Galache, J.L., McBride, V.A., Corbet, R.H.D., Markwardt, C.B., Laycock, S., 2004. Three new X-ray pulsars detected in the Small Magellanic Cloud and the positions of two other known pulsars determined. Mon. Not. R. Astron. Soc. 353 (4), 1286-1292. http://dx.doi.org/10.1111/j.1365-2966.2004.08150.x, arXiv: astro-ph/0406580.

Eggum, G.E., Coroniti, F.V., Katz, J.I., 1988. Radiation hydrodynamic calculation of super-eddington accretion disks. Astrophys. J. 330, 142. http://dx.doi.org/10.1086/ 166462.

Ekşi, K.Y., Andaç, I.C., Çıkintoğlu, S., Gençali, A.A., Güngör, C., Öztekin, F., 2015. The ultraluminous X-ray source NuSTAR J095551+6940.8: a magnetar in a high-mass X-ray binary. Mon. Not. R. Astron. Soc. 448, L40-L42. http://dx.doi.org/10.1093/ mnrasl/sl199, arXiv:1410.5205.

El Mellah, I., Sundqvist, J.O., Keppens, R., 2019. Wind Roche lobe overflow in high-mass X-ray binaries. A possible mass-transfer mechanism for ultraluminous X-ray sources. Astron. Astrophys. 622, L3. http://dx.doi.org/10.1051/0004-6361/ 201834543, arXiv:1810.12937.

Erkut, M.H., Türkoğlu, M.M., Ekşi, K.Y., Alpar, M.A., 2020. On the magnetic fields, beaming fractions, and fastness parameters of pulsating ultraluminous X-ray sources. Astrophys. J. 899 (2), 97. http://dx.doi.org/10.3847/1538-4357/aba61b, arXiv:2007.08102.

Evans, I.N., Primini, F.A., Glotfelty, K.J., Anderson, C.S., Bonaventura, N.R., Chen, J.C., Davis, J.E., Doe, S.M., Evans, J.D., Fabbiano, G., Galle, E.C., Gibbs, I., Grier, J.D., Hain, R.M., Hall, D.M., Harbo, P.N., He, X.H., Houck, J.C., Karovska, M., Kashyap, V.L., Lauer, J., McCollough, M.L., McDowell, J.C., Miller, J.B., Mitschang, A.W., Morgan, D.L., Mossman, A.E., Nichols, J.S., Nowak, M.A., Plummer, D.A., Refsdal, B.L., Rots, A.H., Siemiginowska, A., Sundheim, B.A., Tibbetts, M.S., Van Stone, D.W., Winkelman, S.L., Zografou, P., 2010. The chandra source catalog. ApJS 189 (1), 37-82. http://dx.doi.org/10.1088/0067-0049/189/ 1/37, arXiv:1005.4665.

Fabbiano, G., 1989. X-rays from normal galaxies. ARAA 27, 87-138. http://dx.doi.org/ 10.1146/annurev.a.a.27.090189.000511.

Fabbiano, G., Zezas, A., Murray, S.S., 2001. Chandra observations of "the antennae" galaxies (NGC 4038/9). Astrophys. J. 554, 1035-1043. http://dx.doi.org/10.1086/ 321397, arXiv:astro-ph/0102256.

Fabian, A.C., Rees, M.J., 1979. SS 433: a double jet in action? Mon. Not. R. Astron. Soc. 187, 13P-16. http://dx.doi.org/10.1093/mnras/187.1.13P.

Fabrika, S., 2004. The jets and supercritical accretion disk in SS433. ASPRv 12, 1-152, arXiv:astro-ph/0603390.

Fabrika, S.N., Atapin, K.E., Vinokurov, A.S., Sholukhova, O.N., 2021. Ultraluminous X-ray sources. Astrophys. Bull. 76 (1), 6-38. http://dx.doi.org/10.1134/ S1990341321010077, arXiv:2105.10537.

Fabrika, S., Ueda, Y., Vinokurov, A., Sholukhova, O., Shidatsu, M., 2015. Supercritical accretion disks in ultraluminous X-ray sources and SS 433. Nat. Phys. 11 (7), 551-553. http://dx.doi.org/10.1038/nphys3348, arXiv:1512.00435.

Falanga, M., Bozzo, E., Lutovinov, A., Bonnet-Bidaud, J.M., Fetisova, Y., Puls, J., 2015. Ephemeris, orbital decay, and masses of ten eclipsing high-mass X-ray binaries. Astron. Astrophys. 577, A130. http://dx.doi.org/10.1051/0004-6361/201425191, arXiv:1502.07126.

Falcke, H., Körding, E., Markoff, S., 2004. A scheme to unify low-power accreting black holes. Jet-dominated accretion flows and the radio/X-ray correlation. Astron. Astrophys. 414, 895-903. http://dx.doi.org/10.1051/0004-6361:20031683, arXiv: astro-ph/0305335.

Farrell, S.A., Webb, N.A., Barret, D., Godet, O., Rodrigues, J.M., 2009. An intermediate-mass black hole of over 500 solar masses in the galaxy ESO243-49. Nature 460, 73-75. http://dx.doi.org/10.1038/nature08083, arXiv:1001.0567.

Fender, R.P., Homan, J., Belloni, T.M., 2009. Jets from black hole X-ray binaries: testing, refining and extending empirical models for the coupling to X-rays. Mon. Not. R. Astron. Soc. 396 (3), 1370-1382. http://dx.doi.org/10.1111/j.1365-2966. 2009.14841.x, arXiv:0903.5166.

Fender, R.P., Pooley, G.G., Brocksopp, C., Newell, S.J., 1997. Rapid infrared flares in GRS 1915+105: evidence for infrared synchrotron emission. Mon. Not. R. Astron. Soc. 290 (4), L65-L69. http://dx.doi.org/10.1093/mnras/290.4.L65, arXiv:astro-ph/9707317.

Feng, H., Kaaret, P., 2008. Optical counterpart of the ultraluminous X-ray source IC 342 X-1. Astrophys. J. 675 (2), 1067-1075. http://dx.doi.org/10.1086/527353, arXiv:0711.4131.

Feng, H., Tao, L., Kaaret, P., Grisé, F., 2016. Nature of the soft ULX in NGC 247: Super- eddington outflow and transition between the supersoft and soft ultraluminous regimes. Astrophys. J. 831 (2), 117. http://dx.doi.org/10.3847/0004-637X/831/ 2/117, arXiv:1608.07212.

Ferland, G.J., Korista, K.T., Verner, D.A., Ferguson, J.W., Kingdon, J.B., Verner, E.M., 1998. CLOUDY 90: Numerical simulation of plasmas and their spectra. PASP 110 (749), 761-778. http://dx.doi.org/10.1086/316190.

Finke, J.D., Razzaque, S., 2017. The binary black hole merger rate from ultraluminous X-ray source progenitors. Mon. Not. R. Astron. Soc. 472, 3683-3691. http://dx.doi. org/10.1093/mnras/stx2248, arXiv:1708.09001.

Fragile, P.C., Blaes, O.M., Anninos, P., Salmonson, J.D., 2007. Global general relativistic magnetohydrodynamic simulation of a tilted black hole accretion disk. Astrophys. J. 668 (1), 417-429. http://dx.doi.org/10.1086/521092, arXiv:0706.4303.

Fragos, T., Lehmer, B.D., Naoz, S., Zezas, A., Basu-Zych, A., 2013. Energy feedback from X-Ray binaries in the early universe. Astrophys. J. Lett. 776 (2), L31. http://dx.doi.org/10.1088/2041-8205/776/2/L31, arXiv:1306.1405.

Frank, J., King, A., Raine, D.J., 2002. Accretion Power in Astrophysics: Third Edition.

Fuerst, F., Walton, D.J., Heida, M., Bachetti, M., Pinto, C., Middleton, M.J., Bright- man, M., Earnshaw, H.P., Barret, D., Fabian, A.C., Kretschmar, P., Pottschmidt, K., Ptak, A., Roberts, T., Stern, D., Webb, N., Wilms, J., 2021. Long-term pulse period evolution of the ultra-luminous X-ray pulsar NGC 7793 P13. arXiv e-prints, arXiv:2105.04229.

Fürst, F., Walton, D.J., Harrison, F.A., Stern, D., Barret, D., Brightman, M., Fabian, A.C., Grefenstette, B., Madsen, K.K., Middleton, M.J., Miller, J.M., Pottschmidt, K., Ptak, A., Rana, V., Webb, N., 2016. Discovery of coherent pulsations from the ultraluminous X-Ray source NGC 7793 P13. Astrophys. J. Lett. 831, L14. http://dx.doi.org/10.3847/2041-8205/831/L14, arXiv:1609.07129.

Fürst, F., Walton, D.J., Stern, D., Bachetti, M., Barret, D., Brightman, M., Harrison, F.A., Rana, V., 2017. Spectral changes in the hyperluminous pulsar in NGC 5907 as a function of super-orbital phase. Astrophys. J. 834 (1), 77. http://dx.doi.org/10. 3847/1538-4357/834/1/77, arXiv:1610.00258.

Galloway, D.K., Morgan, E.H., Levine, A.M., 2004. A frequency glitch in an accreting pulsar. Astrophys. J. 613 (2), 1164-1172. http://dx.doi.org/10.1086/423265, arXiv:astro-ph/0401476.

Gandhi, P., Dhillon, V.S., Durant, M., Fabian, A.C., Kubota, A., Makishima, K., Malzac, J., Marsh, T.R., Miller, J.M., Shahbaz, T., Spruit, H.C., Casella, P., 2010. Rapid optical and X-ray timing observations of GX339-4: multicomponent optical variability in the low/hard state. Mon. Not. R. Astron. Soc. 407 (4), 2166-2192. http://dx.doi.org/10.1111/j.1365-2966.2010.17083.x, arXiv:1005.4685.

Gao, Y., Wang, Q.D., Appleton, P.N., Lucas, R.A., 2003. Nonnuclear hyper-luminous X-ray sources in the starburst cartwheel ring galaxy. Astrophys. J. Lett. 596, L171-L174. http://dx.doi.org/10.1086/379598, arXiv:astro-ph/0309253.

Ghosh, P., Lamb, F.K., 1979. Accretion by rotating magnetic neutron stars. II. Radial and vertical structure of the transition zone in disk accretion. Astrophys. J. 232, 259-276. http://dx.doi.org/10.1086/157285.

Giacomazzo, B., Perna, R., 2013. Formation of stable magnetars from binary neutron star mergers. Astrophys. J. Lett. 771 (2), L26. http://dx.doi.org/10.1088/2041- 8205/771/L26, arXiv:1306.1608.

Gies, D.R., Huang, W., McSwain, M.V., 2002. The Spectrum of the Mass Donor Star in SS 433. Astrophys. J. Lett. 578 (1), L67-L70. http://dx.doi.org/10.1086/34443610. 48550/arXiv:astro-ph/0208044, arXiv:astro-ph/0208044.

Gilfanov, M., Churazov, E., Revnitsev, M., 2000. Frequency-resolved spectroscopy of Cyg X-1: fast variability of the reflected emission in the soft state. Mon. Not. R. Astron. Soc. 316 (4), 923-928. http://dx.doi.org/10.1046/j.1365-8711.2000.03686.x, arXiv:astro-ph/0001450.

Gladstone, J.C., Copperwheat, C., Heinke, C.O., Roberts, T.P., Cartwright, T.F., Levan, A.J., Goad, M.R., 2013. Optical counterparts of the nearest ultraluminous X-ray sources. ApJS 206 (2), 14. http://dx.doi.org/10.1088/0067-0049/206/2/14, arXiv:1303.1213.

Gladstone, J.C., Roberts, T.P., Done, C., 2009. The ultraluminous state. Mon. Not. R. Astron. Soc. 397 (4), 1836-1851. http://dx.doi.org/10.1111/j.1365-2966.2009. 15123.x, arXiv:0905.4076.

Good, M.R., Roberts, T.P., Knigge, C., Lira, P., 2002. The optical counterpart of the ultraluminous X-ray source NGC 5204 X-1. Mon. Not. R. Astron. Soc. 335 (3), L67-L70. http://dx.doi.org/10.1046/j.1365-8711.2002.05852.x, arXiv:astro-ph/0207428.

Godet, O., Lombardi, J.C., Antonini, F., Barret, D., Webb, N.A., Vingless, J., Thomas, M., 2014. Implications of the delayed 2013 outburst of ESO 243-49 HLX-1. Astrophys. J. 793, 105. http://dx.doi.org/10.1088/0004-637X/793/2/105, arXiv:1408.1819.

González Hernández, J.I., Suárez-Andrés, L., Rebolo, R., Casares, J., 2017. Extremely fast orbital decay of the black hole X-ray binary Nova Muscae 1991. Mon. Not. R. Astron. Soc. 465 (1), L15-L19. http://dx.doi.org/10.1093/mnrasl/slw182, arXiv: 1609.02961.

