Another possible indication of the different nature of the smallest clouds with respect to the largest ones is shown by their behaviour in the velocity dispersion vs. radius relation. This relation, known as the first Larson relation (Larson 1981), is expected to be of the form σv ∝ Rβ. The observed non-thermal motions in MCs are always supersonic (thermal motions for gas at T = 10 K is ≃0.1 km s−1), and the expected value of β, if the origin of these motions is purely supersonic turbulence, the so-called Burger turbulence, is β = 0.5 (McKee & Ostricker 2007). Various values of β in MCs have been derived by several authors, ranging from β ∼ 0.38 (Larson 1981) to β = 0.6 ± 0.3 (Miville-Deschênes et al. 2017). Restricting the evaluation of the relation to the interstellar clouds of the outer Galaxy, previous estimates give β = 0.47 ± 0.08 (Sodroski 1991), β = 0.53 ± 0.03 (Brand & Wouterloot 1995), β = 0.45 ± 0.04 (May et al. 1997), and β = 0.53 ± 0.06 for MCs in the third quadrant of the Galaxy (Rice et al. 2016), all in agreement with the a Burger-like turbulence. However, the nature of the non-thermal motions in MCs is still debated (Krumholz et al. 2019), and it is not yet clear whether they originate solely from turbulence or from large-scale gravitational collapse (Ballesteros-Paredes et al. 2011; Traficante et al. 2018a,b; Merello et al. 2019). We plot the σv–R relation for clouds of the FQS catalogue in Fig. 15. Two different regimes appear for clouds with R ≥ 2 pc and clouds with R   2 pc. For MCs with R ≥ 2 pc the velocity dispersion increases with radius with an exponent β = 0.59, similar to what is expected from pure supersonic turbulence, and to that previously measured. On the other hand, for MCs with R   2 pc the relation is almost flat, with β = 0.08. The non-thermal motions in the smallest clouds seem to be independent of cloud size. These condensations, likely to be only transient structures, are probably not formed by the turbulent ISM, which would lead to a Burger-like spectrum. It may be possible that these structures are the result of a large-scale effect, such as spiral-arm density-wave shock that injects the same amount of kinetic energy to all these objects. This large-scale effect would dominate over the local turbulence or the self-gravity within the smallest clouds, becoming increasingly irrelevant in the larger clouds.


More interestingly, there are hints suggesting that the impacts of projection effects extend beyond richness misidentification. First, when Miyatake et al. (2016) reported a possible detection of assembly bias for subsamples of clusters divided based on the concentration of member galaxies, the signal appeared too large compared to theoretical predictions (Wechsler et al. 2006; Dalal et al. 2008) for the ΛCDM model. Subsequent works found that this large apparent signal might be due to projection effects (Busch & White 2017; Zu et al. 2017; Sunayama & More 2019). Secondly, when More et al. (2016) reported a detection of the so-called ‘splashback’ radius, a physically motivated boundary of cluster haloes, for redMaPPer clusters, the location of the splashback radius was found to be smaller than theoretical expectations (also see Chang et al. 2018, for a similar detection). Follow-up studies (Shin et al. 2019; Zürcher & More 2019) used samples of clusters selected based on the Sunyaev-Zel’dovich effect and found a different location of the splashback radius consistent with theoretical expectations, albeit with larger errors, suggesting that the original location may have been impacted by projection effects. The recent analysis in Murata et al. (2020) further indicated that previous analyses of the splashback radius for optically selected clusters may suffer from projection effects. Third, Murata et al. (2018) developed a forward modelling approach to calibrate the richness–mass relation from a joint measurement of cluster abundances and cluster lensing. However, they found that a population of less massive haloes, down to 1012h−1M⊙, had to be introduced in order for the ΛCDM model prediction to match the observations. Overall, these studies indicate that projection effects may impact not only cluster richnesses but also other cluster observables such as cluster lensing, which, if true, can render problematic the standard approach for cluster cosmology employed by photometric surveys.


IRIS always takes short exposure (with the shortest possible exposure time of 2.2 s) and long exposure with specified exposure time (14.5 s) one by one. In order to estimate and subtract the sky background, each field was observed in 10 dithered positions. Raw exposures were sky-subtracted and flat-fielded using standard IRAF (Tody 1986) routines. An astrometric solution was performed with Sextractor (Bertin & Arnouts 1996) and SCAMP (Bertin 2006), and then 10 dithered frames were resampled and combined with SWARP (Bertin 2010) into a single, final image (details of the pipeline used for calibrations can be found in Watermann 2012). Aperture photometry was performed with the DAOPHOT (Stetson 1987) package, and instrumental photometry was tied to the 2MASS system using the constant stars present in a given field as standards (usually more than 3 stars of brightness similar to our target with quality flag AAA in the 2MASS catalog). If there were no comparison stars of similar magnitude in a given field (cases of VY Pyx, SW Tau, and AL Vir), we used long exposures (14.5 s) to measure the brightness of comparison stars while the target was measured in the short exposure (2.2 s). We found a non-negligible color term in J band, and it amounts to −0.07 (J − K

s
). Internal precision of our photometry is at a level of 0.02 mag. In order to check correctness of our transformation to the 2MASS system, we compared the magnitudes of the constant stars present in the observed fields (transformed to the 2MASS system using an approach identical to our scientific objects) with the corresponding magnitudes from the 2MASS catalog. The observed fields offered very limited numbers of bright constant stars; thus for this test, we mostly used sources that were adopted as comparison stars in the transformation of the photometry of science targets. Each considered star was excluded from the set of comparison stars while transforming its own photometry. This test is presented in Figure 2. The mean difference between IRIS and 2MASS photometry is zero with the error on the mean of 0.002 mag in each band. We adopt this value as our zero-point uncertainty, which contributes to the systematic error of our calibration of PLRs.


The problem of imaging global magnetic fields through helioseismology has been relatively underexplored, as studies have mainly focused on the solar rotational profile and other global and local flow fields (Lavely & Ritzwoller 1992; Basu et al. 1999; Giles 2000; Zhao & Kosovichev 2004; Hanasoge et al. 2012b, 2017). Some studies have analyzed the effects of local fields, such as those contained in a sunspot, on the reduction of wave power (Cally 2000; Schunker & Cally 2006), and changes in wave speed and flow patterns (Gizon et al. 2009; Švanda et al. 2014; Khomenko & Collados 2015; Rabello-Soares et al. 2018; Braun 2019). Nevertheless, early attempts (e.g., Gough 1990) that were made to study the impact of global magnetic fields (Lorentz-stress perturbations) on the eigenfrequencies and eigenfunctions of the standard solar model (model S in Christensen-Dalsgaard et al. 1996) focused on the details of the forward problem of frequency shifts induced by an axisymmetric magnetic field not aligned with the rotation axis. Dziembowski & Goode (2004) considered near-surface, small-scale as well as a large-scale deep toroidal fields at the tachocline. However, lacking a formal relation between Lorentz stresses and the consequent seismic signatures (sensitivity kernels), these efforts suffered from the drawback of restricting the field geometry to make the problem tractable. Several numerical studies have also considered small perturbations around a magnetized background medium (Cameron et al. 2008, 2010; Hanasoge et al. 2012a; Schunker et al. 2013). Attempts at deducing temporal changes in magnetic field configurations from variations in angular velocity have been met with limited success (Antia et al. 2013). In a recent analysis, Cutler (2017) explored the potential of learning about magnetic fields from mode-coupling theory. Hanasoge (2017) derived analytical forms of the Lorentz-stress sensitivity kernels in the context of normal-mode coupling. This has made it possible to consider the treatment of a completely general magnetic field configuration as a perturbation around a hydrostatic background state. This forms the basis of the current study.


We then used the fxcor task to determine the redshifts of selected objects in the field. This task allows to calculate the radial velocity through Fourier cross-correlation between the spectrum of the object under analysis and a reference (template) spectrum (Tonry & Davis 1979). Both spectra are continuum subtracted and Fourier filtered before doing the correlation, while dispersions are equalized by rebinning to the smallest dispersion. For this work, we used two reference spectra: that of NGC 4449 (Kennicutt 1992), an irregular galaxy that has well-defined emissions, and the spectrum of NGC 4387 (Gavazzi et al. 2004), an elliptical galaxy showing strong absorptions. Both templates were downloaded from NED. For those spectra where it was possible to establish a tentative redshift value, typical emission lines were identified, such as H γ, [O ii] (3727 Å), H β, [O iii] (4959 Å) and [O iii] (5007 Å), and/or absorptions, like Ca ii (H+K), Ca+Fe, Na i and H α. Finally, the redshift adopted for each object was computed from Gaussian fits to two or more such features in its spectrum. Three objects (slits #6, #19 and #23) turned out to be Galactic stars5 (we give their radial velocities in Table 1), while no reliable redshift value could be obtained for other five objects (slits #5, #11, #13, #17 and #20), due to the low S/N ratio of their spectra (we will return to objects #5 and #11 in Section 3.2). Tentative redshifts for two of them (slits #17 and #20) were measured through just one emission line each, which we assumed to be [O ii] (3727 Å) and H δ, respectively (based on their colours and spiral morphology). So, their tentative redshift values would be $z_{\#17} \simeq 0.476$ and $z_{\#20} \simeq 0.479$. No clear emission or absorption lines could be identified in the blazar's spectrum, besides telluric lines and diffuse interstellar bands (DIBs), so no definite redshift value could be established in this way for 3C 66A (see, however, Section 3.3 for our analysis on probable foreground absorptions on the blazar's spectrum). Redshifts were thus established for 15 (plus two just tentative) out of the 24 selected objects. Our results are shown in Table 1, where we also include the only galaxy with a previously published redshift within our GMOS field (G2 in Bow97).


Here, we present new Very Large Telescope (VLT) VIMOS (Le Févre et al. 2003) observations of two star-forming dwarf galaxies using the integral field unit (IFU) spectroscopy mode (hereafter VIMOS-IFU). UM 461 (the upper panel in Fig. 1) is a well-studied H ii/BCD galaxy (e.g. Taylor et al. 1995; van Zee, Skillman & Salzer 1998; Lagos et al. 2011). This galaxy has been described as formed by two compact and off-centre giant H ii regions (GH iiR), some smaller star-forming regions spread across the galaxy disc and an external stellar envelope that is strongly skewed towards the south-west (Lagos et al. 2011). It has been classified as having a cometary-like morphology with an integrated subsolar metallicity of 12 + log(O/H) = 7.73–7.78 (Masegosa, Moles & Campos-Aguilar 1994; Izotov & Thuan 1998; Pérez-Montero & Díaz 2003). As in most H ii/BCD galaxies, UM 461 has an underlying component of old stars (Telles & Terlevich 1997; Lagos et al. 2011) that exhibits an elliptical outer morphology. Deep Near-Infrared observations with the Gemini/NIRI camera (Lagos et al. 2011) revealed that the star-formation activity in this galaxy is taking place in several star clusters with masses typically between ∼104 M⊙ and ∼106 M⊙. Fig. 1 shows the Kp band image of UM 461 obtained by Lagos et al. (2011). Using the same notation as Lagos et al. (2011), the main GH iiR (the brightest one in Fig. 1) in our study is composed of the star clusters nos. 2 and 3, while the faintest one is formed by star clusters nos. 5–7. Taylor et al. (1995) proposed that the SE tail in their H i image of UM 461 was formed as a result of a tidal interaction with UM 462. However, higher resolution H i maps of UM 461 by van Zee, Skillman & Salzer (1998) did not show the extended SE H i tail seen in the Taylor H i map. This discrepancy is attributed to solar interference in the Taylor map (van Zee, Skillman & Salzer 1998). Moreover, the age distribution of the star cluster population in UM 461 indicates that the current starburst has begun within the last few million years (Lagos et al. 2011). This current starburst time-scale is too short to realistically be attributed to a UM 461/UM 462 interaction.


