Current sheet drift is implemented following the approach proposed by Burger (2012) to calculate the drift velocity Vd in Equation (7). The heliospheric current sheet angle is modeled as by Kóta & Jokipii (1983), but now with a time-dependent tilt angle from Equation (8) such that
12

where, after Burger et al. (2008), we employ
13

with ϕ0 = 0°, thereby allowing for the inclusion in the model of the effects of a fully time-dependent heliospheric current sheet. Diffusion coefficients are modeled as by Moloto et al. (2018). A composite slab/2D model for transverse magnetostatic turbulence is assumed (see, e.g., Matthaeus et al. 1995), as well as slab/2D turbulence power spectra with wavenumber-independent energy-containing ranges, and Kolmogorov inertial ranges. This latter assumption does not perfectly reflect spacecraft observations of the same (see, e.g., Bieber et al. 1993; Matthaeus et al. 2007; Bruno & Carbone 2013), but leads to relatively simple, tractable expressions for the parallel and perpendicular MFPs. For more detail on diffusion coefficients derived assuming more realistic forms for the turbulence power spectra, see Shalchi et al. (2010), Engelbrecht & Burger (2015b), and Strauss et al. (2016). In brief, then, the parallel MFP expression used here is that constructed by Burger et al. (2008) from the quasilinear theory results presented by Teufel & Schlickeiser (2003), and given by
14

where s = 5/3, R = RLkm, and km = 1/λsl the wavenumber at which the slab spectrum inertial range commences, and RL is the maximal proton Larmor radius. To model the perpendicular MFP, we use the Nonlinear Guiding Center result of Shalchi et al. (2004), as modified by Burger et al. (2008) to take into account a general ratio of slab to 2D energies (see, e.g., Bieber et al. 1994, 1996). This expression is similar to that derived by Zank et al. (2004), and is given by
15

where ν = 5/6 denotes half the Kolmogorov inertial range spectral index, and we assume that α2 = 1/3 (Matthaeus et al. 2003). Drift coefficients, reduced in the presence of turbulence, are modeled following the approach of Engelbrecht et al. (2017), so that the lengthscale corresponding to the drift coefficient is given by
16

with

 being the total magnetic variance. This expression is chosen as it provides results in reasonable agreement with numerical test particle simulations done by Minnie et al. (2007) and Tautz & Shalchi (2012) for the range of turbulence conditions expected in the supersonic solar wind, and due to the fact that its use in a CR modulation code has been shown by Moloto et al. (2018) to lead to computed CR intensities in reasonable agreement with spacecraft observations.


Rocky planets are the only harbour for life form in the Solar system, so unravelling their origin and history is fundamental for understanding the habitability of planets other than Earth (Lineweaver & Chopra 2012; Cockell et al. 2016). For example, mantle–crust differentiation on Earth has set boundary conditions through redox conditions and early degassing processes that liquid water can occur on the surface of Earth. Geochemical studies, mainly elemental and isotopic compositions, on the specimens from these planets provide significant information about differentiation processes and their timing. Sample-return missions represent one way to obtain these specimens from the differentiated planets (e.g. Anand et al. 2020), but at great time and expense. Non-chondrite meteorites (including achondrites) also originate from differentiated asteroids and planets, e.g. from Moon, Mars, and Vesta, and the angrite and ureilite parent bodies (Binzel & Xu 1993; Weiss et al. 2008; Agee et al. 2013; Marchi et al. 2013; Bischoff et al. 2014). Some non-chondritic meteorites have a unique mineralogy and bulk composition, indicative of core, mantle, and crustal domains of their parent bodies, and thus, these samples record large-scale early planetary differentiation events. For instance, ureilites (Mg-rich, dominated by olivine and pyroxene) and iron meteorites (Fe–Ni metal) are from the mantle and core of asteroids, respectively, and record planetary mantle differentiation and core formation (Goodrich, Scott & Fioretti 2004; Goldstein, Scott & Chabot 2009). In contrast, shergottite and howardite–eucrite–diogenite meteorites, which are inferred to have derived from Mars, 4 Vesta, and related bodies, reflect a variety of crustal compositions and processes (Mezger, Debaille & Kleine 2013; Mittlefehldt 2015). In addition to the well-known achondrite groups with numerous members, ungrouped achondrites, e.g. Northwest Africa (NWA) 011 (Yamaguchi et al. 2002), Graves Nunatak (GRA) 06128/06129 (Day et al. 2009), NWA 11119 (Srinivasan et al. 2018), and NWA 7325 (Koefoed et al. 2016) expand the compositional range of achondrites towards chemically more evolved compositions (e.g. higher SiO2 contents), and thus, showcase the diversity of planetary and asteroidal crusts in the Solar system. Some achondrites, e.g. NWA 11119 and NWA 7325, yield evidence for their accretion and differentiation within the first ∼5 Myr after the formation of Ca–Al-rich inclusions (CAIs); (Koefoed et al. 2016; Srinivasan et al. 2018; Zhu et al. 2019b; Barrat et al. 2021). Hence, dating more achondrites is beneficial to map the early history of Solar system.


As shown in Fig. 3, the differences in metallicity between different SN subclasses are not significant. This is in contradiction with what is expected from single-star evolution theory, where metallicity-driven winds are crucial: type Ic SNe, which are the most highly stripped, would show the highest metallicity, followed by type Ib, and finally the H-rich type II SNe. The observations, on the other hand, reveals that this is not the case. Some SNe Ic are even located in the low-metallicity part of the distribution in the current sample. This result strengthens the notion that metallicity may not play an important role in deciding theresulting SN type, in agreement with other works based on SN environments (Anderson et al. 2010, 2015; Leloudas et al. 2011; Galbany et al. 2016a). The environments of broad-lined SNe IcBL are found to be relatively metal poor compared to the normal CCSNe, in agreement with previous studies (Modjaz et al. 2011; Galbany et al. 2016a). However, we note that there are only two such SNe in the current sample. The explosion site of SN 1998bw (the first SN to be associated with a GRB: 980425; Galama et al. 1998; Krühler et al. 2017) in this study shows a lower metallicity of 12 + log(O/H) = 8.30 dex compared to the GRB-less SN 2009bb (Pignata et al. 2011), 12 + log(O/H) = 8.49 dex. Levesque et al. (2010a), using slit spectroscopy of the explosion site, concluded that the high metallicity of SN 2009bb site is consistent with typical GRB-less SNe IcBL and not with GRB hosts. Their metallicity value recalculated on the Marino et al. (2013) N2 scale is 12 + log(O/H) = 8.52 dex. These two different cases illustrate the importance of metallicity in deciding whether an SN IcBL progenitor would also produce GRB or not (Modjaz et al. 2008; Levesque et al. 2010b). Progenitors with higher metallicity are not able to spin fast enough and thus produce high angular momentum essential for GRB jet production, eventually producing a GRB-less SN IcBL (Woosley & Bloom 2006).


The Lindblad–Oort idea of a rotation of the Galaxy around the Galactic Centre (GC) proposes that for any type of Galactic object there is at each point in the plane a mean circular, differential motion (Oort 1927a,b). In the conventional lowest order approach to the determination of the rotation parameters of the system, a strictly circular model is adopted (Mihalas & Binney 1998). Small non-axisymmetric spiral-like perturbations of the basic axisymmetric gravitational potential induce non-circular variations of stellar velocities proportional to $\widetilde{v}_r \cos \phi$ and $\widetilde{v}_\varphi \sin \phi$, and we are looking for these systematic motions in our study. Here, $\widetilde{v}_r$ and $\widetilde{v}_\varphi$ are the amplitudes of the radial and tangential wave motions that depend weakly on the Galactocentric distance r, and ϕ is the phase of the wave (Lin et al. 1969; Yuan 1969; Rohlfs 1977; Griv et al. 2020, annexure B therein). The method of analysis used for this purpose follows the development of Crézé & Mennessier (1973), Byl & Ovenden (1978), Mishurov, Pavlovskaya & Suchkov (1979), and Grivnev (1981). Specifically, in addition to the ordinary circular rotation of the system that is axisymmetric in the mean, Galactic objects have small streaming wave motions. The radial and tangential components of the velocity of a star in the plane are represented as
(1)$$\begin{eqnarray*}
V_r = \widetilde{v}_r \cos \phi ,
\end{eqnarray*}$$(2)$$\begin{eqnarray*}
V_\varphi = r \Omega + \widetilde{v}_\varphi \sin \phi ,
\end{eqnarray*}$$where Ω(r) is the angular velocity of the mean motion at the star’s distance r from the GC for the type of object considered, and the amplitudes $\widetilde{v}_r$, $\widetilde{v}_\varphi$ and the phase ϕ are to be found. Distinct populations of Galactic objects will have different average velocities Vφ at r, so the value of Ω should vary from population to population. An observed value of heliocentric line-of-sight velocity of a star $v$los corrected for solar motion towards the apex may be modeled in the following form:
(3)$$\begin{eqnarray*}
v_{\mathrm{los}} &=& \left\lbrace r_0 \left[ \Omega - \Omega _0 \right] \sin \ell - \widetilde{v}_r \cos \phi \cos (\ell +\varphi) \right. \nonumber \\
&&\left. \quad + \widetilde{v}_\varphi \sin \phi \sin (\ell +\varphi) + u_0 \cos \ell - v_0 \sin \ell \right\rbrace \cos b \nonumber \\
&&\quad - w_0 \sin b ,
\end{eqnarray*}$$where ℓ and b are the Galactic coordinates, the angle φ is measured clockwise in the direction of overall rotation from the radius passing through the location of the Sun, Ω0(r0) is the angular velocity of the mean motion at the Sun’s distance r0, ϕ = ϕ0 − m[φ − (1/tan p)ln (r/r0)], ϕ0 is the phase of the wave at the Sun’s location of the different Fourier m-modes, and the constants u0, $v$0, $w$0 are the components of solar peculiar motion relative to the mean linear speed of rotation at the Sun’s distance r0Ω0 (Mihalas & Binney 1998). To reiterate, the terms ∝(Ω − Ω0) and u0, $v$0, $w$0 describe the mean rotation of the system under study and the peculiar motion of the Sun. The deviation of the motion of objects from the circular motion due to a wave perturbation is characterized by terms ${\propto} \widetilde{v}_r \cos \phi$ and $\widetilde{v}_\varphi \sin \phi$.


One of the most astonishing characteristics of Liller 1 is the extremely large value of the collision rate parameter. Verbunt & Hut (1987) showed that Liller 1 has the second-highest value of stellar encounter rate (after Terzan 5; see also Lanzoni et al. 2010) among all star clusters in the Galaxy, thus suggesting that it represents an ideal environment where exotic objects, generated by collisions, can form. In fact, it is commonly believed that dynamical interactions in GCs facilitate the formation of close binary systems and exotic objects such as cataclysmic variables (CVs), low-mass X-ray binaries (LMXBs), millisecond pulsars (MSPs), and blue straggler stars (BSSs) (e.g., Bailyn 1992; Paresce et al. 1992; Ferraro et al. 2001, 2009a, 2012; Ransom et al. 2005; Pooley & Hut 2006). Moreover, Hui et al. (2010) found that clusters with large collisional parameters and high metallicity (see also Bellazzini et al. 1995) usually host more MSPs. Indeed, Terzan 5 hosts the largest population of MSPs among all Galactic GCs (Ransom et al. 2005).
6

6

Note that Terzan 5 is suspected to not be a genuine GC, because it harbors at least three stellar populations with different iron abundances (Ferraro et al. 2009a; Origlia et al. 2011, 2013; Massari et al. 2014).
 A strong γ-ray emission has been recently detected in the direction of Liller 1 by the Large Area Telescope (LAT) on board Fermi (Tam et al. 2011). This is the most intense emission detected so far from a Galactic GC, again suggesting the presence of a large number of MSPs. However, no direct radio detection of these objects has been obtained so far in this system (Ransom et al. 2005). The only exotic object identified in the cluster is the rapid burster MXB 1730-335, an LMXB observed to emit radio waves and type I and type II X-ray bursts (Hoffman et al. 1978). It seems to be located in the central region of Liller 1, but no optical/IR counterpart of this object has been found so far (Homer et al. 2001).