Greene, J.E., Strader, J., Ho, L.C., 2020. Intermediate-mass black holes. ARAA 58, 257-312. http://dx.doi.org/10.1146/annurev-astro-032620-021835, arXiv:1911. 09678.

Grisé, F., Kaaret, P., Corbel, S., Cseh, D., Feng, H., 2013. A long-term X-ray monitoring of the ultraluminous X-ray source NGC 5408 X-1 with Swift reveals the presence of dips but no orbital period. Mon. Not. R. Astron. Soc. 433 (2), 1023-1038. http://dx.doi.org/10.1093/mnras/stt783, arXiv:1305.1810.

Grisé, F., Kaaret, P., Corbel, S., Feng, H., Cseh, D., Tao, L., 2012. Optical emission of the ultraluminous X-ray source NGC 5408 X-1: Donor star or irradiated accretion disk? Astrophys. J. 745 (2), 123. http://dx.doi.org/10.1088/0004-637X/745/2/ 123, arXiv:1109.4423.

Grisé, F., Pakull, M.W., Motch, C., 2006. The ultraluminous X-ray source in Holmberg IX and its environment. In: Meurs, E.J.A., Fabbiano, G. (Eds.), Populations of High Energy Sources in Galaxies. Vol. 230, pp. 302-303. http://dx.doi.org/10.1017/ S1743921306008519, arXiv:astro-ph/0603768.
Grisé, F., Pakull, M.W., Soria, R., Motch, C., Smith, I.A., Ryder, S.D., Böttcher, M., 2008. The ultraluminous X-ray source NGC 1313 X-2. Its optical counterpart and environment. Astron. Astrophys. 486 (1), 151–163. http://dx.doi.org/10.1051/0004-6361/200809557, arXiv:0805.4011.

Gültekin, K., Cackett, E.M., Miller, J.M., Di Matteo, T., Markoff, S., Richstone, D.O., 2009. The fundamental plane of accretion onto black holes with dynamical masses. Astrophys. J. 706 (1), 404–416. http://dx.doi.org/10.1088/0004-637X/706/1/404, arXiv:0906.3285.

Gúrpide, A., Godet, D., Koliopanos, F., Webb, N., Olive, J.-F., 2021. Long-term X-ray spectral evolution of Ultraluminous X-ray sources: implications on the accretion flow geometry and the nature of the accretor. arXiv e-prints, arXiv:2102.11159.

Hameury, J.M., 2020. A review of the disc instability model for dwarf novae, soft X-ray transients and related objects. Adv. Space Res. 66 (5), 1004–1024. http://dx.doi.org/10.1016/j.asr.2019.10.022, arXiv:1910.01852.

Hameury, J.M., Lasota, J.P., 2020. Models of ultraluminous X-ray transient sources. Astron. Astrophys. 643, A171. http://dx.doi.org/10.1051/0004-6361/202038857, arXiv:2010.00365.

Harrison, F.A., Craig, W.W., Christensen, F.E., Hailey, C.J., Zhang, W.W., Boggs, S.E., Stern, D., Cook, W.R., Forster, K., Giommi, P., Grefenstette, B.W., Kim, Y., Kitaguchi, T., Koglin, J.E., Madsen, K.K., Mao, P.H., Miyasaka, H., Mori, K., Perri, M., Pivovaroff, M.J., Puccetti, S., Rana, V.R., Westergaard, N.J., Willis, J., Zoglauer, A., An, H., Bachetti, M., Barrière, N.M., Bellm, E.C., Bhalerao, V., Brejhnholz, N.F., Fuerst, F., Liebe, C.C., Markwardt, C.B., Nynka, M., Vogel, J.K., Walton, D.J., Wik, D.R., Alexander, D.M., Cominsky, L.R., Hornscheimer, A.E., Hornstrup, A., Kaspi, V.M., Madejski, G.M., Matt, G., Molendi, S., Smith, D.M., Tomsick, J.A., Ajello, M., Ballantyne, D.R., Baloković, M., Barret, D., Bauer, F.E., Blandford, R.D., Brandt, W.N., Brenneman, L.W., Chiang, J., Chakrabarty, D., Chenevez, J., Comastri, A., Dufour, F., Elvis, M., Fabian, A.C., Farrah, D., Fryer, C.L., Gottelfh, E.V., Grindlay, J.E., Helfand, D.J., Krivonsos, R., Meier, D.L., Miller, J.M., Natalucci, L., Ogle, P., Ofek, E.O., Ptak, A., Reynolds, S.P., Rigby, J.R., Tagliaferri, G., Thorsett, S.E., Treister, E., Urry, C.M., 2013. The nuclear spectroscopic telescope array (NuSTAR) high-energy X-ray mission. Astrophys. J. 770 (2), 103. http://dx.doi.org/10.1088/0004-637X/770/2/103, arXiv:1301.7307.

Hashizume, K., Ohsuga, K., Kawashima, T., Tanaka, M., 2015. Radiation hydrodynamics simulations of wide-angle outflows from super-critical accretion disks around black holes. PASJ 67 (4), 58. http://dx.doi.org/10.1093/pasj/psu132, arXiv:1412.4521.

Heida, M., Harrison, F.A., Brightman, M., Fürst, F., Stern, D., Walton, D.J., 2019a. Searching for the donor stars of ULX pulsars. Astrophys. J. 871 (2), 231. http://dx.doi.org/10.3847/1538-4357/aafa77, arXiv:1901.03776.

Heida, M., Jonker, P.G., Torres, M.A.P., Kool, E., Servillat, M., Roberts, T.P., Groot, P.J., Walton, D.J., Moon, D.S., Harrison, F.A., 2014. Near-infrared counterparts of ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 442 (2), 1054–1067. http://dx.doi.org/10.1093/mnras/stu928, arXiv:1405.1733.

Heida, M., Jonker, P.G., Torres, M.A.P., Roberts, T.P., Walton, D.J., Moon, D.S., Stern, D., Harrison, F.A., 2016. Keck/MOSFIRE spectroscopy of five ULX counterparts. Mon. Not. R. Astron. Soc. 459 (1), 771–778. http://dx.doi.org/10.1093/mnras/stw695, arXiv:1603.07024.

Heida, M., Lau, R.M., Davies, B., Brightman, M., Fürst, F., Grefenstette, B.W., Kennea, J.A., Tramper, F., Walton, D.J., Harrison, F.A., 2019b. Discovery of a red supergiant donor star in SN2010da/NGC 300 ULX-1. Astrophys. J. Lett. 883 (2), L34. http://dx.doi.org/10.3847/2041-8213/ab4139, arXiv:1909.02171.

Heil, L.M., Vaughan, S., 2010. The linear rms-flux relation in an ultraluminous X-ray source. Mon. Not. R. Astron. Soc. 405 (1), L86–L89. http://dx.doi.org/10.1111/j.1745-3933.2010.00864.x, arXiv:1003.5825.

Heil, L.M., Vaughan, S., Roberts, T.P., 2009. A systematic study of variability in a sample of ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 397 (2), 1061–1072. http://dx.doi.org/10.1111/j.1365-2966.2009.15068.x, arXiv:0905.1265.

Hernández-García, L., Vaughan, S., Roberts, T.P., Middleton, M., 2015. X-ray time lags and non-linear variability in the ultraluminous X-ray sources NGC 5408 X-1 and NGC 6946 X-1. Mon. Not. R. Astron. Soc. 453 (3), 2877–2884. http://dx.doi.org/10.1093/mnras/stv1830, arXiv:1508.01328.

Herold, H., 1979. Compton and Thomson scattering in strong magnetic fields. Phys. Rev. D 19 (10), 2868–2875. http://dx.doi.org/10.1103/PhysRevD.19.2868.

Hu, H., Inayoshi, K., Haiman, Z., Quataert, E., Kuiper, R., 2022. Long-term evolution of supercritical black hole accretion with outflows: a subgrid feedback model for cosmological simulations. arXiv e-prints, arXiv:2203.14994.

Hu, C.-P., Li, K.L., Kong, A.K.H., Ng, C.Y., Lin, L.C.-C., 2017. Swift detection of a 65 day X-Ray period from the ultraluminous pulsar NGC 7793 P13. Astrophys. J. Lett. 835 (1), L9. http://dx.doi.org/10.3847/2041-8213/835/1/L9, arXiv:1701.02449.

Ilkiewicz, K., Mikołajewska, J., Belczyński, K., Wiktorowicz, G., Karczmarek, P., 2019. Wind Roche lobe overflow as a way to make Type Ia supernovae from the widest symbiotic systems. Mon. Not. R. Astron. Soc. 485 (4), 5468–5473. http://dx.doi.org/10.1093/mnras/stz760, arXiv:1812.02602.

Inayoshi, K., Ostriker, J.P., Haiman, Z., Kuiper, R., 2018. Low-density, radiatively inefficient rotating-accretion flow on to a black hole. Mon. Not. R. Astron. Soc. 476 (1), 1412–1426. http://dx.doi.org/10.1093/mnras/sty276, arXiv:1709.07452.

Inoue, A., Ohsuga, K., Kawashima, T., 2020. Pulsed fraction of super-critical column accretion flows on to neutron stars: Modeling of ultraluminous X-ray pulsars. PASJ 72 (2), 34. http://dx.doi.org/10.1093/pasj/psa010, arXiv:2003.07569.

Irwin, J.A., Brink, T.G., Bregman, J.N., Roberts, T.P., 2010. Evidence for a stellar disruption by an intermediate-mass black hole in an extragalactic globular cluster. Astrophys. J. Lett. 712 (1), L1–L4. http://dx.doi.org/10.1088/2041-8205/712/1/L1, arXiv:0908.1115.

Israel, G.L., Belfiore, A., Stella, L., Esposito, P., Casella, P., De Luca, A., Marelli, M., Papitto, A., Perri, M., Puccetti, S., Castillo, G.A.R., Salvetti, D., Tiengo, A., Zampieri, L., D'Agostino, D., Greiner, J., Haberl, F., Novara, G., Salvaterra, R., Turolla, R., Watson, M., Wilms, J., Wolter, A., 2017a. An accreting pulsar with extreme properties drives an ultraluminous X-ray source in NGC 5907. Science 355 (6327), 817–819. http://dx.doi.org/10.1126/science.aai8635, arXiv:1609.07375.

Israel, G.L., Papitto, A., Esposito, P., Stella, L., Zampieri, L., Belfiore, A., Rodríguez Castillo, G.A., De Luca, A., Tiengo, A., Haberl, F., Greiner, J., Salvaterra, R., Sandrelli, S., Lisini, G., 2017b. Discovery of a 0.42-s pulsar in the ultraluminous X-ray source NGC 7793 P13. Mon. Not. R. Astron. Soc. 466, L48–L52. http://dx.doi.org/10.1093/mnrasl/slw218, arXiv:1609.06538.

Ivanova, N., Chaichenets, S., Fregeau, J., Heinke, C.O., Lombardi, J., Woods, T.E., 2010. Formation of black hole X-ray binaries in globular clusters. Astrophys. J. 717 (2), 948–957. http://dx.doi.org/10.1088/0004-637X/717/2/948, arXiv:1001.1767.

Jaisawal, G.K., Naik, S., 2016. Detection of cyclotron resonance scattering feature in high-mass X-ray binary pulsar SMC X-2. Mon. Not. R. Astron. Soc. 461 (1), L97–L101. http://dx.doi.org/10.1093/mnrasl/slw108, arXiv:1705.05544.

Jansen, F., Lumb, D., Altieri, B., Clavel, J., Ehle, M., Erd, C., Gabriel, C., Guainazzi, M., Gondoin, P., Much, R., Munoz, R., Santos, M., Schartel, N., Texier, D., Vancanti, G., 2001. XMM-Newton observatory. I. The spacecraft and operations. Astron. Astrophys. 365, L1–L6. http://dx.doi.org/10.1051/0004-6361/20000036.

Jaroszynski, M., Abramowicz, M.A., Paczynski, B., 1980. Supercritical accretion disks around black holes. A&A 30 (1), 1–34.

Jenke, P., Wilson-Hodge, C.A., 2017. Fermi GBM detects pulsations from Swift J0243.6+6124. Astronomer's Telegr. 10812, 1.

Jiang, Y.-F., Stone, J.M., Davis, S.W., 2013. On the thermal stability of radiation-dominated accretion disks. Astrophys. J. 778 (1), 65. http://dx.doi.org/10.1088/0004-637X/778/1/65, arXiv:1309.5646.

Jiang, Y.-F., Stone, J.M., Davis, S.W., 2014. A global three-dimensional radiation magneto-hydrodynamic simulation of super-eddington accretion disks. Astrophys. J. 796, 106. http://dx.doi.org/10.1088/0004-637X/796/2/106, arXiv:1410.0678.

