Still, to further rule out a stellar origin, we attempt to fit the transit spectrum with a stellar contamination model. Following Rackham et al. (2018) we consider the hypothesis that the observed transit depth variations are due to inhomogeneities on the stellar surface. The observed wavelength-dependent transit depths

D

λ
,
obs

 are modeled as:
4

D

λ
,
obs

=

D

λ

1
−

f

spot

1
−

F

λ
,
spot

F

λ
,
phot

−

f

fac

1
−

F

λ
,
fac

F

λ
,
phot

,

where Dλ is the geometric radius ratio

R

p

/

R

⋆

2

, assumed here to be constant with wavelength (=D), fspot and ffac are the spot and faculae covering fractions, and the Fλ refer to bandpass-integrated PHOENIX model spectra of the photosphere, spots, and faculae (Hauschildt et al. 1999). Using K2-18b stellar parameters (Table 2), we explore a wide range of possible stellar contamination spectra for M2–M3 stars with spot and faculae covering fractions consistent with 1% I-band variability. Based on Rackham et al. (2018), we then explore scenarios with giant spots and solar-like spots as well as with and without faculae, resulting in spot fractions of up to 20%. However, none of those models can explain the amplitude of the observed transit spectrum. The amplitude of resulting transit depth variations due to the stellar inhomogeneities are up to 3–8 parts-per-million (ppm), about an order of magnitude smaller than the observed 80–90 ppm transit depth variations in the observed WFC3 spectrum (Figure 3). Finally, we also explore the most extreme scenarios where the spot and faculae covering fractions can be as high as 100%, but even those stellar inhomogeneity models fail to explain the amplitude of the observed transit depth variation. They deliver an absolute maximum of 20 ppm at 1.4 μm, which still only corresponds to less than a quarter of the transit depth variation in the observations. We conclude that stellar inhomogeneities and activity cannot explain the measured transmission spectrum.


The results presented in this work answer a number of questions regarding the character of the GG Tau A system, while raising others and leaving others untouched. First among the questions raised by our results are the questions of whether the detailed morphology of features in the circumbinary torus as seen in our simulations are actually present in the GG Tau A system. The current best resolution observations of the torus provide tantalizing hints that such features do exist, but a definitive statement that such features are present must await higher resolution observations of quality similar to those described by the ALMA Partnership (2015), for the HL Tau circumstellar disk. Another important question concerns planet formation in multiple systems. Whether or not any theoretical mechanism presently exists to explain the formation of giant planets in binary systems, the fact remains that at least a few binary systems, such as γ Cephei (Neuhauser et al. 2007), GI86 (Queloz et al. 2000), and HD 41004 (Zucker et al. 2004), do harbor planets. Therefore, some formation mechanism does in fact exist. While we find that accretion into the circumstellar disks occurs rapidly enough so that they can survive for the comparatively long timescales needed to form planets, other conditions, such as temperatures, remain quite unfavorable. What are the mechanisms still missing from our models that permit such objects to form? Finally, our simulations model the evolution of the “A” component of the full GG Tau system over a time span extending over only a tiny fraction of its formation timescale and in only two spatial dimensions. We neglected the full dynamical effects expected to be present in the system, insofar as our results include neither the distant binary “B” component of the GG Tau system, nor the newly discovered tight binary nature of the GG Tau Ab component. Even so, we find large scale morphological changes even over this short time span, and restricted dimensionality and physical system. Given the vigor of the activity over such a short timescale, we would expect activity of similar scale to occur over longer time spans as well, with correspondingly large consequences on the system morphology. To what extent will 3D effects also play a role in the evolution? What will be the end state configuration of the GG Tau system as a whole? Will the components eventually break apart? Merge? Future investigations extending the work presented here will be required in order to answer these questions.


Our formula can be used to confront the curvature effect with observations and estimate the decay timescale of the steep decay phase. In observations, the steep decay phase has been observed in the decay phase of the prompt emission phase and flares in GRBs. Since the value of E0 (

∼
0.3
–
1

MeV

) in the prompt emission phase is significantly larger than

10

keV

, the β in the steep decay phase of prompt emission would be a linear function of observer time based on Equation (38). This behavior has been observed in a number of bursts, such as GRBs 050814 (Zhang et al. 2009, please see the spectral evolution in the

β
−

t

obs

 space), 051001 etc. The linear relation between β and

t

obs

 is also found in the steep decay of flares (e.g., Mu et al. 2016). For a linear function β of

t

obs

, one can obtain the slope of the linear function, which is equal to

7.9

κ

ˆ

/

t

c

=
2.37

keV

/

[

E

0

(

t

obs

=
0
)

t

c

]

 based on Equations (38) or (39). Then, the decay timescale

t

c

 of our studying phase can be estimated if the value of

E

0

(

t

obs

=
0
)

 is known. We fit the spectral evolution in the decay phase of a flare (

∼
172

s

) in GRB 060904B (Mu et al. 2016) with a linear function. The fitting result, i.e.,

β
=
0.84
+
0.020

t

obs

 with

t

obs

=

t

obs

−

t

p

, is shown in the left panel of Figure 4 with  a red solid line. Then, we have

E

0

(

t

obs

=
0
)

t

c

=
119

keV

s

, which is around that found in Mu et al. (2016), i.e.,

2.54

keV
×
65.39

s

. For a flare (

∼
116

s

) in GRB 131030A, the spectrum at the beginning of the steep decay phase can be fitted with a Band function. With the fitting result found in Mu et al. (2016), i.e.,

α

ˆ

=
−
0.91

,

β

ˆ

=
−
3.19

, and

E

0

(

t

obs

=
0
)
=
1.95

, we plot the evolution of β based on Equation (38) in the right panel of Figure 4 with a red solid line. Here, we adopt

t

c

=
54

s

 (Mu et al. 2016), which can also be roughly estimated based on the flux evolution. It can be found that Equation (38) describes the spectral evolution approximately, which may reveal that a more appropriate value of parameters (e.g.,

t

c

) may be required for this source. The agreement of our analytical formula and observational data shows that the assumption (2) given at the beginning of Section 2 (i.e., the jet shell has no θ-dependent spectral parameters or Lorentz factor) is applicable in reality.


, i.e.,

α

ˆ

=
−
0.91

,

β

ˆ

=
−
3.19

, and

E

0

(

t

obs

=
0
)
=
1.95

, we plot the evolution of β based on Equation (38) in the right panel of Figure 4 with a red solid line.


Then, we have

E

0

(

t

obs

=
0
)

t

c

=
119

keV

s

, which is around that found in


We fit the spectral evolution in the decay phase of a flare (

∼
172

s

) in GRB 060904B


The linear relation between β and

t

obs

 is also found in the steep decay of flares (e.g.,


In the single cloud simulations presented in Paper I and Paper II, the system was treated in isolation, i.e. with no external forces acting upon it. In reality, such a binary would be placed deep in the potential well of a galaxy, where stars and dark matter exert their gravitational influence. To mimic the presence of the galactic spheroid, we include an external potential with a Hernquist profile (Hernquist 1990), which can be written as
(1)
\begin{eqnarray*}
\rho (r) = \frac{M_*}{2\pi}\frac{a_*}{r}\frac{1}{(r+a_*)^3},
\end{eqnarray*}
and an enclosed mass given by
(2)
\begin{eqnarray*}
m(r) = M_*\frac{r^2}{(r+a_*)^2},
\end{eqnarray*}
where M* and a* are scaling constants that represent the total mass of the spheroid and the size of core, respectively. Based on a typical MBH–Mbulge relation (Magorrian et al. 1998) and a radius-to-stellar-mass relation (Dabringhausen, Hilker & Kroupa 2008), we choose MH = 4.78 × 102M0 and rH = 3.24 × 102a0, thus implying
(3)
\begin{eqnarray*}
m(a_0) \approx 5\times 10^{-3} M_0.
\end{eqnarray*}
As a consequence, this external force represents only a small perturbation to the dynamics of the interaction that is still dominated by the binary’s gravitational potential. Moreover, because this external potential is spherically symmetric, orbits experience precession only, where energy and angular momentum are conserved. In principle, this precession could enhance stream collisions, prompting more gas onto the binary, although the time-scales are too long with respect to the frequency of cloud infall, which is the dominant effect in our models. Based on this, we do not expect the oscillations induced by this potential to have a secular effect in the overall evolution of the system during the stages modelled. In practice, this potential maintains the binary close to the centre of the reference frame by applying a restoring force when it drifts away due to the interaction with the incoming material. It is important to mention that the gas also feels this external force.


For the new observations described in Sect. 3, the spectra are renormalised by applying a linear fit to two wavelength regions, 6455–6559 Å and 6567–6580 Å, on either side of the Hα line. The value for pEW (Hα) is measured over the wavelength range 6560–6565 Å. The selected wavelength range is sufficiently narrow to exclude nearby spectral lines and sufficiently broad to measure the Hα line of a fast rotating star. The value of pEW(Hα) is calculated from

(1)

${\rm{pEW}(H\alpha)} = \int^{\lambda_2}_{\lambda_1}
\left(1-\frac{F(\lambda)}{F_{\rm{pc}}}\right){\rm{d}}\lambda,$pEW(Hα)= ∫ λ1λ2 1-F(λ)Fpc dλ,

where Fpc is the average of the median flux in the pseudo-continuum in the ranges [6545:6559] and [6567:6580], λ1  = 6560Å, λ2  = 6565Å, and the error is determined with the method of Vollmann & Eversberg (2006), which is applied as follows:

(2)

$\sigma_{\rm{pEW}} = \frac{\mathrm\Delta \lambda -
\rm{pEW(H\alpha)}}{\rm{S/N}} \sqrt{1 + \frac{F_{\rm{pc}}}{F_{1,2}}},$σpEW=Δλ-pEW(Hα)S∕N1+  Fpc   F1,2,

where Δλ = λ2 − λ1 and F1,2  is the mean flux in the wavelength range between λ1 and λ2. For Hα active stars, i.e. where pEW(Hα) is negative, the normalised Hα luminosity can be expressed as

(3)

$\log \left(\frac{L_{{\rm{H}}\alpha}}{L_{\rm{bol}}}\right) = \log \chi
+ \log (-{\rm{pEW}}({\rm{H}}\alpha)),$logLHαLbol = logχ+ log(-pEW(Hα)),

where log χ is given as a function of the effective temperature (e.g. Reiners & Basri 2008). Lines with Hα in absorption have positive pEW(Hα) values and lines with Hα in emission have negative pEW(Hα) values. The minimum level of emission in Hα that we are sensitive to is pEW(Hα) ≤−0.5Å, which is the definition for an active star in this work and is indicated by the term Hα active. This detection threshold was determined by visually inspecting the spectra and is consistent with values obtained by Newton et al. (2017) and West et al. (2015). The values derived from the new observations are tabulated in Table A.2.