Half a century ago, a series of theorems laid the ground for the Kerr hypothesis (Israel 1967; Carter 1971; Robinson 1975); according to these no-hair theorems, the only stationary, axisymmetric, asymptotically flat, regular outside of the horizon solution to four-dimensional GR when the matter fields feature the same isometries as the spacetime is the Kerr BH. Notwithstanding their significance, there are many ways with which to circumvent them and discover different solutions. Still, in four dimensions, hairy BHs have been described in different theories of gravity, such as Einstein–Yang–Mills (Bizon 1990; Künzle & Masood-ul-Alam 1990; Volkov & Galtsov 1990; Breitenlohner et al. 1992; Kleihaus & Kunz 1998, 2001; Kleihaus et al. 2004), scalar-tensor (Bocharova et al. 1970; Bekenstein 1974; Kleihaus et al. 2015; Collodel et al. 2020a), and Gauss–Bonnet theories (Kanti et al. 1996; Kleihaus et al. 2011, 2016; Antoniou et al. 2018; Doneva & Yazadjiev 2018; Silva et al. 2018; Cunha et al. 2019; Collodel et al. 2020b; Herdeiro et al. 2021; Berti et al. 2021). Remarkably, by dropping the assumption that the matter fields must be stationary and axisymmetric, Herdeiro and Radu found solutions in the context of GR where BHs have hair (Herdeiro & Radu 2014b, 2015), by minimally coupling to gravity a complex scalar field that depends on time and on the axial coordinate while its energy-momentum tensor still possesses the respective isometries; see Herdeiro et al. (2015, 2016a, 2016b), Brihaye et al. (2016), and Delgado et al. (2016) for generalizations. These are known as scalarized Kerr black holes (KBHsSH) and they are the object of study of this paper. In their domain of existence, they connect Kerr BHs (that is, with no hair) with pure solitonic solutions, also known as boson stars (BS), which are regular everywhere and feature no horizons. In this sense, one can think of the KBHsSH indeed as a combined system of a BS with a horizon at its center, and therefore it shares traits of both objects.


The high interaction rates in globular clusters, especially at their centres, lead to the efficient formation of exotic binaries like accreting compact objects – cataclysmic variables (white dwarfs) and X-ray binaries (neutron stars and black holes; Clark, Markert & Li 1975). Soon after the first X-ray missions, it was recognized that X-ray transients in globular clusters were disproportionately associated with neutron stars, with no confirmed black holes (Verbunt et al. 1995), a fact that remains true to this day (Bahramian et al. 2014). In contrast, about a third of the X-ray transients in the rest of the Galaxy contain black holes (Miller-Jones et al. 2015; Tetarenko et al. 2016). Originally it was proposed that due to mutual gravitational interactions that all black holes would have been ejected from globular clusters (Kulkarni, Hut & McMillan 1993; Sigurdsson & Hernquist 1993). However, there are several recent indications that a number of black holes may still exist within clusters, based on X-ray observations of extragalactic clusters (Maccarone et al. 2007; Brassington et al. 2010; Irwin et al. 2010; Shih et al. 2010; Maccarone et al. 2011), radio/X-ray observations of Galactic clusters (Maccarone & Knigge 2007; Strader et al. 2012; Chomiuk et al. 2013; Miller-Jones et al. 2015), as well as theoretical simulations (Sippel & Hurley 2013; Morscher et al. 2015; Peuten et al. 2016). The reason why these black holes are so elusive could perhaps be due to the nature of the X-ray binaries they form, rather than their number. If the majority of accreting black holes in globular clusters have very low-mass, possibly degenerate, donors, they will have short, faint outbursts, making them undetectable by current and past all-sky X-ray surveys (Knevitt et al. 2014). Indeed, the dynamics in globular clusters are thought to effectively produce ultracompact X-ray binaries (Verbunt 1987; Deutsch et al. 1996; Deutsch, Margon & Anderson 2000; Ivanova et al. 2005, 2010), in which a black hole or neutron star accretes matter from an H-poor donor in a system with a very short orbital period (≲1  h; Nelson, Rappaport & Joss 1986).


Major nearby galaxy cold gas mapping surveys (Regan et al. 2001; Wilson et al. 2009; Rahman et al. 2011; Leroy et al. 2009; Donovan Meyer et al. 2013; Bolatto et al. 2017; Sorai et al. 2019; Sun et al. 2018) have focused on observations of the molecular gas (through CO lines). Despite a few notable exceptions (e.g. Alatalo et al. 2013; Saintonge et al. 2017), these surveys observed mainly spiral or infrared-bright galaxies (i.e. galaxies with significant star formation) and have furthered our understanding of how star formation happens, rather than how it stops. This boils down to quantifying the relation between molecular gas and star formation rate (SFR), which appears nearly linear in nearby discs (Kennicutt 1998; Bigiel et al. 2008; Leroy et al. 2013; Lin et al. 2019). This relationship is often parametrised via the ratio between the SFR and the molecular gas mass (Mmol), which is called the molecular star formation efficiency (SFE = SFR/Mmol = 1∕τdep), where the inverse of the SFE is the depletion time, τdep. The depletion time indicates how much time is necessary to convert all the available molecular gas into stars at the current star formation rate. On kpc scales and in the discs of nearby star-forming galaxies, τdep is approximately constant around 1–2 Gyr (Bigiel et al. 2011; Rahman et al. 2012; Leroy et al. 2013; Utomo et al. 2017), and it appears to weakly correlate with many galactic properties such as stellar mass surface density or environmental hydrostatic pressure (Leroy et al. 2008; Rahman et al. 2012). Nevertheless, small but important deviations for a constant SFE have been noticed, which can be the first hints of star formation quenching. In some galaxies, the depletion time in the centres appear shorter (Leroy et al. 2013; Utomo et al. 2017) or longer (Utomo et al. 2017) with respectto their discs. These differences may correlate with the presence of a bar or with galaxy mergers (Utomo et al. 2017; see also Muraoka et al. 2019) and do not seem to be related to unaccounted variation in the CO-to-H2 conversion factor (Leroy et al. 2013; Utomo et al. 2017). Spiral arm streaming motions have also been observed to lengthen depletion times (Meidt et al. 2013; Leroy et al. 2015).


Silicon monoxide (SiO) is predicted to be the most abundant Si-bearing molecule in the entire 1–10 R* range in the atmospheres of M stars. In S-type atmospheres, the calculated abundance of SiO decreases by two orders of magnitude in the 1–5 R* but retains a very high abundance beyond, and the same occurs in C-rich atmospheres, although in this case, the abundance drop in the 1–5 R* is even more pronounced (see Fig. 2; see also Agúndez & Cernicharo 2006). Observations indicate that the abundance of SiO does not differ significantly between envelopes around M-, S-, and C-type stars, although in all them the SiO abundance decreases with increasing mass-loss rate (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). This decline in the SiO abundance with increasing envelope density is not a consequence of chemical equilibrium (Massalkhi et al. 2019), but has been interpreted as evidence that SiO disappears from the gas phase at high densities to be incorporated into dust grains (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). It therefore appears that the gradual abundance decline calculated for SiO in the 1–5 R* region from stellar type in the sense M → S → C does not have a direct consequence in the SiO abundance that is injected into the expanding wind. However, this behavior predicted by chemical equilibrium probably explains why SiO masers are observed in M-type stars but not toward carbon stars (e.g., Pardo et al. 2004). Except for these details, chemical equilibrium and observations agree in the fact that SiO is one of the most abundant carriers of silicon in the atmospheres of M-, S-, and C-type stars. Calculations and observations also agree for SiS in that it is an abundant molecule regardless of the C/O. However, observations indicate a differentiation between C- and O-rich envelopes, with SiS being on average one order of magnitude more abundant in carbon-rich sources (Schöier et al. 2007; Danilovich et al. 2018; Massalkhi et al. 2019, 2020). Moreover, in some oxygen-rich envelopes, the fractional abundance of SiS relative to H2 is as low as ~10−8, which is well below the predictions of chemical equilibrium (Danilovich et al. 2019; Massalkhi et al. 2020).


At this juncture in cosmology, independent and complementary probes with considerable precision are very helpful for providing clues about the origin of the abovementioned crises. Strong-lensing systems are one of the most promising probes for investigating these issues. The time delay between images of strongly lensed time-variable sources was proposed to directly determine H0 (Refsdal 1964; Treu 2010). Recently, with elaborate time-delay measurements and lens modeling for five selected strongly lensed quasar systems, the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW) team yielded an estimation of H0 that is also 2.3σ higher than the Planck-calibrated value (Birrer et al. 2019). It should be mentioned that this result is completely independent of all rungs of the distance ladder. Moreover, on the basis of the distance sum rule (DSR), distance ratios derived from angular separation measurements of images in strong-lensing systems were proposed to test the FLRW metric and model-independently determine ΩK (Räsänen et al. 2015). This method has been intensively implemented with updated observations (Xia et al. 2017; Li et al. 2018a; Liu et al. 2020; Zhou & Li 2020). In order to reduce the systematics resulting from oversimplified lensing modeling in the distance ratio method, Liao et al. (2017b) reformulated the DSR in terms of the time-delay distance, which is a combination of three angular diameter distances in a strong-lensing system. With the latest strongly lensed quasar observations and type Ia supernovae (SNe Ia) luminosity distance measurements, H0 and ΩK were simultaneously and model-independently determined to a precision of ∼6% and ∼0.3 (Collett et al. 2019), respectively. Meanwhile, strongly lensed gravitational waves (GWs) and their electromagnetic (EM) counterparts from the binary of compact object coalescence are proposed as a powerful tool for precision cosmology since the time delay between images in these systems can be precisely measured (Liao et al. 2017a; Li et al. 2019). However, both traditional strongly lensed quasar and proposed strongly lensed GW systems face shortages. For lensed quasars, the precision of time-delay measurements is limited to ∼3% and lens modeling is difficult to improve because of the bright active-galactic nuclei (AGNs) contamination in the source host galaxy. For the expected lensed GWs, the main challenges may be the event rate and localization ability for images of GW signals, which is crucial for lens modeling.


