of periapsis ω , and time of periastron t peri ). These can be used to calculate the projected position of both components on the sky at any moment in time. In all previous cases of binary events with significant binary motion, Keplerian orbital motion provided only a small improvement relative to the linear approximation ( Skowron et al. 2011 ; Shin et al. 2012 ). This is not the case here, because, as we show below, the orbital period of the lens is similar to the duration of the event (e.g. Penny et al. 2011 ). Modelling of this event is an iterative process: for given microlensing parameters, we estimated the angular radius and distance to the source, we calculated best-fit microlensing parameters, and we repeated the procedure until all parameters converged. The best-fit microlensing parameters are presented in Table 5 . Uncertainties were calculated using the Markov chain Monte Carlo approach (MCMC; Foreman-Mackey et al. 2013 ) and represent 68% confidence intervals of marginalized posterior distributions. We note that another degenerate solution exists for the microlensing model that differs only by the signs of s z and γ z (( s z , γ z ) → − ( s z , γ z )). The second solution has the same physical parameters (except for Ω → π − Ω and ω → ω − π ) and differs by the sign of the radial velocity. Thus, the degeneracy can be broken with additional radial velocity measurements of the lens ( Skowron et al. 2011 ). Table 5. Best-fit microlensing model parameters of the Gaia16aye binary event. Notes. HJD′=HJD-2450000. We adopt t 0, par = t 0, kep = 7675. 4.3. Source star Spectroscopic observations of the event indicate that the source is a K5-type giant or a super-giant. If the effective temperature of the source were higher than 4250 K, TiO absorption features would be invisible. If the temperature were lower than 3800 K, these features would be stronger than those in the observed spectra. Spectral modelling indicates that the effective temperature of the source is 3933 ± 135 K. According to Houdashelt et al. (2000) , the intrinsic Johnson–Cousins colours of a star of this spectral type and solar metallicity should be , and (error bars correspond to the source of K4- and M0-type, respectively). We used a model-independent regression to calculate the observed colours of the source (we used observations collected in the Bialkow Observatory, which were calibrated to the standard system): V − R = 0.99 ± 0.01 and V − I = 1.91 ± 0.01. Thus, the colour excess is E ( V − I ) = 0.31 and E ( V − R ) = 0.16, consistent with the standard reddening law ( Cardelli et al. 1989 ) and A V = 0.62. According to the best-fitting microlensing model, the amount of light coming from the magnified source is V s = 16.61 ± 0.02 and I s = 14.70 ± 0.02. The V -band brightness of the source after correcting for extinction is therefore V 0 = 15.99 mag. Subsequently, we used the colour–surface brightness relations for giants from Adams et al. (2018) to estimate the


scale height (Klahr Henning 1997; Pinilla et al. 2012; Testi et al. 2014; Johansen et al. 2014) . The regions in the disk midplane that correspond to the snowlines of major volatiles are particularly interesting. These may promote locally efficient grain growth through recondensation across the snowline or by changing the sticking properties of ice-coated grains and, in addition, the local release of volatiles from the ices may induce a local pressure bump that could trap large grains (e.g., Supulver Lin 2000; Wada et al. 2009; Ros Johansen 2013; Gundlach Blum 2015) . The dense regions of disk midplanes can be investigated at submillimeter and millimeter wavelengths, where the dust emission is more optically thin and can now be spatially resolved with present-day facilities, such as the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA). These facilities allow us to obtain sensitive and high angular resolution observations of the dust continuum and gas emission lines from protoplanetary disks and therefore study the radial variations of the physical parameters of the disk. Recent results include the study of the dust properties as a function of radius in disks (e.g., Guilloteau et al. 2011; Banzatti et al. 2011; Pérez et al. 2012, 2015; Menu et al. 2014; Tazzari et al. 2016) , and the clear identification of the CO snowline in nearby disks (Mathews et al. 2013; Qi et al. 2013, 2015) , through its effects on DCO and NH abundances. It is thus becoming possible to directly investigate the effect of the CO snowline on grain growth observationally. This snowline is thought to be one of the most important after that of water, because the CO abundance in protostellar ices is found to be about 3040% of HO (Öberg et al. 2011) . In this work we focus on the Herbig Ae star HD 163296, a bright and isolated object at a distance of parsec (van den Ancker et al. 1998) with a relatively massive disk (~0.1 M⊙: Qi et al. 2011; Isella et al. 2007) and an excellent prototype for gas- and dust-rich protoplanetary disks. An estimated age of 5 Myr was obtained from the comparison between H ipparcos astrometric measurements and pre-main sequence evolutionary models by van den Ancker et al. (1998) . The stellar parameters computed by Natta et al. (2004) are , , K. To study the dust properties in the protoplanetary disk around HD 163296, we re-analyse the ALMA science verification observations (de Gregorio-Monsalvo et al. 2013; Mathews et al. 2013; Rosenfeld et al. 2013) and for the first time discuss the continuum emission in Band 6, combined with new VLA observations from the Disks@EVLA collaboration. In Sect. 2 we describe the observational data, in Sect. 3 we report the main new results of our analysis, in Sect. 4 we present the result of our disk modeling, and in Sect. 5 we discuss the main implications for grain properties. Fig. 1 Continuum maps at different wavelengths, from the left : 850 m, 1.3 mm, and 9 mm, the