In this work, we consider four different galaxy models from Smirnov & Sotnikova (2018). Full details of the simulations can be found in that work and we refer an interested reader to it. Here, we briefly describe some important aspects of the simulations. Initially, each model consists of an axisymmetric exponential disc:
(11)$$\begin{eqnarray}
\rho (R,z) = \frac{M_\mathrm{d}}{4\pi R_\mathrm{d}^2 z_\mathrm{d}} \exp \left(-\frac{R}{R_\mathrm{d}}\right) \operatorname{sech}^2\left(\frac{z}{z_\mathrm{d}}\right) \, ,
\end{eqnarray}$$where Md is the total mass of the disc, Rd is the disc scale length, and zd is the disc scale height, plus spherically symmetric dark halo of NFW-type (Navarro, Frenk & White 1996). The halo is characterized by the ratio Mh(r  4Rd)/Md, where Mh(r  4Rd) is the dark halo mass inside the sphere with a radius of 4Rd. One model also includes a Hernquist type bulge (Hernquist 1990):
(12)$$\begin{eqnarray}
\rho _\mathrm{b}(r) = \frac{M_\mathrm{b}\, r_\mathrm{b}}{2\pi \, r\, (r_\mathrm{b} + r)^3} \, ,
\end{eqnarray}$$where rb is the scale parameter and Mb is the total bulge mass. Disc and halo components are represented by several millions of particles (see Table 1). Bulge particle number is chosen such that the mass of one particle from the bulge is equal to the mass of one particle from the disc. Some important physical parameters of the models are specified in Table 1. The initial equilibrium state of each multicomponent model was prepared via script mkgalaxy (McMillan & Dehnen 2007) from the toolbox for N-body simulation NEMO (Teuben 1995). Evolution of the models was followed for about 8 Gyr using the fastest N-body code for one CPU gyrfalcON (Dehnen 2002). Each model gives rise to a bar after 1−2 Gyr from the beginning of the simulation. Each bar gradually thickens in the vertical direction (clear buckling events can occur depending on the model) and takes a B/PS shape if seen side-on. Fig. 1 shows the end-state of the bulgeless model with μ = 1.5 and Q(2Rd) = 1.2. This model is our fiducial or ‘main’ model. On the example of this model, we consider below how various projection effects affect the extracted parameters of the B/PS bulge. For each of the models, we prepared a set of Flexible Image Transport System (FITS) images obtained from the corresponding density distribution of disc/bulge particles. Such images can then be decomposed using a usual decomposition procedure analogous to that used for images of real galaxies.


The poor theoretical knowledge of the stellar mass loss history represents one of the main uncertainties in the computation of AGB stellar models. Low- and intermediate-mass stars lose the majority of their mass during the red giant branch (RGB) and the AGB phases. In 1D stellar evolutionary codes, the mass-loss rate during the RGB phase is commonly parameterized according to the formulation proposed by Reimers (1975):
2

where

 is in units of M

 yr−1 and other quantities are in solar units. The uncertainty affecting this formula was originally quoted by Reimers to be at least a factor of two either way. Later, Fusi-Pecci  Renzini (1976) introduced a normalization constant in order to reproduce the horizontal branch morphology of globular clusters (

 = 0.4).10

10
FRUITY models adopt this value.
 Depending on the mass lost during the RGB phase (and thus on the value of

), stars attain the AGB phase with different envelope masses. Thus, in principle, the RGB mass loss could have an effect on the subsequent AGB nucleosynthesis. Those effects are expected to be important for low-mass stars (M

 1.5 M

) because they spend more time in the RGB phase than do larger masses. Moreover, their envelopes are thinner than in more massive stars, so even a small amount of material lost (e.g., 0.1 M

) can produce sizeable effects on the occurrence of TDU in the subsequent AGB phase (see, e.g., Straniero 2003). To properly determine the effects of RGB mass-loss rate on AGB nucleosynthesis (and thus on the solar s-only distribution), we calculate a set of M = 1.3 M

 models at different metallicities with

. In Figure 10 we report the variations of the surface abundances (

) with respect to the corresponding FRUITY cases. We find that

 are larger at low metallicities (in particular for the heaviest s-only isotopes). This is because at large metallicities this mass experiences a few TDU episodes, even using a milder RGB mass-loss rate. Thus, the final surface s-process enhancement is, in any case, low. By comparison, we also report data relative to a M = 2

 Z = 10−2 ([Fe/H] = −0.15) model. The low variations found in this case confirm that for massive-enough AGB stars a reduced mass-loss rate during the RGB phase has practically no effect. In Figure 11 we report a GCE model computed with

 in stars with M

M

 (hereinafter the Reimers case). We find minor variations in the s-only distribution (see also Table 1), with slightly larger enhancements for the heaviest s-only isotopes (

). Our results reinforce the evidence that the major contributors to the solar system s-process inventory are AGB stars in the mass range (1.5–3.0)

, as already inferred in Section 3. Their nucleosynthesis is strongly affected by the rate at which they lose mass during the AGB. A viable method to estimate AGB mass loss is based on the observed correlation with the pulsation period (Vassiliadis  Wood 1993). Because the evolution of the pulsation period depends on the variations of radius, luminosity, and mass, this relation provides a simple method to estimate the evolution of the mass-loss rate from basic stellar parameters. In our models, the AGB mass loss is determined according to a procedure similar to the one adopted by Vassiliadis  Wood (1993), but revising the mass loss–period and the period–luminosity relations, taking into account more recent infrared observations of solar-metallicity AGB stars (see Straniero et al. 2006 and references therein). It has been demonstrated that AGB mass-loss rates are mildly dependent on the metallicity (Groenewegen et al. 2007; Lagadec et al. 2008), and thus we applied the same period–mass loss relation for all AGB models present in the FRUITY database. Nevertheless, it is worth noting that, when a fixed period is defined, the observational data show quite a large scatter. In a period–mass loss plot, a theoretical curve constructed when reducing by a factor of two the mass-loss rate at a fixed period still lies within the observed spread (see Figure 8.10 of Cristallo 2006). This still holds for a mass-loss rate increased by a factor of two. In order to quantify the effects on the s-only distribution induced by a variation of the AGB mass-loss rate, we compute some AGB models with a milder and stronger period–mass loss relations. In Figure 12 we show the results on the final surface distributions of 2 M

 stellar models at various metallicities. In the plot,

 represents the difference between models computed with the standard

–period relation (Straniero et al. 2006) and the modified ones. Obviously, positive differences are obtained with a milder mass-loss rate, while negative differences with the stronger one. Heavy-element surface variations are below 0.1 dex (25%) for the whole s-process distribution, being slightly larger at low metallicity. Thus, we expect that a modified

–period relation in the AGB phase will produce an almost rigid shift (upward or downward, depending on the adopted mass-loss law) of the s-process isotopes. In order to verify this statement, we compute a GCE model with a milder

–period relation during the AGB phase (hereinafter the Mloss AGB case). The results are shown in Figure 13; the corresponding data are reported in Table 1. As expected, for s-only isotopes with A ≥ 96, there is an almost rigid upper shift of solar percentages (∼25%). In summary, a rigid shift (upward or downward) of the s-process isotopic inventory can be obtained by adopting a different prescription for the AGB mass-loss rate within the intrinsic observed scatter in the

–period relation.


In order to establish the completeness and purity of the RR Lyrae stars confirmed by the SOS Cep&RRL pipeline and to estimate the number of new discoveries by Gaia, we performed a deep and careful comparison with the literature. As a first step, the catalogue of 140 784 confirmed sources was cross-matched against all major catalogues of known RR Lyrae stars that are available. We primarily used the OGLE catalogues for RR Lyrae stars (version IV of the survey, Soszyński et al. 2014, 2016), but we also used RR Lyrae stars by CTRS (Drake et al. 2013a,b, 2014, 2017; Torrealba et al. 2015), ASAS (Pojmanski 1997; Richards et al. 2012), ASAS-SN (Jayasinghe et al. 2018), ATLAS (Tonry et al. 2018), IOMC (Alfonso-Garzón et al. 2012), LINEAR (Palaversa et al. 2013), NSVS (Kinemuchi et al. 2006), Pann-Stars (PS1 Sesar et al. 2017), and from the works based on Kepler/K2 (Debosscher et al. 2011; Nemec et al. 2011; Molnár et al. 2015a,b, 2016) and on the Simbad database (Wenger et al. 2000). These cross-matches returned a list of 88 578 known RR Lyrae stars in our sample of 140 784 stars. The SOS Cep&RRL confirmed RR Lyrae stars were also cross-matched against catalogues of candidate RR Lyrae stars discovered by the VVV survey (Gran et al. 2016; Minniti et al. 2017; D. Minniti, priv. comm.) in the MW disc and bulge. This returned 319 VVV cross-identified sources in the MW disc and 222 in the MW bulge. We thus confirm these VVV candidates. For known RR Lyrae stars in GCs, the main reference was the catalogue of Clement et al. (2001), which was updated to the latest literature as described in Garofalo et al. (in prep.). For variables in dSphs, we used the following references: Kaluzny et al. (1995), Clementini et al. (2005), Kinemuchi et al. (2008), Dall’Ora et al. (2012) and Garofalo et al. (2013). These latter cross-matches returned a list of 1986 further known RR Lyrae stars. At the end of this cross-match procedure, of the 140 784 RR Lyrae stars that are confirmed by the SOS Cep&RRL pipeline, 90 564 were shown to be known previously, and 50 220 are new discoveries by Gaia.


The SOS Cep&RRL confirmed RR Lyrae stars were also cross-matched against catalogues of candidate RR Lyrae stars discovered by the VVV survey


In Figure 7, we find a trend between

 and SFR over about 3 orders of magnitude in far-IR luminosity/SFR. The solid line shows the best-fit (a logarithmic linear least-squares bisector fit) correlation for the whole sample of QSOs, with a power law of

. The Spearman rank correlation coefficient for this correlation is 0.77 with a high significance (P  10−5) but substantial scatter. Our result is in general agreement with the correlation found between AGN activity and star formation, i.e.,

 (α ∼ 1.1–1.7; see Netzer 2009; Chen et al. 2013; Hickox et al. 2014; Duras et al. 2017; Dai et al. 2018; Izumi et al. 2019 and references therein). As noted in previous works (see e.g., Dai et al. 2018), the variation of slope might be attributed to different sample compositions and/or methods of analysis. However, all of these studies, including our own, reveal a significant trend between the SFR and BH accretion spanning a wide range of luminosity, implying that there may be a direct connection between the AGN and star formation activities over galaxy evolution timescales. In addition, there is evidence that SMBHs have grown in step with their host galaxies since z ∼ 2 (Daddi et al. 2007; Mullaney et al. 2012). The median value of

/SFR is 6.0 × 10−3 for IR QSOs, consistent with the value derived in Xia et al. (2012). In contrast, the

/SFR values for high-z QSOs are found to be about a factor of 10 higher (a median of 7.3 × 10−2) than the local IR QSOs. This is consistent with the “overmassive” BH revealed for z > 5 QSOs (Walter et al. 2004; Wang et al. 2010, 2013, 2016), for which a plausible interpretation is likely related to the different efficiency of gas accretion to the central SMBHs, i.e., faster gas consumption in the most massive SMBHs. Similar results have been reported by Hao et al. (2008), who found a trend that the SFR increases with the accretion rate for both low- and high-redshift IR-luminous QSOs, and the relative growth of BHs and their host spheroids may depend on the intensity of QSO activities.


There are several possible physical processes to reconcile these discrepancies between the models and the observations at z ∼ 10–13. As discussed in Harikane et al. (2021b), less efficient mass quenching and/or lower dust obscuration than assumed in the models can explain the existence of these UV-bright galaxies. Active galactic nucleus (AGN) activity may also boost the UV luminosity in these galaxies. Previous studies indicate that the AGN fraction starts to increase at M
UV ≃ −22 mag (Ono et al. 2018; Stevans et al. 2018; Adams et al. 2020; Harikane et al. 2022; see also Piana et al. 2022). If we assume that the UV luminosities of HD1 and HD2 are solely powered by black holes, the inferred black hole masses are ∼108
M
⊙, assuming accretion at the Eddington rate (Pacucci et al. 2022), in accordance with expectations for high-redshift quasars (see, e.g., Haiman & Menou 2000 and Willott et al. 2010). In addition, note that a ∼108
M
⊙ black hole at z ∼ 12 could be the progenitor of z ∼ 7 quasars, as the growth time to reach a mass of 109–1010
M
⊙, typical of z > 6 quasars detected thus far, is shorter than the cosmic time between z = 12–13 and z = 7, for an Eddington-limited accretion. It is also possible that the observed bright sources at z ∼ 10–13 are galaxies in a short-time starburst phase that is not captured in the models whose outputs are averaged over a time interval (see also Dayal et al. 2013). Finally, a top-heavier IMF would explain the discrepancies by producing more UV photons at the same stellar mass. It is possible that these bright galaxies (especially HD1 and HD2) are merging systems that are not resolved in the ground-based images. However, even if they are major mergers, the UV luminosity will decrease only by a factor of a few, which would not explain the discrepancy at z ∼ 13 (see also discussions in Harikane et al. 2022; Shibuya et al. 2022). In any case, if these bright z ∼ 10–13 galaxies are spectroscopically confirmed, the discrepancies will motivate the exploration of new physical processes that are responsible for driving the formation of these bright galaxies in the early universe.