Theoretically, the production, propagation, and escape of LyC photons are related to the physical properties of the galaxies. Firstly, the production of LyC radiation implies the presence of young, massive stars, and therefore of on-going star formation. Because of the fast recombination timescale of the HI atoms, previous episodes of star formation have no significant impact on the production of ionizing photons eventually escaping the galaxy (e.g. Paardekooper et al. 2015). Secondly, the propagation of LyC photons within the ISM is favoured by a negligible amount of dust and low column density of HI (N(HI) ≤ 1018 cm-2) in a 10-pc scale region around the emitting star clusters. This could be the case for galaxies embedded in dark-matter halos with masses less than 108 M⊙ (Yajima et al. 2011; Wise et al. 2014; Paardekooper et al. 2015). However, even galaxies residing in more massive halos can have lines of sight favourable to the propagation and the escape of LyC photons (Gnedin et al. 2008; Roy et al. 2015). Supernova explosions could have cleared their ISM, and star-formation episodes could occur in their outskirts. In addition, “runaway” OB stars up to 1 kpc away from the initial-origin regions are proposed to significantly contribute to the amount of LyC photons finally emitted into the IGM (Conroy & Kratter 2012). Thirdly, LyC photons emitted into the IGM can affect the galaxy environment, changing the ratio of neutral vs ionized gas, eventually fuelling the ISM (e.g. Martin et al. 2012, for a study of ionized-metal outflows and inflows). Simulations at intermediate redshift have shown that the LyC escape fraction (fesc(LyC)) steeply decreases as the dark-matter halo mass (Mh) increases at 3 z 6 (e.g. Yajima et al. 2011) and that the median fesc(LyC) also changes with redshift at z = 4−6 (e.g., Cen & Kimm 2015). It is worth stressing that while some authors find that the LyC escape fraction decreases with the increase in the halo mass (see also Ferrara & Loeb 2013), other works find the opposite trend: fesc(LyC) is found to range from a few percent (e.g. Gnedin et al. 2008) up to
        20−30% (e.g. Mitra et al. 2013) or even higher (e.g. Wise & Cen 2009).


Gaia 1 is a star cluster that was recently discovered by Koposov et al. (2017) in the first Gaia data release (Gaia Collaboration 2016), alongside with another system of lower mass. Its observation and previous detections were seriously hampered by the nearby bright star Sirius, which emphasized the impressive discovery power of the Gaia mission. This object was first characterized as an intermediate-age (6.3 Gyr) and moderately metal-rich (−0.7 dex) system, based on isochrone fits to a comprehensive combination of Gaia, 2MASS (Cutri et al. 2003), WISE (Wright et al. 2010), and Pan-STARRS1 (Chambers et al. 2016) photometry. Hence, this object was characterized by Koposov et al. (2017) as a star cluster, most likely of the globular confession. Further investigation of Gaia 1 found a metallicity higher by more than 0.5 dex, which challenged the previous age measurement and rather characterized it as a young (3 Gyr), metal-rich (−0.1 dex) object, possibly of extragalactic origin given its orbit that leads it up to ~1.7 kpc above the disk (Simpson et al. 2017). Subsequently, Mucciarelli et al. (2017) measured chemical abundances of six stars in Gaia 1, suggesting an equally high metallicity, but based on their abundance study, the suggestion of an extragalactic origin was revoked. While a more metal-rich nature found by the latter authors conformed with the results by Simpson et al. (2017), the evolutionary diagrams of both studies are very dissimilar and could not be explained by one simple isochrone fit. In particular, it was noted that “the Simpson et al. (2017) stars do not define a red giant branch in the theoretical plane, suggesting that their parameters are not correct” (Fig. 1 of Mucciarelli et al. 2017). Such an inconsistency clearly emphasizes that a clear-cut chemical abundance scale is inevitable for fully characterising Gaia 1, and to further allow for tailored age determinations, even more so in the light of the seemingly well-determined orbital characteristics, Thus, this work focuses on a detailed chemical abundance analysis of four red giant members of Gaia 1, based on high-resolution spectroscopy, which we complement with an investigation of the orbital properties of this transition object. Combined with the red clump sample of Mucciarelli et al. (2017) and reaching down to the subgiant level (Simpson et al. 2017), stars in different evolutionary states in Gaia 1 are progressively being sampled.


We study here the Sco OB1 association (Figs. 1 and 2), using this and other techniques. The general properties of this large OB association, which spans almost 5° on the sky, and is surrounded by a ring-shaped HII region called Gum 55, are reviewed by Reipurth (2008). Its central cluster NGC 6231 contains several tens of OB stars, which have been extensively studied. On the other hand, many fewer studies, all recent, were devoted to the full mass spectrum, using optical photometry (Sung et al. 1998, 2013) and X-rays (Sana et al. 2006, 2007; Damiani et al. 2016; Kuhn et al. 2017a,b). The currently accepted distance of NGC 6231 is approximately 1580 pc, and its age is between 2and 8 Myr, with a significant intrinsic spread (Sung et al. 2013; Damiani et al. 2016). No ongoing star formation is known to occur therein, however. Approximately one degree North of the cluster, the loose cluster Trumpler 24 (Tr 24) also belongs to the association. There is little literature on this cluster (Seggewiss 1968; Heske & Wendker 1984, 1985; Fu et al. 2003, 2005) which unlike NGC 6231 lacks a well-defined center and covers about one square degree on the sky. Its age is  10 Myr according toHeske & Wendker (1984, 1985), who find several PMS stars, and its distance is 1570–1630 pc according to Seggewiss (1968). Other studies of the entire Sco OB1 association include MacConnell & Perry (1969 – Hα-emission stars), Schild et al. (1969 – spectroscopy), Crawford et al. (1971 – photometry), Laval (Laval 1972a,b – gas and star kinematics, respectively), van Genderen et al. (1984 – Walraven photometry), and Perry et al.(1991 – photometry). At the northern extreme of Sco OB1, the partially obscured HII region G345.45+1.50 and its less obscured neighbor IC4628 were studied by Laval (1972a), Caswell & Haynes (1987), López et al. (2011), and López-Calderón et al. (2016). They contain massive young stellar objects (YSOs; Mottram et al. 2007), maser sources (Avison et al. 2016), and the IRAS source 16562-3959 with its radio jet (Guzmán et al. 2010), outflow (Guzmán et al. 2011), and ionized wind (Guzmán et al. 2014), and are therefore extremely young (1 Myr or less). The distance of G345.45+1.50 was estimated as 1.9 kpc by Caswell & Haynes (1987), and 1.7 kpc by López et al. (2011), in fair agreement with distances of Sco OB1 stars. In Fig. 1 of Reipurth (2008) a strip of blue stars is visible, connecting NGC 6231 to the region of IC4628.


We ignore the density stratification effect in Case I, II, and IIa, because the width of the horizontal current sheet in our simulations is much shorter than the length. The simulation domain extends from x = 0 to x = L0 in the x-direction, and from

y
=
−
0.5

L

0

 to

y
=
0.5

L

0

 in the y-direction, in the three cases, with

L

0

=

10

6

 m. Outflow boundary conditions are used in the x-direction and inflow boundary conditions in the y-direction. For the inflow boundary conditions, the fluid is allowed to flow into the domain but not to flow out; the gradient of the plasma density vanishes; the total energy is set such that the gradient in the thermal energy density vanishes; a vanishing gradient of parallel components plus divergence-free extrapolation of the magnetic field. For the outflow boundary conditions, the fluid is allowed to flow out of the domain but not to flow in, and the other variables are set by using the same method as the inflow boundary conditions. The horizontal force-free Harris current sheet is used as the initial equilibrium configuration of magnetic fields in Case I,
13

B

x
0

=
−

b

0

tanh
[
y

/

(
0.05

L

0

)
]

14

B

y
0

=
0

15

B

z
0

=

b

0

/

cosh
[
y

/

(
0.05

L

0

)
]
.

The magnetic fields in the low solar atmosphere could be very strong (Jin et al. 2009, 2012; Khomenko et al. 2014; Peter et al. 2014; Vissers et al. 2015) and the magnetic field can exceed 0.15 T in both the intranetwork and the network quiet region (e.g., Orozco Suárez et al. 2007; Martínez González et al. 2008; Jin et al. 2009, 2012). In the work by Jin et al. 2012, the maximum of the field strength was found to be 0.15 T. The magnetic field could be even stronger in the active region near the sunspot. Therefore, we set b0 = 0.05 T in Case I and Case II, and b0 = 0.15 T in Case IIa. Due to the force-freeness and neglect of gravity, the initial equilibrium thermal pressure is uniform. The initial temperature and plasma density are set as T0 = 4200 K and ρ0 = 1.66057 × 10−6 kg m−3 in Case I, and T0 = 4800 K and ρ0 = 3.32114 × 10−5 kg m−3 in Case II and Case IIa. Therefore, the initial plasma β is calculated as β ≃ 0.0583 in Case I, β ≃ 1.332 in Case II, and β ≃ 0.148 in Case IIa. The initial ionization degree is assumed as Yi = 10−3 in Case I, and Yi = 1. 2 × 10−4 in Case II and IIa. The magnetic diffusion in this work matches the form computed from the solar atmosphere model in Khomenko & Collados (2012), and we set

η
=

[

5
×

10

4

(
4200

/

T
)

1.5

+
1.76
×

10

−
3

T

0.5

Y

i

−
1

]

 m2 s−1 in Case I, and

η
=
[
5
×

10

4

(
4800

/

T
)

1.5

+
1.76

×

10

−
3

T

0.5

Y

i

−
1

]

 m2 s−1 in Case II and IIa. The first part ∼ T−1.5 is contributed by collisions between ions and electrons, the second part

∼

T

0.5

Y

i

−
1

 is contributed by collisions between electrons and neutral particles. Small perturbations for both magnetic fields and velocities at t = 0 make the current sheet to evolve and secondary instabilities start to appear later in the three cases. The forms of perturbations are listed below:
16

b

x
1

=
−
pert
·

b

0

·
sin

2
π

y
+
0.5

L

0

L

0

·
cos

2
π

x
+
0.5

L

0

L

0

17

b

y
1

=
pert
·

b

0

·
cos

2
π

y
+
0.5

L

0

L

0

·
sin

2
π

x
+
0.5

L

0

L

0

18

v

y
1

=
−
pert
·

v

A
0

·
sin

π

y

L

0

·

random

n

Max

(

∣

random

n

∣

)

,

where pert = 0.08, vA0 is the initial Alfvén velocity, randomn is the random noise function in our code, and

Max
(
∣

random

n

∣
)

 is the maximum of the absolute value of the random noise function. This random noise function makes the initial perturbations for the velocity in the y-direction to be asymmetric, and such an asymmetry makes the current sheet gradually become more tilted, especially after secondary islands appear. The reconnection process is not really symmetrical in nature (Murphy et al. 2012), this is one of the reasons that we use such a noise function. Another reason is that the asymmetric noise function makes the secondary instabilities develop faster. Figure 1(a) shows the distributions of the current density and magnetic fields at t = 0 in case I.