Swift J1734.5-3027 was detected by INTEGRAL for the first time during the observations performed toward the Galactic bulge in the satellite revolution 1329, i.e., about half a day before the BAT discovery (from 56 535.85950 MJD to 56 536.01338 MJD; see Table 1). It remained within the field of view (FoV) of the instruments on-board INTEGRAL until satellite revolution 1348 (from 56 592.54664 MJD to 56 593.31612 MJD), when the window of seasonal visibility toward the Galactic center closed. We analyzed all INTEGRAL data by using version 10.1 of the Off-line Scientific Analysis software (OSA) distributed by the ISDC (Courvoisier et al. 2003). INTEGRAL observations are divided into science windows (SCWs), i.e., pointings with typical durations of ~2−3 ks. To limit the ISGRI calibration uncertainties (Lebrun et al. 2003), we made use of all public SCWs from the Galactic bulge, Scutum/Sagittarium, and Perseus/Norma monitoring programs during which the source was located to within 12 deg from the center of the IBIS FoV (Ubertini et al. 2003). We also included in our dataset the observations of the Galactic center and 4U 1728-34 for which our group was awarded data rights in revolutions 1329−1348. A summary of the total exposure-time available in each revolution is provided in Table 1 for IBIS/ISGRI and the two JEM-X telescopes (Lund et al. 2003). We extracted the mosaics and spectra in each revolution for the two JEM-X and ISGRI. All JEM-X spectra were extracted by using the standard 16-channel response matrix, while a customized 37 energy bin response matrix was created for ISGRI in order to optimize the signal-to-noise ratio (S/N) in the energy range (20−50 keV). Only in revolution 1329, was the ISGRI spectrum extracted with a reduced energy binning (8 channels), as the source was relatively faint (see Sect. 3). JEM-X lightcurves with a time resolution of 2 s were extracted from all observations to search for Type-I X-ray bursts, but none was found. We did not perform other timing analyses of the INTEGRAL data as the source was too faint to extract meaningful power spectra. In Fig. 1 we show the ISGRI mosaic realized by using all available data.


To derive the equipartition magnetic field of J1146+4037, we predict the rest-frame 8.4 GHz (redshifted to 1.4 GHz at z = 5.0059) flux density from our spectral model. However, there is no source size measurement at 1.4 GHz. We make use of the full width at half maximum (FWHM) source size of 0.74 ± 0.01 mas derived by the Gaussian fit from 5 GHz VLBI mas angular resolution observations (Frey et al. 2010). We note that in our calculations, we assume a source size that is 1.8 times larger than the FWHM, following the approach of Readhead (1994) and Orienti & Dallacasa (2008). The derived equipartition magnetic field is

34

−
7

+
8

$ 34^{+8}_{-7} $

 mG. This is within the range of the equipartition magnetic fields of 17 HFP radio sources (7–60 mG; quasars and galaxies at 0.22   z   2.91; Orienti & Dallacasa 2012) and 5 HFPs at 0.084   z   1.887 (18–160 mG; Orienti & Dallacasa 2008). The magnetic field calculated from the turnover information listed in Table 4 is

1
.

8

−
2.7

+
2.3

$ 1.8^{+2.3}_{-2.7} $

 G assuming an SSA origin with Eq. (3), however the uncertainty is very large. The large uncertainty is caused by the fact that we only have four data points to constrain the turnover information and we do not have source size measurements at the turnover frequency, but rather we assume the source size measured at another frequency. More data taken in other wavelength bands are needed to meaningfully constrain the turnover peak, and mas resolution observations at the peak frequency are needed to give reliable magnetic field strength measurements. This may indicate that the turnover is not caused by SSA, by comparing the large magnetic field strength measured from the spectral turnover (

1
.

8

−
2.7

+
2.3

$ 1.8^{+2.3}_{-2.7} $

 G) with the equipartition magnetic field strength (

34

−
7

+
8

$ 34^{+8}_{-7} $

 mG). As J1146+4037 is a strong blazar, the turnover may be caused by its strong variability. Another possible explanation for the spectral turnover is that high-density plasma in the nuclear region attenuates the radio emission from the central active BH. High-resolution, interstellar medium observations of the nuclear region of this target may address the latter issue.

and 5 HFPs at 0.084   z   1.887 (18–160 mG


The spectral analysis above 3 keV allows us to characterise the hot corona and the relativistic reflection emission properties. The deep January 2017 NuSTAR observation was also included in the simultaneous fit (Ezhikode et al. 2020; Panagiotou & Walter 2020). From the RELXILL reflection model, and assuming a primary exponential cutoff power-law continuum, we find moderate reflection strengths, ℛ ∼ 0.1−0.2, and high cutoff energies, Ecut ∼ 110−120 keV. These values are in very good agreement with those measured from the average long-term Swift/BAT (Burst Alert Telescope) spectrum (Vincentelli et al. 2021). Applying relativistic reflection models that assume a primary Comptonisation continuum, we infer the hot corona temperature to be kThot ∼ 26−31 keV (kThot ∼ 21−22 keV) and the optical depth to be τhot ∼ 2 (τhot ∼ 6−7) for the slab (or spherical) geometry. From the spectral analysis, it is not possible to discriminate between either of the hot corona geometries, although the slab geometry provides a better fit. In the near future, X-ray polarimetry is expected to play an important role within such a framework (e.g. Schnittman & Krolik 2010; Beheshtipour et al. 2017; Tamborra et al. 2018; Marinucci et al. 2019) thanks to, for example, IXPE (Imaging X-Ray Polarimetry Explorer; Weisskopf et al. 2016) and eXTP (Enhanced X-ray Timing and Polarimetry observatory; Zhang et al. 2016). While the corona temperatures found for Mrk 110 are broadly consistent with the average ones found by Middei et al. (2019) from a sample of 26 AGN (with ⟨kThot⟩ = 50 ± 21 keV and ⟨kThot⟩ = 53 ± 23 keV for the slab and spherical geometry, respectively), it is likely to be located in the lower range of this distribution. However, its hot coronal temperature is not as low as the temperatures inferred for some AGN with much lower high-energy cutoffs, such as GRS 1734–292 (Tortosa et al. 2017), Ark 564 (Kara et al. 2017), and PDS 456 (Reeves et al. 2021b), where kT could be as low as 15 keV.


Today, at least three known populations of gap transients are recognized in the luminoisty gap. These include classical luminous blue variable (LBV) outbursts, intermediate-luminosity red transients (ILRTs), and luminous red novae (LRNe). LBVs are thought to be related to eruptions of massive luminous stars (see Smith et al. 2011). As shown in greater detail in Stritzinger et al. (2020, hereafter Paper I), the ILRT subtype is well represented by NGC 300-2008-OT and SN 2008S, and has been linked to asymptotic giant branch (S-AGB) stars (Prieto et al. 2008, 2009; Thompson et al. 2009; Botticella et al. 2009; Kochanek 2011; Adams et al. 2016; Doherty et al. 2017) that die as electron-capture supernovae (Miyaji et al. 1980; Nomoto 1984; Miyaji & Nomoto 1987; Hashimoto et al. 1993; Kitaura et al. 2006; Poelarends et al. 2008). Other models appearing in the literature for ILRTs consist of moderately massive stars experiencing super-Eddington winds and/or giant outbursts (e.g., Smith et al. 2009; Humphreys et al. 2011), or massive stars donating material to a main-sequence star, leading to the release of gravitational energy (e.g., Kashi et al. 2010). Finally, a leading model for the origins of LRNe, which all display a ubiquitous double-humped light curve (Pastorello et al. 2019a), consists of the ejection of a common envelope by a massive binary system (e.g., Blagorodnova et al. 2017) upon coalescence (Smith et al. 2016; Metzger & Pejcha 2017; Lipunov et al. 2017; Mauerhan et al. 2018). However, other models have also been proposed in the past to account for LRNe, particularly within articles that have studied the Galactic LRN archetype V838 Mon. These include, among others, outbursts from massive stars (Tylenda 2005), accretion of low-mass stars onto solar-mass main-sequence companions (Soker & Tylenda 2003; Tylenda & Soker 2006; Kashi et al. 2010; Kashi & Soker 2016; Soker 2020), or even giant stars that accrete relatively massive planets (Retter & Marom 2003).


Time domain structures (TDSs; electrostatic or electromagnetic electron holes, ion holes, solitary waves, double layers, nonlinear whistlers, etc.) are ∼1 ms pulses having significant electric fields parallel to the background magnetic field (Mozer et al. 2015). They are abundant through space, occurring along auroral zone magnetic field lines (Temerin et al. 1982; Mozer et al. 1997; Ergun et al. 1998), in the magnetospheric tail and plasma sheet (Cattell et al. 2005; Tong et al. 2018; Lotekar et al. 2020), at reconnection sites (Cattell et al. 2005; Steinvall et al. 2019; Lotekar et al. 2020), in the solar wind (Mangeney et al. 1999; Malaspina et al. 2013), in collisionless shocks (Wilson et al. 2010; Vasko et al. 2020; Wang et al. 2020), and in the magnetospheres of other planets (Pickett et al. 2015). TDSs are also expected along the Parker Solar Probe orbit (Mozer et al. 2020a). According to theoretical estimates and simulations (Cranmer & van Ballegooijen 2003; Valentini et al. 2011, 2014), these nonlinear structures can provide thermalization of electron and ion beams produced in the course of the turbulence cascade development at scales the order of the electron inertial length and down to the Debye length. This paper discusses such observations at a heliocentric distance of 35 solar radii. The electric field experiment on the Parker Solar Probe measures electric fields from DC to 20 MHz. A general description of the instrument and its electronics appears elsewhere (Bale et al. 2016). In this paper, the data from DC to 2 MHz are discussed. These measurements are obtained from the potentials of the four antennas, V1 through V4, that are located in the plane perpendicular to the Sun–satellite line. They produce E12 = (V1−V2)/3.5 and E34 = (V3−V4)/3.5, which are then rotated into the spacecraft coordinate system to produce EX and EY. The direction, X, is perpendicular to the Sun–spacecraft line, in the ecliptic plane, and pointing in the direction of solar rotation (against the ram direction), Y is perpendicular to the ecliptic plane, pointing southward, and Z points toward the Sun. The numerical factor, 3.5, is the effective antenna length (Mozer et al. 2020a). The uncertainties of the amplitudes of the waves and time domain structures reported in this paper are estimated to be about a factor of 2. These amplitudes are underestimated because the capacitive divider that couples the antennas to the electronics decreases the measured electric field relative to that on the antennas. They are often overestimated because short antennas produce overestimates of the electric field by factors of 2–4, as was observed during antenna deployment on the Cluster satellite and as is observed on the Parker Solar Probe from the ratio of the electric field to the magnetic field in whistlers.


NGC 2110. NGC 2110 is another nearby (z = 0.00779, Gallimore et al. 1999), X-ray bright Seyfert galaxy. Diniz et al. (2015) report a black hole mass of

2
.

7

−
2.1

+
3.5

×

10
8

M
⊙

$ 2.7^{+ 3.5}_{- 2.1} \times 10^{8}\,{{M}_{\odot}} $

, from the relation with the stellar velocity dispersion. From BeppoSAX data, Malaguti et al. (1999) found the X-ray spectrum to be affected by complex absorption. This has been later confirmed by Evans et al. (2007), who find the Chandra+XMM–Newton data to be well fitted with a neutral, three-zone, partial-covering absorber. Rivers et al. (2014) find the Suzaku data to be well fitted with a stable full-covering absorber plus a variable partial-covering absorber. A soft excess below 1.5 keV is also present (Evans et al. 2007), and possibly due to extended circumnuclear emission seen with Chandra (Evans et al. 2006). No Compton reflection hump has been detected with Suzaku (Rivers et al. 2014) or NuSTAR (Marinucci et al. 2015), despite the presence of a complex Fe Kα line. According to the multi-epoch analysis of Marinucci et al. (2015), the Fe Kα line is likely the sum of a constant component (from distant, Compton-thick material) and a variable one (from Compton-thin material). Concerning the high-energy cut-off, ambiguous results have been reported in literature (see Table 1). Ricci et al. (2017) report a value of

448

−
55

+
63

$ 448^{+63}_{-55} $

 keV, while Lubiński et al. (2016) report a coronal temperature of

230

−
57

+
51

$ 230^{+51}_{-57} $

 keV and an optical depth of

0
.