For the distance to the source of HESS J1825−137 of 4 kpc (based on dispersion measure using the models for Galactic electrons by Taylor & Cordes 1993; Cordes & Lazio 2002), the measured angular size of the latter corresponds to the 70 pc linear size of the gamma-ray production region. Although the gamma-ray image deviates from the spherically symmetric shape; below for simplicity we will assume that the radius of the source is 35 pc. The detection of a Hα rim at a distance of

 from the pulsar PSR J1826-1334 has been interpreted as a signature of the progenitor SNR (see Stupar et al. 2008; Voisin et al. 2016). As illustrated in Figure 4, in the case of an ISM density gradient, the measured radius does not coincide with the radius, Rsnr . If the pulsar is still located inside the SNR then the SNR radius cannot be significantly smaller than the observed distance:

. Thus, with a factor of two uncertainty one can estimate the radius based on Sedov’s solution:
40

where

 are the density, the hydrogen number density, and the proton mass, respectively. Thus, the SNR shell can be located at the distance of

 pc, provided that the following condition is fulfilled:
41

where the numerical value corresponds to

. The ejecta energy at SN type II is constrained by

, while the age of the source is limited by

 (for

). Thus, Sedov’s solution is consistent with the observed size of the SNR when

. Note that de Jager & Djannati-Ataï (2009) derived a somewhat smaller upper limit for

 assuming the braking index n = 2. This upper limit seems to be below the typical density of the interstellar gas in the Galactic Plane. Moreover, Voisin et al. (2016) reported the presence of several molecular clouds in the small angular proximity to the nebula with an average number density

 and characteristic size

. It is likely that one of these clouds is responsible for the anisotropic expansion of the nebula, thus it should be located close to the nebula. The gas density in molecular clouds is expected to follow the King’s profile:
42

Thus, the density to the south of the pulsar can hardly be as low as it is required by Sedov’s solution. Instead, it should be comparable to the upper limit of

 obtained by Voisin et al. (2016).


In some cases, the precursor emission has a nonthermal spectrum, especially GRB111117510 and GRB160804180 with ΔBIC ≳ 6. These cases may be explained by the NS magnetospheric interaction model (assuming that the sources are nearby). For NS mergers with the surface magnetic field

 for the primary NS, the typical spectrum may be approximately described by a synchrotron radiation spectrum of a photon index around −2/3 peaking at ∼MeV, because of the effect of synchrotron-pair cascades (Wang et al. 2018a, 2018b). Such a model can well explain the photon indices and peak energies of the nonthermal precursor bursts, e.g., GRB111117510, GRB140209313, and GRB160804180 (Wang et al. 2018b). The precursor emission time for this magnetospheric interaction model roughly coincides with the gravitational-wave radiation chirp signal time. So the waiting time between the precursor and the main burst should correspond to the time delay between the GW signal and the SGRB signal. This timescale consists of three parts (Zhang 2019): the time (

) for the jet to be launched by the central engine, the time (Δtbo) for the jet to propagate through and break out from the circumburst medium, and the time (ΔtGRB) for the jet to reach the energy dissipation radius (e.g., the photospheric radius or the internal shock radius). The last term is

, while the first two terms depend on the jet-launch models. According to the Table 1 in Zhang (2019), for most models,

 = 0.01–1 s. Consequently, one would also expect

 ∼

. An exception is the SMNS/SNS magnetic model, in which a uniform-rotation-supported supramassive NS (SMNS) is formed after the NS merger, which subsequently becomes a stable NS (SNS). In this model, the waiting time is dominated by the term

, which is mainly contributed by the time needed to clean the environment to launch a relativistic jet (Metzger et al. 2011; Zhang 2019). In this case, one expects

 ≫

. In our sample, we find most events satisfy

 ∼

, except GRB191221802, which has

/

 ≈ 52 and

 s. We also notice that for GRB090510016, Troja et al. (2010) found two precursors in the Swift data, but only the second precursor can be found in Fermi data (consistent with our results). Its first precursor is found to be of

/

 ≈ 40 and

 ≈ 12 s, while its second precursor in our analysis is consistent with the photospheric radiation of the fireball. Therefore, its first precursor with a long waiting time (

/

 ≫ 1) could originate from NS magnetospheric interaction, and such long waiting times are caused by the jet-launch mechanism in the SMNS/SNS magnetic model. In conclusion, according to this model, an SNS engine might have been formed after the merger in events with

/

 ≫ 1, e.g., GRB090510016 and GRB191221802.


, for most models,

 = 0.01–1 s. Consequently, one would also expect

 ∼

.


In this model, the waiting time is dominated by the term

, which is mainly contributed by the time needed to clean the environment to launch a relativistic jet


For the first time, we detected [C ii] 158-μm emission from a GRB host galaxy at z > 2. This is the second detection of [C ii] 158-μm emission among known GRB host galaxies, following GRB 980425 (Michałowski et al. 2016). The [C ii] 158-μm fine structure line is the dominant cooling line of the cool interstellar medium, arising from photodissociation regions (PDR) on molecular cloud surfaces. It is one of the brightest emission lines from star-forming galaxies from FIR to metre wavelengths, almost unaffected by dust extinction. [C ii] 158-μm luminosity, L[C II], has been discussed as an indicator of SFR (e.g. Stacey et al. 2010). If L[C II] scales linearly with SFR, the ratio to FIR luminosity, L[C II]/LFIR, is expected to be constant, since LFIR is a linear function of SFR (e.g. Kennicutt 1998a). However, LC II/LFIR is not constant, but declines with increasing LFIR, known as the ‘[C ii] deficit’ (e.g. Luhman et al. 1998, 2003; Malhotra et al. 2001; Sargsyan et al. 2012; Díaz-Santos et al. 2013, 2017; Spilker et al. 2016). The [C ii] deficit persists when including high-z galaxies (e.g. Stacey et al. 2010; Wang et al. 2013; Rawle et al. 2014). In Fig. 5, we compare the [C ii] deficit in the GRB 080207 host and other star-forming galaxies. Two GRB hosts are shown by stars: GRB 080207 (orange star) and 980425 (blue star). The comparison sample is compiled from the literature up to z ∼ 3 (Malhotra et al. 2001; Cormier et al. 2010, 2014; Ivison et al. 2010; Stacey et al. 2010; Sargsyan et al. 2012; Farrah et al. 2013; Magdis et al. 2014; Brisbin et al. 2015; Gullberg et al. 2015; Schaerer et al. 2015). Active galactic nuclei are separated from star-forming galaxies based on either (i) the explicit description in the literature or (ii) EWPAH 6.2μm  0.1 (Sargsyan et al. 2012). As reported by previous studies (e.g. Maiolino et al. 2009; Stacey et al. 2010), high-z galaxies are located at a different place from local galaxies in the L[C II]/LFIR–LFIR plane.


The comparison sample is compiled from the literature up to z ∼ 3


Active galactic nuclei are separated from star-forming galaxies based on either (i) the explicit description in the literature or (ii) EWPAH 6.2μm  0.1


Jiang et al. (1975) estimated the infrared band strength of CO ice deposited at high pressure compared to modern setups: their deposition rate of 0.5 to 2 μm requires a pressure about 16 to 66 times higher than typical experiments performed at 1 × 10−6 mbar during deposition. To obtain this band strength, Jiang et al. (1975) also adopted a literature value of the CO ice density measured at a relatively high temperature, 30 K (Vegard 1930). According to Luna et al. (2022) and this work, the CO ice density depends on the temperature and pressure during deposition, and therefore, the value of the CO infrared band strength in Jiang et al. (1975) needs a revision. We propose to use $\mathcal {A}(\rm CO)$  = (8.7 ± 0.5) × 10−18 cm  molecule−1 for future column density estimations. This value is valid in the experimental range from 11 to 28 K deposition temperatures investigated in this work, for which no variations of the integrated absorbance area and sticking probability were found (Cazaux et al. 2017). The CO ice column density values reported in previous experimental and observational papers might thus be underestimated, they would be about 23  per cent lower than the actual value. Most of the CO ice column densities reported in the literature adopted a band strength of $\mathcal {A}(\rm CO)$  = 1.1 × 10−17 cm  molecule−1 (Jiang et al. 1975), they would need to be multiplied by a factor of 1.3 for correction. An example is the number of monolayers on the surface, or just beneath the surface of the ice, involved in the photodesorption of CO, i.e. N  = 5 × 1015 molecules cm−2 or about 5 monolayers (ML) where 1 ML  = 1 × 1015 molecules cm−2 (Muñoz Caro et al. 2010; Fayolle et al. 2011; Chen et al. 2014). After correction, this becomes 6.5 ML. Considering our average density value of CO ice deposited at 11 K, 0.837 g cm−3, and equation (24), it is found that the thickness of one monolayer is 0.56 nm, and 3.36 nm for the top 6.5 ML of ice. The UV photons emitted by the MDHL that are absorbed deeper than 3.36 nm would not lead us to photodesorption of CO molecules.


SFR and

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

 can be derived from observations, but the molecular gas mass, MH2 = αCO ×

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

, is the key quantity of interest. The observed SFR/

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

 ratio is related to both the depletion time (τdep) and the CO-to-H2 conversion factor (αCO) as SFR/

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

 = SFR/(MH2/αCO) = αCO/τdep. Many studies have shown that αCO increases rapidly at low metallicity theoretically and observationally (Israel 1997; Glover & Mac Low 2011; Leroy et al. 2011; Narayanan et al. 2012; Elmegreen et al. 2013; Shi et al. 2016). If τdep is constant, as is found for the nearby disc galaxies (Leroy et al. 2008; Bigiel et al. 2011), then the dependence of the SFR/

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

 ratio on metallicity is the direct consequence of the variation of αCO. However, τdep in dwarf galaxies remains uncertain and tends to be shorter at a lower mass and at a higher specific SFR (sSFR; Saintonge et al. 2011; Shi et al. 2014; Hunt et al. 2020). IZw18, as a dwarf galaxy with a relatively high sSFR and low mass, is likely to have low τdep. We speculates that as αCO = τdep ×

SFR

L

CO
(
1
−
0
)

′

$ \frac{\mathrm{SFR}}{L^\prime_{\mathrm{CO(1{-}0)}}} $

, the high SFR/

L

CO(1-0)
′

$ L^\prime_{\rm CO(1{-}0)} $

 ratio of IZw18 would overwhelm the possibly low τdep, and this would result in a high αCO. Moreover, considering the dependence of αCO on both sSFR and metallicity for the metal poor galaxies, IZw18 follows the empirical relation found in Hunt et al. (2020) within the uncertainty of the stellar mass, as shown in the bottom right corner of Fig. 5. This relation was derived based on a recent compilation of ∼400 metal poor galaxies (Ginolfi et al. 2020, MAGMA). We note that the individual star-forming regions of the metal-poor galaxies from Shi et al. (2015, 2016) all fall slightly above the relation, but well within the scatter of the global measurements of the galaxies. This indicates that αCO changes continuously with metallicity and sSFR. A further constraint on the conversion factor (αCO) of IZw18 is beyond the scope of this paper.