inferred from the shell modeling reported in Sect. 3.1 and Fig. 11 must be considered as strict lower limits. This is because the emerging spectrum is strongly weighted by sightlines with the lowest column densities, given that Ly α escapes through the paths of least resistance (e.g., Eide et al. 2018 ), generally orthogonal to the stream velocities in case of infall ( Gronke et al. 2017 ). Nevertheless, we note that an alternative scenario suggested by recent modeling is that radiation is emitted through the cooling of mixed gas occurring at the boundary between the phases ( Mandelker et al. 2019 ; Cornuault et al. 2018 ). In that case, Ly α radiation would originate from the combined dissipation of the kinetic energy of the stream and the thermal energy from the mixed gas that cools down ( Gronke Oh 2020a ). This scenario, and our calculations of gas mass flows in Sect. 3.1 , also imply a total cold gas mass present at each moment in the diffuse streams of the order of 10 11 M ⊙ (to be compared to the lower limit of ≈10 8 M ⊙ of neutral hydrogen). Is that a reasonable gas mass to be diffused into the intra-group gas? On the one hand, this is comparable to or smaller than the ISM mass of all group galaxies combined, and less than 10% of all baryons expected to be in the group given its DM estimate and assuming a universal baryon fraction. Assuming pressure equilibrium, the flowing gas would need to be confined in clouds with quite a small volume filling factor, of order 10 −3 to 10 −5 , which is qualitatively similar to what is discussed in theoretical works (e.g., Cornuault et al. 2018 ; McCourt et al. 2018 ; Gronke Oh 2020b ). This is required to reach a high-enough density to compensate for the much larger temperature of the hot medium. Such dense gas clouds would produce copious recombination Ly α photons following photoionization, if a source emitting enough ionizing photons towards this medium were to be present. This does not appear to be the case for RO-1001, at least given the evidence presented here. 5. Summary and conclusions The main findings of this work can be summarized as follows: RO-1001 is a group at z = 2.91 defined by four galaxies with stellar masses above 10 11 M ⊙ , originally selected as an overdensity of faint radio sources (12 σ excess) over a small, 10′′ region. The group contains an ongoing SFR of 1200 M ⊙ yr −1 mostly spread among three ALMA-detected, IR-luminous sources characterized by very compact IR sizes, for which we reported CO[3−2] detections with NOEMA. RO-1001 does not contain any detectable evidence of ongoing AGN activity, down to limits that are consistent with a cosmic average co-existence of an AGN and SFR at typical levels. The hosting DM halo mass is estimated to be typical for a group, with ∼4 × 10 13 M ⊙ consistently derived using three methods, including a blind X-ray measurement with significance of 3.1 σ . RO-1001 hosts a giant Ly α halo with a luminosity of 1.3 × 10 44 erg s −1 as


on the low branch. Mass is being fed into the annulus at a greater rate than it is able to process it and so mass accumulates and Σ increases. Eventually, the annulus reaches the low-temperature bifurcation point and leaps to the high hot state. The annulus, now above the Σ-nullcline, begins losing mass because its accretion rate exceeds the supply rate. Once the high-temperature bifurcation point is reached, the annulus drops to the low-temperature state and the process is repeated. The red curve in Fig. 4 (a) corresponds to a numerical simulation of equations ( 15 ) and ( 17 ) and illustrates this basic behaviour quite clearly. In Fig. 4 (b), we plot the evolution of Σ and T c as a function of time. Here, one can observe the two time-scales at work, especially in the (blue) T c curve. In between outbursts there is little change in temperature, but a build up in mass (seen in the red curve) occurring on the slow viscous time-scale t Σ . Interleaving these phases are the abrupt bursts occurring on the short thermal time-scale t th . 3.2.2 Z Cam type simulations Z Cam variables intermittently behave in a similar manner to U Gem variables but occasionally remain on the high-temperature branch in a quasi-steady state for months to years before dropping to quiescence and undergoing a fresh batch of outbursts. This is attributed to a shift in the Σ-nullcline upwards (due to a change in mass transfer, δ ≠ 0), so that the intersection is beyond the saddle node. Of course, the system must be close to criticality if this is to be possible. To demonstrate this in our model, and δ are chosen such that the fixed point oscillates between the stable high-temperature branch and the unstable branch. When the fixed point is on the upper branch the system is stable and will remain in a standstill. A decrease in pushes the fixed point on to the unstable branch and the system undergoes periodic orbits resulting in trains of outbursts. In Fig. 5 , we show an example of standstill–outburst-train cycles. Figure 5. Time evolution of the surface density and central temperature with and b 0 = 0 with mass transfer variation. The variation amplitude is δ = 0.1 and t I = 5 × 10 6 s. The system clearly switches between outburst trains and standstills. 3.3 Results: stochastic With the basics established, we include a fluctuating viscosity (β ≠ 0). The fluctuation time-scale is taken to be 10 t orb , which is motivated by MRI shearing box simulations (Hawley et al. 1995 ). The amplitude is set at b 0 = 0.1. First, we consider the case where there is no mass transfer variability (δ = 0). To obtain a fixed point on the high-temperature branch close to the bifurcation point we choose . A deterministic system with this configuration would remain in the high-temperature state indefinitely. A stochastic system however will see the fixed point jostle about as the two nullclines fluctuate with α, sometimes sitting on the upper branch, sometimes dropping to the middle branch