52

−
0.13

+
0.14

$ 0.52^{+ 0.14}_{- 0.13} $

. From 2008–2009 INTEGRAL data, Beckmann & Do Cao (2010) report a cut-off of ∼80 keV with a hard photon index, but these results are not confirmed by NuSTAR (Marinucci et al. 2015). Indeed, only lower limits to the high-energy cut-off have been found with NuSTAR (210 keV: Marinucci et al. 2015), Suzaku (250 keV: Rivers et al. 2014) and BeppoSAX (143 keV: Risaliti 2002). No hard X-ray spectral variability has been detected by Caballero-Garcia et al. (2012) and Soldi et al. (2014) from BAT data, despite the significant flux variability.


As the most luminous persistent sources in the Universe, quasars are bright enough to be detected up to redshifts z > 7 (Mortlock et al. 2011; Banados et al. 2018; Wang et al. 2018; Yang et al. 2020). According to the currently accepted model, quasars are extremely luminous active galactic nuclei (AGNs), where the observed intense energy release are related to the accretion of a gaseous disk onto a supermassive black hole (SMBH). Quasars have a wide spectral energy distribution, which normally contains a significant emission component in the optical-UV band LUV, the so-called big blue bump, with a softening at higher energies (Sanders et al. 1989; Elvis et al. 1994; Trammell et al. 2007; Shang et al. 2011). It has long been discussed that there is a nonlinear relationship between LUV and the quasar’s X-ray luminosity LX, parametrized as log(LX) = γlog(LUV)+β (Vignali et al. 2003; Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007; Green et al. 2009; Young et al. 2010; Jin et al. 2012). From the theoretical point of view, this relation could be intrinsic since the UV emission is usually thought to originate from the optically thick disk surrounding the SMBH and the X-ray photons are thought to be generated through the inverse-Compton scattering of these disk UV photons by a plasma of hot relativistic electrons (the so-called corona) around the accretion disk. Such a relation is found to be independent of redshift (Lusso & Risaliti 2016), so that it could be used as a distance indicator to estimate cosmological parameters. The initial dispersion of the LUV − LX relation is relatively large (δ ∼ 0.35−0.4, Just et al. 2007; Young et al. 2010), but after a detailed study, Lusso & Risaliti (2016) suggest that most of the observed dispersion is not intrinsic, but it is rather due to observational effects. By gradually refining the selection technique and flux measurements, Risaliti & Lusso (2019) collected a complete sample of quasars, whose dispersion of the LUV − LX relation is smaller than 0.15 dex. The sample of main quasars is composed of 1598 data points in the range from 0.036  z  5.1. With this sample, they constructed a Hubble diagram of quasars in redshift range of 0.5  z  5.5, which is in excellent agreement with the analogous Hubble diagram for SNIa in the redshift range of 0.5  z  1.4. Moreover, this Hubble diagram of quasars has been studied in cosmological applications (Zheng et al. 2020, 2021). Considering that objects at the same redshift should have the same luminosity distance in any cosmology, here we first fit the model-independent cosmography formula that reflects the Hubble relation between the luminosity distance and redshif using the quasar sample, and then we obtained the distance moduli (also the luminosity distance) for GRBs at a given redshift with the best fit results.


When the characteristic time of variability of the mass flux along the accretion disk is longer than the relaxation time of the local disk equilibrium, it is possible to use the approximation of local equilibrium Shakura (1972), see also Bisnovatyi-Kogan (2011), to calculate the transient disk structure. The equilibrium along a radius of the accretion disk around a star with a mass M is determined by the Keplerian rotational velocity ΩK(1)\begin{equation} \Omega=\Omega_{\rm K}=\left(\frac{GM}{r^3}\right)^{1/2}\cdot \label{omega} \end{equation}Ω=ΩK=GMr31/2·Writing the equation of the vertical equilibrium in approximate algebraic form, we obtain (2)\begin{equation} h=\sqrt 2 \frac{v_{\rm s}}{\Omega}, \label{h} \end{equation}h=2vsΩ,where \hbox{$v_{\rm s}=\sqrt{P/\rho}$}vs=P/ρ is the speed proportional to the sound velocity, P and ρ are the (gas + radiation) pressure and density at the symmetry plane of the accretion disk, and h is the semi-thickness of the accretion disk. The specific angular momentum l of the matter in the accretion disk is connected to the rotation velocity as(3)\begin{equation} l=r\,v_\phi=r^2\Omega. \label{l} \end{equation}l=r vφ=r2Ω.The mass flux through the disk at radius r is connected to the radial velocity vr as (4)\begin{equation} \dot M=-4\pi h\rho r v_r, \quad \dot M>0,\quad v_r<0. \label{mflux} \end{equation}Ṁ=−4πhρrvr, Ṁ>0, vr0.We use an α approximation for the turbulent viscosity (Shakura 1972) when the (rφ) component of the stress tensor trφ is written as (5)\begin{equation} t_{r\phi}=\alpha\, P, \label{trphi} \end{equation}trφ=α P,where the phenomenological non-dimensional parameter α ≤ 1. The condition of stationarity of the angular momentum, in which the outward viscous radial flux of the angular momentum is balanced by the angular momentum of the inward flux of the mass, is written as (see, e.g., Bisnovatyi-Kogan 2011) (6)\begin{equation} r^2 h \alpha P=\frac{\dot M}{4\pi}(l-l_{\rm in}). \label{angmom} \end{equation}r2hαP=Ṁ4π(l−lin).The main input into the time lag comes from the outer regions of the disk with l ≫ lin. Then we have from Eqs. (4) and (6) the expression for the radial velocity in the form (7)\begin{equation} v_r=-\alpha\frac{v_{\rm s}^2}{v_\phi}\cdot \label{vr} \end{equation}vr=−αvs2vφ·We also define the surface density Σ, and write Eq. (6) in light of Eq. (3), using condition l ≫ lin, in the form (8)\begin{equation} \Sigma=2\rho h,\quad \dot M \Omega=4\pi \alpha P h. \label{sigma} \end{equation}Σ=2ρh, ṀΩ=4παPh.The equation of the local thermal balance in the accretion disk, when the heat produced by viscosity Q+ is entirely emitted through the sites of the optically thick accretion disk with a total flux Q−, at l ≫ lin is written as (see, e.g., Bisnovatyi-Kogan 2011)(9)\begin{equation} \frac{3}{2}\dot M \Omega^2=\frac{16\pi ac T^4}{3\varkappa \Sigma}\cdot \label{theq} \end{equation}32ṀΩ2=16πacT43ϰΣ·Here T is the temperature in the symmetry plane of the accretion disk, a is the constant of the radiation energy density, c is the speed of light, and ϰ is the Thompson (scattering) opacity of the matter.


Recent technological advances related to 3D Integral Field Spectroscopy (IFS), which produces data cubes where each pixel on the image has a spectrum, have opened a new window for examining the CGM gas. This approach combines the information gathered in absorption against background sources (whose lines of sight pass through a galaxy’s CGM) with traditional emission-based properties of galaxies. Following at least two decades of limited success in identifying the galaxies associated with quasar absorbers, IFS have open a new era in establishing the relation between absorption and emission with high success rates. Early efforts with near-infrared IFS VLT/SINFONI (Bouché et al. 2007; Péroux et al. 2011; Péroux et al. 2013, 2016) led to efficient discoveries of star-forming galaxies associated with Mg ii and H i absorbers at z ∼ 2 (see also Rudie, Newman & Murphy 2017; Joshi et al. 2021). The optical IFS VLT/MUSE (Bacon et al. 2010) has proved to be a true game-changer in the field. Early on, the MUSE Guaranteed Time Observations (GTO) team established surveys including MUSE-QuBES (Muzahid et al. 2020) and MEGAFLOW (Bouché et al. 2016; Schroetter et al. 2016; Schroetter et al. 2019; Zabl et al. 2019) to relate gas traced by absorbers to galaxies. In a parallel effort, the MAGG survey targets higher redshift galaxies (Fumagalli, O’Meara & Prochaska 2016; Dutta et al. 2020; Lofthouse et al. 2020). The Cosmic Ultraviolet Baryon Survey CUBS instead is absorption-blind and uncovers new quasar absorbers in a wide range of column densities (ranging from few times 16.0  $\rm{log}\,\,{\it N}(\rm{H\,\,{\small I}})$20.1) at z1 (Chen et al. 2020; Boettcher et al. 2021; Cooper et al. 2021; Zahedy et al. 2021). By extending to bluer wavelengths, the optical IFS Keck/KCWI (Martin et al. 2010) has enabled similar studies at higher spectral resolution (Martin et al. 2019; Nielsen et al. 2020). BlueMUSE, a blue-optimized, medium spectral resolution IFS based on the MUSE concept and proposed for the Very Large Telescope is also under planning (Richard et al. 2019). Contemporary to these works, ALMA - which can be viewed as an IFS at mm-wavelengths - has enabled the detections of both CO and [CII] emission in galaxies associated with strong quasar absorbers at intermediate and high redshifts, respectively (Neeleman et al. 2016; Kanekar et al. 2018; Klitsch et al. 2018; Neeleman et al. 2018; Neeleman et al. 2019; Péroux et al. 2019; Klitsch et al. 2021; Szakacs et al. 2021a). These lines enable us to trace the colder (∼100K) and denser phase of the neutral gas: the molecular hydrogen, H2. The molecular gas constitutes the ultimate phase of the gas reservoir from which stars form and hence is an essential link to the baryon cycle. Together, these IFS observations have provided unique information on the resolved galaxy kinematics which can then be combined with the gas dynamics to probe gas flows in the CGM regions (Bouché et al. 2013; Rahmani et al. 2018a; Schroetter et al. 2019; Zabl et al. 2019; Neeleman et al. 2020; Szakacs et al. 2021a).


Topological estimators such as the Minkowski functionals (MFs) are also important diagnostics in this direction as they carry information at all orders. The MFs have been extensively developed as a statistical tool in a cosmological setting for both two-dimensional (2D; projected) and 3D (redshift) surveys. The MFs have analytically known results for a Gaussian random field, making them suitable for studies of non-Gaussianity. Examples of such studies include CMB data (Schmalzing & Górski 1998; Novikov, Schmalzing & Mukhanov 2000; Hikage et al. 2008; Natoli et al. 2010; Ducout et al. 2013; Planck Collaboration 2016b; Planck Collaboration IX, 2020a), LSS (Gott, Mellot & Dickinson 1986; Coles 1988; Gott et al. 1989, 1992; Melott 1990; Moore et al. 1992; Canavezes et al. 1998; Schmalzing & Diaferio 2000; Kerscher et al. 2001; Hikage et al. 2002, 2008 Park et al. 2005; Hikage, Komatsu & Mastubara 2006), weak lensing (Matsubara & Jain 2001; Sato et al. 2001; Taruya et al. 2002; Munshi et al. 2011d), Sunyaev–Zel’dovich maps (Munshi et al. 2011c), 21cm (Gleser et al. 2006), and N-body simulations (Schmalzing & Diaferio 2000; Kerscher et al. 2001). Note that this is an incomplete list of references and we have selected a sample of representative papers from the literature. The MFs are spatially defined topological statistics and, by definition, contain statistical information of all orders. This makes them complementary to the polyspectra methods that are defined in Fourier space. It is also possible that the two approaches will be sensitive to different aspects of non-Gaussianity and systematic effects, although in the weakly non-Gaussian limit it has been shown that the MFs reduce to a weighted probe of the bispectrum (Hikage et al. 2006). In addition to providing cosmological information, MFs can also be useful diagnostics of any unknown systematics as well as baryonic contamination which are expected to affect weak lensing observables (Herenois-Deraps et al. 2016).