The behaviour of the radio emission from the early-type magnetic stars has been definitively quantified by the empirical scaling relationship between the radio spectral luminosity and the magnetic flux rate: $L_{\nu ,\mathrm{rad}} {\propto } (\Phi / P_{\mathrm{rot}})^2 = {B_{\mathrm{p}}^2 R_{\ast }^{4}} / {P_{\mathrm{rot}}^2}$, found by Leto et al. (2021) and confirmed by Shultz et al. (2022). This empirical relationship is the consequence of the physical mechanism supporting the non-thermal acceleration able to produce the electrons responsible for the magnetospheric radio emission of early-type magnetic stars. It was recently demonstrated by Owocki et al. (2022) that the power provided by centrifugal breakout events, continuously occurring within the stellar magnetosphere, is directly related to the power of the radio emission. From this point of view, the CBOs are non-random events. Breakouts occur continuously in a well-constrained magnetospheric region, where the resulting reconnection of the magnetic fields drives the acceleration of the local electrons. The CBO luminosity is related to the stellar parameters by the relation (Owocki et al. 2022):
$$\begin{eqnarray*}
L_{\mathrm{CBO}} = \frac{B_{\mathrm{p}}^2 R_{\ast }^3}{P_{\mathrm{rot}}} \times W {\mathrm{~~(erg \, s^{-1}),}}
\end{eqnarray*}$$with Bp in gauss, R* in centimetres, and Prot in seconds. In the above relation $W=2 \pi R_{\ast } / P_{\mathrm{rot}} \sqrt{G M_{\ast }/R_{\ast }}$ is the dimensionless critical rotation parameter calculated as the ratio between the equatorial stellar velocity and the corresponding orbital velocity, defined by the gravitational law at the stellar equator (G = 6.67408 × 10−8 cm3 g−1 s−2 is the gravitational constant). Once the explicit relation of W is substituted within the LCBO definition, we find that $L_{\mathrm{CBO}} \propto {B_{\mathrm{p}}^2 R_{\ast }^{4.5} M_{\ast }^{-0.5}} / {P_{\mathrm{rot}}^2} \propto L_{\nu ,\mathrm{rad}}$, which in practice is almost the same relation empirically found, except for the term related to the mass, that in any case has negligible effect. The maximum possible value of W is W = 1, which, due to magnetic braking, would have to be at the beginning of the star’s life; however no magnetic star has ever been found with W⪆0.5 (Shultz et al. 2019b). In fact, this parameter progressively decreases as the star loses angular momentum throughout its life (Keszthelyi et al. 2019, 2020).


The CBO luminosity is related to the stellar parameters by the relation

$$\begin{eqnarray*}
L_{\mathrm{CBO}} = \frac{B_{\mathrm{p}}^2 R_{\ast }^3}{P_{\mathrm{rot}}} \times W {\mathrm{~~(erg \, s^{-1}),}}
\end{eqnarray*}$$with Bp in gauss, R* in centimetres, and Prot in seconds.


The presence of neutral lines in the IRIS spectra allow us an accurate absolute wavelength calibration, and therefore a more accurate determination of line Doppler shifts, as compared to some other spectral observations; e.g., with EIS. For the post-flare loops, we find that the Fe xii emission is largely unshifted at the loop tops and predominantly redshifted at both loop footpoints, as expected for the draining of plasma in the later phases of the flare, when the heating has ceased. For the moss observations, we find that the distribution of Doppler shifts is peaked at a redshift of a few km s−1, but with significant wings on both the red and the blue sides. In our interpretation, guided by the Bifrost 3D models, Fe xii appears redshifted for hotter coronal temperatures (≳4 MK), while blueshifted when the corona is at cooler temperatures. The distribution of Doppler shift we observe shows a wide range of blue- and redshifts, and it suggests that there may be a continuous mix of heating and cooling in the moss we observed. For cooler TR lines (

[K]

), the dominance of redshift is well established (e.g., Doschek et al. 1976; Dere et al. 1984; Achour et al. 1995; Chae et al. 1998b; Peter & Judge 1999). The physical processes causing the observed redshifts are still debated, and several models have been proposed (e.g., Hansteen 1993; Patsourakos & Klimchuk 2006; Peter et al. 2006; Hansteen et al. 2010). Hansteen et al. (2010) use 3D radiative MHD models of the solar atmosphere to investigate the TR redshifts, and find that in their model the heating is dominated by rapid intermittent events at low heights which heat the plasma locally to coronal temperature and produces downflows at TR temperature due to the local overpressure. The model analyzed by Hansteen et al. (2010) reached modest coronal temperatures (≲2.5 MK), therefore with significant Fe xii emission in loop structures rather than at the loop footpoints, as in the case for moss. Here we used a different Bifrost 3D MHD simulation, which reaches higher coronal temperatures and represents a better model for moss observations. We find that the moss Fe xii (mostly) redshifted emission we observe with IRIS is reproduced in the model when the corona gets hot enough and most of the Fe xii is confined in the TR loops. The Fe xii then behaves like a TR line, and is redshifted, in the model, as a consequence of the local heating at low heights which causes upflows in the hotter lines and downflows in the cooler (TR) lines.


After crossing the bow shock, neutral atoms can interact with the shocked protons. The interaction length is given by

(2)

\begin{equation}
\lambda = \frac{V_{\rm NS}}{X_{\rm ion} n_{\rm ISM} r_{\rm c} \langle \sigma (v_{\rm rel}) v_{\rm rel} \rangle },
\end{equation}

where Xion is the ionization fraction of the ISM, rc is the compression ratio of the bow shock, σ(vrel) is the relevant cross-section of the process under consideration and 〈σvrel〉 is the collision rate averaged over the ion distribution function. When the ion distribution is a Maxwellian, 〈σvrel〉 is well approximated (within 20 per cent) by the expression (Zank et al. 1996; Blasi et al. 2012)

(3)

\begin{equation}
\langle \sigma v_{{\rm rel}} \rangle \approx \sigma (U^*) U^*,
\end{equation}

where

(4)

\begin{equation}
U^*= \sqrt{\frac{8}{\pi } \frac{2 k_{\rm B} T}{m_{\rm p}} }
\end{equation}

is the average, relative speed between the incoming hydrogen atom and ions (T is the temperature of the shocked ISM determined by the Rankine–Hugoniot jump conditions, assumed to be ≫TISM). Using the fiducial values nISM = 0.1 cm−3 and VNS = 300 km s−1, together with an ionization fraction of 90 per cent and rc = 4 (the typical value for strong shocks), leads to the following estimates for the mean free paths:

(5)

\begin{eqnarray}
\lambda _{{\rm ion},{\rm p}} & \approx 3.0 \times 10^{20} \, \rm cm,
\end{eqnarray}

(6)

\begin{eqnarray}
\lambda _{{\rm ion},{\rm e}} & \approx 2.2 \times 10^{16} \, \rm cm,
\end{eqnarray}

(7)

\begin{eqnarray}
\lambda _{\rm CE} & \approx 1.5 \times 10^{15} \, \rm cm
\end{eqnarray}

for the ionization due to collisions with protons, electrons and CE, respectively. Note that λion, e has been calculated under the assumption that the electrons downstream of the shock equilibrate rapidly with protons, thereby acquiring the same temperature. If this assumption does not hold, the collisional length scale for ionization due to electrons can become much larger than the value reported in equation (6). In addition, the values (5)–(7) are to be taken as lower limits as they are valid just ahead of the nebula, where the compression ratio and the temperature obtain their maximum values.


The driving mechanism and physical nature of large-scale EUV waves have been hotly debated over the past 20 years (Chen 2017). Because chromospheric Moreton waves were believed to be driven by the flare pressure pulses for a long time after Uchida (1968), solar physicists naturally thought at the beginning that EUV waves also have the same driving mechanism (e.g., Khan & Aurass 2002; Hudson et al. 2003; Warmuth et al. 2004). However, more and more recent high-resolution observational studies have shown that EUV waves are in fact bow shocks driven by CMEs instead of flare pressure pulses (e.g., Chen 2006; Kienreich et al. 2009; Patsourakos & Vourlidas 2009; Patsourakos et al. 2010; Liu et al. 2011b; Shen & Liu 2012a, 2012c; Xue et al. 2013; Long et al. 2017a; Shen et al. 2017a; Cunha-Silva et al. 2018). Further investigations indicated that EUV waves can also be excited by other kinds of slightly different processes, such as newly formed expanding loops, coronal jets, and mini-filament eruptions on small scales (e.g., Podladchikova et al. 2010; Zheng et al. 2012, 2013; Su et al. 2015; Shen et al. 2017a), and the sudden expansion of transequatorial loops driven by coronal jets on large scales (Shen et al. 2018e, 2018d). In these scenarios, those authors found that such EUV waves often have a shorter lifetime (a few minutes) compared to those driven by CMEs (tens of minutes). Moreover, Shen et al. (2018a) reported an interesting non-CME-associated homologous EUV wave event in which the initial speeds of the waves are about 1000 km s−1, and the authors proposed that the observed EUV waves were large-amplitude nonlinear fast-mode magnetosonic waves or shocks directly driven by the associated recurrent coronal jets, resembling the generation of a piston shock in a tube. These new observations suggest that EUV waves can be excited by different kinds of coronal disturbances, e.g., CMEs, coronal jets, and mini-filament eruptions.


Further investigations indicated that EUV waves can also be excited by other kinds of slightly different processes, such as

and the sudden expansion of transequatorial loops driven by coronal jets on large scales


reported an interesting non-CME-associated homologous EUV wave event in which the initial speeds of the waves are about 1000 km s−1, and the authors proposed that the observed EUV waves were large-amplitude nonlinear fast-mode magnetosonic waves or shocks directly driven by the associated recurrent coronal jets, resembling the generation of a piston shock in a tube. These new observations suggest that EUV waves can be excited by different kinds of coronal disturbances, e.g., CMEs, coronal jets, and mini-filament eruptions.


The HD 189733 system offers the possibility to study these various interactions (Table 1). It is a binary system with a K2V dwarf (HD 189733 A, hereafter HD 189733) and a M4V dwarf (HD 189733 B; Bakos et al. 2006) at a mean separation of ∼220 au. The bright primary (V = 7.7) hosts a transiting hot Jupiter at 0.03 au (Bouchy et al. 2005), whose strong irradiation and large occultation area make it particularly favourable for atmospheric characterization (see Pino et al. 2018 and references inside for observations of the lower atmospheric layers). Recent transit observations in the near-infrared (Salz et al. 2018) revealed absorption by helium in an extended but compact thermosphere. Transit observations in the far-ultraviolet (FUV) previously revealed absorption by a dense and hot layer of neutral oxygen at higher altitudes (Ben-Jaffel & Ballester 2013). The close distance of HD 189733 to the Sun (19.8 pc) enables observations of the stellar Lyman α line with the Hubble Space Telescope (HST). Atmospheric escape of neutral hydrogen was first detected in the unresolved line with the HST Advanced Camera for Surveys (ACS) in two out of three epochs (Lecavelier des Etangs et al. 2010), and in the line resolved with the HST Space Telescope Imaging Spectrograph (STIS) in one out of two epochs (Lecavelier des Etangs et al. 2012; Bourrier et al. 2013). These observations provided the first indication of temporal variations in the physical conditions of an evaporating planetary atmosphere. Bourrier & Lecavelier des Etangs (2013) attributed the high-velocity, blueshifted absorption signature detected by Lecavelier des Etangs et al. (2012) to intense charge-exchange between the planet exosphere and the stellar wind, proposing that an X-ray flare observed before the transit increased the atmospheric mass-loss and/or increased the density of the stellar wind. The latter scenario is favoured by thermal escape simulations from Chadney et al. (2017), who found that the energy input from a flare would not increase sufficiently the mass-loss. Interestingly the tentative detection of absorption by ionized carbon (Ben-Jaffel & Ballester 2013) and excited hydrogen (Jensen et al. 2012; Cauley et al. 2015, 2016; Cauley, Redfield & Jensen 2017; Kohl et al. 2018) before and during the transit of HD 189733b could be explained by the interaction of the stellar wind with the planetary magnetosphere or escaping material. The observed temporal variability in the atmospheric escape of neutral and excited hydrogen is likely linked to the high-level of activity from the host star, which results in a fast-changing radiation, particle, and magnetic environment for the planet. Enhanced activity in the stellar chromosphere and transition region have also been observed after the planetary eclipse, and attributed to signatures of magnetic star–planet interactions (Pillitteri et al. 2010, 2011, 2014, 2015). Evidence for modulation in the Ca ii lines at the orbital period of the planet, during an epoch of strong stellar magnetic field, further supports this scenario (Cauley et al. 2018). The detectability of star–planet interactions in the HD 189733 system however remain uncertain, and intrinsic stellar variability and inadequate sampling has been proposed to explain the observed variations (Route 2019). These results show the need to study contemporaneously and in different epochs the upper atmosphere of HD 189733b and its high-energy environment.