χ 2 ), constrained by all of the photometric detections and upper limits from NIR to radio wavelengths (Figure 4 ). Parameters are analyzed under a Bayesian approach generating a posterior probability distribution function. The SED fitting failed to tightly constrain fracAGN given the lack of mid-IR photometric points (which differentiate between AGN and star-forming galaxies) and the loose constraint from the NIR. The posterior probability distribution suggests that the AGN component contributes at most ∼20% to the total IR luminosity, with the highest probability being assigned to a contribution of 0%–5%. This is consistent with the estimation from the L X / L FIR ratio in Section 3.1 . The model SED with the maximum 20% AGN fraction is also plotted in Figure 4 , which is inconsistent with the 100 μ m Herschel /PACS upper limit. Figure 4. Best-fit SED (black) from CIGALE PYTHON. Different components are color-coded. The data points from left to right are HST /WFC3 F110W+F160W, Spitzer /IRAC 3.6 μ m + 4.5 μ m, Herschel /PACS 100 μ m + 160 μ m, Herschel /SPIRE 250 μ m + 350 μ m + 500 μ m, APEX/LABOCA 870 μ m, SPT 1.4 mm + 2.0 mm, and ATCA 5.5 GHz + 2.1 GHz. We do not include the ATCA 9.0 GHz upper limit, which is less constraining, because the source may be resolved at this frequency. The inset plot shows the normalized probability distribution function of the AGN fraction in the total IR luminosity. The AGN most probably contributes less than 5%. The dash–dotted line is the model curve with the maximum 20% AGN contribution to the IR. In this model, the AGN contribution does not extend to the radio part of the SED. The ATCA radio continuum upper limits at 2.1 and 5.5 GHz are consistent with the FIR-to-radio correlation for star-forming galaxies. The radio part of the SED for radio-loud AGN would be at least a factor of ∼2 higher (e.g., Rush et al. 1996a , 1996b ; Morić et al. 2010 ). 3.3. Theoretical Expectations We have provided evidence that SPT0346-52 is star formation dominated in the IR. Since our SFR is mainly constrained by the FIR photometric data, L IR being almost all from star formation suggests that the inferred SFR reflects the true SFR. We examine whether this observed high SFR can be physically explained in the framework of “maximum” starbursts (Elmegreen 1999 ) where a substantial fraction of available gas is consumed to make stars. Following Tacconi et al. ( 2006 ), the maximum (“Schmidt-law”) SFR can be written aswhere Elmegreen ( 1999 ) defines as the star formation efficiency, f g is the gas fraction, M tot is the total (dynamical) mass of the system, t dyn is the dynamical time, and v c is the circular velocity in km s −1 . We use the definition in Tacconi et al. ( 2006 ), v c = 0.67 × v FWHM = 410 km s −1 ( v FWHM = 613 ± 30 km s −1 measured from the low- J CO(2-1) line; Aravena et al. 2016 ). Assuming a gas fraction of 0.3–0.8, we utilize the observed SFR of 3600 ± 300 M yr −1 to 19 19 Here we adopt the SFR


( 2010 ). They have also shown that when these are combined with lower limits required to avoid the compactness problem, values of Γ 0 are in the range 10 2 –10 3 . Concerning direct estimates (rather than limits) of Γ 0 , a spectral break in the prompt component has been observed only in a few cases (Ackermann et al. 2011 ; Tang et al. 2015 ). Most of the available estimates of the value of Γ 0 have been inferred from the detection of an early peak in the afterglow lightcurve. Ghirlanda et al. ( 2012 ) collected all GRBs with known redshift and with an early peak in the optical lightcurve, and inferred Γ 0 under the assumption that the peak corresponds to the blast wave deceleration time. The Γ 0 values have been derived both for a constant and wind-like medium, and are shown in Fig. 4 as star symbols (the green colour refers to optical lightcurves, while the yellow colour refers to a similar analysis applied to GeV lightcurves of LAT GRBs with temporally extended GeV emission). The most stringent limits derived in this work lie above most of the values inferred from GRBs with an optical peak. This implies that the non-detection of synchrotron afterglow radiation is consistent with the simplest model, and there is no evidence that mechanisms producing a suppression of the GeV flux (see Section 2.2 ) are at work. The possibility of testing the relevance of these processes is however limited by the instrument sensitivity. We can conclude that present instrument capabilities are not pointing to the need for a relevant suppression of the high-energy afterglow synchrotron flux. On the other hand, the upper limits lie not far from (and sometimes below) the estimated values of Γ 0 . This suggests that the LAT should be able to detect the synchrotron afterglow component for those GRBs with the largest bulk Lorentz factors and largest energetics. A fraction of the LAT-detected GRBs are indeed characterized by the presence of an emission above 100 MeV lasting much longer than the prompt radiation, whose flux decays in time as a PL (Ackermann et al. 2013 ). These are the brightest GBM GRBs, and a large Lorentz factor Γ 0 > 500 has been inferred for them. An association with synchrotron afterglow radiation has been claimed to be consistent also with their spectral and temporal properties (Kumar Barniol Duran 2009 , 2010 ; De Pasquale et al. 2010 ; Ghirlanda, Ghisellini Nava 2010 ; Ghisellini et al. 2010 ; Lemoine, Li Wang 2013 ; Nava et al. 2014 ; Beniamini et al. 2015 ), although photons with particularly large energies (>10 GeV) detected at late times (>10 2 s) are in excess of the synchrotron limit and require a different explanation (Piran Nakar 2010 ; Wang, Liu Lemoine 2013 ; Ackermann et al. 2014 ). Finally, we comment on the dependence of these results on the unknown parameters ε e and η γ , with reference to a homogeneous density medium (similar considerations hold also for a wind-shaped density medium). In the first regime, where observations