How does the propagation of radiation and the ISM composition affect ISM observables in low-metallicity galaxies? Addressing this question is important to understand the evolution of low-metallicity galaxies, which undergo more bursty star formation than normal galaxies. Nearby star-forming dwarf galaxies present distinct observational signatures compared to well-studied disk galaxies. Dwarfs are usually metal poor, H i rich, and molecule poor as a result of large-scale photodissociation (e.g., Kunth & Östlin 2000; Hunter et al. 2012; Schruba et al. 2012). Mid-IR (MIR) and far-IR (FIR) observations have revealed bright atomic lines from H ii regions ([S iii], [Ne iii], [Ne ii], [O iii], etc.) and PDRs ([C ii], [O i]) (e.g., Hunter et al. 2001; Madden et al. 2006; Wu et al. 2008; Hunt et al. 2010; Cormier et al. 2015). Their spectral energy distributions (SEDs) are also different from spiral and elliptical galaxies and indicative of altered dust properties, with a relatively low abundance of polycyclic aromatic hydrocarbons (PAHs) and perhaps a different dust composition (e.g., Madden et al. 2006; Galliano et al. 2008; Rémy-Ruyer et al. 2013). It is still unknown, however, whether these differences between dwarf and disk galaxies are the direct result of recent star formation activity shaping the ISM or instead a consequence of the low-metallicity ISM that is independent of star formation activity. To answer this, one needs to observe tracers of the interplay between the ISM and various stages of star formation activity. While there are now a number of important studies available on PDR properties modeling FIR lines on large scales in various extragalactic environments (e.g., Kaufman et al. 2006; Vasta et al. 2010; Graciá-Carpio et al. 2011; Cormier et al. 2012; Parkin et al. 2013) or in our Galaxy under solar-metallicity conditions (e.g., Cubick et al. 2008; Bernard-Salas et al. 2012, 2015), only a few studies are published on individual extragalactic regions (Mookerjea et al. 2011; Lebouteiller et al. 2012). Of particular interest are dwarf galaxies, where the effect due to radiative feedback is expected to be most significant. The goal of this paper is to investigate how the low-metallicity ISM reacts under the effects of star formation in regions that have undergone different histories. The nearby low-metallicity galaxy NGC 4214 provides an excellent environment to perform this experiment because it has well-separated star-forming centers, one hosting a super star cluster, which allows us to study the effects of extreme star-forming conditions on the surrounding ISM.


This work improves the efficiency of component by component modelling that has been successful in recovering the physical conditions for various individual absorbers (e.g. Churchill & Charlton 1999; Charlton et al. 2000, 2003; Ding et al. 2003a, 2003b; Zonak et al. 2004; Ding, Charlton & Churchill 2005; Masiero et al. 2005; Lynch & Charlton 2007; Misawa et al. 2008; Jones et al. 2010; Lacki & Charlton 2010; Muzahid et al. 2015; Richter et al. 2018; Rosenwasser et al. 2018). Rather than averaging over components and phases, it is possible to determine how much of the H i is associated with these different phases in order to derive separate metallicities for various clouds. Resolving the individual clouds allows us to break the degeneracy for components on the flat part of the Lyα curve of growth, even with coverage of just saturated H i lines, and derive metallicity constraints for different parcels of gas along the line of sight. It is important to do so because different processes, e.g. outflows (Bouché et al. 2012; Bordoloi et al. 2014; Rubin et al. 2014; Schroetter et al. 2016), pristine accretion (Martin et al. 2012; Rubin et al. 2012; Danovich et al. 2015), recycled accretion (Ford et al. 2014), minor and major mergers (Martin et al. 2012; Anglés-Alcázar et al. 2017), are surely contributing to the same system, and it is expected that conditions will vary significantly along a line of sight which can span hundreds of kpc spatially (Churchill et al. 2015; Peeples et al. 2019). This will lead to a more meaningful comparison to galaxy properties. For example, Pointon et al. (2019) did not find a difference between the metallicities of absorbers found within an impact parameter of 200 kpc along the major and the minor axes of isolated galaxies. Based on cosmological hydrodynamic simulations, a larger metallicity is expected along the minor axis due to outflows and a lower metallicity along the major axis due to inflows (Peroux et al. 2020). However, an observational trend could exist, for example, for the minor axis to have some, but not all, high metallicity components, or for the minor axis to have one or more low metallicity components. Such results would be ‘washed out’ by deriving an average metallicity for all gas along a line of sight, which clearly often has multiple complex origins. For some data sets/projects, the new analysis could be transformative, however, to make it feasible to use for large statistical studies it is important that the analysis is semi-automated and robust.


The question whether electrons are able to penetrate into deep and dense layers of the solar atmosphere is currently under scrutiny. Calculations by Emslie (1978) showed that for electrons and/or protons to reach the

 level, their energy has to be of the order of a few MeV, while electron energy in the strongest flares only reaches several hundreds of keV. Considering the continuity equation for electron precipitation, Syrovatskii & Shmeleva (1972) and Dobranskis & Zharkova (2015) calculated that beam electrons with energies above 100 keV can reach the lower chromosphere with a column depth of 2 × 1021 cm−2, while those with energies of the order of 200 keV are even capable of penetrating to the photosphere (1022 cm−2; see also Zharkova & Gordovskyy 2006). Works by other authors seem to support the idea that power-law beam electrons may precipitate throughout the entire flaring atmosphere down to the photosphere (Brown 1971; Syrovatskii & Shmeleva 1972), causing its heating via inelastic collisions with the ambient plasma via a hydrodynamic response (Somov et al. 1981; Nagai & Emslie 1984; Fisher et al. 1985; Zharkova & Zharkov 2007). These power-law electrons also cause nonthermal excitation and ionization of hydrogen and other elements, combined with radiative transfer, leading to occurrence of emission in the lines and continua during flaring events (Aboudarham & Henoux 1986; Zharkova & Kobylinskii 1993). Observations indicate that CE may be a combination of radiation that originates (i) in an optically thin chromospheric layer owing to heating caused by beam electrons (thermal model), with subsequent recombination producing enhanced Balmer and Paschen continuum, and (ii) in the photosphere and TMR, where the plasmas are excited and ionized directly by collisions with high-energy electrons, resulting in radiative transfer processes in spectral lines and continua, combined with backwarming radiation supplied by the heated chromosphere and corona (e.g., Hudson 1972; Metcalf et al. 1990; Babin et al. 2016; Kleint et al. 2016). Indeed, since the early 1980s the enhanced Balmer continuum has been observed close to the Balmer cutoff at 3646 Å (Neidig 1989; Kerr & Fletcher 2014), and more recently a strong increase of Balmer continuum has been detected over a wide spectral range using IRIS data (Heinzel & Kleint 2014; Kleint et al. 2016).


Douchin & Haensel (2001; DH) formulated a unified EoS for NS on the basis of the SLy4 Skyrme nuclear effective force (Chabanat et al. 1998), where some parameters of the Skyrme interaction were adjusted to reproduce the Wiringa et al. calculation of neutron matter (Wiringa et al. 1988) above saturation density. Hence, the DH EoS contains certain microscopic input. In the DH model the inner crust was treated in the CLDM approach. More recently, unified EoSs for NS have been derived by the Brussels-Montreal group (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013). They are based on the BSk family of Skyrme nuclear effective forces (Goriely et al. 2010). Each force is fitted to the known masses of nuclei and adjusted among other constraints to reproduce a different microscopic EoS of neutron matter with different stiffness at high density. The inner crust is treated in the extended Thomas-Fermi approach with trial nucleon density profiles including perturbatively shell corrections for protons via the Strutinsky integral method. Analytical fits of these neutron-star EoSs have been constructed in order to facilitate their inclusion in astrophysical simulations (Potekhin et al. 2013). Quantal Hartree calculations for the NS crust have been systematically performed by (Shen et al. 2011b,a). This approach uses a virial expansion at low density and a RMF effective interaction at intermediate and high densities, and the EoS of the whole NS has been tabulated for different RMF parameter sets. Also recently, a complete EoS for supernova matter has been developed within the statistical model (Hempel & Schaffner-Bielich 2010). We shall adopt here the EoS of the BSk21 model (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) as a representative example of contemporary EoS for the complete NS structure, and a comparison with the other EoSs of the BSk family (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013) and the RMF family (Shen et al. 2011b,a) shall be left for future study.


The origin of kiloparsec scale magnetic fields observed in the nearby galaxies through the polarized radio synchrotron emission (e.g. Fletcher 2010; Beck 2012, etc.) is attributed to the large-scale dynamo operating in the interstellar medium (ISM). This is driven mainly via the helical turbulent motions in the interstellar medium, coupled with the differential shear and vertical density stratification. This mechanism, along with some phenomenological approximations about the properties of background turbulence, in principle explains the growth of magnetic fields from small initial strengths to large-scale equipartition strengths against the diffusive losses (Beck et al. 1996; Shukurov 2005; Beck & Wielebinski 2013), and the characteristic times it takes for the field to reach the equipartition strength turn out to be of the order of $\sim \, {\rm Gyr}\,$. This is perhaps a much too slow to account for the strong equipartition strength magnetic fields observed in the high-redshift galaxies with z > 1 (e.g. Bernet et al. 2008) or even for that in the slowly rotating nearby galaxies. This discrepancy leads one to invoke some additional mechanism such as cosmic rays (CRs) boosting the typical dynamo action. The idea of CR driven dynamo was initially discussed by Parker (1992), this predicted the possibility of enhanced dynamo action by the virtue of additional CR buoyant instability, that inflates the magnetic field structures (see also Brandenburg 2018). Based on the conventional dynamo formulation Parker further suggested a simple model for the flux loss through the gaseous disc due to buoyancy by substituting the transport terms Bϕ/td. These terms are supposed to encapsulate the non advective flux transport associated with the buoyant instability, and leads to the fast dynamo action in characteristic field mixing times. Hanasz & Lesch (2000) indirectly verified such a dynamo action via the numerical simulations of rising magnetic flux tubes and found e-folding times of mean field of the order of $100\, {\rm Myr}\,$. Supplementing this Hanasz, Wóltański & Kowalik (2009), Siejkowski et al. (2010), Kulpa-Dybeł et al. (2015), Girichidis et al. (2016), etc. also demonstrated the fast amplification of regular magnetic fields via the direct magnetohydrodynamic (MHD) simulation of global galactic ISM including CR driven turbulence, along with the differential shear (but excluding the viscous term). To complement this, we aim here to extend our previous analysis of dynamo mechanism in SN driven ISM turbulence (Bendre, Gressel & Elstner 2015) by including the CR component and investigate the influence of magnetic field dependent propagation of CR on the dynamo. Here we focus on estimating the dynamo coefficients from the direct MHD simulations and effect CR component has on them by comparing with our previous analysis without the CR.