Due to recent major advances in the observational studies of active galactic nuclei (AGN), evidence is growing that massive black holes (MBHs) heavier than $10^5\, \rm {M_\odot }$ form in nature and power AGN activity at the centres of galaxies through gas accretion (Schmidt 1963; Hopkins, Richards & Hernquist 2007; Merloni & Heinz 2008; Ueda et al. 2014; Aird et al. 2015). The demographic study of AGN and the dynamics of stars and gas around the centre of nearby galaxies, further provided evidence that most (if not all) massive galaxies in the Universe host MBHs in their nuclei (Genzel & Townes 1987; Dressler & Richstone 1988; Kormendy 1988; Kormendy & Richstone 1992; Genzel, Hollenbach & Townes 1994; Salucci et al. 1999; Peterson et al. 2004; Vestergaard & Peterson 2006). Even more, the existing correlations between the mass of MBHs and key properties of their host galaxies hint for their co-evolution (Haehnelt & Rees 1993; Faber 1999; O’Dowd, Urry & Scarpa 2002; Häring & Rix 2004; Kormendy & Ho 2013; Savorgnan et al. 2016). Even though these findings sharpened our knowledge on the role of MBHs in the formation and evolution of galaxies, there is a need to contextualize galaxies and MBHs within the broad cosmological context. It is commonly accepted that the Universe behaves in a hierarchical way. Cosmic structure formed through the hierarchical assembly of dark matter (DM) haloes, and the galaxies observed nowadays assembled through mergers with smaller companions and accretion of matter from the cosmic filaments (White & Rees 1978; White & Frenk 1991; Haehnelt & Rees 1993; Kauffmann et al. 1999; Guo et al. 2011; Vogelsberger et al. 2014a,b; Schaye et al. 2015; Nelson et al. 2018; Pillepich et al. 2018). Consequently, the existence of MBHs at the centre of galaxies and the main role of mergers in the Universe, hint for the existence of massive black hole binary systems (MBHBs) that might have formed and coalesced throughout the whole Universe lifetime.

Kormendy 1988
O’Dowd, Urry & Scarpa 2002


Due to recent major advances in the observational studies of active galactic nuclei (AGN), evidence is growing that massive black holes (MBHs) heavier than $10^5\, \rm {M_\odot }$ form in nature and power AGN activity at the centres of galaxies through gas accretion


Cosmic structure formed through the hierarchical assembly of dark matter (DM) haloes, and the galaxies observed nowadays assembled through mergers with smaller companions and accretion of matter from the cosmic filaments


The two components in V593 Cen are early-type stars that contain the convective core and the radiative envelope. This suggests that the period oscillation cannot be explained by the magnetic activity cycle mechanism, which is usually adopted to explain the cycle period change of later-type binary stars (e.g., Applegate 1992; Lanza et al. 1998). Therefore, the light-travel-time effect via the presence of a tertiary body is adopted to explain the cyclic change of the orbital period (e.g., Irwin 1952; Chambliss 1992; Borkovits & Hegedüs 1996; Liao & Qian 2010). Using this method, tertiary bodies have been detected orbiting massive close binary stars. Some examples are V701 Sco (Qian et al. 2006), V382 Cyg, TU Mus (Qian et al. 2007), and AI Cru (Zhao et al. 2010). Though it seems that binaries favor a more uniform distribution of eccentricities (Tokovinin 1997, 2008; Raghavan et al. 2010; Moe & Di Stefano 2017), we still assume that the tertiary wanders in the circular orbit. This is because the period change (in Figure 2) displays a periodic oscillation, and this oscillation is fitted either by a sine curve without eccentricities, or by using the value of the outer orbital period and the inner binary period (Pouter and Pinner). The period ratio for this multiple system is about Pouter/Pinner = 2.5 × 104. For this kind of multiple star system with a very large period ratio, the outer orbit usually has very low or no eccentricities (Shatsky 2001; Tokovinin 2004, 2008). Moreover, in large Pouter/Pinner ratio multiple system (commonly found in triple systems) the Kozai effect becomes too weak (Tokovinin 2008). For brevity, considering that the third body in the V593 Cen system is moving in a circular orbit, the projected radius of the orbit of the eclipsing pair rotating around the mass central of the triple system, the mass function, and the masses of the third component could be computed with these equations as follows:
5

6

where A3 is the amplitude of the O − C oscillation, c is the light speed, P3 is the period of the O − C oscillation, and i′ is the inclination of the tertiary orbital plane. Finally, when the inclination i′ = 90°, it is calculated that the lowest mass of the tertiary companion is 4.3 (0.3) M⊙ and the separation between the binary and the tertiary companion is about 25.5(2.2) au. For the other inclinations, the third body should have a larger mass and a shorter separation. When the inclination i′ = 826, which shows that the third body is in the same plane with the inner binary, its mass is calculated to be 4.7 (0.4) M⊙ and the separation is 25.2(2.8) au.


For this kind of multiple star system with a very large period ratio, the outer orbit usually has very low or no eccentricities


The two components in V593 Cen are early-type stars that contain the convective core and the radiative envelope. This suggests that the period oscillation cannot be explained by the magnetic activity cycle mechanism, which is usually adopted to explain the cycle period change of later-type binary stars (e.g.,


The binary characteristics of early-type magnetic stars may provide crucial clues, allowing one to test alternative fossil field hypotheses. The non-magnetic chemically peculiar stars of Am (A-type stars with enhanced lines of Fe-peak elements) and HgMn (late-B stars identified by strong lines of Hg and/or Mn) types are frequently found in close binaries (Gerbaldi, Floquet & Hauck 1985; Ryabchikova 1998; Carquillat & Prieur 2007), including eclipsing systems (Nordstrom & Johansen 1994; Strassmeier et al. 2017; Takeda et al. 2019). In contrast, only about ten close (Porb  20 d) spectroscopic binaries containing at least one magnetic ApBp star are known (Landstreet et al. 2017). The overall incidence rate of magnetic upper main sequence stars in close binaries is less than 2 per cent (Alecian et al. 2015), although this fraction is significantly higher if one includes wide long-period systems (Mathys 2017). This low incidence of magnetic ApBp stars in close binaries is frequently considered as an argument in favour of the stellar merger origin of fossil fields (de Mink et al. 2014; Schneider et al. 2016). In this context, confirmation of magnetic ApBp stars in short-period binary systems gives support to alternative theories or, at least, demonstrates that early-type stars may acquire magnetic fields through different channels. In addition, detached close binary stars, particularly those showing eclipses, are valuable astrophysical laboratories that provide model-independent stellar parameters and allow one to study pairs of co-evolving stars formed in the same environment. Until recently, no early-type magnetic stars in eclipsing binaries were known. The first such system, HD 66051, was identified by Kochukhov et al. (2018). The second system, HD 62658 containing twin components of which only one is magnetic, was found by Shultz et al. (2019). Several other eclipsing binaries containing candidate ApBp stars were proposed (Hensberge et al. 2007; González, Hubrig & Castelli 2010; Skarka et al. 2019), but the magnetic nature of these stars has not been verified by direct detections of their fields using the Zeeman effect. In this paper, we put a spotlight on another candidate eclipsing magnetic Bp star, which received little attention prior to our work despite being significantly brighter than the confirmed magnetic eclipsing systems HD 62658 and HD 66051.


The first such system, HD 66051, was identified by


The second system, HD 62658 containing twin components of which only one is magnetic, was found by


The non-magnetic chemically peculiar stars of Am (A-type stars with enhanced lines of Fe-peak elements) and HgMn (late-B stars identified by strong lines of Hg and/or Mn) types are frequently found in close binaries


This low incidence of magnetic ApBp stars in close binaries is frequently considered as an argument in favour of the stellar merger origin of fossil fields


In our model atom, singlet and triplet terms are often separated, and thus we would
            like to estimate how this total cross-section is distributed among final spin states. We
            considered a representation where the spin of the Rydberg electron is coupled to the
            spin of the other electrons in the target atom Sc (assuming
            this to be a good quantum number) to give the total electronic spin of the Rydberg atom,
              S.
            Recoupling of angular momenta gives the required spin-changing scattering amplitude in
            terms of the singlet and triplet scattering amplitudes (i.e. in the representation in
            which the Rydberg electron spin and the hydrogen atom spin are coupled), and the
            differential cross-section for change of spin S → S′, S ≠ S′,
            is found to be \begin{eqnarray} |f_{\rm e}(p,\theta,S \rightarrow S')|^2 & = & \frac{(2S'+1)}{8(2S_{\rm c}+1)} |f^+ - f^-|^2 \\[3mm]  & = &\frac{(2S'+1)}{2(2S_{\rm c}+1)} \sigma_{\rm exch} \end{eqnarray}

|

f

e

(
p,θ,S
→

S

′

)

|

2

=

(
2

S

′

+
1
)

8
(
2

S

c

+
1
)

|

f

+

−

f

−

|

2

=

(
2

S

′

+
1
)

2
(
2

S

c

+
1
)

σ

exch

where σexch is the
            differential cross-section for electron exchange in elastic e−+H  collisions (e.g. Field 1958; Burke
              & Schey 1962). The derivation essentially follows Dalgarno & Rudge (1965), except that in our case the electron
            spin is coupled to the core electronic spin and not to the nuclear spin. We note that
              S′ =
                Sc ± 1/2 and the factor
              (2S′ + 1) /
                2(2Sc + 1) is always in the range 0 to
            1 and represents the probability that an electron exchange leads to a change in the
            total electronic spin of the Rydberg atom. In the limit p → 0, − f± →
                a±, where a± are the
            scattering lengths, which have values of a+ = 5.965 and a− = 1.769
            atomic units (Schwartz 1961). In this limit, for
            the case of Sc =
              1/2, via comparison of the expressions for the cross sections we
            find that \begin{eqnarray} \sigma_{nl,S=0 \rightarrow n'l',S'=0} = 0.706 \: \sigma_{nl \rightarrow n'l'}, \\ \sigma_{nl,S=0 \rightarrow n'l',S'=1} = 0.294 \: \sigma_{nl \rightarrow n'l'}, \\ \sigma_{nl,S=1 \rightarrow n'l',S'=0} = 0.098 \: \sigma_{nl \rightarrow n'l'}, \\ \sigma_{nl,S=1 \rightarrow n'l',S'=1} = 0.902 \: \sigma_{nl \rightarrow n'l'}. \end{eqnarray}

σ

nl,S
=
0
→

n

′

l

′

,

S

′

=
0

=
0.706

σ

nl
→

n

′

l

′

,

σ

nl,S
=
0
→

n

′

l

′

,

S

′

=
1

=
0.294

σ

nl
→

n

′

l

′

,

σ

nl,S
=
1
→

n

′

l

′

,

S

′

=
0

=
0.098

σ

nl
→

n

′

l

′

,

σ

nl,S
=
1
→

n

′

l

′

,

S

′

=
1

=
0.902

σ

nl
→

n

′

l

′

.