pulsars. Timing noise manifests as a red-noise (time-correlated) process in the TOAs, and is typically described by a wide-sense stationary stochastic process (Groth 1975 ), modelled as either random walks in the pulsar spin parameters, or with a more general power spectrum. The origin of this noise is unclear. While some of it may be caused by variable torques associated with changes in the pulsar magnetosphere state (Lyne et al. 2010 ), a significant fraction is likely associated with rotational irregularities interior to the star (Melatos Link 2014 ). The properties of timing noise vary markedly across the pulsar population, with its strength depending on the pulsar spin frequency ν and frequency derivative (Shannon Cordes 2010 ), and likely other factors because of the large dispersion levels of timing noise between pulsars. For example, the most stable MSP, PSR J1909−3744 shows no evidence for instabilities with phase variations limited ≲100 ns (≈0.3 per cent of pulse phase) over 11 yr (Shannon et al. 2015 ). In contrast, the timing noise in young pulsars and magnetars can contribute many cycles of pulse phase on week to month time-scales (Livingstone et al. 2011 ), both making it difficult to find a phase-coherent solutions in poorly sampled data and presenting challenges to TOA-modelling algorithms. While finding the origin of timing noise is important for understanding neutron stars, it is also necessary to account for timing noise as part of a general timing model for the pulsar. This is necessary to eliminate, or at least mitigate, bias in the estimation of other parameters in the model (Coles et al. 2011 ; van Haasteren Levin 2013 ; Lentati et al. 2014 ; Kerr et al. 2015 ). In addition to exhibiting timing noise, pulsars can experience glitch events (e.g. Espinoza et al. 2011 ; Yu et al. 2013 ), in which they are observed to suddenly change spin state, with the most significant component being increases in spin frequency that can exceed 1: 10 5 (Manchester Hobbs 2011 ). Glitches have been modelled with permanent changes in ν and , as well as transient components, in which changes in ν are modelled to decay (typically exponentially) on time-scales τ. Occasionally multiple glitch-decay components (with different time-scales) are invoked, particularly when high cadence (daily or higher) observations (e.g. Dodson, McCulloch Lewis 2002 ). Glitch components are often identified and characterized by searching for variation of spin frequency and frequency derivative in subsets of the data (Lyne et al. 2015 ). This method is suboptimal because it does not utilize the phase coherence of the pulse arrival times. The study of glitches is further complicated by the presence of timing noise. There are two prevailing theoretical models for glitches. In the first, glitches are associated with the transfer of angular momentum between the superfluid interior and solid crust of the neutron star (Anderson Itoh 1975 ; Alpar et al. 1984 ). A


power. In AGN and LI(N)ER galaxies, the molecular component is more dominant than in star-forming galaxies. There is, however, significant variation from galaxy to galaxy. Studying the relative contribution of different phases to the outflow rate and the kinetic power as a function of SFR or α bol revealed no clear trends (see e.g. Section B1 ). Figure 6. Relative contribution of the molecular (blue), ionized (green), and neutral atomic (red) phases to the total kinetic power of the outflow. The galaxies whose names are in red are star-forming galaxies. Next we investigate the mass outflow rate of the three different phases, ionized, neutral atomic, and molecular for galaxies which have measurements (or upper limits) for at least two phases. This comparison can be seen in Fig. 7 , where we plot the different mass outflow rates against each other. The samples in the three plots are slightly different. To increase the statistics, in each plot we show the galaxies with measurements in both of the phases plotted. We distinguish between high-redshift sources ( z > 1, green) and low-redshift sources ( z 0.2, black). The data points with a red edge have no reliable extinction correction for the ionized phase and thus should be treated as lower limits. These figures clearly show that the ionized mass outflow rate is much smaller (up to 2–3 orders of magnitude smaller) than the neutral atomic or molecular mass outflow rate. A major caveat is that some ionized outflow rates might be underestimated because of an uncertain extinction correction. But even if these points are ignored, the ionized outflow rates are significantly lower (cf. Fig. 5 , which only includes galaxies with proper extinction correction). This confirms previous findings which estimate the ionized phase to contribute only minimally (Rupke Veilleux 2013 ; Carniani et al. 2015 ; Ramos Almeida et al. 2019 ). The figure on the top right highlights that outflow rates in the molecular and neutral atomic phase are similar (usually within 1 dex). This picture might be slightly skewed, however, as we include upper limits in the molecular and ionized, but not in the atomic neutral outflow phase. However, the relative contribution of the ionized outflow rate to the total outflow rate varies from galaxy to galaxy (from ≤ 1 to 10’s of ) and a simple prescription as in Fluetsch et al. ( 2019 ) might not be fully appropriate to determine the total outflow budget. If electron densities from auroral or trans-auroral lines are a better estimate than the densities based on the [S ii ] doublet (as suggested by Davies et al. 2020 , see Section 3.2.1 ), then the contribution of the ionized phase would drop even further by additional 1–2 orders of magnitude and hence it would become negligible also in star-forming galaxies. Figure 7. Comparison between the outflow rates in the ionized, molecular, and neutral gas phases. The black symbols represent the low-redshift ( z 0.2) sources while the green symbols


normalized to unity at 1 keV, this is seen as a decrease of the reflection amplitude. Figure A2. An example illustration of the effect of the emission of the bottom lamp and of the emission of the top lamp circling around the BH (i.e. crossing twice the equatorial plane). The blue solid and red dashed curves show the observed reflection spectra computed with reflkerr_lp for δ = 0 and 1, respectively, for h = 2, a = 0.998, r in = 4.9, r out = 1000, Γ = 1.7, kT e = 200 keV, ξ = 1, kT bb = 50 eV, and θ o = 9° (thick curves) and 30° (thin curves). The black dotted curve shows the observed primary spectrum. We see the actual reflected spectra may be much weaker with respect to the observed primary emission than those in the approximate (δ = 0) case. In the shown case, this is due mostly to the primary emission of the bottom lamp gravitationally focused toward the observer, which enhances the observed primary flux by as much as a factor of 10 in the case of θ o = 9°. Since our plotted primary spectra are normalized to unity at 1 keV, this enhancement is seen here as a decrease of the amplitude of the reflection. We emphasize that properly assessed reflection amplitude gives an important constraint on the lamppost model, where both the fraction and the radial distribution of photons illuminating the disc surface are fully determined by the height of the primary X-ray source. Then, the radial emission profile is strictly related to assumed geometry, and treating the fraction of reflected photons as a free parameter leads to results which are not self-consistent. Still, our model allows the user to make it free. APPENDIX B: <monospace>hreflect</monospace> We describe here details of our hybrid reflection model. In particular, we apply rescaling of the xillver spectra to account for an angular distribution of reflection predicted by this model, which is different than that of ireflect (with the reflection strength in ireflect larger by a factor of ≃1.5 for edge-on directions). In some cases, we apply also a minor rescaling related with differences of the incident spectra. We explain the criteria which we use to establish the rescaling factor, denoted below by f . We follow an approach similar to that of Done Gierliński ( 2006 ). We use xillver , which applies a more accurate absorption model, as a reference for the spectral shape below ∼20 keV, and ireflect , which correctly describes the angular distribution of the reflected radiation using the exact Klein–Nishina cross-section, as a reference for the reflection amplitude. The absorption model applied in ireflect assumes that the absorption coefficient above 12 keV is ∝ E −3 , then, the depth of its absorption edge at these energies can be matched to that predicted by xillver by modifying any parameter (we choose ξ) affecting the absorption level at 12 keV. As can be seen below, the shapes of ireflect spectra with such an adjusted ξ typically agree very well with those of xillver in the ∼10–30