We use the microlensing magnification estimates for 27 quasar image pairs in 19 lens systems from MED09. In order to have the largest possible sample, but with a similar range of observed rest wavelengths, we include all of the objects from MED09 with magnifications measured in the wavelength range between LyÎ± (1216âÃ) and Mgâii (2798âÃ). With this choice, the average rest wavelength is Î» = 1736 Â± 373âÃ, but we still keep 27 out of 29 image pairs from 19 out of 20 lensed quasars. Only the system RXS J1131â1231 is excluded, as it was observed in [Oâiii] at a much larger wavelength of â¼5000âÃ. These microlensing magnification estimates are calculated after subtracting the emission line flux ratios, which are little affected by microlensing (see, e.g., Guerras etÂ al. 2013), from the continuum flux ratios, and are therefore virtually free from extinction, substructure, and macro model effects (as these affect the line and continuum flux ratios equally). Our strategy is to compare the observed microlensing magnification for a given image pair  with a statistical sample of simulated values for that measurement as a function of the source size (rs) and the fraction of surface mass density in stars (Î±). This will allow us to calculate the likelihood of the parameters (rs, Î±) given the observations . The procedure is repeated for each of the 27 image pairs. We calculate magnification maps for each image using a grid with 11 values for the fraction of the surface mass density in stars, Î±, logarithmically distributed between 0.025 and 0.8 as Î±j = 0.025 Ã 2j/2 with j = 0, â¦, 10. The 517 magnification maps were created using the Inverse Polygon Mapping algorithm described by Mediavilla etÂ al. (2006, 2011a). We used equal mass microlenses of 1âM. All of the linear sizes can be scaled for a different microlens mass as . The maps have a size of 2000 Ã 2000 pixels with a pixel size of 0.5 light-days. The maps therefore span 1000 lt-days. The individual sizes of maps and pixels in (more natural) units of Einstein radii for microlenses of 1âM are given in TableÂ 1. On average, the maps span approximately 50 Einstein radii with a pixel scale of roughly 0.025 Einstein radii.


Furthermore, well-defined large samples of white dwarfs are an extremely useful starting point for identifying rare white dwarf types like magnetic white dwarfs (Gänsicke, Euchner & Jordan 2002; Schmidt et al. 2003; Külebi et al. 2009; Kepler et al. 2013), pulsating white dwarfs (Castanheira et al. 2004; Greiss et al. 2014), high/low-mass white dwarfs (Vennes & Kawka 2008; Brown et al. 2010; Hermes et al. 2014), white dwarfs with unresolved low-mass companions (Farihi, Becklin & Zuckerman 2005; Girven et al. 2011; Steele et al. 2013), white dwarfs with rare atmospheric composition (Schmidt et al. 1999; Dufour et al. 2010; Gänsicke et al. 2010), close white dwarf binaries (Marsh, Nelemans & Steeghs 2004; Parsons et al. 2011), metal polluted white dwarfs (Sion, Leckenby & Szkody 1990; Zuckerman & Reid 1998; Dufour et al. 2007; Koester, Gänsicke & Farihi 2014) or white dwarfs with dusty or gaseous planetary debris discs (Gänsicke et al. 2006; Farihi, Jura & Zuckerman 2009; Debes et al. 2011; Wilson et al. 2014). Because of their intrinsic low luminosities identifying a large, complete and well-defined sample of white dwarfs still remains a challenge. Much progress has been made in recent years thanks to large area surveys, first and foremost the Sloan Digital Sky Survey (SDSS; York et al. 2000; Harris et al. 2003; Eisenstein et al. 2006; Kleinman et al. 2013). The largest published catalogue of white dwarfs to date (Kleinman et al. 2013) fully exploited the spectroscopic data available at the time of SDSS Data Release 7 (DR7) and contains over 20 000 white dwarfs (of which 7424 with g ≤ 19). However not only is DR7 now outdated, but SDSS spectroscopy is only available for less than 0.01 per cent of all SDSS photometric sources. Furthermore most of SDSS's white dwarfs are only serendipitous spectroscopic targets. The true potential of SDSS's vast multiband photometric coverage still remains to be fully mined for white dwarf research, but this requires a reliable method able to select white dwarfs candidates without recourse to spectroscopy. Proper motion has been traditionally used to distinguish white dwarfs from other stellar populations. In particular many studies that contributed to the census of white dwarfs in the solar neighbourhood specifically targeted high proper motion objects (Holberg et al. 2002; Sayres et al. 2012; Limoges, Lépine & Bergeron 2013). In this paper we present a novel method which makes use of photometric data and proper motions to calculate a probability of being a white dwarf (PWD) for any photometric source within a broad region in colour space. Unlike any previous similar work, our method does not use a specific cut in colour or proper motion to generate a list of white dwarf candidates; instead it provides a catalogue of sources with an associated PWD. These PWD can then be used to create samples of white dwarf candidates best suited for different specific uses. By applying our method to the full photometric footprint of SDSS Data Release 10 (DR10), we created a catalogue which includes ∼23 000 bright (g ≤ 19) high-fidelity white dwarfs candidates (Table 1). Using this catalogue, we assess the spectroscopic completeness of the SDSS white dwarf sample.


The stochastic accretion of gas and galaxy merger-driven gas inflows are both known triggers of supermassive black hole (SMBH) growth and nuclear activity, but the relative contributions of each is still unclear. Simulations of galaxy mergers show that they drive gas to the centers of merger-remnant galaxies (e.g., Springel et al. 2005; Hopkins & Hernquist 2009), predicting that merger-driven SMBH mass growth occurs when the black hole nears the center of the merger remnant. Observations have shown that the AGN fraction does increase with decreasing distance between two merging galaxies (Ellison et al. 2011; Koss et al. 2012; Ellison et al. 2013), but this has not been well tested at the very centers of merger-remnant galaxies because of the observational difficulty of detecting and resolving two AGNs with separations 10 kpc. This is known as the “dual AGN” phase.4

4
The separation scale expected for dual AGNs is between 0.1 and 10 kpc. The SMBHs in a merger stay at these separations for a few hundred megayears before evolving into a gravitationally bound, parsec-scale separation binary AGN system (Begelman et al. 1980).
 Hundreds of AGN pairs with >10 kpc separations have been discovered (Myers et al. 2008; Hennawi et al. 2010; Liu et al. 2011). However, there are only a few confirmed kiloparsec-scale dual AGNs (Junkkarinen et al. 2001; Komossa et al. 2003; Hudson et al. 2006; Rodriguez et al. 2006; Bianchi et al. 2008; Fu et al. 2011b; Koss et al. 2011, 2012; Mazzarella et al. 2012; Liu et al. 2013; Comerford et al. 2015). Dual AGNs are an intermediate evolutionary stage between first encounter and final coalescence of two merging gas-rich galaxies (e.g., Comerford et al. 2009; Liu et al. 2012), in which strong tidal interactions are more likely to influence the nuclear accretion and star formation in both galaxies (Barnes & Hernquist 1996). Indeed, galaxy merger simulations and observations clearly show that the dual AGN phase is the critical stage when SMBH growth and star formation activity are the most vigorous (e.g., Koss et al. 2012; Van Wassenhove et al. 2012; Blecha et al. 2013).


Hydrocarbons also show a variety of deuterated molecules in L483. We detected C4D, with an isotopic ratio of 1.9 ± 0.6%, which is slightly above that found in TMC-1 (0.43; Turner 1989) and similar to that derived in L1527 (1.8; Sakai et al. 2009b). We also detected the singly and doubly deuterated forms of c-C3H2, with isotopic ratios of 5.1 ± 1.5% and 0.97 ± 0.29%, respectively, which are similar to the values found in L1544 (Spezzano et al. 2013) and L1527 (Sakai et al. 2009b; Yoshida et al. 2019). Moreover, c-C3HD and c-C3D2 have been surveyed in a sample of low-mass prestellar and protostellar cores (Chantzos et al. 2018), finding that the corresponding isotopic ratios are relatively uniform, within a factor of a few, and similar to those in L1544 and L483. Thanks to the high sensitivity of our line survey, we detected the different deuterated forms of the two 13C substituted isotopologs of c-C3H2, that is, c-H13CCCD, c-HCC13CD, and c-HC13CCD; the latter only tentatively. This is to our knowledge the first time these species have been detected in space. The deuterium ratios derived for c-H13CCCD and c-HCC13CD are in line with that found for c-C3HD. We also detected the deuterated form of the linear isomer of C3H2, l-C3HD, which was recently observed for the first time toward TMC-1 and L1544 (Spezzano et al. 2016). The isotopic ratio we find in L483, 3.8 ± 1.1%, is similar to the values derived in TMC-1 and L1544. Moreover, it seems that the linear isomer of C3H2 shows very similar levels of deuterium fractionation to the cyclic isomer in both low-mass prestellar and protostellar cores. The two deuterated forms of methyl acetylene, CH2DCCH and CH3CCD, which have previously been observed in TMC-1 with isotopic ratios of a few percent (Gerin et al. 1992a; Markwick et al. 2005), are also detected in L483 with slightly higher deuterium ratios (~6%). The deuterium ratio found for CH2DCCH in L483, 6.5 ± 1.9%, is similar to that derived in L1527 (4.7%; Yoshida et al. 2019).


Major differences between our approach and a full re-calculation of the hydrodynamics were not expected since the changes in the 14N and 22Ne abundances at the different metallicities do not alter the energy release in the hydrodynamic simulations significantly. The situation is different for deflagrations where the buoyancy, and therefore the Rayleigh-Taylor instabilities, depend on Ye. In contrast to detonations, the propagation of a deflagration front is thus affected by the metallicity (e.g., Meakin et al. 2009). The assumption we made here is confirmed by the comparison of the models presented in Table 1. Model M2a is taken from Gronow et al. (2020). The model was calculated at zero metallicity and has a total mass of 1.05 M⊙ with a He shell of 0.07 M⊙ at He ignition. Model M10_05_1, on the other hand, has a similar mass configuration, though it was calculated at solar metallicity (Model M10_05 in Gronow et al. 2021). Model M2a_pp is the same model as Model M2a, but the postprocessing step was calculated with solar metallicity instead of zero metallicity. An inspection of the abundances of Models M2a_pp and M10_05_1 at t = 100 s after He detonation ignition shows that the results of the postprocessing step with varying metallicities are in reasonably good agreement with a full re-calculation of the hydrodynamic model. The maximum difference in the yields produced in the core detonation is only 10%, while the maximum difference is 50% in the He detonation (excluding 12C in both). However, differences in the yields produced in the He detonation can in part be attributed to the slightly different setups of Model M2a (and therefore Model M2a_pp) and Model M10_05_1 at the beginning of the relaxation simulation, with the differences in the total and shell masses being less than 1% (see Gronow et al. 2021 for an explanation of the difference). Generally, the contribution of the yields from the He detonation to the total nucleosynthetic yields are small compared to those of the core detonation. Our approach is thus sufficient to derive nucleosynthetic yields for GCE studies. It saves significant computational costs as additional 3D hydrodynamical simulations of the explosion do not need to be carried out. Nevertheless, there might be slight differences visible in the observables because they are sensitive to the products of the He shell detonation (Höflich et al. 1996; Nugent et al. 1997; Kromer et al. 2010).