However, two recent pieces of evidence may suggest that standard disk accretion is not the only process at work in growing a BH to the (super)massive regime. The first is the discovery of an increasing number of active BHs with masses M
• ≳ 109
M
⊙ at very high redshifts, z ≳ 7 (e.g., Mortlock et al. 2011; Wu et al. 2015; Venemans et al. 2017, 2018; Reed et al. 2019; Banados et al. 2018, 2021; Wang et al. 2019, 2021), when the age of the universe was shorter than 0.8 Gyr. The second is the robust measurements of extreme BH masses M
• ≳109−10
M
⊙ at the center of early-type galaxies with stellar mass M
⋆ ≳ 1011
M
⊙ (e.g., McConnell et al. 2011; Ferre-Mateu et al. 2015; Thomas et al. 2016; Mehrgan et al. 2019; Dullo et al. 2021) that formed most of their old stellar component during a star formation episode lasting some 108 yr at z ≳ 1, as demonstrated by astroarcheological measurements of their stellar ages and α-enhanced metal content (e.g., Thomas et al. 2005, 2010; Gallazzi et al. 2006, 2014; Johansson et al. 2012; Maiolino & Mannucci 2019; Morishita et al. 2019; Saracco et al.2020). These observations concur to raise the issue of how billion-solar-mass BHs may have grown in less than a gigayear. In fact, this is somewhat challenging if standard disk accretion starts from a light seed of ∼102
M
⊙ of stellar origin and proceeds with the typical Eddington ratios λ ≲ 1 as estimated out to z ∼ 6 in active BHs (see Vestergaard & Osmer 2009; Nobuta et al. 2012; Kelly & Shen 2013; Dai et al. 2014; Kim & Im 2019; Duras et al. 2020; Ananna et al. 2022), which would require an overall time ≳0.8/λ Gyr to attain ∼109
M
⊙. Solutions may invoke mechanisms able to rapidly produce heavy BH seeds of 103−5
M
⊙, thus reducing the time required to attain the final masses by standard disk accretion (see Natarajan 2014, Mayer & Bonoli 2019, Inayoshi et al. 2020, and Volonteri et al. 2021 for recent and exhaustive reviews). Viable possibilities comprise direct collapse of gas clouds within a (proto)galaxy, possibly induced by galaxy mergers or enhanced matter inflow along cosmic filaments (e.g., Lodato & Natarajan 2007; Mayer et al. 2010, 2015; Di Matteo et al. 2012, 2017); merging of stars inside globular or nuclear star clusters (e.g., Portegies Zwart et al. 2004; Devecchi et al. 2012; Latif & Ferrara 2016; Kroupa et al. 2020); and migration of stellar BHs toward the nuclear galaxy regions via dynamical friction against the dense gas-rich environment in strongly star-forming progenitors of local massive galaxies (e.g., Boco et al. 2020, 2021).
11

11
When referring to the dynamical friction mechanism, the term “seeds” is used in a broader sense with respect to the classic meaning in the literature. A seed is usually referred to as the first compact object on which subsequent disk accretion occurs, eventually leading to the formation of a supermassive BH. The heavy seeds formed with the dynamical friction mechanism are by-products of multiple mergers of already-existing stellar mass BHs (that in turn could be referred to as light seeds) forming across a wide redshift range.


In contrast to previous studies, the MFP expressions employed here are defined to include independent rigidity and nonlinear radial dependences. Furthermore, this approach does not make the simplifying assumption that λ
⊥ is proportional to λ
∥ (see, e.g., Ferreira et al. 2001). In order to study the radial and rigidity dependences of MFPs required to fit observations, as well as the values of these quantities at 1 au so as to compare these with theoretical predictions of the same, this study still implements simplified parametric expressions for these MFPs, motivated by the fact that the transport code here employed is written to perform on graphic processing units GPUs in CUDA, which allows for the vast performance increase required of such a study, but limits the number of definable variables due to memory constraints (see Dunzlaff et al. 2015, for additional information). Subsequently, λ
∥ and λ
⊥ are defined as
5

λ∥=λ∥,0PP0αrreβ,

6

λ⊥=λ⊥,0PP0γrreδ,

where r

e
 = 1 au, and P
0 = 1 GV, in an approach similar to that employed by Engelbrecht & Di Felice (2020). Here, parameters α and β specify the respective rigidity and radial dependences of the parallel MFP, which assumes a value of λ
0,∥ (in astronomical units) at Earth, with γ, δ, and λ
0,⊥ playing the same roles with respect to the perpendicular MFP. In the parameter studies employed here, these quantities are varied over a broad range of values, chosen so as to include, as well as extend beyond, various theoretical predictions for these quantities. In terms of MFP values at 1 au, the ranges λ
0,∥ ∈ [0.05, 1.0]  au and λ
0,⊥ ∈ [0.001, 0.5]  au are chosen, so as to include values reported in previous such studies for the parallel MFP (e.g., Palmer 1982; Bieber et al. 1994; Dröge et al. 2014) as well as for the perpendicular MFP (e.g., Ferrando et al. 1993; Giacalone 1998; Burger et al. 2000; Zhang et al. 2007; Vogt et al. 2020), while taking into account various theoretical predictions and expressions previously used in modeling studies for these MFPs (e.g., Ferreira et al. 2003; Engelbrecht & Burger 2013b; Nndanganeni & Potgieter 2018; Engelbrecht 2019). For the rigidity dependences, it is assumed that α ∈ [−0.1, 0.67] and γ ∈ [−0.1, 0.33], incorporating the flat rigidity dependence expected of λ
∥ for low-energy electrons (e.g., Dröge 1994; Potgieter 1996; Evenson 1998) within a range that includes dependences expected at higher rigidities as well as from different scattering theories (e.g., Dröge 2000; Teufel & Schlickeiser 2002; Shalchi & Schlickeiser 2004; Burger et al. 2008; Engelbrecht & Burger 2010). The range of rigidity dependences for λ
⊥ was chosen following similar reasoning, with the aim of incorporating a flat rigidity dependence within a range that incorporates moderate rigidity dependences expected from various theories (e.g., Shalchi et al. 2004a; Gammon & Shalchi 2017; Dempers & Engelbrecht 2020) as well as prior particle transport studies (e.g., Zhang et al. 2007; Dröge & Kartavykh 2009) and numerical test particle simulations of diffusion coefficients (e.g., Minnie et al. 2007a; Dundovic et al. 2020). Lastly, radial dependences were varied such that β ∈ [0.5, 1.5] and δ ∈ [0.5, 1.5], taking into account various possible radial dependences for these MFPs reported by studies employing turbulence quantities yielded by various turbulence transport models as inputs for several theoretical expressions (see, e.g., Engelbrecht & Burger 2013b; Wiengarten et al. 2016; Chhiber et al. 2017; Zhao et al. 2017; Adhikari et al. 2021). In order to study the various dependencies in Equations (5) and (6), four initial electron energies are chosen, motivated by the fact that for these energies spacecraft data is available for periods of good and bad magnetic connection to the Jovian source as well as at the Jovian source itself. The three higher energies furthermore correspond to the three lowest-energy channels of the ISEE 3 data by Moses (1987). As the results of the parameter studies have to be compared to spectral fits (given by the dotted lines in Figure 1), this choice allows for the most transparent analysis of the deviation of the simulation results from in situ data. The six parameters governing the MFP expressions used in this study, along with the relevant initial energies, are
7

E=[0.0025,0.006,0.0085,0.0125]GeVλ∥,0=[0.05,0.106,0.224,0.473,1.0]auλ⊥,0=[0.001,0.00473,0.02236,0.1057,0.5]auα=[−0.1,−0.01,0.01,0.04,0.165,0.67]γ=[−0.1,−0.01,0.01,0.03,0.1,0.33]β=[0.5,0.658,0.866,1.397,1.5]δ=[0.5,0.658,0.866,1.397,1.5],

which form a parameter space of consisting of 90,000 grid points, resulting in 180,000 simulations for comparison with observational points both well and badly connected to the Jovian source as shown in Figure 1.


The range of rigidity dependences for λ
⊥ was chosen following similar reasoning, with the aim of incorporating a flat rigidity dependence within a range that incorporates moderate rigidity dependences expected from various theories (e.g.,


Furthermore, this approach does not make the simplifying assumption that λ
⊥ is proportional to λ
∥ (see, e.g.,


In order to study the radial and rigidity dependences of MFPs required to fit observations, as well as the values of these quantities at 1 au so as to compare these with theoretical predictions of the same, this study still implements simplified parametric expressions for these MFPs, motivated by the fact that the transport code here employed is written to perform on graphic processing units GPUs in CUDA, which allows for the vast performance increase required of such a study, but limits the number of definable variables due to memory constraints (see


Lastly, radial dependences were varied such that β ∈ [0.5, 1.5] and δ ∈ [0.5, 1.5], taking into account various possible radial dependences for these MFPs reported by studies employing turbulence quantities yielded by various turbulence transport models as inputs for several theoretical expressions (see, e.g.


Torques caused by a misalignment between the spin axis of a black hole and the angular momentum of the accretion disc can also induce jet precession. In an overall misaligned system the inner part of the accretion disc is aligned with the black hole spin axis by the combined effect of Lense–Thirring precession and internal viscosity of the disc. This process is known as the Bardeen–Petterson effect (Bardeen & Petterson 1975). The outer disc will maintain its angular momentum direction. Through the accretion of material of the outer disc on to the black hole, the black hole spin axis will precess and align with the outer disc. The precession time-scale is of the same order as the alignment time-scale (Scheuer & Feiler 1996). Two aspects of the disc-induced precession, namely the relatively slow precession rate and the single possible precession cycle in the alignment lifetime (Scheuer & Feiler 1996; Lodato & Pringle 2006), make this process less likely to be a cause of jet precession for the given radio sources. For example, following Lodato & Pringle (2006), adopting their numerical values for accretion efficiency ε and disc viscosity parameters α1, 2 and assuming black hole spin a ≈ 1, we obtain a precession period of
(3)
\begin{eqnarray*}
\begin{split} t_\mathrm{prec} &\approx t_\mathrm{align} \approx 7\, \, \mathrm{Myr} \\
&\times \, a^{11/16} \left(\frac{\epsilon }{0.1}\right)^{7/8} \left(\frac{L}{0.1 L_\mathrm{Edd}}\right)^{-7/8} M_9^{-1/16} \\
&\times \left(\frac{\alpha _1}{0.03}\right)^{15/16} \left(\frac{\alpha _2}{0.3}\right)^{-11/16} \, .\\
\end{split}
\end{eqnarray*}
This is larger than the precession period we estimated for Cygnus A. Simulations show that if the precession time-scale becomes comparable to the source age, very asymmetric lobe morphologies result (Donohoe & Smith 2016). As discussed in Section 3.3, the sources in our sample do not show such asymmetries, but often show smooth, ring-like hotspot features that suggest a local impact time-scale short compared to the source ages and thus many precession cycles. This is not consistent with precession induced by a misaligned accretion disc. A process that produces one precession cycle only, where the period of the cycle can be much shorter than the source age (equation 3), would have only a limited probability to be detected at the time a given source is observed. However, we also find precession frequently in comparatively old sources, e.g. 3C 33.1, 3C 303, and 3C 436. These are three of the seven sources with modelled ages of log(age/yr) ≥ 7.9. This makes disc-induced precession less likely for this subpopulation.


Two aspects of the disc-induced precession, namely the relatively slow precession rate and the single possible precession cycle in the alignment lifetime

make this process less likely to be a cause of jet precession for the given radio sources.


Simulations show that if the precession time-scale becomes comparable to the source age, very asymmetric lobe morphologies result

As discussed in Section 3.3, the sources in our sample do not show such asymmetries, but often show smooth, ring-like hotspot features that suggest a local impact time-scale short compared to the source ages and thus many precession cycles. This is not consistent with precession induced by a misaligned accretion disc.