constrain the escape fraction of the ionizing radiation and/or the presence of faint satellite galaxies during the late stages of cosmic reionization. We have predicted radial surface brightness profiles that include the contribution from (i) fluorescent emission powered by ionizing radiation leaking from the central galaxy (as in Mas-Ribas Dijkstra 2016 , for two different CGM prescriptions), and (ii), nebular emission from faint satellite sources that possibly resided within the halo of the central galaxies (as in Mas-Ribas et al. 2017 ). We have compared our predictions with observations of Ly α halos at z = 5.7 and z = 6.6, and have also predicted H α and visible continuum surface brightness profiles may be detectable within future JWST observations. We present and discuss our findings below. 1. Our comparison of models to observations favors the model with a very low escape fraction of ionizing radiation, , from galaxies within the range of magnitudes . This scenario implies that these galaxies do not contribute significantly to the reionization process. Therefore, if galaxies are the major contributors to the reionization process, as recently restated by Parsa et al. ( 2017 ), a large population of faint sources with a high ionizing escape fraction is necessary. 2. The presence of faint satellite sources is unclear. Two out of four comparisons with current Ly α data indicate that satellite sources might contribute to the extended Ly α emission, but the effect of systematics and uncertainties in the observations do not allow for a clear conclusion. Given the required existence of faint sources driven by the low escape fraction results, if the presence of satellite sources around brighter galaxies is ruled out by the observations, this might imply that the population of faint objects is spread out within the IGM, making its detection more challenging. 3. JWST will be able to probe the ionizing escape fraction from one bright, galaxy up to distances of a few tens of pkpc from the center. Fainter galaxies and/or a high S/N for the continuum observations require the observation and stacking of several objects. We stress that we have adopted and extrapolated two CGM models that were derived to match observables at redshifts around . The validity of our results therefore depends on the ability of these two models to realistically describe the medium surrounding galaxies. While a more detailed parameterization of the CGM at high redshift (if currently feasible) is beyond the scope of our work, future observations of extended emission, together with absorption studies (e.g., Dijkstra Kramer 2012 ; Hennawi Prochaska 2013 ; Prochaska et al. 2013 , see also Steidel et al. 2010 , 2011 ), will clearly enable us to use our proposed method to further constrain the escape fraction. The prospects for doing this experiment at lower redshifts, , are interesting, as the surface brightness for emission lines depends on redshift as . However, the contribution


a low self-interaction cross section). However, it seems unlikely that this same model could then be responsible also for the much larger dark matter core reported in Fornax (e.g. Goerdt et al. 2006 ; Walker Peñarrubia 2011 ; Cole et al. 2012 ; Pascale et al. 2018 ) and the similarly large cores reported in nearby gas-rich isolated dwarf irregulars (e.g. Moore 1994 ; Flores Primack 1994 ; Read et al. 2017 ). By contrast, models in which dark matter is heated by bursty stellar feedback could naturally account for such a diversity of central dark matter densities, at least in principle. Recall that whether or not a dark matter core can form from such ‘heating’ depends on: (i) the pre-infall dark matter halo mass, M 200 ; (ii) the halo concentration parameter, c 200 ; (iii) the total stellar mass, M * ; and (iv) the size of the dark matter core (e.g. Di Cintio et al. 2014 ; Read et al. 2016a ; Contenta et al. 2018 ; Bermejo-Climent et al. 2018 ). (Smaller cores require less energy to form and form more rapidly.) Dark matter cores are also easier to form at high redshift when the star formation rates are high and the halo masses are smaller (Madau, Shen Governato 2014 ). This suggests that small (pc) dark matter cores may indeed form very early in the Universe even in ultra-faint dwarfs. This effect could be ubiquitous, or it could be stochastic, depending on the merger history, spin and/or concentration of any given dwarf (e.g. Laporte Peñarrubia 2015 ). We will return to this issue in more detail in a forthcoming paper where we present GravSphere models for all of the Milky Way classical dwarfs. 8 CONCLUSIONS We have used a new mass modelling method, GravSphere , to measure the central dark matter density profile of the Draco dwarf spheroidal galaxy. Our key findings are as follows: Using mock data with sampling, binary star population, and foreground contamination similar to that for the real Draco dwarf, we showed that GravSphere is able to successfully recover the dark matter density profile of a tidally stripped Draco-like dwarf within its 95 per cent confidence intervals (Fig. 4 ). However, while we were able to distinguish the amplitude of the central density, , of our cored and cusped mocks at 95 per cent confidence, the logarithmic slope of the density profile, , depended on our choice of priors. This sensitivity to the prior diminishes with improved spectroscopic sampling (Appendix B ). We then applied GravSphere to the real Draco data. We inferred a high central density of with logarithmic slope at 95 per cent confidence, consistent with expectations from pure-dark matter structure formation simulations in ΛCDM (Fig. 7 ). We tested the robustness of this result, showing that even using a rather extreme prior on γ DM that biases us towards cored models, our GravSphere models still favour a logarithmic slope of at 95 per cent confidence, steeper than that of a uniform-density core. Dark matter models with a high central density and a