Jiang, Y.-F., Stone, J.M., Davis, S.W., 2019. Super-eddington accretion disks around supermassive black holes. Astrophys. J. 880 (2), 67. http://dx.doi.org/10.3847/1538-4357/ab29ff, arXiv:1709.02845.

Jones, D.I., Andersson, N., 2001. Freely precessing neutron stars: model and observations. Mon. Not. R. Astron. Soc. 324 (4), 811–824. http://dx.doi.org/10.1046/j.1365-8711.2001.04251.x, arXiv:astro-ph/0011063.

Kaaret, P., Corbel, S., 2009. A photoionized nebula surrounding and variable optical continuum emission from the ultraluminous X-ray source in NGC 5408. Astrophys. J. 697 (1), 950–956. http://dx.doi.org/10.1088/0004-637X/697/1/950, arXiv:0903.5329.

Kaaret, P., Corbel, S., Prestwich, A.H., Zezas, A., 2003. Radio emission from an ultraluminous X-ray source. Science 299 (5605), 365–368. http://dx.doi.org/10.1126/science.1079610, arXiv:astro-ph/0302182.

Kaaret, P., Feng, H., 2007. Confirmation of the 62 day X-Ray periodicity from M82. Astrophys. J. 669 (1), 106–108. http://dx.doi.org/10.1086/521598, arXiv:0707.1055.

Kaaret, P., Feng, H., Roberts, T.P., 2017. Ultraluminous X-ray sources. ARAA 55, 303–341. http://dx.doi.org/10.1146/annurev-astro-091916-055259, arXiv:1703.10728.

Kaaret, P., Feng, H., Wong, D.S., Tao, L., 2010. Direct detection of an ultraluminous ultraviolet source. Astrophys. J. Lett. 714 (1), L167–L170. http://dx.doi.org/10.1088/2041-8205/714/1/L167, arXiv:1003.4257.

Kaaret, P., Simet, M.G., Lang, C.C., 2006. The orbital period of the ultraluminous X-ray source in M 82. Science 311, 491. http://dx.doi.org/10.1126/science.1121067, arXiv:astro-ph/0603653.

Kaaret, P., Ward, M.J., Zezas, A., 2004. High-resolution imaging of the Hell J4686 emission line nebula associated with the ultraluminous X-ray source in Holmberg II. Mon. Not. R. Astron. Soc. 351 (3), L83–L88. http://dx.doi.org/10.1111/j.1365-2966.2004.08020.x, arXiv:astro-ph/0407031.

Kajava, J.J.E., Poutanen, J., 2008. Spectral variability of ultraluminous X-ray sources. In: Axelsson, M. (Ed.), American Institute of Physics Conference Series. Vol. 1054, pp. 39–47. http://dx.doi.org/10.1063/1.3002507, arXiv:0809.4634.

Kajava, J.J.E., Poutanen, J., 2009. Spectral variability of ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 398, 1450–1460. http://dx.doi.org/10.1111/j.1365-2966.2009.15925.x, arXiv:0906.1485.

Kara, E., Pinto, C., Walton, D.J., Alston, W.N., Bachetti, M., Barret, D., Brightman, M., Canizares, C.R., Earnshaw, H.P., Fabian, A.C., Fürst, F., Kosec, P., Middleton, M.J., Roberts, T.P., Soria, R., Tao, L., Webb, N.A., 2020. Discovery of a soft X-ray lag in the ultraluminous X-ray source NGC 1313 X-1. Mon. Not. R. Astron. Soc. 491 (4), 5172–5178. http://dx.doi.org/10.1093/mnras/stz3318, arXiv:1911.09582.

Kawashima, T., Mineshige, S., Ohsuga, K., Ogawa, T., 2016. A radiation-hydrodynamics model of accretion columns for ultra-luminous X-ray pulsars. PASJ 68 (5), 83. http://dx.doi.org/10.1093/pasj/psw075, arXiv:1608.04211.
Kawashima, T., Ohsuga, K., 2020. Super-critical column accretion on to strongly magnetized neutron stars in ULX pulsars. PASJ 72 (1), 15. http://dx.doi.org/10.1093/pasj/psz136.

Kennea, J.A., Lien, A.Y., Krimm, H.A., Cenko, S.B., Siegel, M.H., 2017. Swift J0243.6+6124: Swift discovery of an accreting NS transient. Astronomer's Astron. 10809, 1.

Khan, N., Middleton, M.J., Wiktorowicz, G., Dauser, T., Roberts, T.P., Wilms, J., 2021. The impact of precession on the observed population of ULXs. Mon. Not. R. Astron. Soc. http://dx.doi.org/10.1093/mnras/stab3049, arXiv:2110.11318.

King, A.R., 2002. The brightest black holes. Mon. Not. R. Astron. Soc. 335, L13-L16. http://dx.doi.org/10.1046/j.1365-8711.2002.05745.x, arXiv:astro-ph/0206117.

King, A.R., 2004. Ultraluminous X-ray sources and star formation. Mon. Not. R. Astron. Soc. 347, L18-L20. http://dx.doi.org/10.1111/j.1365-2966.2004.07403.x, arXiv:astro-ph/0309450.

King, A.R., 2009. Masses, beaming and Eddington ratios in ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 393 (1), L41-L44. http://dx.doi.org/10.1111/j.1745-3933.2008.00594.x, arXiv:0811.1473.

King, A., 2011. The brightest cluster X-ray sources. Astrophys. J. Lett. 732, L28. http://dx.doi.org/10.1088/2041-8205/732/2/L28, arXiv:1104.0751.

King, A., 2020. GSN 069 - A tidal disruption near miss. Mon. Not. R. Astron. Soc. 493 (1), L120-L123. http://dx.doi.org/10.1093/mnrasslaa020, arXiv:2002.00970.

King, A., 2022. Quasi-periodic eruptions from galaxy nuclei. Mon. Not. R. Astron. Soc. http://dx.doi.org/10.1093/mnras/stac1641, arXiv:2206.04698.

King, A.R., Begelman, M.C., 1999. Radiatively driven outflows and avoidance of common-envelope evolution in close binaries. Astrophys. J. Lett. 519 (2), L169-L171. http://dx.doi.org/10.1086/312126, arXiv:astro-ph/9904105.

King, A.R., Davies, M.B., Ward, M.J., Fabbiano, G., Elvis, M., 2001. Ultraluminous X-ray sources in external galaxies. Astrophys. J. Lett. 552, L109-L112. http://dx.doi.org/10.1086/320343, arXiv:astro-ph/0104333.

King, A., Lasota, J.-P., 2016. ULXs: Neutron stars versus black holes. Mon. Not. R. Astron. Soc. 458, L10-L13. http://dx.doi.org/10.1093/mnraslslw011, arXiv:1601.03738.

King, A., Lasota, J.-P., 2019. No magnetars in ULXs. Mon. Not. R. Astron. Soc. 485, 3588-3594. http://dx.doi.org/10.1093/mnras/stz720, arXiv:1903.03624.

King, A., Lasota, J.-P., 2020. Pulsing and non-pulsing ULXs: the iceberg emerges. arXiv e-prints, arXiv:2003.14019.

King, A., Lasota, J.-P., 2021. One for the Future: measuring the mass transfer rate in the ULX M82 X-2 by using orbital period changes will take milenia. arXiv e-prints, arXiv:2112.03779.

King, A., Lasota, J.-P., Kluźniak, W., 2017. Pulsing ULXs: tip of the iceberg? Mon. Not. R. Astron. Soc. 468, L59-L62. http://dx.doi.org/10.1093/mnraslslx020, arXiv:1702.00808.

King, A., Muldrew, S.I., 2016. Black hole winds II: Hyper-Eddington winds and feedback. Mon. Not. R. Astron. Soc. 455 (2), 1211-1217. http://dx.doi.org/10.1093/mnras/stw2347, arXiv:1510.01736.

King, A., Nealon, R., 2019. Supermassive black hole demographics: evading M - σ. Mon. Not. R. Astron. Soc. 487 (4), 4827-4831. http://dx.doi.org/10.1093/mnras/stz1569, arXiv:1906.00064.

King, A.R., Pounds, K.A., 2003. Black hole winds. Mon. Not. R. Astron. Soc. 345 (2), 657-659. http://dx.doi.org/10.1046/j.1365-8711.2003.06980.x, arXiv:astro-ph/0305541.

King, A., Pounds, K., 2015. Powerful outflows and feedback from active galactic nuclei. ARAA 53, 115-154. http://dx.doi.org/10.1146/annurev-astro-082214-122316, arXiv:1503.05206.

King, A.R., Ritter, H., 1998. The light curves of soft X-ray transients. Mon. Not. R. Astron. Soc. 293 (1), L42-L48. http://dx.doi.org/10.1046/j.1365-8711.1998.01295.x.

King, A.R., Ritter, H., 1999. Cygnus X-2, super-Eddington mass transfer, and pulsar binaries. Mon. Not. R. Astron. Soc. 309, 253-260. http://dx.doi.org/10.1046/j.1365-8711.1999.02862.x, arXiv:astro-ph/9812343.

King, A.R., Taam, R.E., Begelman, M.C., 2000. The evolutionary status of SS 433. Astrophys. J. Lett. 530 (1), L25-L28. http://dx.doi.org/10.1086/312475, arXiv:astro-ph/9912396.

Kippenhahn, R., Weigert, A., 1967. Entwicklung in engen Doppelsternsystemen I. Massenaustausch vor und nach Beendigung des zentralen Wasserstoff-Brennens. Z. Astrophys. 65, 251.

Kitaki, T., Mineshige, S., Ohsuga, K., Kawashima, T., 2018. Systematic two-dimensional radiation-hydrodynamic simulations of super-Eddington accretion flow and outflow: Comparison with the slim disk model. PASJ 70 (6), 108. http://dx.doi.org/10.1093/pasj/psy110, arXiv:1809.01151.

Kitaki, T., Mineshige, S., Ohsuga, K., Kawashima, T., 2021. The origins and impact of outflow from super-Eddington flow. PASJ 73 (2), 450-466. http://dx.doi.org/10.1093/pasj/pasb011.

Klencki, J., Moe, M., Gladysz, W., Chruslinska, M., Holz, D.E., Belczynski, K., 2018. Impact of inter-correlated initial binary parameters on double black hole and neutron star mergers. Astron. Astrophys. 619, A77. http://dx.doi.org/10.1051/0004-6361/201833025, arXiv:1808.07889.

Klochkov, D., Staubert, R., Postnov, K., Shakura, N., Santangelo, A., 2009. Continuous monitoring of pulse period variations in Hercules X-1 using Swift/BAT. Astron. Astrophys. 506 (3), 1261-1267. http://dx.doi.org/10.1051/0004-6361/200912791, arXiv:0908.0053.

Kluźniak, W., Lasota, J.-P., 2015. An ultraluminous nascent millisecond pulsar. Mon. Not. R. Astron. Soc. 448, L43-L47. http://dx.doi.org/10.1093/mnrasl/sl200, arXiv:1411.1005.

Koliopanos, F., Vasilopoulos, G., Buchner, J., Maitra, C., Haberl, F., 2019. Investigating ULX accretion flows and cyclotron resonance in NGC 300 ULX1. Astron. Astrophys. 621, A118. http://dx.doi.org/10.1051/0004-6361/201834144, arXiv:1811.06251.

Koliopanos, F., Vasilopoulos, G., Godet, O., Bachetti, M., Webb, N.A., Barret, D., 2017. ULX spectra revisited: Accreting, highly magnetized neutron stars as the engines of ultraluminous X-ray sources. Astron. Astrophys. 608, A47. http://dx.doi.org/10.1051/0004-6361/201730922, arXiv:1710.04953.

Kong, A.K.H., Di Stefano, R., 2003. A luminous recurrent supersoft X-ray source in NGC 300. Astrophys. J. Lett. 590 (1), L13-L16. http://dx.doi.org/10.1086/376552, arXiv:astro-ph/0304510.

Kong, A.K.H., Hu, C.-P., Lin, L.C.-C., Li, K.L., Jin, R., Liu, C.Y., Yen, D.C.-C., 2016. A possible 55-d X-ray period of the ultraluminous accreting pulsar M82 X-2. Mon. Not. R. Astron. Soc. 461, 4395-4399. http://dx.doi.org/10.1093/mnras/stw1558, arXiv:1606.08520.

Kong, L.-D., Zhang, S., Zhang, S.-N., Ji, L., Doroshenko, V., Santangelo, A., Chen, Y.-P., Lu, F.-J., Ge, M.-Y., Wang, P.-J., Tao, L., Qu, J.-L., Li, T.-P., Liu, C.-Z., Liao, J.-Y., Chang, Z., Peng, J.-Q., Shui, Q.-C., 2022. Insight-HXMT discovery of the highest-energy CRSF from the first galactic ultraluminous X-ray pulsar swift J0243.6+6124. ApJL 933 (1), L3. http://dx.doi.org/10.3847/2041-8213/ac7711, arXiv:2206.04283.