We end by studying the BH mass versus stellar velocity dispersion, σ, in Fig. 7. This is also a benchmark scaling, and it is considered to be one of the best predictors for BH masses, i.e. to have a small intrinsic scatter (0.3 dex). This is perhaps the most problematic for Horizon-AGN. If we fit a single logarithmic slope to the BH mass versus stellar velocity dispersion, we find a value of 4.02 for galaxies with σ > 60 km s−1, compared to 4.38 found by Kormendy & Ho on a culled subsample of the galaxies shown in Fig. 7. The main reason is that velocity dispersions in the simulation are underestimated at Mbulge  1011 M⊙ (σ  200 km s−1), and overestimated above, when comparing to the observed Faber–Jackson relation (Bernardi et al. 2003). The dearth of BHs with MBH  5 × 107  M⊙ in intermediate-mass galaxies highlighted in the discussion of Fig. 5 also contributes, but given the good agreement in the MBH versus Mbulge relation, it is a minor contribution, for this specific comparison. One contribution to the discrepancy is that galaxy sizes in the simulation are larger than for observed galaxies with mass ≲ 1011 M⊙. In fact, the galaxy sizes are in good agreement with observed low-mass late-type galaxies, but are larger, by a factor of ∼ 3–4, than observed low-mass early-type galaxies (Dubois et al., in preparation). Since the complete sample is a mix of late- and early-type galaxies, there appears to be an overall mismatch at σ  200 km s−1 of a factor of ${\sim } \sqrt{2}$ in the velocity dispersion (roughly corresponding to an average overestimate of the galaxy size of a factor of 2). The velocity dispersion is also sensitive to the DM halo central profile, which depends not only on DM halo mass but also on a subtle interplay with the baryons and AGN feedback. Indeed, the central DM densities in Horizon-AGN are lower than for the Horizon-noAGN simulation, which differs only in that AGN are not included in the latter. We defer a more detailed study quantifying the exact contribution of this effect as a function of galaxy mass and assembly history to another paper (Peirani et al., in preparation).


We defer a more detailed study quantifying the exact contribution of this effect as a function of galaxy mass and assembly history to another paper


In fact, the galaxy sizes are in good agreement with observed low-mass late-type galaxies, but are larger, by a factor of ∼ 3–4, than observed low-mass early-type galaxies


However, our understanding of the scaling relations in lower-mass galaxies is lacking. This includes galaxies near the break of the galaxy stellar-mass function

 (e.g., Baldry et al. 2012) like the Milky Way (MW), as well as galaxies at lower masses. Measurements of black hole (BH18

18
In this article, we use the abbreviations SMBH and BH interchangeably.
) masses are lacking in these galaxies. Despite the MW’s precisely measured central BH mass of

 (Boehle et al. 2016; Gillessen et al. 2017), we actually know very little about the demographics of BHs in galaxies of this mass. In particular, there are only 11 published

 in spiral galaxies within ∼1 dex in stellar mass of the MW, but there are strong indications that the relations between

 and galaxy properties that hold at higher mass (Kormendy & Ho 2013; McConnell et al. 2013; Saglia et al. 2016; van den Bosch et al. 2016) break down for M⋆ spiral galaxies (Greene et al. 2010, 2016; Läsker et al. 2016). For instance, Andromeda is only ≲2 times more massive than the MW, but its SMBH is two orders of magnitude higher,

 ∼1.4 × 108M⊙ (Bender et al. 2005). At even lower galaxy masses, the changes in the inferred

 are twofold: not only does the scatter increase enormously at low mass (e.g., Reines et al. 2013), but it also seems that the

 are lower at fixed stellar mass or σ of the lower-mass systems (e.g., Kormendy & Ho 2013; Scott et al. 2013; Greene et al. 2016; Saglia et al. 2016; Nguyen et al. 2017, 2018, 2019, hereafter N17, N18, N19). Despite the incomplete sample of

 at lower masses, there are already two intriguing findings from the limited data available: (1) a factor of 2 difference in normalization seen in the

–σ correlations for early-type (ETGs) and late-type (LTGs) galaxies (McConnell et al. 2013) and (2) a large scatter up to two orders of magnitude of MBH seen around the global scaling relations for low-mass systems (Greene et al. 2010; Scott et al. 2013; Graham & Scott 2015; Greene et al. 2016; Läsker et al. 2016; Chilingarian et al. 2018).


there are already two intriguing findings from the limited data available:

a large scatter up to two orders of magnitude of MBH seen around the global scaling relations for low-mass systems


The 21-cm line is the transition line of atomic hydrogen between two hyperfine states that are split from the ground state due to the spin coupling of the nucleus and electron. The 21-cm brightness temperature from a bulk of hydrogen gas depends on the matter density, the neutral fraction, the velocity gradient, and the spin temperature. During the EoR, it is reasonable to assume that X-ray heating and Ly α-pumping effects are so efficient that the H i spin temperature is much greater than the CMB temperature. In this limit, the power spectrum of 21-cm brightness temperature fluctuations can be written as (Datta et al. 2012; Mao et al. 2013)
(3)
\begin{eqnarray*}
P_{\Delta T}({\boldsymbol k},{\boldsymbol n},z) = \widetilde{\delta T}_b^2 \bar{x}_{\rm H\,{\small I}}^2\, \left[ b_{\rho _{\rm H\,{\small I}}}(z) + \mu _{\boldsymbol k}^2 \right]^2\, P_{\zeta }(k,{\boldsymbol n},z),
\end{eqnarray*}
at large scales, with
(4)
\begin{eqnarray*}
\widetilde{\delta T}_b(z) = (23.88\, {\rm mK}) (\frac{\Omega _b h^2}{0.02}) \sqrt{\frac{0.15}{\Omega _M h^2} \frac{1+z}{10}}.
\end{eqnarray*}
Note that $\bar{x}_{\rm H\,{\small I}}$ is the global neutral fraction that implicitly depends on the redshift, and μk ≡ k · n/|k| (cosine of angle between line of sight n and wave vector k of a given Fourier mode). We can relate the neutral hydrogen density fluctuations to the total matter density fluctuations with a simple bias parameter, the neutral density bias, $b_{\rho _{\rm H\,{\small I}}}(k,z) \equiv \tilde{\delta }_{\rho _{\rm H\,{\small I}}}({\boldsymbol k},z)/\tilde{\delta }_{\rho }({\boldsymbol k},z)$. At large scales, the bias approaches to a scale-independent value, $b_{\rho _{\rm H\,{\small I}}}(z)$. Here, we assume that the baryonic distribution traces the cold dark matter distribution at large scales, so $\delta _{\rho _{\rm H}} = \delta _{\rho }$. Also, we assume that no additional hemispherical power asymmetry was generated during the evolution of the Universe, so the dipolar modulation of the curvature perturbation is transferred to the 21-cm power spectrum with the same form.


The sensitivity of dwarfs to galaxy formation physics, like the gas density at which stars form (e.g. Kravtsov 2003; Saitoh et al. 2008) or the details of galactic outflows (e.g. Read et al. 2006b), makes them a natural ‘rosetta stone’ for constraining galaxy formation models. Early work simulating dwarf galaxies focused on high resolution small box simulations, stopping at high redshift (z ∼ 5–10) to avoid gravitational collapse on the scale of the box (e.g. Abel et al. 1998; Gnedin & Kravtsov 2006; Read et al. 2006b; Mashchenko, Wadsley & Couchman 2008). These simulations demonstrated that stellar winds, SN feedback, and ionizing radiation combine to prevent star formation in halo masses below ∼107–8 M⊙ (Read et al. 2006b; Bland-Hawthorn, Sutherland & Webster 2015). Furthermore, once cooling below 104 K is permitted and gas is allowed to reach high densities $n_{\rm max} {\gtrsim}10\,{\rm cm}^{-3}$ (requiring a spatial and mass resolution better than $\Delta x {\lesssim}100$ pc and mmin  103 M⊙; Pontzen & Governato 2012; Benitez-Llambay et al. 2019; Bose et al. 2019; Dutton et al. 2019), star formation becomes much more stochastic and violent (Mashchenko et al. 2008; Pontzen & Governato 2012; Dutton et al. 2019). The repeated action of gas cooling and blow-out due to feedback expels DM from the galaxy centre, transforming an initially dense DM cusp to a core (e.g. Read & Gilmore 2005; Pontzen & Governato 2012). Finally, independent of any internal sources of feedback energy, cosmic reionization can halt star formation in low-mass galaxies (e.g. Gnedin & Kravtsov 2006). Dwarfs that have not reached a mass of $M_{200} {\gtrsim}10^8$ M⊙ (see Section 2.4 for a definition of M200) by the redshift that reionization begins (z ∼ 8–10; Gnedin & Kaurov 2014; Ocvirk et al. 2018) are gradually starved of fresh cold gas, causing their star formation to shut down by a redshift of z ∼ 4 (Oñorbe et al. 2015). This is similar to the age of nearby ‘ultra-faint’ dwarf galaxies (UFDs) that have $M_* {\lesssim}10^5$ M⊙, suggesting that at least some of these are likely to be relics from reionization, inhabiting pre-infall halo masses in the range M200 ∼ 108–9 M⊙ (Gnedin & Kravtsov 2006; Bovill & Ricotti 2009, 2011; Brown et al. 2014; Weisz et al. 2014; Jethwa, Erkal & Belokurov 2018; Read & Erkal 2019).


Furthermore, once cooling below 104 K is permitted and gas is allowed to reach high densities $n_{\rm max} {\gtrsim}10\,{\rm cm}^{-3}$ (requiring a spatial and mass resolution better than $\Delta x {\lesssim}100$ pc and mmin  103 M⊙


Moreover, there could also be some contribution to the detected temperature asymmetry from high-latitude gas clouds in our Galaxy along the line of sight toward M 81. In this respect we note that M 81 is at about 40.9° north of the Galactic disk, where contamination from the Milky Way is expected to be low. However, interpretation of astronomical observations is often hampered by the lack of direct distance information. Indeed, it is often not easy to judge whether objects on the same line of sight are physically related or not. Since the discovery of the Arp’s Loop (Arp 1965) the nature of the interstellar clouds in this region has been debated; in particular whether they are related to the tidal arms around the galaxy triplet (Sun et al. 2005; de Mello et al. 2008) or to Galactic foreground cirrus (Sollima et al. 2010; Davies et al. 2010). Already Sandage et al. (1976) presented evidence showing that we are observing the M 81 triplet through widespread Galactic foreground cirrus clouds and de Vries et al. 1987 built large-scale HI, CO, and dust maps that showed Galactic cirrus emission toward the M 81 region with NH ≃ 1−2  ×  1020 cm-2. The technique used to distinguish between the emission from extragalactic or Galactic gas and dust relies on spectral measurements and on the identification of the line of sight velocities, which are expected to be different in each case. Unfortunately, in the case of the M 81 Group, this technique appears hardly applicable since the radial velocities of extragalactic and Galactic clouds share a similar LSR (local standard of rest) velocity range (Heithausen 2012). Several small-area molecular clouds (SAMS), that is, tiny molecular clouds in a region where the shielding of the interstellar radiation field is too low (so that these clouds cannot survive for a long time), have been detected by Heithausen (2002) toward the M 81 Group. More recently, data from the Spectral and Photometric Imaging Receiver (SPIRE) instrument onboard Herschel ESA space observatory and Multiband Imaging Photometer for Spitzer (MIPS) onboard Spitzer allowed the identification of several dust clouds north of the M 81 galaxy with a total hydrogen column density in the range 1.5–5 × 1020 cm-2 and dust temperatures between 13 and 17 K (Heithausen 2012). However, since there is no obvious difference among the individual clouds, there was no way to distinguish between Galactic or extragalactic origin although it is likely that some of the IR emission both toward M 81 and NGC 3077 is of Galactic origin. Temperature asymmetry studies in Planck data may be indicative of the bulk dynamics in the observed region provided that other Local (Galactic) contamination in the data is identified and subtracted. This is not always possible, as in the case of the M 81 Group, and therefore it would be important to identify and study other examples of dust clouds where their origin, either Galactic or extragalactic, is not clear. One such example might be provided by the interacting system toward NGC 4435/4438 (Cortese et al. 2010) where the SAMS found appear more consistent with Galactic cirrus clouds than with extragalactic molecular complexes. Incidentally, the region A1 within R0.50 has been studied by Barker et al. (2009), who found evidence for the presence of an extended structural component beyond the M 81 optical disk, with a much flatter surface brightness profile, which might contain ≃10–15% of the M 81 total V-band luminosity. However, the lack of both a similar analysis in the other quadrants (and at larger distances from the M 81 center) and the study of the gas and dust component associated to this evolved stellar population, hamper our understanding of whether this component may explain the observed temperature asymmetry toward the M 81 halo.