Since the star-formation histories of galaxies (ETGs included, e.g. De Lucia et al. 2006; Maraston et al. 2009) can be stochastic and include multiple bursts, we also verify the full-spectrum fitting capabilities to retrieve more complex SFHs. In particular, we take an 11 Gyr old composite stellar population with an exponentially delayed SF (τ = 0.3 Gyr) as the main SF episode (this age is compatible with the age of the Universe at z ~ 0.15, which is the median redshift of our sample, see Sect. 3). We then define more complex SFHs by combining this single CSP with a burst of SF at different ages (5, 6, 7 Gyr) and with different mass contributions (3, 5, 10 %). In all cases, we consider a solar metallicity for the main SF episode and, according to the results of Maraston et al. (2009), a subsolar metallicity (Z = 0.004) for the later one. We do not mask any spectral feature of the input spectra, we assume AV  =  0.1 mag for the two components and apply a velocity dispersion of 200 km s-1. We show the results for a S/N of 80, which matches the typical S/N of the SDSS median stacked spectra analyzed in the following (see Sect. 3). Useful information can be derived from the comparison between the output SFH obtained from these input simulated spectra and the one provided when the single CSP alone is taken as input SFH. Fig. 5 shows that the single CSP alone is well recovered by the full spectrum fitting. In particular, ~80% of the stellar mass is retrieved within ~1 Gyr from the SFH peak. When a burst is added to this major episode of SF, the full-spectrum fitting is able to recognize the presence of a more complex SFH, as indicated by the tail appearing at smaller ages, and the total mass percentage of the later burst is retrieved within 1 Gyr from the expected age. However, we note that the main episode of SF is spread on a time interval longer than expected, and 50% of the stellar mass is retrieved around ~1 Gyr from the SFR peak. We also find that, in this case, the mean properties of the global stellar population are well retrieved, with a percentage accuracy larger than 10% starting from S/N ~ 15 for age, ~7 for metallicity, ~20 for AV, ~8 for σ and that the metallicities of the two SF episodes are separately recovered. These S/Ns are well below those typical of the stacked spectra analyzed in the following sections.


Galactic winds have been ubiquitously observed in galaxies at both low and high redshifts, and they are critical to galaxy formation and evolution. Simulations calibrated to match these observations predict that a large amount of galactic material is ejected as a wind before reaccreting to either form stars or be ejected once again (Oppenheimer et al. 2010; Anglés-Alcázar et al. 2017). Current cosmological hydrodynamic simulations of galaxy formation employ a variety of subgrid models (e.g. Springel & Hernquist 2003; Oppenheimer & Davé 2006; Stinson et al. 2006; Dalla Vecchia & Schaye 2008; Agertz et al. 2013; Schaye et al. 2015; Davé, Thompson & Hopkins 2016; Tremmel et al. 2017; Pillepich et al. 2018; Davé et al. 2019; Huang et al. 2020a) that artificially launch galactic winds, but the results are sensitive to numerical resolution and the exact subgrid model employed (Huang et al. 2019, 2020a). Simulations without these subgrid wind models (e.g. Hopkins et al. 2018; Kim & Ostriker 2015; Martizzi et al. 2016) allow winds to occur ‘naturally’, but these simulations may not resolve the scales necessary to resolve the important known physical processes (Scannapieco & Brüggen 2015; Brüggen & Scannapieco 2016; Schneider & Robertson 2017; McCourt et al. 2018; Huang et al. 2020b). Hence, modelling galactic winds accurately remains a theoretical challenge for even the most refined high-resolution simulations of galaxies (see Naab & Ostriker 2017, for a review). Even if one were able to accurately model the formation of galactic winds, the subsequent propagation in galactic haloes depends on a complicated interplay of many physical processes that occur on a wide range of physical scales that cannot be simultaneously resolved in a single simulation. For example, to robustly model the propagation and disintegration of moving clouds in various situations requires cloud-crushing simulations with at least sub-parsec scale resolution (Schneider & Robertson 2017; McCourt et al. 2018), which is orders of magnitudes below the resolution limits of cosmological simulations. Furthermore, most cosmological hydrodynamic simulations concentrate their resolution in the dense, star-forming regions of galaxies and thus have lower resolution in the circumgalactic medium (CGM, but see Hummels et al. 2019; Mandelker et al. 2019; Peeples et al. 2019; Suresh et al. 2019; van de Voort et al. 2019). To date, cosmological simulations do not include physically motivated subgrid models for galactic wind evolution, which are required to capture these small-scale physical processes.


Submillimetre galaxies (SMGs) are ultraluminous dusty star-forming galaxies (SFGs) with the vast majority of radiation energy in the far-infrared (FIR) and submillimetre bands (Smail, Ivison & Blain 1997; Barger et al. 1998; Hughes et al. 1998; Michałowski et al. 2012; Casey, Narayanan & Cooray 2014). They are extreme starbursts with high star formation rate (SFR) of $\sim 10^2\, -\, 10^3$ M⊙ yr−1 and high stellar mass of ∼1010–11 M⊙, located preferentially at z ∼ 2–3 (Chapman et al. 2005; Wardlow et al. 2011; Smolčić et al. 2012; Simpson et al. 2014; Brisbin et al. 2017; Danielson et al. 2017; Michałowski et al. 2017; Smith et al. 2017; Hodge & da Cunha 2020, and references therein). The physical properties of SMGs derived from detailed studies of individual sources and large sky area submillimetre surveys suggest that SMGs represent an early evolutionary phase of all local ellipticals (Smail et al. 2002; Swinbank et al. 2006; Fu et al. 2013; Toft et al. 2014; Ikarashi et al. 2015; Miettinen et al. 2017; An et al. 2019; Gullberg et al. 2019; Dudzevičiūtė et al. 2020; Rennehan et al. 2020). Although SMGs are a rare population (∼400 deg−2 down to S850 = 4 mJy; Simpson et al. 2019; Shim et al. 2020), they contribute a significant fraction (∼20 per cent) of the cosmic SFR density at z > 2 (Bourne et al. 2017; Koprowski et al. 2017; Zavala et al. 2021). Their extreme SFRs are correlated with higher gas fractions compared to normal SFGs at the same epoch (Bothwell et al. 2013; Scoville et al. 2016; Decarli et al. 2016; Tacconi et al. 2018). The large amount gas is thought to be supplied by gas infall via cold streams from surrounding gas reservoirs (Narayanan et al. 2015; Ginolfi et al. 2017). The extreme starbursts of this population are partially triggered by galaxy major mergers (Tacconi et al. 2008; Engel et al. 2010, but see Davé et al. 2010; Narayanan et al. 2015; McAlpine et al. 2019), while a diversity of morphologies unveiled from the rest-frame ultraviolet (UV) and optical imaging indicate galaxy interactions and disc instabilities to be important mechanisms for enhancing star formation in SMGs (Swinbank et al. 2010; Kartaltepe et al. 2012; Chen et al. 2015), as well as AGN activities (Chapman et al. 2005; Wang et al. 2013). Because the rarity and high SFR of SMGs are sensitive to the physical processes governing galaxy formation (e.g. star formation, stellar and AGN feedback, gas infall, metal enrichment, and galaxy merging/interactions), the SMG population is used to constrain cosmological models. It remains challenging to reproduce the SMG population with high SFRs matching observations at high z (Davé et al. 2010; McAlpine et al. 2019; Hayward et al. 2021; Lovell et al. 2021).


NLFFF extrapolation provides the reconstructed coronal magnetic field for AR 11158 from 2011 February 13 − 2011 February 15 (Figures 1(d)–(f)). The field lines (yellow lines) within the core of the AR have arcade-like structure with a relatively strong twist mainly near the PIL. These figures show that the magnetic field evolved during this period. Although we did not quantitatively compare the field lines with the observation, in general, the reconstructed coronal field morphologies match with the observations in Figures 1(a)–(c). The general morphologies and the locations of the high-twist fields are also in agreement with many previous studies (Jing et al. 2012; Sun et al. 2012; Dalmasse et al. 2013; Inoue et al. 2013, 2014a; Liu et al. 2013; Wang et al. 2013; Aschwanden et al. 2014; Malanushenko et al. 2014; Zhao et al. 2014). Unlike Zhao et al. (2014) who could identify the twisted flux rope from the topology of the reconstructed coronal field, we could not find an obvious topological signature of a flux rope existing in our NLFFF during our analysis time window. It might be due to the fact that there was little magnetic flux with twist higher than one turn in our NLFFF and it is difficult to topologically define it as a flux rope. However, our result is consistent with other NLFFF results (Jing et al. 2012; Sun et al. 2012; Liu et al. 2013; Wang et al. 2013; Inoue et al. 2014a; Malanushenko et al. 2014). The high-twist region in our result is also in agreement with the region with high helicity flux (Dalmasse et al. 2013) and the location of the flare ribbons (Bamba et al. 2013; Liu et al. 2013), as well as the high current density region (Janvier et al. 2014). Figures 1(g)–(i) show the evolution of the twist distribution map, with the magnetic twist of the field lines plotted at the footpoints of field lines according to a color scale. This shows that the high-twist (strongly right-handed twist corresponding to Tw > 0.5) areas are concentrated in only a limited part of the AR. The high-twist area grew and became even more twisted just before the X2.2 flare (Figure 1(i)). Most parts of the AR have twist values less than 0.25, but near the PIL the twist can reach more than 0.5, even up to about a full turn. This is consistent with the results of Sun et al. (2012) and Inoue et al. (2014a). A high-twist (strong negative/left-handed twist) area also developed in the eastern part of the AR, which did not exist initially on February 13. Both of these high-twist areas produced several flares. However, here we focus on the flares that resulted from the high-twist core region near the center of the AR, where the M6.6 and X2.2 flares occurred.