sampling rate. 4. Discussion 4.1. Prominences From the H α tomogram, we can estimate the size and location of the satellite emission that we associate with prominences by assuming that they are corotating with the secondary star. The projected distance of these features from the center of mass (CM) of the binary is simply r = v /Ω, where v is the inclination-corrected velocity amplitude of the emission and Ω is the angular velocity of the secondary. The orbital inclination is expected to be ∼75° based on our assumed stellar masses and the mass function measured by Marsh et al. ( 2016 ). Therefore, the correction between the radial velocity and space velocity is less than 10%. For the orbital period from Marsh et al. ( 2016 ), the inverse angular velocity is 2043 s rad −1 . Assuming a mass for the WD of 0.8 M ⊙ , then the mass ratio of the system is q ≈ 0.3 for a secondary with a mass typical for an M5 dwarf. The radius of the secondary’s Roche lobe is (Eggleton 1983 ). Since the secondary is probably close to filling its Roche lobe, we use this as the stellar radius and compare it to the size of the prominences. The brightest emission from the prominences is seen around 500 km s −1 , corresponding to 4.4 Roche radii from the CM. The prominences precede and trail the secondary by ± 0.15 in phase, meaning that the prominences extend 3 stellar radii from the surface of the secondary. The faint emission behind the secondary at 1000 km s −1 corresponds to 8.7 stellar radii from the CM, or about 5 stellar radii from the backside of the red dwarf. In isolated magnetized stars, the corotation radius is where the gravitational pull of the star balances the centrifugal acceleration of plasma trapped in the field. Prominences found at or beyond the corotation radius are called “slingshot” prominences (Steeghs et al. 1996 ). In binary systems the balance between centrifugal and gravitational forces is found at the Lagrangian points. The L 4 and L 5 points are actually rather broad regions that make an equilateral triangle with the primary and secondary stars. For the assumed parameters of the AR Sco binary, the L 4 and L 5 points are 370 km s −1 from the CM. The prominences extend more than 30% farther than L 4 and L 5 points. The trailing prominence differs in phase from the L 5 point by 20°. The L 2 point is expected to be at 4.5 Roche radii from the CM, or a velocity of 500 km s −1 , while the faint prominence behind the secondary is seen at twice that distance. We conclude that the prominence emission extends well beyond the outer Lagrangian points. The stability of slingshot prominences has been modeled by Ferreira ( 2000 ). Such prominences can be stable out to ∼5 stellar radii if the dipole surface magnetic field is larger than ∼100 G, and out to 10 stellar radii for a 500 G field. A quadrupole field would require ∼500 G for prominence stability at 5 stellar radii. The WD field at the secondary is expected to have an average field strength of order


the evolution after 18.25 days but underpredicts the millimeter-band data and the observations above ≈10 GHz before 8.55 days. Figure 10. Same as Figure 8 , but now including energy injection between 0.15 and 0.26 days (Section 4.3 ), a standard RS contributing to the optical/NIR light curve before 2 × 10 −3 days and to the radio at 1.5 days (Section 5.1 ), and a refreshed RS contributing to the millimeter-band light curve (Section 5.3 ). Figure 11. Same as Figure 9 , but for the model (solid) shown in Figure 10 decomposed into FS (dashed) and RS (dotted) contributions. The two RS components are best distinguished at 1.5 days, where the lower-frequency component arises from an RS in the original shell producing the GRB, while the higher-frequency component arises from the collision of two shells at 0.15 days, which also produces the X-ray rebrightening. The red shaded regions represent the expected variability due to scintillation. To summarize, the continued high flux density of the X-ray detections after ≈1 day suggests that the X-ray excess at ≈0.26 days is not due to late-time central engine activity, but is caused by a rebrightening of the FS radiation. The multiband data are consistent with a wind-like circumburst medium, requiring a single episode of energy injection at ≈0.2 days. The resultant model fits the optical and X-ray evolution and matches the radio SED after 18 days. However, this model underpredicts the CARMA light curve, as well as the 5–83 GHz SED at 1.5 and 8.55 days. To account for these deficits, we next investigate the effect of including emission from additional components. We delineate the evidence for their presence and consider their possible physical origins. 5. Multicomponent Models 5.1. Reverse Shock In Section 3.2 , we discussed the apparent multicomponent structure of the radio SEDs between 1.5 and 18.2 days. In the previous section, we have shown that while a single FS model can reproduce the gross features of the radio light curves, such a model cannot explain the multiple peaks in the SED at 1.5 days, the ≈14 GHz peak at 4.5 days, and the SED at 8.55 days. Of these, the greatest discrepancy between data and model arises in the radio SEDs at 1.5 and 4.55 days. We now consider whether each spectral peak at 1.5 days can in turn be ascribed to radiation from an RS. An RS propagating into GRB ejecta is expected to produce synchrotron radiation with its own set of characteristic frequencies, ν a,r , , and ν c,r , and peak flux . These quantities are related to those of the FS at the deceleration time, ec , when the RS just crosses the ejecta, and the relation between the two sets of break frequencies and fluxes allows for a determination of the ejecta Lorentz factor and magnetization. After the RS crosses the ejecta, the flux above ν c,r declines rapidly, 16 16 The angular time delay effect prevents abrupt disappearance of flux above ν c,r ; instead, we expect (Kobayashi Zhang 2003 ). as no electron is