The objective of this article is to study the spatial distribution and possible changes in the properties of carbon nano-dust in protoplanetary disks (PPDs). Carbon nanodust, detected under more or less organised structures and different ionisation states, constitutes a major component of dust in the interstellar and circumstellar environments. Vibrational emission bands in the near- to mid-IR from nanocarbon dust have been observed towards PPDs around most of the Herbig Ae stars, about half of the Herbig Be stars, and a few T-Tauri stars (e.g. Brooke et al. 1993; Acke & van den Ancker 2004; Acke et al. 2010; Seok & Li 2017). In contrast to large grains, these tiny and numerous carbon grains are well coupled to the gas and do not settle towards disk midplanes. This results in different spatial distributions in which tiny grains are present at the disk surfaces (e.g. Meeus et al. 2001; Habart et al. 2004; Lagage et al. 2006) and in the cavity or gaps from which the pebbles are missing (e.g. Geers et al. 2007; Kraus et al. 2013; Klarmann et al. 2017; Kluska et al. 2018; Maaskant et al. 2013). The very small carbon grains in the irradiated disk layers may have strong consequences (e.g. Gorti & Hollenbach 2008). As in the irradiated regions of the interstellar medium, they are the prevalent contributors to the energetic balance because they are very efficient at absorbing UV photons and heating the gas through the photoelectric effect. The highest fluxes of lines tracing the warm gas (e.g. [OI] 63 and [OI] 145 μm, H2 0-0 S(1), and high-J CO) are found in PPDs that show a large amount of flaring and high aromatic band strength (e.g. Meeus et al. 2013). Moreover, due to their large effective surface area, they may dominate the catalytic formation of key molecules as H2 and the charge balance. The disk structure may further depend on the level of nanograins that are coupled with the gas. Characterising the size and properties of these tiny grains through the disks, from internal to external regions, is thus of prime importance to understand the structure and evolution of PPDs.


Our first attempt to derive the $PL_{K_\mathrm{s}}$ relation has revealed a number of RRLs brighter than the main relation. We investigated their spatial distribution and found that they are mainly located in the central part of the LMC. This is shown in Fig. 5 which presents in the bottom panel the spatial distribution of the whole sample of RRLs considered in this paper (${\sim}29\, 000$), in the top panel the distribution of the RRLs which appear to be overluminous in the $PL_{K_\mathrm{s}}$ relation, and, in the middle panel, the distribution of the RRLs which were actually used to fit our final $PL_{K_\mathrm{s}}$ relation. Further investigations, performed using the Fourier parameters (ϕ31, ϕ21, R21, and R31) of the light curves available in the OGLE IV catalogue did not show any particular properties of the overluminous RRLs. On the other hand, in the period–amplitude diagram based on the I amplitudes available in the OGLE IV catalogue, the bright RRLs all show small, in some cases near-zero amplitudes, compared with regular RRLs of the same period. The decrease in amplitude at a given period can be owing to these RRLs being blended with non-variable stars. We expect the centroid of a blended source to be determined with poor accuracy (see e.g. Ripepi et al. 2014, 2015). For this reason as a further test we plotted the distribution of distances in arcsec of the VMC sources cross-matched with the OGLE IV RRLs. A clear separation is now seen in the two samples, for 94 per cent of the RRLs lying on the PL/PW relations the cross-match radius is less than 0.2 arcsec, whereas for 68 per cent of the overluminous RRLs the cross-match radius is larger than 0.2 arcsec. The average accuracy of the VMC astrometry is of the order of 0.080 arcsec both in RA and in Dec. (Cioni et al. 2011). We therefore discarded the RRLs with a cross-match radius larger than 0.2 arcsec. A total of 3252 objects were discarded. This procedure allowed us to significantly reduce the scatter on the PL/PW relations. We visually inspected the VMC images of some of the discarded RRLs, confirming that they all are clearly blended with stars and/or background galaxies. Similar investigations were performed in the past and the same effects were noted, e.g. by Ripepi et al. (2015) for Type II Cepheids. The final sample of LMC RRLs after this cleaning procedure contains 25 795 objects. This is the sample that was used as a starting point to investigate the PL and PW relations presented in the following sections. Additional RRLs were later discarded from the final fit based on a 3σ clipping procedure leading to $PL_{K_\mathrm{s}}$ relations using a clean sample of ${\sim}22\, 000$ RRLs.


In direct relation to the interplay between the structure of the dark matter distribution and the baryon physics, galaxies are found in a wide range of structural hierarchies, from low-density regions to groups and clusters (see e.g. Tully 1987; Berlind et al. 2006; Yang et al. 2007), and during their lifetime they experience merging events (e.g. Mamon 1988; Tempel et al. 2017). In some cases, the mergers eventually devoid their entire neighbourhood, leaving behind a single elliptical galaxy of group-scale mass, called a fossil group galaxy (Ponman et al. 1994; Jones et al. 2003). Numerical simulations by Barnes (1989) first motivated such a hierarchical merging scenario (see also Díaz-Giménez, Muriel & Mendes de Oliveira 2008). Since then, there have been several supporting reports of X-ray sources identified as fossil groups (Santos, Mendes de Oliveira & Sodré 2007; La Barbera et al. 2009). Because most fossil systems found to date lie within z  0.2, fossil galaxy groups most likely are old, undisturbed systems due to the lack of major mergers. While some luminous galaxies experience major merger events in their evolution, fossil group galaxies acquire their mass typically through minor merger events, where the mass ratio stays below 0.3 (DOnghia et al. 2005). Simulations show that a fossil system may assemble half of its mass in dark matter by redshift z > 1, and that the assembled mass at any redshift is generally higher in a fossil than in regular groups (Dariush et al. 2007). Since this merging process is relatively fast compared to the cooling time of the surrounding gas, comparable to one to several Hubble times, fossil groups are usually found embedded in giant, X-ray luminous gas haloes (Mulchaey 2000). If a fossil system has not yet fully merged, it can be identified by another criterion, a gap in brightness of at least 2.5 mag (usually defined in the r band) between the first and fourth brightest galaxies in the group (Dariush et al. 2010; Zarattini et al. 2014) within half its virial radius.


At present, however, kinematical studies of the nearby late-type stars have become somewhat foreshadowed with the advent of deep, wide-field SDSS (York et al. 2000), SDSS/SEGUE (Yanny et al. 2009) and RAVE (Steinmetz et al. 2006) surveys which have made it possible to study K–M dwarfs to much greater distances from the Sun. Using their spectroscopic catalog with radial velocities measured with an external accuracy of 7–10 km s-1 and applying photometric parallax relations, the SDSS teams have traced K–M dwarfs in the distance range up to ~2 kpc, thus providing valuable information on the spatial, velocity, and metallicity distributions with respect to vertical distance from the Galactic plane (Bochanski et al. 2007, 2011; Jurić et al. 2008; Fuchs et al. 2009; Bond et al. 2010; West et al. 2011; Schlesinger et al. 2012; Zhang et al. 2013), as well as on the luminosity and mass functions of low-mass dwarfs in the Galactic disk (Covey et al. 2008; Bochanski et al. 2010). Relatively local (| z |   500 pc) samples of late-type dwarfs from the RAVE survey, based on radial velocities accurate to ~2 km s-1 and photometrically determined distances, have been used to deduce the solar space velocity with respect to the Local Standard of Rest (Coşkunoǧlu et al. 2011; Pasetto et al. 2012a; Golubov et al. 2013). The RAVE survey has also resulted in a catalog of ~44 000 candidate active stars (Žerjal et al. 2013) which makes a major contribution to the data on chromospheric emission of cool dwarfs. In the context of these massive surveys, as well as of present-day models of the Galaxy, the samples of nearby late-type dwarfs with most accurate trigonometric parallax and radial-velocity measurements, as well as other high-quality observational data, still remain important, as they provide a fundamental framework for calibration and tests of relations between low-mass star parameters (such as, e.g., color-luminosity, mass-luminosity, activity-age, chemo-kinematic relations).


There are several reasons to suspect that the (galaxy-sourced) ionizing background during reionization may have been somewhat harder than the estimates given here. First, our calculations neglect the filtering effects of optically thick H i in the ISM of the host galaxy, and within the cosmic web. Absorption by this gas would have hardened the spectrum of the ionizing radiation as it escaped the galaxy and traveled through the IGM (e.g., Madau 1995; Faucher-Giguère et al. 2009; Haardt & Madau 2012). These effects were likely strongest during the last stages of reionization, when the radiation typically had to travel large distances to reach the I-fronts. Second, our calculations neglect the effects of binary star systems. Mass transfers and mergers between binary companions can extend the period over which ionizing photons are produced by the stellar population, which would harden the time-integrated spectrum (Eldridge & Stanway 2009; Stanway et al. 2016). Lastly, recent studies have suggested that the IMF in starburst galaxies may be more top-heavy than the IMF assumed here (Baugh et al. 2005; Gunawardhana et al. 2011; Marks et al. 2012; Zhang et al. 2018). Most recently, Schneider et al. (2018) measured a logarithmic slope of

 in the mass range 15–200 M⊙, using spectroscopic measurements of the 30 Doradus star-forming region in the Large Magellanic Cloud. (The IMF adopted here has a slope of 2.3 for M > M⊙, and a cutoff of 120 M⊙.) Each of the provided effects would work in the direction of making

 smaller. Based on these considerations, we argue that the lower half of Figure 2, with

 ≲ 1.5, is likely the most relevant region of parameter space for

. In what follows, we adopt

 = 1.5 as our fiducial value, but we note that

 is only mildly sensitive to

 except at the fastest I-front speeds. In the next section we find that

 = 104 km s−1 is close to the upper limit achieved by I-fronts in cosmological simulations, which yields

 = 26,200 K, assuming

 = 1.5 (see Figure 2). This result varies by Δ

 = −4200 (+1600) K if we instead assume

 = 2.5(0.5).


Recently, the EHT Collaboration completed an analysis of the linear polarization of M87*, providing novel insights into its magnetic field structure in particular (Event Horizon Telescope Collaboration 2021a,b; Goddi et al. 2021). Synchrotron emission, which dominates the millimetre image, is initially generated perpendicular to the local magnetic field, such that its polarization carries with it an imprint of the field geometry (Palumbo, Wong & Prather 2020). Then, as this polarization propagates, it is further modified by Faraday effects, important for depolarizing accretion flows down to observed levels and generating the observed rotation measure (Ballantyne, Özel & Psaltis 2007; Mościbrodzka et al. 2017; Jiménez-Rosales & Dexter 2018; Ricarte et al. 2020). Fully polarized radiative transport simulations on EHT scales have been developed in the past few decades, allowing us to link polarized images to the detailed physics of the underlying plasma and the space–time producing them (Bromley, Melia & Liu 2001; Broderick & Loeb 2006; Broderick & McKinney 2010; Porth et al. 2011; Shcherbakov, Penna & McKinney 2012; Dexter 2016; Mościbrodzka & Gammie 2018). This enabled (Event Horizon Telescope Collaboration 2021b) to discriminate between two major classes of accretion disc: a ‘Magnetically Arrested Disk’ (MAD) and ‘Standard and Normal Evolution’ (SANE). MAD accretion discs have magnetic fields strong enough to affect the disc dynamics and exhibit stronger poloidal (or non-toroidal) magnetic field components (Bisnovatyi-Kogan & Ruzmaikin 1974; Igumenshchev, Narayan & Abramowicz 2003; Narayan, Igumenshchev & Abramowicz 2003; Chael, Narayan & Johnson 2019). Meanwhile, the weaker magnetic fields of a SANE disc are sheared out by the motion of the plasma into a mostly toroidal configuration (Narayan et al. 2012; Sądowski et al. 2013; Ryan et al. 2018). The fractional linear polarization of M87*, the upper limit on its circular polarization, and most importantly the ‘twisty pattern’ of its spatially resolved linear polarization map favour ‘MAD’ models of M87* (Event Horizon Telescope Collaboration 2021b).