This analysis searches for a GW signal compatible with the inspiral of a BNS or NSBH binary—collectively NS binaries—within 6 s of data associated with an observed short GRB. This stretch of data is the on-source window and runs from −5 s to +1 s around the start of the GRB emission (i.e., the GRB trigger time). The surrounding ∼30–90 minutes of data are split into 6 s off-source trials which are also analyzed in order to build a background. Around 30 minutes allows the modeled search to accurately estimate the power spectral density of the available instruments and ensures that it can assess at sub-percent level accuracy the significance of any candidate events found in the on-source window. All the data are processed using PyGRB (Harry & Fairhurst 2011; Williamson et al. 2014), a coherent matched filtering pipeline that is part of the general open-source software PyCBC (Nitz et al. 2020) and has core elements in the LALSuite software library (LIGO Scientific Collaboration 2018). We scan each trial of data and the on-source window in the 30–1000 Hz frequency band using a predefined bank of waveform templates (Owen & Sathyaprakash 1999) created with a hybrid geometric–stochastic method (Capano et al. 2016; Dal Canton & Harry 2017) and using a phenomenological inspiral-merger-ringdown waveform model for non-precessing point-particle binaries (IMRPhenomD; Husa et al. 2016; Khan et al. 2016).210

210
All waveforms mentioned in this section are generated with the LALSimulation package that is part of the LALSuite software library (LIGO Scientific Collaboration 2018).
 The waveform template bank includes waveforms corresponding to a range of masses ([1.0, 2.8]M for NSs, [1.0, 25.0]M for BHs) and dimensionless spin magnitudes ([0, 0.05] for NSs, [0, 0.998] for BHs) for aligned-spin, zero-eccentricity BNS or NSBH systems that may produce an electromagnetic counterpart via the tidal disruption of the NS (Pannarale & Ohme 2014). Aside from the updated sensitivity of our detectors, the only difference with respect to the second LIGO–Virgo observing run (Abbott et al. 2019b) is that the generation of the bank has been updated to apply more accurate physics to determine whether an NSBH system could produce an accretion disk from this disruption (Foucart et al. 2018). We only search for circularly polarized GWs, which may be emitted by binaries with inclinations of 0° or 180°: such systems have GW amplitudes that are consistent (Williamson et al. 2014) with those of binary progenitors with inclination angles over the full range of viewing angles that we expect for typical brightness GRBs (≲30°; Fong et al. 2015), such as those in our sample.


Figure 1 shows the NGC 419 CMD after field-star decontamination. The cluster has an eMSTO at 20 ≤ V ≤ 22 mag. We adopted the Padova stellar evolution models (PARSEC CMD 2.7, v. 1.2S; Bressan et al. 2012),8

8

http://stev.oapd.inaf.it/cgi-bin/cmd_2.7

 for Z = 0.004 (Glatt et al. 2008; Girardi et al. 2009), and fitted the eMSTO extremes with isochrones of log(t yr−1) = 9.12 (1.32 Gyr; blue line) and log(t yr−1) = 9.31 (2.02 Gyr; red line), adopting a distance modulus (m − M)0 = 18.90 mag and a visual extinction AV = 0.181 mag (Rubele et al. 2010). The maximum possible age spread implied by the extent of the eMSTO is ∼700 Myr, similar to the results of Rubele et al. (2010; ∼700 Myr) and Girardi et al. (2013; ∼670 Myr). However, the cluster exhibits an SGB that is broad on the blue side and that becomes significantly narrower on the red side. Previous studies of intermediate-age star clusters with eMSTOs usually showed tight SGBs throughout (Mackey & Broby Nielsen 2007; Li et al. 2014b; Bastian & Niederhofer 2015; but see Goudfrooij et al. 2015). This feature is, however, already apparent in the NGC 419 data before field-star decontamination and is, hence, not caused by our data reduction. In addition, the significance level of our field-star decontamination is very high along the SGB, while the good agreement between our iraf/daophot and dolphot stellar catalogs further confirms the reality of the SGB morphology. Examination of the SGB stars’ spatial distribution reveals that blending is unlikely responsible for the observed narrowing either. The NGC 419 CMD of Goudfrooij et al. (2014) shows a similar trend, although that of Glatt et al. (2008) resembles an SSP more closely. The latter CMD is, however, composed of HST ACS/High Resolution Channel observations covering a small stellar sample located in the cluster’s central region only. Our data are consistent with the Glatt et al. (2008) CMD for stars drawn from inside the cluster’s core radius. We thus conclude that the observed narrowing of the NGC 419 SGB is real and not caused by artifacts associated with our data reduction (see the Appendix).


Some studies have used the 2.5D mean-field dynamo approach to do so, extending solar mean-field dynamo models to other stellar spectral types (Chabrier & Küker 2006; Jouve et al. 2010; Küker et al. 2011; Kitchatinov et al. 2018, and references therein). While these studies are very helpful, most of them lack the full nonlinearity and genuine parametric dependence of 3D magnetohydrodynamic (MHD) simulations. Recent developments by Pipin (2021) are starting to overcome these limits and have extended the work of Rempel (2006) on the Sun to solar-type stars with various rotation rates. Nevertheless, with the arrival of more powerful supercomputers, other authors have used instead global 3D MHD simulations to model DR and stellar magnetism in the convection zone of solar-like stars (Glatzmaier & Gilman 1982; Miesch et al. 2000, 2006; Brun et al. 2004, 2011; Brown et al. 2008, 2010; Ghizaru et al. 2010; Käpylä et al. 2011, 2014; Gastine et al. 2014; Augustson et al. 2015; Karak et al. 2015). These studies pointed out the large magnetic temporal variability and the critical effect of stellar rotation and mass on magnetic field generation through dynamo mechanism, leading in some parameter regimes to configurations with cyclic activity (Gilman & Miller 1981; Gilman 1983; Glatzmaier 1985a; Brown et al. 2011; Racine et al. 2011; Augustson et al. 2013, 2015; Käpylä et al. 2013; Nelson et al. 2013; Beaudoin et al. 2016; Guerrero et al. 2016, 2019; Strugarek et al. 2017, 2018; Viviani et al. 2018, 2019; Warnecke 2018; Matilsky & Toomre 2020). Several studies pointed out the positive effect of a stable region underneath the convection zone (Parker 1993) on the efficient storage of intense toroidal field and the lengthening of the stellar dynamo cycle period (Glatzmaier 1985b; Browning et al. 2006; Lawson et al. 2015; Beaudoin et al. 2016; Guerrero et al. 2016, 2019; Käpylä et al. 2019; Bice & Toomre 2020). Over the last decade, significant progress has been made in successfully simulating large-scale mean flows and stellar activity cycle using different numerical codes and methods (Jones et al. 2011). This is quite reassuring that a global consensus is growing on the nature of solar-like star dynamos. It is common knowledge that there are still key transitions in Rossby number (at low and high values of this parameter) that need to be understood further, as well as what is the exact type of convective dynamos realized in solar-like stars as their global parameters are varied. This study continues this effort by doing an even broader systematic parametric study of solar-like star dynamos coupled to a stably stratified layer below than what have been published so far. It extends the work published in Varela et al. (2016) and Brun et al. (2017) with the MHD anelastic spherical harmonic code (ASH) (Brun et al. 2004). In particular, we wish to better characterize energy transfers and how much of a star’s energy (luminosity) is converted into magnetic energy by nonlinear global convective dynamos over a wide range of Rossby numbers, generalizing to solar-like stars the work by Starr & Gilman (1966) and Rempel (2006).


At each heliocentric distance rh, the activity model (Fulle et al. 2020b) is defined by five analytical equations fixing (i) the gas pressure P(s) depending on the depth s from the nucleus surface (Fig. 1 for the CO2 case), (ii) the gas flux Q from the nucleus surface, (iii) the temperature gradient ∇T at depths of a few cm, (iv) the heat conductivity λs at depths of a few cm below the nucleus surface, and (v) the temperature Ts of the nucleus surface
(3)$$\begin{eqnarray*}
P(s) = P_0 ~f(s) ~\exp \left[{- {T_0 \over {T_s - s ~\nabla T}}}\right]
\end{eqnarray*}$$(4)$$\begin{eqnarray*}
Q = {{14 ~r ~P(R)} \over {3 ~R}} \sqrt{{2 ~m} \over {\pi k_B ~(T_s - R ~\nabla T)}}
\end{eqnarray*}$$(5)$$\begin{eqnarray*}
\nabla T = {\sqrt{\Lambda ~Q ~/ ~\sigma _B} \over {8 ~(T_s - R ~\nabla T) ~R}}
\end{eqnarray*}$$(6)$$\begin{eqnarray*}
\lambda _s = {32 \over 3} ~(T_s - R ~\nabla T)^3 ~\sigma _B ~R
\end{eqnarray*}$$(7)$$\begin{eqnarray*}
(1 - A) ~I_\odot ~\cos \theta ~r_h^{-2} = \epsilon \sigma _B T_s^4 + \lambda _s ~\nabla T + \Lambda ~Q
,
\end{eqnarray*}$$where P0, T0, and Λ values are listed in Table 1, s is the depth from the nucleus surface, $f(s) = 1 - (1 - {s \over R})^4$ for s ≤ R, f(s) = 1 elsewhere, r ≈ 50 nm and R ≈ 5 mm are the radii of the grains of which cometary dust consists (Levasseur-Regourd et al. 2018; Güttler et al. 2019; Mannel et al. 2019) and of the pebbles of which cometary nuclei consist (Blum et al. 2017; Fulle et al. 2020b), m is the mass of the gas molecule, kB is the Boltzmann constant, σB is the Stefan–Boltzmann constant, A is the nucleus Bond albedo (e.g. A = 1.2 per cent measured at 67P; Fornasier et al. 2015), I⊙ is the solar flux at the heliocentric distance of Earth, θ is the solar zenithal angle, and ϵ ≈ 0.9 is the nucleus emissivity. Since the gas originates from the superficial pebbles and is assumed to share the temperature Ts − s ∇T of refractories and ices, the thermal diffusion due to gas convection is negligible with respect to the sublimation sink Λ Q. A nucleus is active if the gas pressure overcomes the tensile strength S bonding dust particles to the nucleus surface (Skorov & Blum 2012), thus defining the activity onset for each ice (Table 2), occurring (i) at rh = 85 au for carbon monoxide (Fulle et al. 2020a); (ii) at rh = 60 au for molecular oxygen; (iii) at rh = 52 au for methane; (iv) at rh = 18 au for ethane; (v) at rh = 13 au for carbon dioxide (dotted line in Fig. 1); and (vi) at rh = 3.8 au for water (Fulle et al. 2020b; Ciarniello et al. 2021). The value R ≈ 5 mm has been constrained by several data collected at comet 67P, by laboratory experiments of dust accretion in conditions expected to occur in the solar protoplanetary disc and by observations of other protoplanetary discs (Blum et al. 2017). Other R-values would not provide the best fit of the 67P water-loss time-evolution (Ciarniello et al. 2021).