metallicity than QGs-A. The median stacked spectra, corrected for dust extinction, of QGs-A and QGs-B have a blue stellar continuum, suggesting a young mean stellar population. The analysis confirms a weak [] emission and that also other high ionization emission lines (such as []) are weak in both QGs stacked spectra, and the [] /H α ratios are consistent with a low ionization level. On the contrary, [], H α and H β (i.e. low ionization lines) are still strong and with an Hα flux slightly weaker () than the one of SF galaxies. We find that QGs have D n 4000 and EW(H α) values intermediate between SF and already quenched galaxies, confirming that they have just stopped their star formation and have a young/intermediate mean stellar population. In the colour-mass diagram, the bulk of the QGs-A and QGs-B resides in the blue cloud region, and only few of them (∼3 per cent) lie in the green valley region. The QGs have masses log( M /M ⊙ ) > 9.5, comparable with those of the SF population, being the QGs-B, on average, more massive. This suggests that, as expected in a downsizing scenario, star formation quenching has not started yet for low-mass galaxies, consistently with a lack of low-mass red galaxies. Their H α emission is compatible with a just quenched SFR of the order of 0.6–10 M ⊙ yr −1 , similar to that of the SF main sequence population, suggesting the presence of residual ionized gas in our QGs. The emission from the median stacked spectra is, however, weaker than that in the SF population, suggesting that the depletion of the gas has started. The morphologyand concentration index (C=R90/R50) of QGs are similar to those of the SF population, suggesting that no morphological transformation has occurred yet, in the early phase after the quenching of the star formation. However, some of them have a concentration index higher than the threshold that divides the early-type from the other galaxy types (i.e. C > 2.6) and they could have experienced morphological transformation during the interruption of the star formation. Compared to the parent SF population, we find an excess of QGs in high-density environments (∼42 per cent), in particular for QGs-B. QGs in high-density environments are preferentially satellites (from ∼60 to 80 per cent). Approximatively 5 per cent of QGs are in groups/clusters which have more than 30 members, but no one of them is the brightest galaxy in its environments. From the fraction of QG candidates ( of the SF population) we estimate the quenching time-scales for these populations to be between 10 and 18 Myr. These values are compatible with the sharp quenching models by C17 . If we assume that at most 50 per cent the entire SF-[]undet population (∼7.5 per cent) is in a low ionization state, as witnessed by the low but not extreme [] /H α ratio in their stacked spectrum, we obtain an upper limit to the quenching time-scale of ≃ 0.76 Gyr. In this case, the quenching time-scale is compatible with galaxies which are


et al. 2017 ; Vallini et al. 2017 ), which may affect the density field of GMCs, and ultimately increase the conversion factor. Finally, we compare our inferred conversion factor with the one resulting from the best-fitting formula, X CO /( cm 2 K km s − 1 ) = 6.3 × 10 19 α CO /(M ⊙ K km s − 1 pc 2 ), obtained by Narayanan et al. ( 2012 ). They simulate the hydrodynamic evolution of both isolated and merging disc galaxies finding that . If we substitute and Z = 0.5 Z ⊙ we obtain α CO = 2.9 M ⊙ /(K km s − 1 pc 2 ) in agreement within a factor ≈2 with our results. 4.5 ALMA observability In Section 4.3 we have shown that the peak of the Althæa CO SLED coincides with the CO(7–6) line. As CO transitions with J up ≥ 6 fall in the ALMA bands from z > 6, in what follows, we use the ALMA Sensitivity Calculator to compute the observing time required to detect the CO(7–6) line from (a galaxy similar to) Althæa. The total CO(7–6) luminosity of Althæa is L CO(7-6) = 10 7.1 L ⊙ , i.e. ≈1/16 of its [C] luminosity. If we assume the line width to be equal to that of [C] observations in LBGs at z ≈ 6 − 7 ( Maiolino et al. 2015 ; Knudsen et al. 2016 ; Pentericci et al. 2016 ; Bradač et al. 2017 ), this yields a peak flux density . 8 The ALMA full-array observing time required to detect (resolve over 1/3 × FWHM) the CO(7–6) line with a signal-to-noise ratio S/N = 5 is ≈13 h (≈38 h), i.e. it would be challenging but doable within the maximum observing time ( ≤ 50 h) allowed for ALMA regular programs. This is in line with what was found by Muñoz Furlanetto ( 2013 ), which pointed out that ALMA observations of high- J CO can be performed with reasonable integration times only in those z ≈ 6 galaxies which, like Althæa, are chemically evolved ( Z Althaea > 0.1 Z ⊙ ) and UV-bright ( M UV, Althaea ≈ −22). 5 CONCLUSIONS In this paper we have studied the CO emission properties of galaxies at the end of the Reionization Epoch. First, we have developed a semi-analytical model that, given the internal density field of a GMC and the impinging FUV flux ( G 0 ) at the cloud surface, computes the CO line emission. The density PDF of the GMC is set both by turbulence (parametrized by the Mach number ) and self-gravity (parametrized by t / t ff ). The radiative transfer is performed with cloudy and includes z = 6 CMB radiation. The model takes the mean gas density n 0 , , t / t ff , G 0 as inputs, and it returns the luminosity of the first nine CO rotational transitions. We validated the model with local observations, demonstrating its capability to reproduce: the M vir - relation; the observed CO excitation in local SB galaxies; and the CO SLED of the low-metallicity ( Z ≈ 0.5 Z ⊙ ) molecular cloud N159W in the LMC. We used our validated CO emission model to post-process a cosmological zoom-in simulation of a prototypical z ≈ 6 galaxy ( M ⋆ ∼ 10 10 M ⊙ , SFR ∼ 100 M ⊙ yr − 1 ), Althæa. We have made the following additional assumptions: (i) we adopt a constant CRIR (cfr.