Körding, E., Colbert, E., Falcke, H., 2005. A radio monitoring survey of ultra-luminous X-ray sources. Astron. Astrophys. 436 (2), 427-436. http://dx.doi.org/10.1051/0004-6361/20042452, arXiv:astro-ph/0502265.

Körding, E., Falcke, H., Markoff, S., 2002. Population X: Are the super-Eddington X-ray sources beamed jets in microblazars or intermediate mass black holes? Astron. Astrophys. 382, L13-L16. http://dx.doi.org/10.1051/0004-6361/20011776, arXiv:astro-ph/0112385.

Kosec, P., Pinto, C., Fabian, A.C., Walton, D.J., 2018a. Searching for outflows in ultraluminous X-ray sources through high-resolution X-ray spectroscopy. Mon. Not. R. Astron. Soc. 473 (4), 5680-5697. http://dx.doi.org/10.1093/mnras/stx2695, arXiv:1710.06438.

Kosec, P., Pinto, C., Reynolds, C.S., Guainazzi, M., Kara, E., Walton, D.J., Fabian, A.C., Parker, M.L., Valtchanov, I., 2012. Ionized emission and absorption in a large sample of ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 508 (3), 3569-3588. http://dx.doi.org/10.1093/mnras/stab2856, arXiv:2109.14683.

Kosec, P., Pinto, C., Walton, D.J., Fabian, A.C., Bachetti, M., Brightman, M., Fürst, F., Grefenstette, B.W., 2018b. Evidence for a variable Ultrafast Outflow in the newly discovered Ultraluminous Pulsar NGC 300 ULX-1. Mon. Not. R. Astron. Soc. 479 (3), 3978-3986. http://dx.doi.org/10.1093/mnras/sty1626, arXiv:1803.02367.

Kotani, T., Kawai, N., Aoki, T., Doty, J., Matsuoka, M., Mitsuda, K., Nagase, F., Ricker, G., White, N.E., 1994. Discovery of the double Doppler-shifted emission-line systems in the X-Ray spectrum of SS 433. PASJ 46, L147-L150.

Kotko, I., Lasota, J.P., 2012. The viscosity parameter α and the properties of accretion disc outbursts in close binaries. Astron. Astrophys. 545, A115. http://dx.doi.org/10.1051/0004-6361/201219618, arXiv:1209.0017.

Kotze, M.M., Charles, P.A., 2012. Characterizing X-ray binary long-term variability. Mon. Not. R. Astron. Soc. 420 (2), 1575-1589. http://dx.doi.org/10.1111/j.1365-2966.2011.20146.x, arXiv:1111.1296.

Kovlakas, K., Fragos, T., Schaerer, D., Mesinger, A., 2022. The ionizing and heating power of ultraluminous X-ray sources under the geometrical beaming model. arXiv e-prints, arXiv:2207.09331.

Kovlakas, K., Zezas, A., Andrews, J.J., Basu-Zych, A., Fragos, T., Hornschemeier, A., Kouroumpatzakis, K., Lehmer, B., Ptak, A., 2021. The heraklion extragalactic catalogue (HECATE): a value-added galaxy catalogue for multimessenger astrophysics. Mon. Not. R. Astron. Soc. 506 (2), 1896-1915. http://dx.doi.org/10.1093/mnras/stab1799, arXiv:2106.12101.

Kovlakas, K., Zezas, A., Andrews, J.J., Basu-Zych, A., Fragos, T., Hornschemeier, A., Lehmer, B., Ptak, A., 2020. A census of ultraluminous X-ray sources in the local Universe. Mon. Not. R. Astron. Soc. 498 (4), 4790-4810. http://dx.doi.org/10.1093/mnras/staa2481, arXiv:2008.10572.

Kozai, Y., 1962. Secular perturbations of asteroids with high inclination and eccentricity. Astron. J. 67, 591-598. http://dx.doi.org/10.1086/108790.

Kozłowski, M., Jaroszynski, M., Abramowicz, M.A., 1978. The analytic theory of fluid disks orbiting the Kerr black hole. Astron. Astrophys. 63 (1-2), 209-220.

Kretschmar, P., Kreykenbohm, I., Wilms, J., Staubert, R., Heindl, W.A., Gruber, D.E., Rothschild, R.E., 2000. Disappearing pulses in Vela X-1. In: McConnell, M.L., Ryan, J.M. (Eds.), The Fifth Compton Symposium: In: American Institute of Physics Conference Series, Vol. 510, pp. 163-167. http://dx.doi.org/10.1063/1.1303195, arXiv:astro-ph/9910539.

Kuranov, A.G., Postnov, K.A., Yungelson, L.R., 2020. Population synthesis of ultraluminous X-ray sources with magnetized neutron stars. Astron. Lett. 46 (10), 658-676. http://dx.doi.org/10.1134/S1063773720100084, arXiv:2010.03488.
Lai, D., 2003. Warping of accretion disks with magnetically driven outflows: A possible origin for jet precession. Astrophys. J. Lett. 591 (2), L119–L122. http://dx.doi.org/10.1086/377163, arXiv:astro-ph/0306012.

Lander, S.K., Jones, D.I., 2009. Magnetic fields in axisymmetric neutron stars. Mon. Not. R. Astron. Soc. 395 (4), 2162–2176. http://dx.doi.org/10.1111/j.1365-2966.2009.14667.x, arXiv:0903.0827.

Lang, C.C., Kaaret, P., Corbel, S., Mercer, A., 2007. A radio nebula surrounding the ultraluminous X-ray source in NGC 5408. Astrophys. J. 666 (1), 79–85. http://dx.doi.org/10.1086/519553, arXiv:0705.1978.

Lasota, J.-P., 2001. The disc instability model of dwarf novae and low-mass X-ray binary transients. New Astron. Rev. 45, 449–508. http://dx.doi.org/10.1016/S1387-6473(01)00112-9, arXiv:astro-ph/0102072.

Lasota, J.-P., 2016. Black hole accretion discs. In: Bambi, C. (Ed.), Astrophysics of Black Holes: From Fundamental Aspects to Latest Developments. In: Astrophysics and Space Science Library, Vol. 440, p. 1. http://dx.doi.org/10.1007/978-3-662-52859-4,1, arXiv:1505.02172.

Lasota, J.-P., King, A.R., Dubus, G., 2015. X-ray transients: Hyper- or hypoluminous? Astrophys. J. Lett. 801, L4. http://dx.doi.org/10.1088/2041-8205/801/1/L4, arXiv:1502.00103.

Lasota, J.-P., Vieira, R.S.S., Sąkowski, A., Narayan, R., Abramowicz, M.A., 2016. The slimming effect of advection on black-hole accretion flows. Astron. Astrophys. 587, A13. http://dx.doi.org/10.1051/0004-6361/201527636, arXiv:1510.09152.

Lau, R.M., Heida, M., Walton, D.J., Kasliwal, M.M., Adams, S.M., Cody, A.M., De, K., Gehrz, R.D., Fürst, F., Jencson, J.E., Kennea, J.A., Masci, F., 2019. Uncovering red and dusty ultraluminous X-Ray sources with spitzer. Astrophys. J. 878 (1), 71. http://dx.doi.org/10.3847/1538-4357/abl1bc, arXiv:1904.09852.

Lehmer, B.D., Eufrasio, R.T., Basu-Zych, A., Doore, K., Fragos, T., Garofali, K., Kovlakas, K., Williams, B.F., Zezas, A., Santana-Silva, L., 2021. The metallicity dependence of the high-mass X-Ray binary luminosity function. Astrophys. J. 907 (1), 17. http://dx.doi.org/10.3847/1538-4357/abccec1, arXiv:2011.09476.

Lewin, W.H.G., van Paradijk, J., van den Heuvel, E.P.J., 1997. X-ray Binaries.

Li, J., Ostriker, J., Sunyaev, R., 2013. Rotating accretion flows: From infinity to the black hole. Astrophys. J. 767 (2), 105. http://dx.doi.org/10.1088/0004-637X/767/2/105, arXiv:1206.4059.

Licquia, T.C., Newman, J.A., 2015. Improved estimates of the milky way's stellar mass and star formation rate from hierarchical Bayesian meta-analysis. Astrophys. J. 806, 96. http://dx.doi.org/10.1088/0004-637X/806/1/96, arXiv:1407.1078.

Lidov, M.L., 1962. The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. PLANSS 9 (10), 719–759. http://dx.doi.org/10.1016/0032-0633(62)090129-0.

Lin, D., Irwin, J.A., Webb, N.A., Barret, D., Remillard, R.A., 2013. Discovery of a highly variable dipping ultraluminous X-Ray source in M94. Astrophys. J. 779 (2), 149. http://dx.doi.org/10.1088/0004-637X/779/2/149, arXiv:1311.1198.

Linden, T., Kalogera, V., Spimpensky, J.F., Prestwich, A., Zezas, A., Gallagher, J.S., 2010. The effect of starburst metallicity on bright X-ray binary formation pathways. Astrophys. J. 725, 1984–1994. http://dx.doi.org/10.1088/0004-637X/725/2/1984, arXiv:1005.1639.

Lipunov, V.M., Shakura, N.I., 1980. Interaction of the accretion disk with the magnetic field of a neutron star. Sov. Astron. Lett. 6, 14–17.

Liu, J.-F., Bregman, J.N., Bai, Y., Justham, S., Crowther, P., 2013. Puzzling accretion onto a black hole in the ultraluminous X-ray source M 101 ULX-1. Nature 503 (7477), 500–503. http://dx.doi.org/10.1038/nature12762, arXiv:1312.0337.

Liu, J.-F., Bregman, J., Miller, J., Kaaret, P., 2007. Optical studies of the ultraluminous X-Ray source NGC 1313 X-2. Astrophys. J. 661 (1), 165–172. http://dx.doi.org/10.1086/516624, arXiv:astro-ph/0703697.

López, K.M., Heida, M., Jonker, P.G., Torres, M.A.P., Roberts, T.P., Walton, D.J., Moon, D.S., Harrison, F.A., 2017. A systematic search for near-infrared counterparts of nearby ultraluminous X-ray sources (II). Mon. Not. R. Astron. Soc. 469 (1), 671–682. http://dx.doi.org/10.1093/mnras/stx857, arXiv:1704.01068.

López, K.M., Heida, M., Jonker, P.G., Torres, M.A.P., Roberts, T.P., Walton, D.J., Moon, D.S., Harrison, F.A., 2020. NIR counterparts to ULXs (III): completing the photometric survey and selected spectroscopic results. Mon. Not. R. Astron. Soc. 497 (1), 917–932. http://dx.doi.org/10.1093/mnras/staa1920, arXiv:2006.02795.

Luangtip, W., Roberts, T.P., Done, C., 2016. The X-ray spectral evolution of the ultraluminous X-ray source Holmberg IX X-1. Mon. Not. R. Astron. Soc. 460 (4), 4417–4432. http://dx.doi.org/10.1093/mnras/stw1282, arXiv:1605.08246.

Luangtip, W., Roberts, T.P., Mineo, S., Lehmer, B.D., Alexander, D.M., Jackson, F.E., Goulding, A.D., Fischer, J.L., 2015. A deficit of ultraluminous X-ray sources in luminous infrared galaxies. Mon. Not. R. Astron. Soc. 446, 470–492. http://dx.doi.org/10.1093/mnras/stu2086, arXiv:1410.1569.

Lutovinov, A.A., Tsygankov, S.S., 2009. Timing characteristics of the hard X-ray emission from bright X-ray pulsars based on INTEGRAL data. Astron. Lett. 35 (7), 433–456. http://dx.doi.org/10.1134/S1063773709070019, arXiv:0907.4288.

Lyubarskii, Y.E., 1997. Flicker noise in accretion discs. Mon. Not. R. Astron. Soc. 292 (3), 679–685. http://dx.doi.org/10.1093/mnras/292/3.679.

Maccarone, T.J., Kundu, A., Zepf, S.E., Rhode, K.L., 2007. A black hole in a globular cluster. Nature 445 (7124), 183–185. http://dx.doi.org/10.1038/nature05434, arXiv:astro-ph/0701310.

Maccarone, T.J., Kundu, A., Zepf, S.E., Rhode, K.L., 2011. A new globular cluster black hole in NGC 4472. Mon. Not. R. Astron. Soc. 410 (3), 1655–1659. http://dx.doi.org/10.1111/j.1365-2966.2010.17547.x, arXiv:1008.2896.

Madhusudhan, N., Rappaport, S., Podsiadlowski, P., Nelson, L., 2008. Models for the observable system parameters of ultraluminous X-Ray sources. Astrophys. J. 688, 1235–1249. http://dx.doi.org/10.1086/592237, arXiv:0710.3854.