Using a single-fluid approach Chian & Oliveira (1994, 1996), and Oliveira & Chian (1996) studied the effects of parametric instabilities on standing waves with applications to the magnetosphere. These authors developed a theory of MHD parametric instabilities driven by a left- or right-hand circularly polarised standing Alfvén wave in a low plasma-β under very specific initial conditions. Israelevich & Ofman (2004) and Israelevich & Ofman (2011) using both the MHD approach and hybrid simulations investigated numerically the generation of an electric field parallel to the magnetic field, due to non-linear induced ion-acoustic waves produced by the presence of a standing Alfvénic pump. In a different context, Mottez (2015) also explored the generation of a parallel electric field using PIC (particle in cell) simulations when two counter-propagating Alfvén waves are excited. However, the mechanism proposed by this author is not related to the ponderomotive force that it is usually operating under such conditions. A ponderomotive force (see the review of Lundin & Guglielmi 2006) generates density enhancements periodically in time and space which are normally called cavities and depend on gradients in density or electric fields. The periodicity depends on the value of gas pressure of the system and the amplitude of these enhancements is related quadratically with the amplitude of the initial transverse excitation (see also Rankin et al. 1994; Tikhonchuk et al. 1995). Interestingly, ponderomotive forces can lead to separation of species, although this topic is not addressed in the present work since the quasi-neutrality condition is imposed for the plasma composed of kinetic protons and the treatment of electrons is that of a fluid. Recently, Martínez-Gómez et al. (2018) used the multi-fluid approach to model high-frequency waves in partially ionised plasmas similar to those in quiescent solar prominences. These authors show that non-linear Alfvén waves generate density and pressure perturbations and that the friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat that raises the temperature of the plasma.

Background Background Background Background


studied the effects of parametric instabilities on standing waves with applications to the magnetosphere. These authors developed a theory of MHD parametric instabilities driven by a left- or right-hand circularly polarised standing Alfvén wave in a low plasma-β under very specific initial conditions.

Using a single-fluid approach Chian & Oliveira (1994, 1996), and


and Israelevich & Ofman (2011) using both the MHD approach and hybrid simulations investigated numerically the generation of an electric field parallel to the magnetic field, due to non-linear induced ion-acoustic waves produced by the presence of a standing Alfvénic pump.


used the multi-fluid approach to model high-frequency waves in partially ionised plasmas similar to those in quiescent solar prominences. These authors show that non-linear Alfvén waves generate density and pressure perturbations and that the friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat that raises the temperature of the plasma.


The X-ray transient MAXI J1820+070 was first detected on 2018 March 11 (Kawamuro et al. 2018) by the Monitor of All-sky X-ray Image (MAXI, Matsuoka et al. 2009) and was associated with the optical transient ASASSN-18ey (Denisenko 2018; Tucker et al. 2018). In the X-rays, the source flux exceeded 3 Crabs (Bozzo et al. 2018; Mereminskiy et al. 2018), and in the optical, the source reached a magnitude of mV = 12 − 13 (Littlefield 2018; Russell et al. 2018). The parallax of the source π = 0.3 ± 0.1 mas was presented in the Gaia DR2 catalogue (Gaia Collaboration 2018). This corresponds to a distance of

3
.

9

−
1.3

+
3.3

$ 3.9^{+3.3}_{-1.3} $

 kpc (Gandhi et al. 2018a). This unusually bright event allows a detailed investigation of multi-wavelength spectral and timing properties. The course of the outburst was monitored in radio (Trushkin et al. 2018; Polisensky et al. 2018), sub-millimeter (Tetarenko et al. 2018a), optical (Baglio et al. 2018), X-rays (Uttley et al. 2018), and γ-rays (Bozzo et al. 2018; Kuulkers et al. 2018). Because the object was sufficiently bright even for small telescopes, the target was almost continuously monitored, and a rich variety of phenomena was observed. Fast variability and powerful flares in the optical and infrared (Littlefield 2018; Sako et al. 2018; Gandhi et al. 2018b; Casella et al. 2018), optical, and X-ray quasi-periodic oscillations (Mereminskiy et al. 2018; Yu et al. 2018a,b; Buisson et al. 2018; Zampieri et al. 2018) as well as low linear polarisation (Berdyugin et al. 2018) were detected in the source. A 17 h photometric period was recently reported (Patterson et al. 2018) and was tentatively associated with the orbital or superhump period (previously, the source showed a 3.4 h periodicity, Richmond 2018). The X-ray spectral and timing properties as well as the optical-to-X-ray flux ratio suggests that the source is a black hole binary (Baglio et al. 2018; Mereminskiy et al. 2018).


We study the impact of secondary outgassing associated with partial melting and volcanism following accretion and a possible magma ocean phase. Raymond et al. (2007) showed that the accretion of planets around M-dwarf stars is faster than around more massive stars, which has also been calculated by Lissauer (2007) and Ida & Lin (2005). We therefore assumed that the accretion of a planet around an M dwarf is very fast (1 Myr), while for the other stellar cases we assumed an accretion time of 20 Myr. This corresponds to the lower limit in accretion times of Raymond et al. (2007) for planets around stars with masses greater than 0.8 MSun. After accretion, the planet may reside in a magma ocean stage, which we assume to last 1 Myr, following the results by Spohn & Schubert (1991) and Lebrun et al. (2013), among others. For high stellar irradiation, the planet may be trapped in a long-term magma ocean stage, which may last from several millions of years to billions of years (see e.g. Hamano et al. 2013, Nikolaou et al. 2019). For planets in a long-term magma ocean stage, Hamano et al. (2013) suggested very low water concentrations in the mantle at the end of the magma ocean stage because the planet can only exit this stage via severe atmospheric water loss because thick, water-rich atmospheres show a thermal blanketing effect suppressing the cooling of the planet via the Planck feedback. Their estimates of interior water reservoirs for such cases correspond to our lower limit of the initial mantle water concentration of 34 ppm. We nevertheless assumed in our calculations that the magma ocean has a short duration. This allows the high-luminosity pre-main sequence phase of the M dwarfs to have a larger impact on the HZ evolution. Any CO2 and H2O outgassed during the magma ocean phase is neglected in our calculations, i.e. we started our outgassing calculations with a 1 bar N2 atmosphere. Neglecting any atmospheric H2O and CO2 from the magma ocean phase results in a very narrow HZ at the beginning of our calculations, which is then only extended by secondary outgassing. This facilitates the evaluation of the potential of secondary outgassing from a stagnant-lid planet to form a HZ.


showed that the accretion of planets around M-dwarf stars is faster than around more massive stars,

We therefore assumed that the accretion of a planet around an M dwarf is very fast (1 Myr), while for the other stellar cases we assumed an accretion time of 20 Myr.


This corresponds to the lower limit in accretion times of

for planets around stars with masses greater than 0.8 MSun.


For planets in a long-term magma ocean stage,

suggested very low water concentrations in the mantle at the end of the magma ocean stage because the planet can only exit this stage via severe atmospheric water loss because thick, water-rich atmospheres show a thermal blanketing effect suppressing the cooling of the planet via the Planck feedback. Their estimates of interior water reservoirs for such cases correspond to our lower limit of the initial mantle water concentration of 34 ppm.


The theory of LK migration with STs involves two important time-scales. The first is the time-scale for quadrupole LK eccentricity oscillations, tLK, given by
(40)
\begin{eqnarray*}
t_{\rm LK} &=& \left(\frac{10^6}{2\pi }\,\text{yr}\right)\left(\frac{M_\mathrm{ b}}{\rm{ M}_\odot }\right)^{-1}\left(\frac{M_*}{\mathrm{ M}_\odot }\right)^{1/2}\left(\frac{a_0}{1\, \text{au}}\right)^{-3/2}\nonumber \\
&&\times \, \left(\frac{a_{\rm b,eff}}{100\, \text{au}}\right)^{3} ,
\end{eqnarray*}
where a0 is the initial semimajor axis of the planet’s orbit, Mb is the mass of the (stellar) companion, and
(41)
\begin{eqnarray*}
a_{\rm b,eff} \equiv a_{\rm b} (1-e_{\rm b}^2)^{1/2} ,
\end{eqnarray*}
with ab and eb the semimajor axis and eccentricity of the companion’s orbit, respectively. The time that the planet spends near the maximum eccentricity, emax, is of the order of (e.g. Anderson et al. 2016)
(42)
\begin{eqnarray*}
\Delta t(e_{\rm max}) \sim (1-e_{\rm max}^2)^{1/2} t_{\rm LK}.
\end{eqnarray*}
The second important time-scale is that of orbital decay due to STs given by (Alexander 1973; Hut 1981).
(43)
\begin{eqnarray*}
t^{-1}_{\rm ST} &=& \left|\frac{\skew4\dot{a}}{a}\right|_{\rm ST} = (6 k_{2\mathrm{ p}} \Delta t_{\mathrm{ L}}) \frac{M_*}{M_\mathrm{ p}} \left(\frac{R_\mathrm{ p}}{a}\right)^{5}\frac{n^{2}}{(1-e^2)^{15/2}} \nonumber \\
&&\times \, \left[f_1(e)\ - \frac{f_2^2(e)}{f_5(e)}\right],
\end{eqnarray*}
where k2p is the tidal Love number of the planet, ΔtL is the lag time, f1(e) = 1 + 31e2/2 + 255e4/8 + 185e6/16 + 25e8/64, and f2(e) and f5(e) are given in equations (30) and (31), respectively. (We have assumed that the planet has a pseudo-synchronous spin rate.) Tidal dissipation is most efficient near the maximum eccentricity. Since the planet only spends a fraction (${\sim } \sqrt{1-e_{\rm max}^2}$) of the time near emax, the effective orbital decay rate during LK migration is
(44)
\begin{eqnarray*}
t^{-1}_{\rm ST,LK} &=& \left(\left|\frac{\skew4\dot{a}}{a}\right|_{\rm ST} \sqrt{1-e^2}\right)_{e_{\rm max}} \nonumber \\
&\approx& \frac{1.27}{{\rm Gyr}} \left(\frac{k_{\rm 2p}}{0.37}\right) \left(\frac{\Delta t_{\rm L}}{1 {\rm s}}\right)\left(\frac{M_\mathrm{ p}}{\mathrm{ M}_{\odot }}\right)^2 \left(\frac{M_\mathrm{ p}}{M_\mathrm{ J}}\right)^{-1} \nonumber \\
&&\times \; \left(\frac{R_\mathrm{ p}}{R_\mathrm{ J}}\right)^5\left(\frac{a_0}{1\, {\rm au}}\right)^{-1} \left(\frac{r_{\rm p, min}}{0.025\, {\rm au}}\right)^{-7} \,,
\end{eqnarray*}
where rp, min = a0(1 − emax) is the minimum pericentre distance (in the second of the above equalities, we have used emax = 0.96). Successful migration within a few Gyr requires rp, min ≲ 0.025 au, corresponding to a final (circularized) planet semimajor axis aF ≲ 0.05 au. A planet would need to be more dissipative than Jupiter (larger ΔtL)5 to become an HJ with a larger aF.