MRI is considered to be the most promising mechanism driving angular-momentum transport in protoplanetary disks (Balbus & Hawley 1991; Brandenburg et al. 1995; Hawley et al. 1995; Balbus et al. 1996; Balbus & Hawley 1998). However, protoplanetary disks are cold, dense, and, therefore, poorly ionized. The low level of ionization tends to decouple the disk gas from magnetic fields, which generates non-ideal MHD effects: Ohmic dissipation, ambipolar diffusion (AD), and the Hall effect (e.g., Armitage 2011; Turner et al. 2014). These effects quench MRI in different ways: Ohmic dissipation originates from collisions between electrons and neutrals, AD from collisions between ions and neutrals, and the Hall effect from drift between electrons and ions (Fleming et al. 2000; Sano & Stone 2002; Bai & Stone 2011). Ohmic dissipation operates in high-density regions with weak field, AD dominates in highly ionized and low-density regions, and the Hall effect lies in between (Fleming & Stone 2003; Bai & Stone 2011; Bai 2014). So far, the effect of Ohmic dissipation has been best studied. Investigations show the layered accretion in the inner disk, where the midplane region is “dead” due to low ionization while the surface layer is “active” due to sufficient ionization (Gammie 1996; Jin 1996; Fleming et al. 2000; Fleming & Stone 2003; Turner et al. 2007; Ilgner & Nelson 2008; Oishi & Mac Low 2009; Okuzumi & Hirose 2011). Recent works that take into account both Ohmic dissipation and AD show that AD may render the surface layer and portions of the outer disk inactive (Bai & Stone 2011; Landry et al. 2013; Kalyaan et al. 2015). Bai & Stone (2013) find that MRI is completely suppressed in the inner disk and a strong magnetocentrifugal wind is launched. Three-dimensional simulations that include all three non-ideal MHD effects are also performed (Bai 2014, 2015; Lesur et al. 2014; Simon et al. 2015). In the inner disk, the influence of the Hall effect on midplane angular-momentum transport depends on the orientation of the vertical magnetic field with the disk rotation axis. When the field is aligned with the axis, the enhanced Maxwell stress promotes angular-momentum transport. When the field is anti-aligned with the axis, the midplane remains quiescent. In the outer disk, the Hall effect has little influence on the disk turbulence. Although the inclusion of AD and the Hall effect substantially changes the level of turbulence in the protoplanetary disks, the feature that the viscosity is low in the inner disk and high in the outer disk is still valid. In this study, we assume that gas giant planets form in situ via the core accretion scenario, which implies that their formation locations are always in the low-viscosity region. Since in this study we focus on the relation between photoevaporation and planet formation and gap opening by planets in the disk, we adopt Ohmic dissipation to represent the non-ideal MHD effects on the MRI. We consider that this simplification has little influence on our main calculation results.


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).


After the disruption phase, the star is tidally stretched into a very long thin stream and the evolution of the stream structure in the transverse and longitudinal directions are decoupled (Kochanek 1994). Thus, the system enters the free-fall phase where each stream segment follows its own geodesic like a test particle (Coughlin et al. 2016). Then, after passing the apocentres of the highly eccentric orbits, the bound debris falls back towards the BH at a rate given by the distribution of specific energy (Evans & Kochanek 1989; Phinney 1989). Due to relativistic apsidal precession, the bound debris, after passing the pericentre, collides violently with the still in-falling stream (see Fig. 1). It has been shown that shocks at the self-intersection point is the main cause of orbital energy dissipation and the subsequent formation of an accretion disc (Rees 1988; Kochanek 1994; Hayasaki, Stone & Loeb 2013; Guillochon, Manukian & Ramirez-Ruiz 2014; Shiokawa et al. 2015; Bonnerot et al. 2016). However, the aftermath of the self-intersection is an extremely complex problem, which depends on the interplay among magnetohydrodynamics, radiation, and general relativity in 3D. No numerical simulations to date have been able to provide a deterministic model for TDEs with realistic star-to-BH mass ratio and high eccentricity (see Stone et al. 2018a, for a review). Many simulations consider either an intermediate-mass BH (e.g. Guillochon et al. 2014, Evans, Laguna & Eracleous 2015; Shiokawa et al. 2015; Sa̧dowski et al. 2016) or the disruption of a low-eccentricity (initially bound) star (e.g. Bonnerot et al. 2016; Hayasaki, Stone & Loeb 2016). It is unclear how to extrapolate the simulation results to realistic configurations and provide an answer to the following questions: How long does it take for the bound gas to form a circular accretion disc (if at all)? How much radiative energy is released from the system? What fraction of the radiation is emitted in the optical, UV, or X-ray bands?


Our approach shares its transdimensional nature with that of Brewer et al. (2015), which implemented an independent transdimensional framework to infer substructure in strong lens systems. However, in addition to differences concerning substructure modeling and the sampling method used, our code and analysis were developed independently of theirs, and hence provide an important cross-check of the method and results. It has become customary in cosmological analyses to have at least two publicly available independent codes to check for numerical accuracy and find bugs. While both codes are public, we understand that this approach is not yet ubiquitous in the field of galaxy-scale strong lensing (for instance, it has been difficult thus far to reproduce/check the results of Vegetti et al. 2014 and Hezaveh et al. 2016), but we hope that our work can help make substructure lensing more reproducible. Given the uniqueness of the constraints it can provide on low-mass substructures and the impact that these detections can have on dark matter physics, we believe it is extremely important to have multiple cross-checks to validate any results. On a more technical level, our approach differs from that of Brewer et al. (2015) in two major ways:

1.
Subhalo lens modeling. We represent subhalos with NFW profiles with a certain mass, scale, and cutoff radius, whereas Brewer et al. (2015) uses so-called blobs, i.e., deflection as a power law in the subhalo-centric radius. We think that choosing a physically motivated basis function set to represent the deflection field due to subhalos is essential for correctly marginalizing them out, i.e., propagating their (rather large) uncertainties to the parameter of interests such as the subhalo mass function.

2.
The sampling method and the sampler used to sample from the posterior probability distribution of the (different) lens models given the data. Brewer et al. (2015) uses Diffusive Nested Sampling (DNS) as implemented in RJObject. We use a homebrew reversible-jump MCMC sampler with Metropolis-type within-model proposals.


Figure 1 shows that in the regions where activity was detected visually, i.e., Hapi, Seth, and Ma’at pits have lower (8–13%/100 nm) spectral slopes than the rest of the comet surface (13–22%/100 nm). In addition to those places, Seth alcoves, the wall of the large Anuket alcove, around the circular features, both clustered and isolated bright features (see Thomas et al. 2015b; Auger et al. 2015; Pommerol et al. 2015b, for definitions) show similar lower spectral slopes than the rest of the surface, even though there was no visual detection of activity features rising from them at the time of the observations used in this study4. This may be because the observing geometry was not suited for their detections during the observations. In the regions we investigated, the Hapi region displays the lowest spectral slopes 8–11%/100 nm (see also Fornasier et al. 2015) together with the isolated bright features (IBFs) and the clustered bright features in the Imhotep region. The locations of the bright features on the Imhotep image (image #4) are shown in Fig. B.4. According to the spectral slope values, the IBFs of Imhotep seem to be more similar to the Hapi region than the active pits of Seth and Ma’at regions. Active pits, alcoves, and the large alcove of Anuket have slope values of typically 10–13%/100 nm. The Ma’at region, which is located on the smaller lobe (head) of the comet, displays higher spectral slope values than the Seth region, which is located on the larger (body) lobe of the comet. In the investigated regions, the highest slope values are detected in the Imhotep region (see Fig. 1d). Here it should be mentioned that the comparison of spectral slopes is performed under the assumption of no spectral reddening between the phase angles of the images we investigated, although the spectral slopes show reddening by phase as presented in Fornasier et al. (2015). Unfortunately, the previous work does not cover all the phase angles of the images we investigated, but the spectral slope variation between 35–54° (Fig. 3 of  Fornasier et al. 2015) is small so that we can make this comparison. However, if we follow the linear trend of the phase reddening, for the image taken in 70.45° phase angle (image #4), the spectral slopes would vary from 15%/100 nm to 18%/100 nm in the observations we used.


Complementary to studies using the integrated emission and angular power spectrum of DM annihilation from a population of Galactic subhalos, in this paper we present a novel strategy using one-point photon statistics to search for the annihilation signature. Our technique takes advantage of the information in the entire population of sources, including both those that are resolved and those that are faint and unresolved. The concept of leveraging the one-point photon-count distribution to search for DM has previously been studied in Dodelson et al. (2009) and Feyereisen et al. (2015) in the context of emission from extragalactic sources and in Lee et al. (2009) and Koushiappas et al. (2010) with application to Galactic subhalos. We introduce a method to search for signatures of DM annihilation from a Galactic subhalo population using the non-Poissonian template fitting (NPTF) framework (Malyshev & Hogg 2011; Lee et al. 2015, 2016; Mishra-Sharma et al. 2017), which has previously been applied to characterize unresolved point sources in the inner Galaxy (Lee et al. 2016; Linden et al. 2016; Leane & Slatyer 2019, 2020a, 2020b; Chang et al. 2020; Buschmann et al. 2020) and at high latitudes (Zechlin et al. 2016; Lisanti et al. 2016; Zechlin et al. 2018). Using simulations, we show that the NPTF can constrain DM annihilation from a population of subhalos in the face of astrophysical background emission. We find that using photon statistics to look for collective emission from a subhalo population can be especially promising when a large number of individual subhalo candidates are identified in point-source catalogs. This establishes a method complementary to the established ones based on characterizing individual resolved point sources as subhalo candidates, as well as those based on using the measured 0-point (overall flux) and two-point (angular power spectrum) statistics to characterize a subhalo population. Moreover, note that our methodology is completely independent of assumptions about, e.g., the location of stellar overdensities, so we are less sensitive to certain uncertainties which can bias dwarf galaxy constraints such as those in modeling tracer populations. Thus, this framework provides an important comparison for the dwarf galaxy analyses as well.


Our model consists of four zones; an inner disk (zone 1, as in Matter et al. 2016), and three zones into which the outer disk is divided (zones 2–4) in order to produce the azimuthal asymmetries seen in our SPHERE observations. The radial extent of these zones were constrained from our images: zone 2 corresponds to the component inside ~14 au observed in the noncoronagraphic J-band image, zone 3 corresponds to the bright ring at 16 au, and zone 4 corresponds to the asymmetrical outer disk. The radial extent of each of these zones, as well as their disk masses, is summarized in Table 2. No gaps were introduced between the three outer disk zones, but the gap between zones 1 and 2 from the Matter et al. (2016) model was kept. We note that these radii are only loosely constrained from our data, and are determined by eye from both the coronographic and noncoronographic data. We ran a grid of models with different inclinations and position angles for zones 1–2 (note that we systematically use the same inclination and position angle for these two zones) and for zone 3 – that is, a total offour free parameters, keeping in mind that the relative inclination between components must be small to allow a single broad shadow to be cast (as opposed to two narrow shadow lanes). The inclination and position angle of zone 4 is set to the values provided in Sect. 3. The grid was sampled in steps of 1° for inclination, and 2° for PA, and later refined to 0.5° steps for inclination and 0.5° for PA after a good initial agreement is found between the average azimuthal profile of the model and the scattered light images. The best fitting model was picked not only based on the location of the shadows cast by the inner components on the outer disk, but also on the shape (slope) of the resulting azimuthal profile of the outer disk. There is also a degeneracy if we consider that the inclinations and PAs of the two inner components (zones 1–2 and zone 3) can be exchanged and produce very similar results. However, doing this would cast a shadow in a different location, and thus produce a different azimuthal profile for zone 3.