Mainieri, V., Vignali, C., Merloni, A., Civano, F., Puccetti, S., Brusa, M., Gilli, R., Bolzonella, M., Comastri, A., Zamorani, G., Aller, M., Carollo, M., Scarlata, C., Elvis, M., Aldcroft, T.L., Cappelluti, N., Fabbiano, G., Finoguenov, A., Fiore, F., Fruscone, A., Koekemoer, A.M., Contini, T., Kneib, J.-P., Le Fèvre, O., Lilly, S., Renzini, A., Scodeggio, M., Bardelli, S., Bongiorno, A., Caputi, K., Coppa, G., Cucatti, O., de la Torre, S., de Ravel, L., Franzetti, P., Garilli, B., Iovino, A., Kampczyk, P., Knobel, C., Kovač, K., Lamareille, F., Le Borgne, J.-F., Le Brun, V., Maier, C., Mignoli, M., Pello, R., Peng, Y., Perez Montero, E., Ricciardelli, E., Silverman, J.D., Tanaka, M., Tasca, L., Tresse, L., Vergani, D., Zucca, E., Capak, P., Ilbert, O., Impey, C., Salvato, M., Scoville, N., Taniguchi, Y., Trump, J., 2010. Ultraluminous X-ray sources out to z 0.3 in the COSMOS field. Astron. Astrophys. 514, A85. http://dx.doi.org/10.1051/0004-6361/200912544, arXiv:1002.4299.

Mapelli, M., Annibali, F., Zampieri, L., Soria, R., 2013. A disrupted bulgeless satellite galaxy as counterpart of the ultraluminous X-ray source ESO 243-49 HLX-1. Astron. Astrophys. 559, A124. http://dx.doi.org/10.1051/0004-6361/201322435, arXiv:1310.0027.

Mapelli, M., Colpi, M., Zampieri, L., 2009. Low metallicity and ultra-luminous X-ray sources in the Cartwheel galaxy. Mon. Not. R. Astron. Soc. 395, L71–L75. http://dx.doi.org/10.1111/j.1745-3933.2009.00645.x, arXiv:0902.3540.

Mapelli, M., Ripamonti, E., Zampieri, L., Colpi, M., Bressan, A., 2010. Ultra-luminous X-ray sources and remnants of massive metal-poor stars. Mon. Not. R. Astron. Soc. 408, 234–253. http://dx.doi.org/10.1111/j.1365-2966.2010.17048.x, arXiv:1005.3548.

Marchant, P., Langer, N., Podsiadlowski, P., Tauris, T.M., de Mink, S., Mandel, I., Moriya, T.J., 2017. Ultra-luminous X-ray sources and neutron-star-black-hole mergers from very massive close binaries at low metallicity. Astron. Astrophys. 604, A55. http://dx.doi.org/10.1051/0004-6361/201630188, arXiv:1705.04734.

Margon, B., Ford, H.C., Grandi, S.A., Stone, R.P.S., 1979. Enormous periodic Doppler shifts in SS433. Astrophys. J. Lett. 233, L63–L68. http://dx.doi.org/10.1086/183077.

Marshall, H.L., Canizares, C.R., Hillwig, T., Mioduszewski, A., Rupen, M., Schulz, N.S., Nowak, M., Heinz, S., 2013. Multiwavelength Observations of the SS 433 Jets. Astrophys. J. 775 (1), 75. http://dx.doi.org/10.1088/0004-637X/775/1/75, arXiv:1307.8427.

Martin, R.G., Nixon, C., Lubow, S.H., Armitage, P.J., Price, D.J., Doğan, S., King, A., 2014. The KozaI-Lidov mechanism in hydrodynamical disks. Astrophys. J. Lett. 792 (2), L33. http://dx.doi.org/10.1088/2041-8205/792/2/L33, arXiv:1409.1226.

Mauerhan, J.C., Muno, M.P., Morris, M.R., Stolovy, S.R., Cotera, A., 2010. Near-infrared counterparts to chandra X-ray sources toward the galactic center. II. Discovery of wolf-rayet stars and O supergiants. Astrophys. J. 710 (1), 706–728. http://dx.doi.org/10.1088/0004-637X/710/1/706, arXiv:0912.1055.

McClintock, J.E., Shafee, R., Narayan, R., Remillard, R.A., Davis, S.W., Li, L.-X., 2006. The spin of the near-extreme Kerr black hole GRS 1915+105. Astrophys. J. 652 (1), 518–539. http://dx.doi.org/10.1086/508457, arXiv:astro-ph/0606076.

McKinney, J.C., Gammie, C.F., 2002. Numerical models of viscous accretion flows near black holes. Astrophys. J. 573 (2), 728–737. http://dx.doi.org/10.1086/340761, arXiv:astro-ph/0204045.

Medvedev, A., Fabrika, S., 2010. Evidence of supercritical disc funnel radiation in X-ray spectra of SS 433. Mon. Not. R. Astron. Soc. 402 (1), 479–491. http://dx.doi.org/10.1111/j.1365-2966.2009.15896.x, arXiv:0910.3186.

Merloni, A., Heinz, S., di Matteo, T., 2003. A Fundamental Plane of black hole activity. Mon. Not. R. Astron. Soc. 345 (4), 1057–1076. http://dx.doi.org/10.1046/j.1365-2966.2003.07017.x, arXiv:astro-ph/0305261.

Mezcue, M., Farrell, S.A., Gladstone, J.C., Lobanov, A.P., 2013a. Milliarcsec-scale radio emission of ultraluminous X-ray sources: steady jet emission from an intermediate-mass black hole? Mon. Not. R. Astron. Soc. 436 (2), 1546–1554. http://dx.doi.org/10.1093/mnras/stt1674, arXiv:1309.4463.

Mezcue, M., Lobanov, A.P., 2011. Compact radio emission in Ultraluminous X-ray sources. Astron. Nachr. 332 (4), 379. http://dx.doi.org/10.1002/asna.201011504, arXiv:1011.0946.

Mezcue, M., Roberts, T.P., Lobanov, A.P., Sutton, A.D., 2015. The powerful jet of an off-nuclear intermediate-mass black hole in the spiral galaxy NGC 2276. Mon. Not. R. Astron. Soc. 448 (2), 1893–1899. http://dx.doi.org/10.1093/mnras/stv143, arXiv:1501.04897.

Mezcue, M., Roberts, T.P., Sutton, A.D., Lobanov, A.P., 2013b. Radio observations of extreme ULXs: revealing the most powerful ULX radio nebula ever or the jet of an intermediate-mass black hole? Mon. Not. R. Astron. Soc. 436 (4), 3128–3134. http://dx.doi.org/10.1093/mnras/stt1794, arXiv:1309.5721.

Middleton, M.J., Brightman, M., Pintore, F., Bachetti, M., Fabian, A.C., Fürst, F., Walton, D.J., 2019a. On the magnetic field in M51 ULX-8. Mon. Not. R. Astron. Soc. 486 (1), 2–9. http://dx.doi.org/10.1093/mnras/stz436, arXiv:1902.04058.
Middleton, M.J., Fragile, P.C., Bachetti, M., Brightman, M., Jiang, Y.F., Ho, W.G.C., Roberts, T.P., Ingram, A.R., Dauser, T., Pinto, C., Walton, D.J., Fuerst, F., Fabian, A.C., Gehrels, N., 2018. Lense-Thirring precession in ULXs as a possible means to constrain the neutron star equation of state. Mon. Not. R. Astron. Soc. 475 (1), 154–166. http://dx.doi.org/10.1093/mnras/stx2986, arXiv:1711.04797.

Middleton, M.J., Fragile, P.C., Ingram, A., Roberts, T.P., 2019b. The Lense-Thirring timing-accretion plane for ULXs. Mon. Not. R. Astron. Soc. 489 (1), 282–296. http://dx.doi.org/10.1093/mnras/stz2005, arXiv:1905.02731.

Middleton, M.J., Heil, L., Pintore, F., Walton, D.J., Roberts, T.P., 2015a. A spectral-timing model for ULXs in the supercritical regime. Mon. Not. R. Astron. Soc. 447, 3243–3263. http://dx.doi.org/10.1093/mnras/stu2644, arXiv:1412.4532.

Middleton, M.J., Heil, L., Pintore, F., Walton, D.J., Roberts, T.P., 2015b. A spectral-timing model for ULXs in the supercritical regime. Mon. Not. R. Astron. Soc. 447 (4), 3243–3263. http://dx.doi.org/10.1093/mnras/stu2644, arXiv:1412.4532.

Middleton, M.J., Higginbottom, N., Knigge, C., Khan, N., Wiktorowicz, G., 2021a. Thermally driven winds in ULXs. Mon. Not. R. Astron. Soc. http://dx.doi.org/10.1093/mnras/stab2991, arXiv:2110.08249.

Middleton, M.J., King, A., 2016. Geometrical beaming of stellar mass ULXs. Mon. Not. R. Astron. Soc. 462 (1), L71–L74. http://dx.doi.org/10.1093/mnras/slw128, arXiv:1606.07811.

Middleton, M.J., King, A., 2017. Predicting ultraluminous X-ray source demographics from geometrical beaming. Mon. Not. R. Astron. Soc. 470 (1), L69–L71. http://dx.doi.org/10.1093/mnras/slx079.

Middleton, M.J., Miller-Jones, J.C.A., Markoff, S., Fender, R., Henze, M., Hurley-Walker, N., Scaife, A.M.M., Roberts, T.P., Walton, D., Carpenter, J., Macquart, J.-P., Bower, G.C., Gurwell, M., Pietsch, W., Haberl, F., Harris, J., Daniel, M., Miah, J., Done, C., Morgan, J.S., Dickinson, H., Charles, P., Burwitz, V., Della Valle, M., Freyberg, M., Greiner, J., Hernanz, M., Hartmann, D.H., Hatzidimitriou, D., Riffeser, A., Sala, G., Seitz, S., Reig, P., Rau, A., Orio, M., Titterington, D., Grainge, K., 2013. Bright radio emission from an ultraluminous stellar-mass microquasar in M 31. Nature 493 (7431), 187–190. http://dx.doi.org/10.1038/nature11697, arXiv:1212.4698.

Middleton, M.J., Roberts, T.P., Done, C., Jackson, F.E., 2011. Challenging times: a re-analysis of NGC 5408 X-1. Mon. Not. R. Astron. Soc. 411 (1), 644–652. http://dx.doi.org/10.1111/j.1365-2966.2010.17712.x, arXiv:1009.2686.

Middleton, M.J., Walton, D.J., Alston, W., Dauser, T., Eikenberry, S., Jiang, Y.F., Fabian, A.C., Fuerst, F., Brightman, M., Marshall, H., Parker, M., Pinto, C., Harrison, F.A., Bachetti, M., Altamirano, D., Bird, A.J., Perez, G., Miller-Jones, J., Charles, P., Boggs, S., Christensen, F., Craig, W., Forster, K., Grefenstette, B., Hailey, C., Madsen, K., Stern, D., Zhang, W., 2021b. NuSTAR reveals the hidden nature of SS433. Mon. Not. R. Astron. Soc. 506 (1), 1045–1058. http://dx.doi.org/10.1093/mnras/stab1280.

Middleton, M.J., Walton, D.J., Fabian, A., Roberts, T.P., Heil, L., Pinto, C., Anderson, G., Sutton, A., 2015c. Diagnosing the accretion flow in ultraluminous X-ray sources using soft X-ray atomic features. Mon. Not. R. Astron. Soc. 454 (3), 3134–3142. http://dx.doi.org/10.1093/mnras/stv2214, arXiv:1509.06760.

Middleton, M.J., Walton, D.J., Fabian, A., Roberts, T.P., Heil, L., Pinto, C., Anderson, G., Sutton, A., 2015d. Diagnosing the accretion flow in ultraluminous X-ray sources using soft X-ray atomic features. Mon. Not. R. Astron. Soc. 454, 3134–3142. http://dx.doi.org/10.1093/mnras/stv2214, arXiv:1509.06760.

Middleton, M.J., Walton, D.J., Roberts, T.P., Heil, L., 2014. Broad absorption features in wind-dominated ultraluminous X-ray sources? Mon. Not. R. Astron. Soc. 438 (1), L51–L55. http://dx.doi.org/10.1093/mnras/sl157, arXiv:1309.3134.

Miller, B.W., 1995. The optical counterpart to the extremely luminous X-Ray source near Holmberg IX: A possible supershell in a tidal tail. Astrophys. J. Lett. 446, L75. http://dx.doi.org/10.1086/187934.

Miller, J.M., Fabian, A.C., Miller, M.C., 2004a. A comparison of intermediate-mass black hole candidate ultraluminous X-Ray sources and stellar-mass black holes. Astrophys. J. Lett. 614 (2), L117–L120. http://dx.doi.org/10.1086/425316, arXiv:astro-ph/0406656.