CMEs are known for large-scale expulsion of magnetized plasma structures from closed magnetic field regions on the Sun. They were first detected in the coronagraphic images taken in 1971 by NASA’s OSO-7 spacecraft (Tousey 1973). However, some definite inferences for the solar wind (Eddington 1910; Birkeland 1916; Biermann 1951) as well as CMEs from the Sun (Chapman & Ferraro 1931; Eddy 1974) were made decades before their formal discovery. Following OSO-7, a series of spacecraft (Skylab, Helios, P78-1 Solwind, SOHO, Coriolis, and STEREO, etc.) have observed thousands of CMEs leading to a vast literature (Munro et al. 1979; Howard et al. 1985; Gosling 1993; Hundhausen 1999; Gopalswamy et al. 2000; Schwenn 2006; Vourlidas et al. 2010; Chen 2011; Wang et al. 2011; Webb & Howard 2012; Mishra & Srivastava 2013; Mishra et al. 2017; Harrison et al. 2018). CMEs have been observed to occur often having spatial and temporal relation with solar flares, eruptive prominences (Munro et al. 1979; Webb & Hundhausen 1987; Zhang et al. 2001; Gopalswamy et al. 2003) and with helmet streamer disruptions (Dryer 1996). Unlike CMEs from the Sun, to observe stellar CMEs are challenging because the close stellar environment cannot be spatially resolved. Although stellar CMEs have not yet been directly detected in Thomson-scattered optical light from other stars, it is believed that the extreme X-ray flares observed on stars may be in conjunction with extreme stellar CMEs (Houdebine, Foing & Rodono 1990; Wheatley 1998; Leitzinger et al. 2011; Aarnio, Matt & Stassun 2012; Osten & Wolk 2015; Vida et al. 2016). Indeed, the stellar X-ray flare, helmet streamers, and prominences observed on T Tauri Stars have shown similarities with those observed on the Sun (Haisch, Antunes & Schmitt 1995; Massi et al. 2008). The CMEs and flares themselves may not be causally related, they both seem to be involved with the reconfiguration of complex magnetic field lines within the corona caused by the same underlying physical processes, e.g. magnetic reconnection (Priest & Forbes 2002; Compagnino, Romano & Zuccarello 2017). But, even for the sun, it has been noted that not all flares are accompanied by CMEs and not all CMEs by flares (Munro et al. 1979; Harrison 1995; Yashiro et al. 2008b; Wang & Zhang 2008).


The first INM of PG 1553+113 to our knowledge was reported by Stalin et al. (2005) – they applied the C-test to the R-band LCs (total duration of about 10 h) and found the source to be variable in one night out of two. Another two nights of INM about 13 h long were presented by Osterman et al. (2006). They found no significant INV, but they did not present statistical tests. To quantify the conclusion of Osterman et al. (2006), we used the C-test in the form C = σ/⟨e⟩, where σ is the standard deviation of the source LC and ⟨e⟩ the mean uncertainty of the source photometric measurements. We applied this test to the data listed in Table 4 of Osterman et al. (2006) and found C = 1.52 and C = 1.28 for the respective nights, which means that PG 1553+113 was non-variable. Andruchow et al. (2007, 2011) reported the results from the INM they carried out during four nights in the VR-bands (April 21 to 24, 2007) and five nights in the BR-bands (April 21 to 25, 2009), respectively. Applying the C-test, the authors found no significant variability. Gopal-Krishna et al. (2011) detected INV during three nights out of three using C- and F-tests (a total monitoring duration of 16 h in the R-band). Gaur et al. (2012) found no INV during six nights of monitoring in the BR-bands (C- and F-tests were applied). Gupta et al. (2016) presented the results from the INM during seven nights in the R-band (a total monitoring duration of about 26 h). The authors found the source to be variable in one night, non-variable in another, and probably variable in the remaining nights (F- and χ2 tests were applied). We, however, should point out that in the latter nights the variability amplitude seems to be quite close to the magnitude uncertainties. In such cases the usage of the C-test could be more appropriate (see Zibecchi et al. 2017, 2020). Pandey et al. (2019) monitored PG 1553+113 for eight nights in the VR-bands for 2–4 h each night. Employing enhanced F- and nested ANOVA tests, the authors found the source to vary on intra-night timescales for three nights. Finally, Pasierb et al. (2020) found no INV in the BVR-bands during a single night of monitoring (duration of about 3.7 h, F-test employed).


In order to assess the impact of the brightness enhancement due to the phase function effects in the light scattering of the coma dust, we apply different phase function corrections to the measured coma brightness of 67P for the 10 000 km aperture radius. In general, the phase function reduces the reflected coma magnitude value. For small phase angles α (typically up to 30°), a linear reduction with α can be applied with typical parameters β for comets between 0.02 and 0.06 (Lamy et al. 2004). Alternatively, the two-parameter phase function of Schleicher, Millis & Birch (1998), based on 1P/Halley measurements, is available or the phase angle correction by Müller (1999) that also considers geometric projection effects by a non-spherical coma, symmetric to the radial direction with respect to the Sun. Fornasier et al. (2015) obtained results for the 67P nucleus surface reflectivity applying a HG-type phase function (Bowell et al. 1989) with a best-fitting G of −0.13. Fig. 5 shows the phase angle-corrected afρ values of 67P for the various phase function solutions. In Fig. 5, β = 0.04 is used as mean value for the linear phase function that is lower than the β value found for the nucleus of 67P (0.059–0.076; Tubiana et al. 2011; Lowry et al. 2012). A second HG-type phase function is applied as well with G = 0.15 that is found from many asteroid light curves (Tedesco 1989). Obviously, the afρ value for zero phase angle depends on the phase darkening and is highest for the Bowell-type phase function with G = −0.13 (as obtained for the 67P nucleus by Fornasier et al. 2015). Two phase functions provide a close to linear decrease of afρ with solar distance over the time interval from the end of 2015 September to the beginning of 2016 April, i.e. the linear phase function with β = 0.04 and the Bowell-HG-type phase function with G = 0.15. The phase functions of Schleicher et al. (1998) and of Müller (1999) can approximate the afρ data well between the end of September and end of December, but do not describe well the 67P dust activity measured in 2016.


The physics of asymmetric inflow reconnection has been investigated in detail for fully ionized plasmas. One of the principal applications of this work has been Earth's dayside magnetopause. Asymmetric inflow reconnection has also been investigated in the context of Earth's magnetotail and elsewhere in the magnetosphere (Oieroset et al. 2004; Muzamil et al. 2014), the solar atmosphere (Murphy et al. 2012; Nakamura et al. 2012; Su & van Ballegooijen 2013; Su et al. 2013), laboratory experiments (Yamada 2007; Murphy & Sovinec 2008; Yoo et al. 2014), and plasma turbulence (Servidio et al. 2009, 2010). Cassak & Shay (2007) performed a scaling analysis for asymmetric inflow reconnection. They found that the outflow is governed by a hybrid upstream Alfvén speed that is a function of the magnetic field strength and density in both upstream regions (see also Birn et al. 2010) and that the flow stagnation point in the simulation frame and magnetic field null were not colocated. The structure and dynamics of asymmetric reconnection in fully ionized collisionless and two-fluid plasmas have been studied previously in several works (e.g., Swisdak et al. 2003; Cassak & Shay 2008, 2009; Mozer et al. 2008; Murphy & Sovinec 2008; Pritchett 2008; Mozer & Pritchett 2009; Pritchett & Mozer 2009; Malakit et al. 2010, 2013; Aunai et al. 2013a, 2013b). Simulations of the plasmoid instability during reconnection with asymmetric upstream magnetic fields by Murphy et al. (2013) showed that the resultant magnetic islands developed primarily into the weak-field upstream region. Because the reconnection jets impacted the islands obliquely rather than directly, the islands developed net vorticity. In addition to asymmetric inflow reconnection, several groups have investigated asymmetric outflow reconnection (e.g., Oka et al. 2008; Murphy 2010; Murphy et al. 2010) and reconnection with three-dimensional asymmetry (e.g., Al-Hachami & Pontin 2010; Wyper & Jain 2013).


The LMC is known to have brought a large population of star clusters as it has been accreted onto the Milky Way (Bica et al. 2008); thus, it is possible that DELVE 2 may share a similar history to the thousands of known star clusters in the Magellanic system. The LMC star cluster formation history is believed to be three-staged, including a period of rapid cluster star formation in the early universe (τ ≳ 10 Gyr), followed by a long quiescent period between ∼10 and ∼2–4 Gyr ago and then by a period of rapid star cluster formation extending to the present day, potentially due to the interaction between the LMC and SMC (Harris & Zaritsky 2009; Weisz et al. 2013; Rubele et al. 2018; Ruiz-Lara et al. 2020). One consequence of this period of quiescence in the LMC cluster formation history is the so-called “age gap” in the age distribution of LMC clusters, with a small (N ≲ 20) population of globular clusters with ages comparable to most known Milky Way globular clusters, separated by the gap from a much larger population of less massive young clusters (e.g., Bertelli et al. 1992; Girardi et al. 1995; Olszewski et al. 1996). These two populations of clusters obey an overarching age–metallicity relation, within which the older clusters (τ > 12 Gyr) are significantly more metal-poor (−2.2 ≲ [Fe/H] ≲ −1.2) compared to the younger population of clusters ([Fe/H] ≳ −0.7; Meschin et al. 2014).38

38
We note that Gatto et al. (2020) recently discovered 16 cluster candidates believed to be within the LMC cluster age gap (4 Gyr ≲ τ ≲ 10 Gyr).
 Therefore, although the photometrically derived metallicity and age for DELVE 2 are limited in accuracy by the small number of red giant branch stars available to precisely constrain these properties through synthetic isochrone fitting, it is clear that DELVE 2 is more consistent with an old, metal-poor stellar population and thus the former class of LMC clusters (provided the system is not a dwarf galaxy, as discussed in the previous subsection).


The experiment was carried out using the VULCAN laser facility at the Rutherford Appleton Laboratory (Danson et al. 1998), using the setup shown in Figure 1(a). A laser pulse of duration ∼1 ns and energy ∼ 70 J, was focused onto a 50 μm thick gold foil, at an incidence angle of

∼
45
°

 to a peak intensity of ∼1015 W cm−2. The interaction of the nanosecond pulse with the gold foil leads to the generation of ablated plasma that is mainly constituted of thermally distributed gold ions and faster lighter ions with an average energy per nucleon of tens of keV (Tan et al. 1984; Gitomer et al. 1986). The lighter ions, such as protons and carbon ions, originate from contaminant layers (water vapor and hydrocarbon) typically present on the surface of the targets (Gitomer et al. 1986). The laser–target interaction was enclosed in a gas cell filled with pure nitrogen at a controlled pressure of ∼10−1 mbar. Hydrodynamic simulations using the code HYADES  (Larsen & Lane 1994) indicate that the gas becomes fully ionized within 100 ps from the start of the laser irradiation by the X-rays emitted from the target (Dean et al. 1971), resulting in a stationary plasma with an electron density and temperature of ∼3 × 1016 cm−3 and

T

e

∼
1

  keV, respectively. These values imply an electron Debye length of

λ

D

∼
1.4

μ
m

 and an ion-acoustic speed of

C

s

∼
2.2
×

10

5

m

s

−
1

. Moreover, the Coulomb logarithm for electron–electron and ion–ion collisions are of the order of 6 and 11, respectively, indicating a characteristic timescale for collisions of

τ

ee

∼
36

ns

 and

τ

ii

∼
600

ns

, respectively. The PPI technique (Borghesi et al. 2002; Sarri et al. 2010) was employed to investigate the interaction of the ablated plasma with the background plasma. The probe proton beam was generated by focusing a second laser pulse of ∼1 ps duration and ∼50 J energy, to an intensity of

∼

10

19

 W cm−2 onto a thin gold foil (thickness ∼20 μm). In the experimental arrangement shown in the Figure 1(a), the distance between proton source and interaction region was

l
≃
4

mm

, and the detector was placed at

L
≃
38

mm

 from the interaction region, giving an intrinsic geometrical magnification of

M
≈
(
l
+
L
)

/

l
∼
10.5

 (Borghesi et al. 2002). A stack of several layers of dosimetrically calibrated (Kirby et al. 2011) RadioChromic Films (RCF), was used to detect the proton beam. The two lasers were temporally delayed so that a proton with an energy of 13 MeV traverses the interaction region at the time

t

0

=
180
±
20

 ps after the start of the long-pulse irradiation, where the start of the interaction corresponds to 1/10 of the peak intensity. The error in defining the beginning of the interaction is mainly due to the systematic error in the synchronization of both laser beams. This does not affect the temporal resolution of the PPI technique, which is on the order of picoseconds (Sarri et al. 2010).