Several predictions for planet(s) shaping the disk of SAO 206462 have been proposed (Muto et al. 2012; Garufi et al. 2013; Fung & Dong 2015; Bae et al. 2016; van der Marel et al. 2016a. Using linear equations from the spiral density wave theory, Muto et al. (2012) suggested two planets with separations beyond ~50 au by fitting independently the two spiral arms seen in Subaru/HiCIAO data and with masses of ~0.5 MJ by using the amplitude of the spiral wave. Garufi et al. (2013) proposed that one planet of mass 5–13 MJ located inside the cavity at a separation of 17.5–20 au could be responsible for the different cavity sizes measured for the small and large dust grains. Fung & Dong (2015) presented scaling relations between the azimuthal separation of the primary and secondary arms and the planet-to-star mass ratio for a single companion on a circular orbit with a mass between Neptune mass and 16 MJ around a 1 M⊙ star. They predicted with 30% accuracy that a single putative planet responsible for both spiral features of SAO 206462 would have a mass of ~6 MJ. Bae et al. (2016) presented dedicated hydrodynamical simulations of the SAO 206462 disk and proposed that both the bright scattered-light feature (Garufi et al. 2013) and the dust emission peak (Pérez et al. 2014) seen for the southwestern spiral arm result from the interaction of the spiral arm with a vortex, although a vortex alone can account for the S1 brightness peak. They suggested that a 10–15 MJ planet may orbit at 100–120 au from the star. However, ALMA observations at two different frequencies seem to contradict a dust particle trapping scenario by a vortex (Pinilla et al. 2015). Stolker et al. (2016) performed new fitting of the spiral arms observed in SPHERE data and found a best-fit solution with two protoplanets located exterior to the spirals: r1 ~ 168 au, θ1 ~ 52° and r2 ~ 99 au, θ2 ~ 355°. van der Marel et al. (2016a) proposed that the features seen in thermal emission in ALMA data and the scattered-light spiral arms are produced by a single massive giant planet located inside the cavity at a separation of ~30 au. Recently, Dong & Fung (2017) used the contrast of the spiral arms to predict a giant planet of ~5–10 MJ at ~100 au.


The question of the evolution of exoplanet systems after the main sequence of their host is generally addressed by studying exoplanets around subgiants, RGB stars, and normal HB (RC) stars (hereafter the ’classical’ evolved stars). These classical evolved stars are typically very large stars, with radii ranging from ~ 5− 10 R⊙ to more than 1000 R⊙. This is much larger than hot subdwarfs, which have radii in the range ~ 0.1−0.3 R⊙ (Heber 2016). Their mass is typically higher than ~ 1.5 M⊙, compared to~0.47 M⊙ for hot subdwarfs. The transit and radial velocity (RV) methods are both challenging for these classical evolved stars because the transit depth is diluted and there are additional noise sources (Van Eylen et al. 2016). Another difficulty forthe question of the fate of exoplanet systems after the RGB phase itself is the difficulty of distinguishing RGB and RC stars based on their spectroscopic parameters alone, which is sometimes hard even with help of asteroseismology (Campante et al. 2019). As a consequence, only large or massive planets are detected around the classical evolved stars (Jones et al. 2021, and references therein). A dearth of close-in giant planets is observed around these evolved stars compared to solar-type main-sequence stars (Sato et al. 2008; Döllinger et al. 2009). This may be caused by planet engulfment by the host star, but current technologies do not allow us to determine whether smaller planets and remnants (such as the dense cores of former giant planets) are present. The lack of close-in giant planets may also be explained by the intrinsically different planetary formation for these intermediate-mass stars (see the discussion in Jones et al. 2021). Ultimately, the very existence of planet remnants may be linked to the ejection of most of the envelope on the RGB that occurs for hot subdwarfs, while for classical evolved stars, nothing stops the in-spiraling planet inside the host star, and in all cases, the planet finally merges with the star, is fully tidally disrupted, or is totally ablated by heating or by the strong stellar wind. In other words, the ejection of the envelope not only enables the detection of small objects as remnants, but most importantly, it may even be the reason for the existence of these remnants by stopping the spiraling-in in the host star.


Kepler transit observations have shown that planets with sizes between those of Earth (1 R
⊕) and Neptune (∼4 R
⊕) are extremely common (Lissauer et al. 2011; Batalha et al. 2013; Fressin et al. 2013; Howard 2013; Fabrycky et al. 2014; Marcy et al. 2014). Demographics analysis suggests that at least 30%–55% of the Sun-like stars host one or more planets within this size range and with orbital periods shorter than 100 days (Mayor et al. 2011; Howard et al. 2012; Fressin et al. 2013; Petigura et al. 2013; Mulders 2018; Mulders et al. 2018; Zhu et al. 2018; He et al. 2019, 2021). Uncertainties in stellar radius estimates from photometric Kepler observations prevented a detailed assessment of the intrinsic planet size distribution (Fulton et al. 2017; Petigura et al. 2017). Specific trends in planet sizes only started to emerge from the data with more precise determination of stellar radii by follow-up surveys (California Kepler Survey, CKS) and the use of Gaia improved parallaxes (Johnson et al. 2017; Van Eylen et al. 2018; Petigura et al. 2022). These studies showed that the size frequency distribution of planets between ∼1 and ∼4R
⊕ is bimodal with peaks at ∼1.4 R
⊕ and ∼2.4 R
⊕, and a valley at ∼1.8 R
⊕ (Fulton et al. 2017; Fulton & Petigura 2018; Petigura 2020). The best-characterized planets with sizes of about ∼1.4 R
⊕ are consistent with rocky composition, as constrained by their estimated bulk densities (Fortney et al. 2007; Adams et al. 2008; Lopez & Fortney 2014; Weiss & Marcy 2014; Dorn et al. 2015; Wolfgang et al. 2016; Zeng et al. 2016, 2019; Bashi et al. 2017; Chen & Kipping 2017; Otegi et al. 2020). These planets are usually referred to as “super-Earths.” Planets with sizes of about ∼2.4R
⊕ are consistent with the presence of volatiles—which could reflect either rocky cores with H-He-rich atmospheres or ice/water-rich planets (Kuchner 2003; Rogers & Seager 2010; Lopez & Fortney 2014; Zeng et al. 2019; Mousis et al. 2020; Otegi et al. 2020). These planets are commonly referred to as “mini-Neptunes.” For a detailed discussion, see reviews by Bean et al. (2021) and Weiss et al. (2022), and references therein.


The energy in the inner crust is largely influenced by the properties of the neutron gas and, therefore, the EoS of neutron matter of the different calculations plays an essential role. The NV calculation (Negele & Vautherin 1973) is based on a local energy density functional that closely reproduces the Siemens-Pandharipande EoS of neutron matter (Siemens & Pandharipande 1971) in the low-density regime. The Moskow calculation (Baldo et al. 2007) employs a semi-microscopic energy density functional obtained by combining the phenomenological functional of Fayans et al. (2000) inside the nuclear cluster with a microscopic part calculated in the Brueckner theory with the Argonne v18 potential (Wiringa et al. 1995) to describe the neutron environment in the low-density regime (Baldo et al. 2004). The BBP calculation (Baym et al. 1971a,b) gives the EoS based on the Brueckner calculations for pure neutron matter of Siemens (Siemens & Pandharipande 1971). The LS-Ska (Lattimer & Swesty 1991; Lattimer 2015) and DH-SLy4 (Douchin & Haensel 2001) EoSs were constructed using the Skyrme effective nuclear forces Ska and SLy4, respectively. The SLy4 Skyrme force (Chabanat et al. 1998) was parametrized, among other constraints, to be consistent with the microscopic variational calculation of neutron matter of Wiringa et al. (1988) above the nuclear saturation density. The Shen-TM1 EoS (Shen et al. 1998b,a; Sumiyoshi 2015) was computed using the relativistic mean field parameter set TM1 for the nuclear interaction. The calculations of LS (Lattimer & Swesty 1991; Lattimer 2015) and Shen et al. (Shen et al. 1998b,a; Sumiyoshi 2015) are the two EoS tables in more widespread use for astrophysical simulations. The BSk21 EoS (Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) is based on a Skyrme force with the parameters accurately fitted to the known nuclear masses and constrained, among various physical conditions, to the neutron matter EoS derived within modern many-body approaches which include the contribution of three-body forces.


Tidal heating of Io has been shown to be responsible for its widespread volcanism. The tidal heating rate of Jupiter’s tidally locked moon,

, driven by forced eccentricities, e, locked by Europa and Ganymede’s Laplace resonance with Io, is the dominant interior heating source. Similarly, the tidal heating of an exomoon will likely dominate the interior energy budget due to the additional stellar tide. Consequently, the tidal heating rate is orders of magnitude higher than at Io, which for an exo-Io of similar rheological properties (

, Rs = RIo, ρs = ρIo) can be written as (Cassidy et al. 2009; Equations (19) and (20))
3

where υ = 3 × 10−7 cm3 erg−1, and τs = τp/5 based on the tidal stability criterion discussed in Section 2. For utility, we describe the exo-Io’s tidal efficiency as

, which can readily be computed for any three-body system as tabulated in Table 4. The enhanced tidal heating described in Equation (3) will also contribute to the surface temperature T0 = Teq + ΔT0, which is very roughly approximated as
4

where σsb is the Stefan–Boltzmann constant and Teq. At Io, the total neutral volcanic content (SO2, SO, NaCl, KCl, Cl, and dissociation products) ejected to space (Section 4.2.1) by the incident plasma is estimated to be, on average, ∼1000 kg s−1 (e.g., Thomas et al. 2004), varying within an order of magnitude over decades of observations (Burger et al. 2001; Wilson et al. 2002; Thomas et al. 2004). While the source of the dominant gas SO2 is ultimately tidally driven volcanism, the near-surface atmosphere is mostly dominated by the sublimation of SO2 frost (Tsang et al. 2016). By observing the atmospheric evolution of the SO2 column density with heliocentric distance, Tsang et al. (2013) estimated the direct volcanic component to be Nvolc ∼ 6.5 × 1016 cm−2, typically

 of the total observed SO2 column density. Ingersoll (1989) demonstrated the relative contributions due to both sublimation and volcanic sources in maintaining Io’s atmosphere and established a relationship relating the volcanic source rate to the volcanically supplied atmospheric pressure:
5

This expression also gives the volcanic column density

, where g is the acceleration due to gravity. Adopting an observed atmospheric temperature of Tatm = 170 K by Lellouch et al. (2015) corresponding to an atmospheric scale height of H = 12 km, a thermal velocity

 equal to 150 m s−1, and a sticking coefficient α = 0.5 for the SO2 mass of 64 amu yields a volcanic source rate of

 ∼ 6.9 × 106 kg s−1 of SO2 integrated over Io’s mass MIo. The average volumetric mixing ratio for NaCl to SO2 at Io is observed to be XNaCl ∼ 3 × 10−3 (Lellouch et al. 2003). This leads to a source rate of

 ∼ 7.4 × 103 kg s−1 of NaCl, somewhat larger than but reasonably consistent with the direct measurement of the NaCl volcanic source rate of (0.8–3.1) × 103 kg s−1 (Lellouch et al. 2003). From these estimates, we will adopt ∼3 × 103 kg s−1 of Na i as the volcanic source rate for Io.