Miller, J.M., Fabian, A.C., Miller, M.C., 2004b. Revealing a cool accretion disk in the ultraluminous X-Ray source M81 X-9 (Holmberg IX X-1): Evidence for an intermediate-mass black hole. Astrophys. J. 607 (2), 931–938. http://dx.doi.org/10.1086/383563, arXiv:astro-ph/0310617.

Miller, J.M., Fabian, A.C., Miller, M.C., 2004c. Revealing a cool accretion disk in the ultraluminous X-Ray source M81 X-9 (Holmberg IX X-1): Evidence for an intermediate-mass black hole. Astrophys. J. 607 (2), 931–938. http://dx.doi.org/10.1086/383563, arXiv:astro-ph/0310617.

Miller, M.C., Hamilton, D.P., 2002. Production of intermediate-mass black holes in globular clusters. Mon. Not. R. Astron. Soc. 330, 232–240. http://dx.doi.org/10.1046/j.1365-8711.2002.05112.x, arXiv:astro-ph/0106188.

Miller, J.M., Walton, D.J., King, A.L., Reynolds, M.T., Fabian, A.C., Miller, M.C., Reis, R.C., 2013. Revisiting putative cool accretion disks in ultraluminous X-Ray sources. Astrophys. J. Lett. 776 (2), L36. http://dx.doi.org/10.1088/2041-8205/776/2/L36, arXiv:1309.4350.

Miller-Jones, J.C.A., Tetarenko, A.J., Sivakoff, G.R., Middleton, M.J., Altamirano, D., Anderson, G.E., Belloni, T.M., Fender, R.P., Jonker, P.G., Körding, E.G., Krimm, H.A., Maitra, D., Markoff, S., Migliari, S., Mooley, K.P., Rupen, M.P.,

Russell, D.M., Russell, T.D., Sarazin, C.L., Soria, R., Tudose, V., 2019. A rapidly changing jet orientation in the stellar-mass black-hole system V404 Cygni. Nature 569 (7756), 374–377. http://dx.doi.org/10.1038/s41586-019-1152-0, arXiv:1906.05400.

Mineo, S., Gilfanov, M., Sunyaev, R., 2012. X-ray emission from star-forming galaxies - I. High-mass X-ray binaries. Mon. Not. R. Astron. Soc. 419 (3), 2095–2115. http://dx.doi.org/10.1111/j.1365-2966.2011.19862.x, arXiv:1105.4610.

Mineshige, S., Hirano, A., Kitamoto, S., Yamada, T.T., Fukue, J., 1994. Time-dependent disk accretion in X-ray nova MUSCAE 1991. Astrophys. J. 426, 308. http://dx.doi.org/10.1086/174065.

Miniutti, G., Alexander, K.D., Bianchi, S., Chiaberge, M., Giustini, M., Laor, A., Read, A., Saxton, R., Uttley, P., 2020. Quasi-periodic eruptions (QPEs) in GSN 069. HST Proposal.

Miniutti, G., Saxton, R.D., Giustini, M., Alexander, K.D., Fender, R.P., Heywood, I., Monageng, I., Coriat, M., Tzioumis, A.K., Read, A.M., Knigge, C., Gandhi, P., Pretorius, M.L., Agfis-González, B., 2019. Nine-hour X-ray quasi-periodic eruptions from a low-mass black hole galactic nucleus. NATURE 573 (7774), 381–384. http://dx.doi.org/10.1038/s41586-019-1556-x, arXiv:1909.04693.

Mitsuda, K., Inoue, H., Koyama, K., Makishima, K., Matsuoka, M., Ogawara, Y., Shibazaki, N., Suzuki, K., Tanaka, Y., Hirano, T., 1984. Energy spectra of low-mass binary X-ray sources observed from Tenma. PASJ 36, 741–759.

Mohamed, S., Podsiadlowski, P., 2007. Wind roche-lobe overflow: a new mass-transfer mode for wide binaries. In: Napiwotzki, R., Burleigh, M.R. (Eds.), 15th European Workshop on White Dwarfs. In: Astronomical Society of the Pacific Conference Series, Vol. 372, p. 397.

Monard, L.A.G., 2010. Supernova 2010da in NGC 300. Central Bureau Electron. Telegr. 2289, 1.

Mondal, S., Belczyński, K., Wiktorowicz, G., Lasota, J.-P., King, A.R., 2020. The connection between merging double compact objects and the ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 491 (2), 2747–2759. http://dx.doi.org/10.1093/mnras/stz3227, arXiv:1909.04435.

Mondal, S., Różańska, A., De Marco, B., Markowitz, A., 2021. Evidence for Fe Kα line and soft X-ray lag in NGC 7456 ultraluminous X-ray source-1. Mon. Not. R. Astron. Soc. 505 (1), L106–L111. http://dx.doi.org/10.1093/mnras/slab061, arXiv:2106.00777.

Moon, D.-S., Harrison, F.A., Cenko, S.B., Shariff, J.A., 2011. Large highly ionized nebulae around ultra-luminous X-ray sources. Astrophys. J. Lett. 731 (2), L32. http://dx.doi.org/10.1088/2041-8205/731/2/L32, arXiv:1103.2773.

Motch, C., 2018. Optical observations of ultra-luminous X-ray pulsars, presentation at “Ultra-luminous X-ray Pulsars”, 6 - 8 june 2018, European Space Astronomy Centre (ESAC), Villafranca del Castillo, Spain. Available at https://www.cosmos.esa.int/documents/1518557/1518574/motch.pdf/a08257a9-9b9b-b56d-63d1-067cd7ae8f8f.

Motch, C., Pakull, M.W., Soria, R., Grisé, F., Pietrzyński, G., 2014. A mass of less than 15 solar masses for the black hole in an ultraluminous X-ray source. Nature 514, 198–201. http://dx.doi.org/10.1038/nature13730, arXiv:1410.4250.

Motta, S.E., Kajava, J.J.E., Sánchez-Fernández, C., Beardmore, A.P., Sanna, A., Page, K.L., Fender, R., Altamirano, D., Charles, P., Giustini, M., Knigge, C., Kuulkers, E., Oates, S., Osborne, J.P., 2017. Swift observations of V404 Cyg during the 2015 outburst: X-ray outflows from super-Eddington accretion. Mon. Not. R. Astron. Soc. 471 (2), 1797–1818. http://dx.doi.org/10.1093/mnras/stx1699, arXiv:1707.01076.

Mukherjee, E.S., Walton, D.J., Bachetti, M., Harrison, F.A., Barret, D., Bellm, E., Boggs, S.E., Christensen, F.E., Craig, W.W., Fabian, A.C., Fuerst, F., Grefenstette, B.W., Hailey, C.J., Madsen, K.K., Middleton, M.J., Miller, J.M., Rana, V., Stern, D., Zhang, W., 2015. A hard X-Ray study of the ultraluminous X-Ray source NGC 5204 X-1 with NuSTAR and XMM-Newton. Astrophys. J. 808 (1), 64. http://dx.doi.org/10.1088/0004-637X/808/1/64, arXiv:1502.01764.

Mushtukov, A.A., Ingram, A., Middleton, M., Nagirner, D.I., van der Klis, M., 2019. Timing properties of ULX pulsars: optically thick envelopes and outflows. Mon. Not. R. Astron. Soc. 484 (1), 687–697. http://dx.doi.org/10.1093/mnras/sty3525, arXiv:1811.02049.

Mushtukov, A.A., Portegies Zwart, S., Tsygankov, S.S., Nagirner, D.I., Poutanen, J., 2020. Pulsating ULXs: large pulsed fraction excludes strong beaming. arXiv e-prints arXiv:2011.09710.

Mushtukov, A.A., Suleimanov, V.F., Tsygankov, S.S., Ingram, A., 2017. Optically thick envelopes around ULXs powered by accreting neutron stars. Mon. Not. R. Astron. Soc. 467, 1202–1208, arXiv:1612.00964.

Mushtukov, A.A., Suleimanov, V.F., Tsygankov, S.S., Poutanen, J., 2015a. On the maximum accretion luminosity of magnetized neutron stars: connecting X-ray pulsars and ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 454, 2539–2548. http://dx.doi.org/10.1093/mnras/stv2087, arXiv:1506.03600.

Mushtukov, A.A., Suleimanov, V.F., Tsygankov, S.S., Poutanen, J., 2015b. The critical accretion luminosity for magnetized neutron stars. Mon. Not. R. Astron. Soc. 447, 1847–1856. http://dx.doi.org/10.1093/mnras/stu2484, arXiv:1409.6457.

Mushtukov, A., Tsygankov, S., 2022. Accreting strongly magnetised neutron stars: X-ray Pulsars. arXiv e-prints, arXiv:2204.14185.
Nandra, K., Barret, D., Barcons, X., Fabian, A., den Herder, J., Piro, L., Watson, M., Adami, C., Aird, J., Afonso, J., Alexander, D., Argiroffi, C., Amati, L., Arnaud, M., Atteja, J., Audard, M., Badenes, C., Ballet, L., Ballo, L., Bamba, A., Bhardwaj, A., Stefano Battistelli, E., Becker, W., De Becker, M., Behar, E., Bianchi, S., Biffi, V., Bïrzan, L., Bocchino, F., Bogdanov, S., Boirin, L., Boller, T., Borgani, S., Borm, K., Bouché, N., Bourdin, F., Bower, R., Braito, V., Brandini, D., Branduardi-Raymont, G., Bregman, J., Brenneman, L., Brightman, M., Brüggen, M., Buchner, J., Bulbul, E., Brusa, M., Bursa, M., Caccianiga, A., Cackett, E., Campana, S., Cappelluti, N., Cappi, M., Carrera, F., Ceballos, M., Christiansen, F., Chu, Y., Churazov, E., Clerc, N., Corbel, S., Corral, A., Comastri, A., Costantini, E., Croston, J., Dadina, M., D'Ai, A., Decourchelle, A., Della Ceca, R., Dennerl, K., Dolag, K., Done, C., Dovciak, M., Drake, J., Eckert, D., Edge, A., Ettori, S., Ezoe, Y., Feigelson, E., Fender, R., Feruglio, C., Finoguenov, A., Fiore, F., Galeazzi, M., Gallagher, S., Gandhi, P., Gaspari, M., Gastaldello, F., Georgakakis, A., Georgantopoulos, I., Gilfanov, M., Gitti, M., Gladstone, R., Goosmann, R., Gosset, E., Grosso, N., Guedel, M., Guerrero, M., Haberl, F., Hardcastle, M., Heinz, S., Alonso Herrero, A., Hervé, A., Holmstrom, M., Iwasawa, K., Jonker, P., Kaastra, J., Kara, E., Karas, V., Kastner, J., King, A., Kosenko, D., Koutroumpa, D., Kraft, R., Kreykenbohm, I., Lallement, R., Lanzuisi, G., Lee, J., Lemoine-Goumard, M., Lobban, A., Lodato, G., Lovisari, L., Lotti, S., McCarthy, I., McNamara, B., Maggio, A., Maiolino, R., De Marco, B., de Martino, D., Mateos, S., Matt, G., Maughan, B., Mazzotta, P., Mendez, M., Merloni, A., Micela, G., Miceli, M., Mignani, R., Miller, J., Miniutti, G., Molendi, S., Montez, R., Moretti, A., Motch, C., Nazé, Y., Nevalainen, J., Micastro, F., Nulsen, P., Ohashi, T., O'Brien, P., Osborne, J., Oskinova, L., Pacaud, F., Paerels, F., Page, M., Papadakis, I., Pareschi, G., Petre, R., Petrucci, P., Piconcelli, E., Pillitteri, I., Pinto, C., de Plaa, J., Pointecouteau, E., Ponman, T., Ponti, G., Porquet, D., Pounds, K., Pratt, G., Predehl, P., Proga, D., Psaltis, D., Rafferty, D., Ramos-Ceja, M., Ranalli, P., Rasia, E., Rau, A., Rauw, G., Rea, N., Read, A., Reeves, J., Reiprich, T., Renaud, M., Reynolds, C., Risaliti, G., Rodriguez, J., Rodriguez-Hidalgo, P., Roncarelli, M., Rosario, D., Rossetti, M., Rozanska, A., Rovilos, E., Salvaterra, R., Salvato, M., Di Salvo, T., Sanders, J., Sanz-Forcada, J., Schawinski, K., Schaye, J., Schwope, A., Sciortino, S., Severgnini, P., Shankar, F., Sijacki, D., Sim, S., Schmid, C., Smith, R., Steiner, A., Stelzer, B., Stewart, G., Strohmayer, T., Strüder, L., Sun, M., Takei, Y., Tatischeff, V., Tiengo, A., Tombesi, F., Trinchieri, G., Tsuru, T., Ud-Doula, A., Ursino, E., Valencic, L., Vanzella, E., Vaughan, S., Vignali, C., Vink, J., Vito, F., Volonteri, M., Wang, D., Webb, N., Willingale, R., Wilms, J., Wise, M., Worrall, D., Young, A., Zampieri, L., In't Zand, J., Zane, S., Zezas, A., Zhang, Y., Zhuravleva, I., 2013. The Hot and Energetic Universe: A White Paper presenting the science theme motivating the Athena+ mission. arXiv e-prints, arXiv:1306.2307.