The simplest two component model (power law + disk) is a phenomenological model often used to describe the spectra of ULXs as an empirical description of a disk plus corona geometry. In the presence of a cool (kT ~ 0.1−0.4 keV) and luminous (L ~ 1039−1040 erg/s) disk, it allows inferring the presence of intermediate-mass black holes (e.g., Makishima et al. 2000). This is not the case for M33 X-8, where the disk component describes the high-energy part of the spectrum well and appears to be hot (kT ~ 1.15 keV), leaving a soft excess that is accounted for by the power law. The overall disk parameters are then inconsistent with a massive black hole, but instead are more typical of an ordinary stellar mass black hole: using the relationship between mass, temperature, and luminosity in a standard disk (see, e.g., Makishima et al. 2000), we derive a mass of ~10 M⊙ for a nonrotating black hole, consistent with the estimation obtained by data from other satellites (e.g., Foschini et al. 2006; Weng et al. 2009; Isobe et al. 2012). Sutton et al. (2013) developed a classification scheme based on a disk+power law fit, to be applied to ULX spectra, according to which the spectral state of an ULX source can be defined by the disk temperature, the power-law slope, and the ratio between the flux contribution of the two spectral components in the 0.3−1 keV band. Our result is consistent with that found by Sutton et al. (2013) using XMM-Newton data, and, according to their classification, it identifies M33 X-8 as a broadened disk source, or in other words, as a source whose spectrum is dominated by emission from a hot disk (see Table 2) and where the additional soft component may be the effect of an unrealistic description of the disk spectrum by the diskbb model. In fact, such hot-disk/soft power-law spectra are difficult to explain in the context of the analogy of ULXs with GBHs: the thermal state of GBHs is indeed characterized by a hot disk, but the presence of a soft power-law-like component in addition to the disk is unusual, and its physical interpretation is not simple: if this component is due to the presence of a Comptonized corona, we do not expect it to be dominant at energies lower than the temperature of the seed photons that come from the disk.


Using all GRBs showing X-ray plateau phases, Dainotti et al. (2008) discovered a tight correlation between L0 and tb (the Dainotti relation). Subsequently, the Dainotti relation has been used to measure cosmological parameters (Cardone et al. 2009, 2010; Dainotti et al. 2013; Postnikov et al. 2014). Cardone et al. (2010) relied on this correlation to build a Hubble diagram of 66 GRBs and present a preliminary constraint on cosmological parameters. The errors on the cosmological constraints are large, which may be related to the nature of GRB light curves and in part due to the sample selection. In previous works, GRBs with X-ray plateaus were used to derive the Dainotti relation, and then to constrain cosmological parameters. However, a newborn magnetar can be spun down through a combination of electromagnetic dipole and gravitational-wave quadrupole emission (Shapiro & Teukolsky 1983). The X-ray luminosity of GRBs is given by the energy input from the electromagnetic and gravitational waves into the surrounding medium (Dai & Lu 1998; Zhang & Mészáros 2001; Metzger et al. 2011). Therefore, in order to standardize GRBs as standard candles through the Dainotti relation, it is recommended that X-ray plateaus caused by the same physical mechanism are used (electromagnetic dipole radiation or gravitational waves). Similar to supernova cosmology, only SNe Ia from accretion channels can be treated as standard candles. Following the Dainotti correlation (Dainotti et al. 2008) between the plateau luminosity and the end time of the plateau in X-ray afterglows, we further confirm this relation out to redshift z = 5.91. In this paper, we perform a first attempt to standardize long GRBs with X-ray plateaus dominated by electromagnetic dipole radiation as reliable standard candles. Using the same method, Hu et al. (2021) considered two other kinds of GRBs to constrain cosmological parameters, i.e., short GRBs with plateau phases dominated by magnetic dipole radiations and long GRBs with gravitational-wave-dominated plateau phases. It is interesting to note that this correlation also holds for the optical sample (Dainotti et al. 2020b).


Figure 6 shows the orbital eccentricities as a function of [M/H] for the metal-rich disc sample. The solid lines correspond to the required eccentricity (see Eq. (2)) for different values of ISM radial metallicity gradients: −0.10 dex kpc−1 (black), −0.07 dex kpc−1 (our measured gradient for young stars in Table 1; see also Minchev et al. 2018, red), −0.04 dex kpc−1 (orange), and −0.06 dex kpc−1 (Cepheids analysis from Genovali et al. 2014, green). For the three first cases, we assumed ISM[M/H](R⊙) = 0.0 to estimate Rbirth from the stellar metallicity. However, Genovali et al. (2014) have their own zero point, defined as: [Fe/H] = −0.06 * Rg + 0.57, with a clear shift in the relation compared to the other ones assumed in this work. The impact of the ISM gradient value and the zero-point assumption on the derived Rbirth, and therefore on the required eccentricity to reach the solar vicinity without the need for churning, is clearly observed. As described in Hayden et al. (2020), given the measured [M/H] and eccentricity, stars lying to the left are able to reach the solar neighbourhood through blurring, while the stars to the right of the line are possible candidates to have migrated through churning. This is the case for most of the SMR stars (70% of the SMR stars lie below the line that corresponds to the Cepheids analysis); they are therefore likely to have been brought to the solar neighbourhood by churning, which is in close agreement with previous studies (e.g., Kordopatis et al. 2015a; Wojno et al. 2016). However, it is worth noting that the observed metallicity distribution function in Fig. 2 peaks around 0.2 dex, which is higher than previous reported solar vicinity MDFs (see e.g., Fuhrmann et al. 2017). A possible ignored bias towards more metal-rich objects in the sample selection could be pulling the percentage of possible migrators to higher values. Among the entire distribution, our churned candidates with [M/H] >  + 0.1 comprise around 17% of the sample. If we constrain the number of migrators to only stars with [M/H] >  + 0.25, the global percentage decreases to 8% of the sample.


While the angular extent of IP shocks can be directly investigated using multi-point in situ measurements, the size of coronal shocks can only be indirectly inferred via remote-sensing observations of the electromagnetic emissions associated with them. According to Nelson & Robinson (1975), the average angle subtended at the solar surface by fundamental metric type II radio emission sources is 43Â°. Aurass et al. (1994) found particular cases with larger, double type II source structures covering a separation angle beyond 90Â°. Type II radio sources often show non-radial propagation trajectories (see Mann et al. 2003, and references therein). Wave-like large-scale disturbances propagating over the solar disk in extreme ultraviolet observations (usually referred to as âEIT wavesâ or âEUV wavesâ) are in close empirical correlation with type II radio bursts (Klassen et al. 2000). Most EIT waves are accompanied by CMEs, and observations and MHD modeling suggest that they are driven by the lateral expansion of CMEs, while the ultimate nature of the phenomenon remains under debate and could consist of true waves, pseudo waves (e.g., reconnection fronts), or a combination of both (Patsourakos & Vourlidas 2012; Nitta et al. 2013b, and references therein). According to Patsourakos & Vourlidas (2012), EIT waves can reach distances up to 1.3 R (850 Mm) from the source. Single-case studies reported some EIT waves covering a whole solar hemisphere (Klassen et al. 2000; Kienreich et al. 2009; Thompson & Myers 2009). Connections between EIT waves and SEP events have been often suggested (e.g., Bothmer et al. 1997; Krucker et al. 1999), and recently Rouillard et al. (2012) hypothesized that the EIT wave can be used to track the expansion of a coronal shock responsible for particle acceleration. Other authors question the EIT wave acceleration scenario for SEPs, with many EIT waves being observed at well-connected positions having no associated SEP increase (Miteva et al. 2014).


The SFG sample was constructed using the Great Observatories All-Sky LIRG Survey (GOALS sample, Armus et al. 2009), from which we extracted 158 galaxies, with data from Inami et al. (2013), who report the fine-structure lines at high resolution in the 10 − 36 μm interval, and Stierwalt et al. (2014), who include the detections of the H2 molecular lines and the PAH features at low spectral resolution. For those galaxies in the GOALS sample that have a single IRAS counterpart, but more than one source detected in the emission lines, we have added together the line or feature fluxes of all components, to consistently associate the correct line or feature emission to the total IR luminosity computed from the IRAS fluxes. To also cover lower luminosity galaxies, as the GOALS sample only includes luminous IR galaxies (LIRGs) and ultra-luminous IR galaxies (ULIRGs), we included 38 galaxies from Bernard-Salas et al. (2009) and Goulding & Alexander (2009), to reach the total sample of 196 galaxies with IR line fluxes in the 5.5 − 35 μm interval in which an AGN component is not detected. For the Bernard-Salas et al. (2009), Goulding & Alexander (2009), and the GOALS samples, we excluded all the composite starburst-AGN objects identified as those with a detection of [NeV] either at 14.3 or 24.3 μm. It is worth noting that the original samples from Goulding & Alexander (2009) and Bernard-Salas et al. (2009) have spectra solely covering the central region of the galaxies. To estimate the global SFR, we corrected the published line fluxes of the Spitzer spectra by multiplying them by the ratio of the continuum reported in the IRAS point source catalogue to the continuum measured on the Spitzer spectra extracted from the CASSIS database (Lebouteiller et al. 2015). We assumed here that the line emission scales (at first order) with the IR brightness distribution. In particular, we considered the continuum at 12 μm for the [NeII]12.8 μm and [NeIII]15.6 μm lines, and the continuum at 25 μm for the [OIV]25.9 μm, [FeII]26 μm, [SIII]33.5 μm, and [SiII]34.8 μm lines. This correction was not needed for the AGN sample and the GOALS sample because of the greater average redshift of the galaxies in the 12MGS and GOALS samples. In particular, the 12MGS active galaxy sample has a mean redshift of 0.028 (Rush et al. 1993), while the GOALS sample has a mean redshift of 0.026. The galaxies presented by Bernard-Salas et al. (2009) have instead an average redshift of 0.0074, while the sample by Goulding & Alexander (2009) has an average redshift of 0.0044. For the other lines in the 10 − 36 μm interval, Goulding & Alexander (2009) did not report a detection, and we used the data presented in Bernard-Salas et al. (2009) for a total of 15 objects. Both Bernard-Salas et al. (2009) and Goulding & Alexander (2009) reported data from the high-resolution Spitzer-IRS spectra. Data in the 50 − 205 μm interval were taken from Díaz-Santos et al. (2017). For the GOALS sample, 20 starburst galaxies were taken from Fernández-Ontiveros et al. (2016), and 23 objects were taken from the ISO-LWS observations of Negishi et al. (2001). As a result, we obtained a total sample of 193 objects. Lastly, the PAH features’ fluxes were measured from the low-resolution Spitzer-IRS spectra by Brandl et al. (2006), including 12 objects from the sample of Bernard-Salas et al. (2009) and 179 objects from Stierwalt et al. (2014).