In recent years, the Atacama Large Millimeter/submillimeter Array (ALMA) has carried out comprehensive surveys of the [C II] 158 μm fine structure line in high-z quasars. For example, Decarli et al. (2018) detected [C II] in 85% of 27 optically selected quasars at z > 5.94. This line is an important coolant that traces the ionized and neutral interstellar medium (ISM) and star-forming activities (Herrera-Camus et al. 2015). The detection of [C II] line and dust continuum emission has revealed a wide range of star formation rates, from a few 10 M⊙ yr−1 to ≥1000 M⊙ yr−1 (Decarli et al. 2018; Izumi et al. 2018). The [C II]–FIR luminosity ratios of these quasar hosts range from 10−4 to a few ×10−3 (Maiolino et al. 2005; Wang et al. 2013; Willott et al. 2017; Decarli et al. 2018), following the trend of decreasing [C II]–FIR ratio with increasing FIR luminosities found with the IR luminous star-forming systems (Malhotra et al. 2001; Luhman et al. 2003; Hailey-Dunsheath et al. 2010; Stacey et al. 2010; Graciá-Carpio et al. 2011; Díaz-Santos et al. 2013, 2017; Muñoz & Oh 2016; Smith et al. 2017; Decarli et al. 2018; Gullberg et al. 2018; Rybak et al. 2019). In particular, the quasar hosts with high FIR luminosities of a few 1012 to 1013 L⊙ show low [C II]–FIR ratios similar to that found in the ultraluminous infrared galaxies (ULIRGs) and submillimeter galaxies (SMGs; Luhman et al. 2003; Díaz-Santos et al. 2013, 2017; Wang et al. 2013; Rybak et al. 2019). The [C II]–FIR ratio is suggested to be related to the local conditions of the ISM; e.g., a decrease of [C II]–FIR ratio could be due to a high gas temperature (i.e., T > ΔE/k ∼ 91 K, ΔE is the energy separation of the two levels of the [C II]158 μm transition) where the upper level of the [C II] transition is saturated (Muñoz & Oh 2016), or a high gas surface density (e.g., the typical density in compact ULIRGs and SMGs) where more gas is in the molecular phase (Narayanan & Krumholz 2017). It is interesting to see how the resolved distributions of the line and continuum surface brightnesses and emission ratios in these FIR luminous quasar hosts compare to that in the ULIRGs and SMGs (Smith et al. 2017; Gullberg et al. 2018; Rybak et al. 2019).


In the second, complimentary method, the line profiles were fitted using the least-squares method with the SCIPY routine CURVE_FIT. Toward B335, the fit was allowed to include up to four Gaussian line profiles, one for each potential transition in the blended emission feature. Bounds on the fits were estimated from the HDO data, and other non-blended emission lines in the dataset. The best fit does not include a fourth component, corresponding to either the CH3OCH3 line at 316.7904 GHz or the CH3OD transition at 316.7916 GHz (i.e., only three Gaussian profiles were included in the final fit). The exclusion of a fourth component has limited impact on the Gaussian profile for D2O. The resulting fit is shown the right panel of Fig. 4. The column density is estimated from the fitted line profile by assuming local thermodynamic equilibrium (LTE) (Mangum & Shirley 2015). We adopted an excitation temperature of 220 K, which is derived from the synthetic spectrum; this method results in a D2O column density of 4.0 × 1015 cm−2. The HDO transitions presented in Jensen et al. (2019) give a HDO column density of 1.9 × 1017 cm−2 at the sameexcitation temperature, when a beam filling factor is applied for a source size of 0.′′ 2. This method then results in a D2O/HDO ratio of (2.1 ± 0.6) × 10−2. Evidently, the D2O/HDO ratios toward B335 are somewhat higher when using the Gaussian fits, however both methods yield high D2O/HDO ratios ≳10−2. We note that the HDO column density is different from that presented in Jensen et al. (2019) because a higher excitation temperature of 220 K and a smaller source size are used in this work. Furthermore, the synthetic model includes an optical depth correction and identifies a slight blending of the H

$_{2}^{18}$218
O line, increasing the HDO/H2O ratio. Because of this, we consider the column densities presented in this work as more accurate. However, this does not impact the results and discussions of the relative HDO/H2O abundances in Jensen et al. (2019), in which identical excitation temperatures were used for all sources. The differences in the reported HDO/H2O ratios in this work and in Jensen et al. (2019) illustrate the dependence on the methodology and assumptions, however, the observed dichotomy between isolated and clustered protostars reported in that paper is robust. To remove the observed dichotomy requires consistently adopting lower excitation temperatures for the isolated sources, independent of the luminosity of the respective sources.


We repeated the plasma pressure calculation presented by Schwadron et al. (2011) and Fuselier et al. (2012) for the new ENA energy spectrum. The results for the downwind hemisphere and for the Voyager 1 region are summarized in Table 3. The measured intensity

j

ENA

 of neutralized hydrogen at a given energy translates into a pressure of the parent ion population in the heliosheath times the integration length along the line of sight, ΔP × l, in the following way:
3

Δ
P
×
l
=

4
π

3

n

H

m

H

v

j

ENA

(
E
)

σ
(
E
)

Δ
E

c

f

4

c

f

=

(
v
+

u

R

)

2

v

4

(

v

2

+
4

u

R

2

+
2

u

R

v
)
.

In Equation (3), ΔE denotes the width of the respective energy bin; for the typical radial velocity of solar wind in the flanks and the downwind hemisphere of the inner heliosheath, we assumed uR = 140 km s−1 as measured by Voyager 2, whereas uR = 40 km s−1 for the heliosheath in the Voyager 1 direction (Schwadron et al. 2011; Gloeckler & Fisk 2015). For the density of neutral hydrogen in the inner heliosheath a constant nH = 0.1 cm−3 is assumed (Schwadron et al. 2011; Gloeckler & Fisk 2015). The charge-exchange cross section between protons and neutral hydrogen decreases from (4 to 2) × 10−15 cm−2 for 0.015 to 1.821 keV (Lindsay & Stebbings 2005). The integration length l for ENA production in the plasma is approximately the thickness of the inner heliosheath. The part of Equation (3) without the velocity factor cf can be interpreted as stationary pressure. The total pressure or dynamic pressure is the stationary pressure times this factor. Integrating over all energy bins in Table 3, we obtain the total plasma pressure times heliosheath thickness as P × l = 304 pdyn cm−2 au for the downwind hemisphere and 66 pdyn cm−2 au for the Voyager 1 region (1 pdyn cm−2 au = 0.015 N m−1). If we want to put these numbers into the context of other studies, we face two problems. First, the uncertainty of the total pressure is large given the upper limits in the two lowest energy bins. Second, heliosheath plasma more energetic than 2 keV will produce ENAs that cannot be detected with IBEX-Lo. We therefore used the observed median j = 0 cm−2 sr−1 s−1 keV−1 for heliospheric ENAs in the two lowest energy bins of IBEX-Lo and relied on the study by Livadiotis et al. (2013). They compared the expected plasma pressure from a kappa distribution of protons with the plasma pressure derived from IBEX-Hi energy spectra: the energy range between 0.03 and 2 keV, roughly corresponding to the IBEX-Lo range, covered more than half of the total plasma pressure predicted from a kappa distribution. The authors found a total plasma pressure of P = 2.1 pdyn cm−2 for all sky directions except for the ENA Ribbon. Gloeckler & Fisk (2015) presented a multi-component plasma model for the heliosheath to explain Voyager and IBEX observations. At low energies they assumed the ENA energy spectra provided by Fuselier et al. (2012). They derived a total pressure of 2.5 pdyn cm−2 in all three plasma regions in the nose of the heliotail (Gloeckler & Fisk 2015). Pressure contributions from the slowed solar wind, magnetic pressure, and the pressure exerted from pickup ions and anomalous cosmic rays all had to be taken into account to obtain this total pressure.


The second issue concerns the fact that inside a given region, coreshine is not detected in all the dense clouds observed by Paladini (2014) and Lefèvre et al. (2014) and that the proportion of clouds exhibiting coreshine varies from one region to another. For instance, 75% of the dense clouds detected in Taurus exhibit coreshine, whereas in most other regions the proportion is closer to 50% (such as Cepheus, Chamaeleon, and Musca)5. On the contrary, there are for instance very few detections in the Orion region. In THEMIS, most of the scattering efficiency originates in the accretion of an a-C:H mantle. This leads to three possible explanations for the absence of detectable coreshine. The first explanation is related to the amount of carbon available in the gas phase. The abundance used by Köhler et al. (2015) relies on the highest C depletion measurements made by Parvathi et al. (2012) towards regions with \hbox{$N_{\rm H} \geqslant 2 \times 10^{21}$}NH⩾ 2 × 1021 H/cm2. Parvathi et al. (2012) highlighted the variability in the carbon depletion in dust depending on the line of sight. Thus, there may be clouds were the amount of carbon available for a-C:H mantle formation is smaller or even close to zero: such regions would be populated with aggregates with a thinner H-rich carbon mantle or no second mantle at all and thus exhibit very little or no coreshine emission. A second explanation is related to the stability of H-rich carbon in the ISM, which depends strongly on the radiation field intensity to local density ratio (Godard et al. 2011; Jones et al. 2014). In low-density regions (according to Jones et al. 2014, \hbox{$A_{V} \leqslant 0.7$}AV⩽ 0.7 for the standard ISRF), UV photons are responsible for causing the photo-dissociation of CH bonds, a-C:H → a-C. In transition regions from diffuse ISM to dense clouds (Jones et al. 2014, \hbox{$0.7 \leqslant A_{V} \leqslant 1.2$}0.7 ⩽ AV⩽ 1.2 for the standard ISRF), better shielded from UV photons and where the amount of hydrogen is significantly higher, H-poor carbon can be transformed into H-rich carbon through H atom incorporation, a-C → a-C:H. Similarly, carbon accreted from the gas phase in these transition regions is likely to be and stay H-rich. Then, in the dense molecular clouds, most of the hydrogen is in molecular form and thus not available to produce a-C:H mantles on the grains. However, this approximately matches the density at which ice mantles start to accrete on the grains, which would partly protect a-C:H layers that had formed earlier (Godard et al. 2011, and references therein). The stability and hydrogenation degree of a-C:H, as well as the exact values of AV thresholds, are both dependent on the timescale and UV field intensity. The resulting a-C ↔ a-C:H delicate balance could explain why in a quiet region such as Taurus most of the clouds exhibit coreshine, whereas in Orion, where on average the radiation field intensity and hardness are much higher, most clouds do not. A third explanation is related to the age and/or density of the clouds. In a young cloud, where dust growth is not advanced, or in an intermediate density cloud (ρC ~ a few 103 H/cm3), the dust population may be dominated by CMM grains instead of AMM(I) dust. Such clouds would be as bright in the IRAC 8 μm band as in the two IRAC bands at 3.6 and 4.5 μm, thus not matching the selection criteria defined by Pagani et al. (2010) and Lefèvre et al. (2014) and would be classified as “no coreshine" clouds.