Narayan, R., Sądowski, A., Soria, R., 2017. Spectra of black hole accretion models of ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 469 (3), 2997-3014. http://dx.doi.org/10.1093/mnras/stx1027, arXiv:1702.01158.

Neilsen, J., Rahoui, F., Homan, J., Buxton, M., 2016. A super-eddington, compton-thick wind in GRO J1655-40? Astrophys. J. 822 (1), 20. http://dx.doi.org/10.3847/0004-637X/822/1/20, arXiv:1603.04070.

Nixon, C.J., Pringle, J.E., 2020. Be star disks: Powered by a nonzero central torque. Astrophys. J. Lett. 905 (2), L29. http://dx.doi.org/10.3847/2041-8213/abd17e, arXiv:2012.04657.

Ohsuga, K., Mineshige, S., 2011. Global structure of three distinct accretion flows and outflows around black holes from two-dimensional radiation-magnetohydrodynamic simulations. Astrophys. J. 736, 2. http://dx.doi.org/10.1088/0004-637X/736/1/2, arXiv:1105.5474.

Ohsuga, K., Mineshige, S., 2014. Outflow launching mechanisms. Space Sci. Rev. 183 (1-4), 353-369. http://dx.doi.org/10.1007/s11214-013-0017-3.

Ohsuga, K., Mori, M., Nakamoto, T., Mineshige, S., 2005. Supercritical accretion flows around black holes: two-dimensional, radiation pressure-dominated disks with photon trapping. Astrophys. J. 628, 368-381. http://dx.doi.org/10.1086/430728, arXiv:astro-ph/0504168.

Okuda, T., 2002. Super-eddington black-hole models for SS 433. PASJ 54, 253-266. http://dx.doi.org/10.1093/pasj/54.2.253, arXiv:astro-ph/0202446.

Okuda, T., Lipunova, G.V., Molteni, D., 2009. The jets and disc of SS 433 at super-Eddington luminosities. Mon. Not. R. Astron. Soc. 398 (4), 1668-1677. http://dx.doi.org/10.1111/j.1365-2966.2009.15169.x, arXiv:0906.3308.

Olausen, S.A., Kaspi, V.M., 2014. The McGill magnetar catalog. Astrophys. J. Suppl. Ser. 212, 6. http://dx.doi.org/10.1088/0067-0049/212/1/6, arXiv:1309.4167.

Olejak, A., Belczynski, K., Bulik, T., Sobolewska, M., 2020. Synthetic catalog of black holes in the Milky Way. Astron. Astrophys. 638, A94. http://dx.doi.org/10.1051/0004-6361/201936557, arXiv:1908.08775.

Oskinova, L.M., 2005. Evolution of X-ray emission from young massive star clusters. Mon. Not. R. Astron. Soc. 361 (2), 679-694. http://dx.doi.org/10.1111/j.1365-2966.2005.09229.x, arXiv:astro-ph/0505512.

Paczynski, B., 1982. Thick accretion disks around black holes (Karl-Schwarzschild-Vorlesung 1981). Mitteilungen Der Astronomischen Gesellschaft Hamburg 57, 27.

Paczynski, B., 1992. GB 790305 as a very strongly magnetized neutron star. AaC 42, 145-153.

Paczynsky, B., Wiita, P.J., 1980. Thick accretion disks and supercritical luminosities. Astron. Astrophys. 500, 203-211.

Pakull, M.W., Grisé, F., 2008. Ultraluminous X-ray sources: Beambags and optical counterparts. In: Bandyopadhyay, R.M., Wachter, S., Gelino, D., Gelino, C.R. (Eds.), A Population Explosion: The Nature & Evolution of X-Ray Binaries in Diverse Environments. In: American Institute of Physics Conference Series, Vol. 1010, pp. 303-307. http://dx.doi.org/10.1063/1.2945062, arXiv:0803.4345.

Pakull, M.W., Grisé, F., Motch, C., 2006. Ultraluminous X-ray sources: Bubbles and optical counterparts. In: Meurs, E.J.A., Fabbiano, G. (Eds.), Populations of High Energy Sources in Galaxies. In: IAU Symposium, Vol. 230, pp. 293-297. http://dx.doi.org/10.1017/S1743921306008489, arXiv:astro-ph/0603771.

Pakull, M.W., Mirioni, L., 2002. Optical counterparts of ultraluminous X-ray sources. arXiv Astrophysics e-prints, arXiv:astro-ph/0202488.

Pakull, M.W., Soria, R., Motch, C., 2010. A 300-parsec-long jet-inflated bubble around a powerful microquasar in the galaxy NGC 7793. Nature 466 (7303), 209-212. http://dx.doi.org/10.1038/nature09168.

Parfrey, K., Spitkovsky, A., Beloborodov, A.M., 2016. Torque enhancement, spin equilibrium, and jet power from disk-induced opening of pulsar magnetic fields. Astrophys. J. 822 (1), 33. http://dx.doi.org/10.3847/0004-637X/822/1/33, arXiv:1507.08627.

Parfrey, K., Tchekhovskoy, A., 2017. General-relativistic simulations of four states of accretion onto millisecond pulsars. Astrophys. J. Lett. 851, L34. http://dx.doi.org/10.3847/2041-8213/aa9c85, arXiv:1708.06362.

Pasham, D.R., Cenko, S.B., Zoghbi, A., Mushotzky, R.F., Miller, J., Tombesi, F., 2015. Evidence for high-frequency QPOS with a 3:2 frequency ratio from a 5000 solar mass black hole. Astrophys. J. Lett. 811 (1), L11. http://dx.doi.org/10.1088/2041-8205/811/1/L11, arXiv:1601.02628.

Pasham, D.R., Remillard, R.A., Fragile, P.C., Franchini, A., Stone, N.C., Lodato, G., Homan, J., Chakrabarty, D., Baganoff, F.K., Steiner, J.F., Coughlin, E.R., Pasham, N.R., 2019. A loud quasi-periodic oscillation after a star is disrupted by a massive black hole. Science 363 (6426), 531-534. http://dx.doi.org/10.1126/science.aar7480, arXiv:1810.10713.

Pasham, D.R., Strohmayer, T.E., 2012. A multi-epoch timing and spectral study of the ultraluminous X-Ray NGC 5408 X-1 with XMM-Newton. Astrophys. J. 753 (2), 139. http://dx.doi.org/10.1088/0004-637X/753/2/139, arXiv:1308.1671.

Pasham, D.R., Strohmayer, T.E., 2013. Can the 62 day X-Ray period of ULX M82 X-1 be due to a precessing accretion disk? Astrophys. J. Lett. 774 (2), L16. http://dx.doi.org/10.1088/2041-8205/774/2/L16, arXiv:1308.1682.

Pasham, D.R., Strohmayer, T.E., Mushotzky, R.F., 2014. A 400-solar-mass black hole in the galaxy M82. Nature 513 (7516), 74-76. http://dx.doi.org/10.1038/nature13710, arXiv:1501.03180.

Pérez-Ramírez, D., Mezcua, M., Leon, S., Caballero-García, M.D., 2011. A search for radio counterparts to Chandra ULX candidates. Astron. Nachr. 332 (4), 384. http://dx.doi.org/10.1002/asna.201011505, arXiv:1010.3851.

Perlman, E.S., Stocke, J.T., Carilli, C.L., Sugiho, M., Tashiro, M., Madejski, G., Wang, Q.D., Conway, J., 2002. The apparent host galaxy of PKS 1413+135: Hubble space telescope, ASCA, and very long baseline array observations. Aj 124 (5), 2401-2412. http://dx.doi.org/10.1086/344109, arXiv:astro-ph/0208167.

Petterson, J.A., 1977. The 35 day cycle of the X-ray binary Hercules X-1. Astrophys. J. 218, 783-791. http://dx.doi.org/10.1086/155735.

Pfeiffer, H.P., Lai, D., 2004. Warping and precession of accretion disks around magnetic stars: Nonlinear evolution. Astrophys. J. 604 (2), 766-774. http://dx.doi.org/10.1086/381967, arXiv:astro-ph/0307324.

Pinto, C., Alston, W., Soria, R., Middleton, M.J., Walton, D.J., Sutton, A.D., Fabian, A.C., Earnshaw, H., Urquhart, R., Kara, E., Roberts, T.P., 2017. From ultraluminous X-ray sources to ultraluminous supersoft sources: NGC 55 ULX, the missing link. Mon. Not. R. Astron. Soc. 468 (3), 2865-2883. http://dx.doi.org/10.1093/mnras/stx641, arXiv:1612.05569.

Pinto, C., Mehdipour, M., Walton, D.J., Middleton, M.J., Roberts, T.P., Fabian, A.C., Guainazzi, M., Soria, R., Kosec, P., Ness, J.U., 2020a. Thermal stability of winds driven by radiation pressure in super-Eddington accretion discs. Mon. Not. R. Astron. Soc. 491 (4), 5702-5716. http://dx.doi.org/10.1093/mnras/stz3392, arXiv:1903.06174.

Pinto, C., Middleton, M.J., Fabian, A.C., 2016. Resolved atomic lines reveal outflows in two ultraluminous X-ray sources. Nature 533 (7601), 64-67. http://dx.doi.org/10.1038/nature17417, arXiv:1604.08593.

Pinto, C., Soria, R., Walton, D.J., D'Ai, A., Pintore, F., Kosec, P., Alston, W.N., Fuerst, F., Middleton, M.J., Roberts, T.P., Del Santo, M., Barret, D., Ambrosi, E., Robba, A., Earnshaw, H., Fabian, A.C., 2021. XMM-Newton campaign on the ultraluminous X-ray source NGC 247 ULX-1: outflows. Mon. Not. R. Astron. Soc. 505 (4), 5058-5074. http://dx.doi.org/10.1093/mnras/stab1648, arXiv:2104.11164.

Pinto, C., Walton, D.J., Kara, E., Parker, M.L., Soria, R., Kosec, P., Middleton, M.J., Alston, W.N., Fabian, A.C., Guainazzi, M., Roberts, T.P., Fuerst, F., Earnshaw, H.P., Sathyaprakash, R., Barret, D., 2020b. XMM-Newton campaign on ultraluminous X-ray source NGC 1313 X-1: wind versus state variability. Mon. Not. R. Astron. Soc. 492 (4), 4646-4665. http://dx.doi.org/10.1093/mnras/staa118, arXiv:1911.09568.

Pintore, F., Esposito, P., Zampieri, L., Motta, S., Wolter, A., 2015. Spectral variability in Swift and Chandra observations of the ultraluminous source NGC 55 ULX1. Mon. Not. R. Astron. Soc. 448 (2), 1153-1161. http://dx.doi.org/10.1093/mnras/stv028, arXiv:1501.01160.
Pintore, F., Motta, S., Pinto, C., Bernardini, M.G., Rodriguez-Castillo, G., Salvaterra, R., Israel, G.L., Esposito, P., Ambrosi, E., Salvaggio, C., Zampieri, L., Wolter, A., 2021. The rare X-ray flaring activity of the Ultraluminous X-ray source NGC 4559 X7. arXiv e-prints, arXiv:2103.14541.

Pintore, F., Zampieri, L., Stella, L., Wolter, A., Mereghetti, S., Israel, G.L., 2017. Pulsator-like spectra from ultraluminous X-ray sources and the search for more ultraluminous pulsars. Astrophys. J. 836 (1), 113. http://dx.doi.org/10.3847/1538-4357/836/1/113, arXiv:1701.03595.

Piro, A.L., Giacomazzo, B., Perna, R., 2017. The fate of neutron star binary mergers. Astrophys. J. Lett. 844 (2), L19. http://dx.doi.org/10.3847/2041-8213/aa7f2f, arXiv:1704.08697.

Ponti, G., Fender, R.P., Begelman, M.C., Dunn, R.J.H., Neilsen, J., Coriat, M., 2012. Ubiquitous equatorial accretion disc winds in black hole soft states. Mon. Not. R. Astron. Soc. 422 (1), L11–L15. http://dx.doi.org/10.1111/j.1745-3933.2012.01224.x, arXiv:1201.4172.

Popov, S.B., 2016. Origins of magnetars in binary systems. Astron. Astrophys. Trans. 29, 183–192, arXiv:1507.08192.

Popov, S.B., 2022. High magnetic field neutron stars and magnetars in binary systems. arXiv e-prints, arXiv:2201.07507.

Portegies Zwart, S.F., McMillan, S.L.W., 2002. The runaway growth of intermediate-mass black holes in dense star clusters. Astrophys. J. 576 (2), 899–907. http://dx.doi.org/10.1086/341798, arXiv:astro-ph/0201055.

Pottschmidt, K., Ballhausen, R., Wilms, J., Zezas, A., Fuerst, F., Nowak, M.A., Grinberg, V., Kuehnel, M., Kretschmar, P., Tomsick, J.A., Antoniou, V., Kennea, J., Hong, J., Haberl, F., Maccarone, T., Hornscheemeier, A., Ptak, A., Yukita, M., Wik, D., Lehmer, B., Fornasini, F., Bodaghee, A., McBride, V., 2016. NuSTAR Observations of SMC X-3. Astronomer's Telegr. 9404, 1.

Poutanen, J., Lipunova, G., Fabrika, S., Butkevich, A.G., Abolmasov, P., 2007. Super-critically accreting stellar black holes as ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 377, 1187–1194. http://dx.doi.org/10.1111/j.1365-2966.2007.11668.x, arXiv:astro-ph/0609274.

Prestwich, A.H., Tsantaki, M., Zezas, A., Jackson, F., Roberts, T.P., Foltz, R., Linden, T., Kalogera, V., 2013. Ultraluminous X-ray sources in the most metal poor galaxies. Astrophys. J. 769, 92. http://dx.doi.org/10.1088/0004-637X/769/2/92, arXiv:1302.6203.

Pringle, J.E., 1975. Period changes in eruptive binaries. Mon. Not. R. Astron. Soc. 170, 633–642. http://dx.doi.org/10.1093/mnras/170.3.633.

Pringle, J.E., 1996. Self-induced warping of accretion discs. Mon. Not. R. Astron. Soc. 281 (1), 357–361. http://dx.doi.org/10.1093/mnras/281.1.357.

Qiu, Y., Feng, H., 2021. Linking soft excess in ultraluminous X-ray sources with optically thick wind driven by supercritical accretion. Astrophys. J. 906 (1), 36. http://dx.doi.org/10.3847/1538-4357/abc959, arXiv:2011.05781.

Ramsey, C.J., Williams, R.M., Gruendl, R.A., Chen, C.H.R., Chu, Y.-H., Wang, Q.D., 2006. An optical study of stellar and interstellar environments of seven luminous and ultraluminous X-ray sources. Astrophys. J. 641 (1), 241–251. http://dx.doi.org/10.1086/499070, arXiv:astro-ph/0511540.

Ransom, S.M., 2001. New search techniques for binary pulsars (Ph.D. thesis). Harvard University.

Ransom, S.M., Eikenberry, S.S., Middleditch, J., 2002. Fourier techniques for very long astrophysical time-series analysis. Astron. J. 124 (3), 1788–1809. http://dx.doi.org/10.1086/342285, arXiv:astro-ph/0204349.

Rao, F., Feng, H., Kaaret, P., 2010. Detection of strong short-term variability in NGC 6946 X-1. Astrophys. J. 722 (1), 620–624. http://dx.doi.org/10.1088/0004-637X/722/1/620, arXiv:1008.2065.

Rappaport, S.A., Podsiadlowski, P., Pfahl, E., 2005. Stellar-mass black hole binaries as ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 356, 401–414. http://dx.doi.org/10.1111/j.1365-2966.2004.08489.x, arXiv:astro-ph/0408032.

Ray, P.S., Guillot, S., Ho, W.C.G., Kerr, M., Enoto, T., Gendreau, K.C., Arzoumanian, Z., Altamirano, D., Bogdanov, S., Campion, R., Chakrabarty, D., Deneva, J.S., Jaisawal, G.K., Kozon, R., Malacaria, C., Strohmayer, T.E., Wolff, M.T., 2019. Anti-glitches in the ultraluminous accreting pulsar NGC 300 ULX-1 observed with NICER. Astrophys. J. 879 (2), 130. http://dx.doi.org/10.3847/1538-4357/ab24d8, arXiv:1811.09218.

Reig, P., Fabregat, J., Alfonso-Garzón, J., 2020. Optical counterpart to Swift J0243.6+6124. Astron. Astrophys. 640, A35. http://dx.doi.org/10.1051/0004-6361/202038333, arXiv:2006.10303.

Revnitvsev, M., Gilfanov, M., Churazov, E., 1999. The frequency resolved spectroscopy of CYG X-1: fast variability of the Fe K_α line. Astron. Astrophys. 347, L23–L26, arXiv:astro-ph/9906198.

Revnitvsev, M., Gilfanov, M., Churazov, E., Sunyaev, R., 2002. Super-Eddington outburst of V4641 Sgr. Astron. Astrophys. 391, 1013–1022. http://dx.doi.org/10.1051/0004-6361:20020865, arXiv:astro-ph/0204132.

Revnitvsev, M., Mereghetti, S., 2016. Magnetic fields of neutron stars in X-Ray binaries. In: The Strongest Magnetic Fields in the Universe: Space Sciences Series of ISSI. Vol. 54, p. 299. http://dx.doi.org/10.1007/978-1-4939-3550-9.

Ritter, H., 1988. Turning on and off mass transfer in cataclysmic binaries. Astron. Astrophys. 202, 93–100.

Ritter, H., King, A.R., 2001. On the spin-up of neutron stars to millisecond pulsars in long-period binaries. In: Podsiadlowski, P., Rappaport, S., King, A.R., D'Antona, F., Burderi, L. (Eds.), Evolution of Binary and Multiple Star Systems. In: Astronomical Society of the Pacific Conference Series, Vol. 229, p. 423, arXiv:astro-ph/0011408.

Robba, A., Pinto, C., Walton, D.J., Soria, R., Kosec, P., Pintore, F., Roberts, T.P., Alston, W.N., Middleton, M., Cusumano, G., Earnshaw, H.P., Fuerst, F., Sathyaprakash, R., Kyritsis, E., Fabian, A.C., 2021. Broadband X-ray spectral variability of the pulsing ULX NGC 1313 X-2. arXiv e-prints, arXiv:2106.04501.

Roberts, T.P., Fabbiano, G., Luo, B., Kim, D.W., Strader, J., Middleton, M.J., Brodie, J.P., Fragos, T., Gallagher, J.S., Kalogera, V., King, A.R., Zezas, A., 2012. A variable ultraluminous X-Ray source in a globular cluster in NGC 4649. Astrophys. J. 760 (2), 135. http://dx.doi.org/10.1088/0004-637X/760/2/135, arXiv:1210.5163.

Roberts, T.P., Gladstone, J.C., Goulding, A.D., Swinbank, A.M., Ward, M.J., Goad, M.R., Levan, A.J., 2011. (No) dynamical constraints on the mass of the black hole in two ULXs. Astron. Nachr. 332 (4), 398. http://dx.doi.org/10.1002/asna.201011508, arXiv:1011.2155.

Roberts, T.P., Goad, M.R., Ward, M.J., Warwick, R.S., 2003. The unusual supernova remnant surrounding the ultraluminous X-ray source IC 342 X-1. Mon. Not. R. Astron. Soc. 342 (3), 709–714. http://dx.doi.org/10.1046/j.1365-8711.2003.06593.x, arXiv:astro-ph/0303110.

Roberts, T.P., Goad, M.R., Ward, M.J., Warwick, R.S., O'Brien, P.T., Lira, P., Hands, A.D.P., 2001. The identification of an optical counterpart to the super-Eddington X-ray source NGC 5204 X-1. Mon. Not. R. Astron. Soc. 325 (2), L7–L11. http://dx.doi.org/10.1046/j.1365-8711.2001.04659.x, arXiv:astro-ph/0105307.

Roberts, T.P., Kilgard, R.E., Warwick, R.S., Goad, M.R., Ward, M.J., 2006. Chandra monitoring observations of the ultraluminous X-ray source NGC 5204 X-1. Mon. Not. R. Astron. Soc. 371 (4), 1877–1890. http://dx.doi.org/10.1111/j.1365-2966.2006.10821.x, arXiv:astro-ph/0607377.

Roberts, T.P., Levan, A.J., Goad, M.R., 2008. New Hubble Space Telescope imaging of the counterparts to six ultraluminous X-ray sources. Mon. Not. R. Astron. Soc. 387 (1), 73–78. http://dx.doi.org/10.1111/j.1365-2966.2008.13293.x, arXiv:0803.4470.

Roberts, T.P., Warwick, R.S., Ward, M.J., Goad, M.R., Jenkins, L.P., 2005. XMM-Newton EPIC observations of the ultraluminous X-ray source NGC 5204 X-1. Mon. Not. R. Astron. Soc. 357 (4), 1363–1369. http://dx.doi.org/10.1111/j.1365-2966.2005.08758.x, arXiv:astro-ph/0412521.

Rodríguez Castillo, G.A., Israel, G.L., Belfiore, A., Bernardini, F., Esposito, P., Pintore, F., De Luca, A., Papitto, A., Stella, L., Tiengo, A., Zampieri, L., Bachetti, M., Brightman, M., Casella, P., D'Agostino, D., Dall'Osso, S., Earnshaw, H.P., Fuerst, F., Haberl, F., Harrison, F.A., Mapelli, M., Marelli, M., Middleton, M., Pinto, C., Roberts, T.P., Salvaterra, R., Turolla, R., Walton, D.J., Wolter, A., 2020. Discovery of a 2.8 s pulsar in a 2 day orbit high-mass X-Ray binary powering the ultraluminous X-Ray source ULX-7 in M51. Astrophys. J. 895 (1), 60. http://dx.doi.org/10.3847/1538-4357/ab8a44, arXiv:1906.04791.

Rosen, S.R., Webb, N.A., Watson, M.G., Ballet, J., Barret, D., Braito, V., Carrera, F.J., Ceballos, M.T., Coriat, M., Della Ceca, R., Denkinson, G., Esquej, P., Farrell, S.A., Freyberg, M., Grisé, F., Guillout, P., Heil, L., Koliopanos, F., Law-Green, D., Lamer, G., Lin, D., Martino, R., Michel, L., Motch, C., Nebot Gomez-Doran, A., Page, C.G., Page, K., Page, M., Pakull, M.W., Pye, J., Read, A., Rodriguez, P., Sakano, M., Saxton, R., Schwope, A., Scott, A.E., Sturm, R., Traulsen, I., Yershov, V., Zolotukhin, I., 2016. The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue. Astron. Astrophys. 590, A1. http://dx.doi.org/10.1051/0004-6361/201526416, arXiv:1504.07051.

Russell, D.M., Yang, Y.J., Gladstone, J.C., Wiersema, K., Roberts, T.P., 2011. New observations of ULX supershells, and their implications. Astron. Nachr. 332 (4), 371. http://dx.doi.org/10.1002/asna.201011502, arXiv:1011.0598.

Sadowski, A., 2011. Slim accretion disks around black holes. arXiv e-prints, arXiv:1108.0396.

Sakurai, Y., Inayoshi, K., Haiman, Z., 2016. Hyper-Eddington mass accretion on to a black hole with super-Eddington luminosity. Mon. Not. R. Astron. Soc. 461 (4), 4496–4504. http://dx.doi.org/10.1093/mnras/stw1652, arXiv:1605.09105.

Sathyaprakash, R., Roberts, T.P., Grisé, F., Kaaret, P., Ambrosi, E., Done, C., Gladstone, J.C., Kajava, J.J.E., Soria, R., Zampieri, L., 2022. A multi-wavelength view of distinct accretion regimes in the pulsating ultraluminous X-ray source NGC 1313 X-2. Mon. Not. R. Astron. Soc. 511 (4), 5346–5362. http://dx.doi.org/10.1093/mnras/stac402, arXiv:2202.06986.

Sathyaprakash, R., Roberts, T.P., Siwek, M.M., 2019a. Observational limits on the X-ray emission from the bubble nebula surrounding Ho IX X-1. Mon. Not. R. Astron. Soc. 488 (4), 4614–4622. http://dx.doi.org/10.1093/mnras/stz2022, arXiv:1907.06439.

Sathyaprakash, R., Roberts, T.P., Walton, D.J., Fuerst, F., Bachetti, M., Pinto, C., Alston, W.N., Earnshaw, H.P., Fabian, A.C., Middleton, M.J., Soria, R., 2019b. The discovery of weak coherent pulsations in the ultraluminous X-ray source NGC 1313 X-2. Mon. Not. R. Astron. Soc. 488 (1), L35–L40. http://dx.doi.org/10.1093/mnrasl/slz086, arXiv:1906.00640.

Sazonov, S.Y., Sunyaev, R.A., Lund, N., 1997. Super-Eddington x-ray luminosity of the bursting pulsar GRO J1744-28: WATCH/Granat observations. Astron. Lett. 23 (3), 286–292.