Comptonization; case 2: partially absorbed pure reflection spectrum; case 3: partially absorbed Comptonization spectrum with reflection; case 4: partially absorbed Comptonization with reflection and variable local absorber. Parameters are: intrinsic column density associated with the direct (Compton) spectrum and relative covering fraction (pcf and pcf), intrinsic column density associated with the reflection spectrum and relative covering fraction (pcf and pcf), electron temperature, Compton parameter (see text), relative reflection factor, ionization parameter (see text), comp PS normalization, Gaussian line energy, Gaussian line equivalent width, power-law photon index (for the dust scattering halo), power-law normalization (for the dust scattering halo), JEM-X calibration constant and ISGRI calibration constant. All the quoted errors are 1 level ones. Notice that all models include an additional absorber to account for the interstellar absorption ( N H 8.310 21 cm 2 ). The FeK line flux has been expressed in terms of ergcm 2 s 1 instead of equivalent width in order to allow direct comparison with the lines flux from Model 2 (see Section 5 , for which measuring the equivalent width is problematic). 4 SPECTRAL MODELLING MODEL 1: PARTIALLY COVERED REFLECTED COMPTON SPECTRUM 4.1 Case 1: partially absorbed Comptonization We initially fitted our data using the Comptonization model comp PS in xspec (see Poutanen Svensson 1996 ) modified by the interstellar absorption ( tbnew in xspec ; Wilms, Allen McCray 2000 ) with a fixed column density of N H 8.310 21 cm 2 . We left the Thomson optical depth electron temperature kT e and the normalization in comp PS free to vary, while we fixed the seed photon temperature to kT bb 0.1keV (i.e. the seed photons are produced by a multicolour disc blackbody with an inner disc temperature of 0.1keV) and the inclination to 67 (see Khargharia etal. 2010 ). We also fixed to zero the ionization parameter since it only affects the reflection component, which is switched off in this case. We left all the remaining comp PS parameters fixed to their default values. Large residuals indicated that a more complex spectral model was required. Therefore, we added a neutral absorber partially covering the source ( tbnew_pcf ). The addition of a narrow Gaussian line to describe the ironK line (see King etal. 2015 ) was required to account for some residuals around 6.4keV. The line is unresolved in both the Swift /XRT and INTEGRAL /JEM-X spectra; therefore we fixed its width to 0.2keV. This model did not provide satisfactory fits, having 2 = 620.12 with 461d.o.f. and null hypothesis probability = 9.8210 8 . Large residuals especially above 10keV indicate that the spectrum likely shows a significant reflection component. 4.2 Case 2: partially absorbed pure reflection Since the emission from the dust scattering halo was at times significant in the sky region around the source, sometimes outshining the source itself (see


K-S tests with respect to the radio properties, and found that the radio sizes of the absorbed and unabsorbed CSO samples could form two populations. In addition, the results of a two-dimensional two-sample K-S test confirmed the possible existence of such two populations. However, we caution that the two-dimensional two-sample K-S test requires a larger number of the absorbed sources (at least twice as many as in the current sample) to be valid. Our results could be interpreted in two ways. It could be that the CSOs with a high intrinsic X-ray absorbing column, N H > 10 23 cm −2 ; 0048+3157, OQ+208, 2021+614, 1511+518, 0108+388) have less evolved radio structures (smaller linear radio size) than X-ray unabsorbed CSOs with the same 5 GHz radio power. Thus, the environment in which a radio source expands might be able to confine the source growth already at the earliest stages of its evolution. This would provide the first observational evidence in the X-ray band that some compact jets may be frustrated by a dense environment and their kinematic ages may be underestimated. An alternative way of explaining the separation visible in Figure 4 is that the X-ray obscured sources have higher radio luminosity than the X-ray unobscured sources for a given radio size. The two factors that drive radio luminosity for a given size of a radio source are environmental density and jet power. Thus, one possible explanation is that the X-ray obscured sources are brighter for a given size because they were born in a denser environment. Another option is that they are brighter than the unobscured CSOs with the same size because they have higher jet power, which is related to central density, through e.g., the accretion rate (e.g., Allen et al. 2006 ; Tchekhovskoy et al. 2011 ; Ghisellini et al. 2014 ), or directly as in the model of Stawarz et al. ( 2008 ). Even though with the current data it is not possible to distinguish between these two explanations, we stress that in both cases the density of the CSO environment plays a key role. Moreover, our results raise a question about the origins of the X-ray emission and the location of the X-ray obscurer. If the CSO X-ray emission originates primarily from an active nucleus that becomes attenuated by obscuring material in the vicinity of the nucleus, then we should also see heavily obscured CSOs with larger radio structures. In contrast, the CSOs in our sample show low intrinsic X-ray absorption for the radio size exceeding a few tens of parsecs. If the CSO X-ray emission is dominated by inverse-Compton emission of the radio lobes (e.g., Stawarz et al. 2008 ; Ostorero et al. 2010 ), then the CSOs would become unobscured once their radio lobes expand beyond the region occupied by the dense material. Thus, it could be that the obscurer is located on scales smaller than a few tens of parsecs. Alternatively, the obscuring material could be destroyed or removed by the expanding radio source. Recently, Ostorero et al.


the marked outliers are not reliable enough for searching for flare candidates alone (see Fig. 1 ): it sometimes also marks the beginning of the light-curve windows. Thus we only used the RANSAC estimate of the inlier points for statistics and calculated the standard deviation of the light curve (with the rotational modulation and most of the flare points removed). We considered those points as first-order flare candidates that were above a given detection level (above 3 σ by default). To achieve more robust results, we shifted the search window through the light curve, by default in steps of one-fourth of the light-curve window (see Fig. 2 , e.g.). In this way, every light-curve point was analyzed multiple times (with the exception of those that are at the beginning or at the end of the data set or large observational gaps), and if a light-curve point is considered as an outlier, that is, a flare point candidate, it received a “vote”. A light-curve section was considered a flare when it received enough votes (≥3, by default) in overlapping search windows and had at least a given number (2, by default) of consecutive points. We note that this last step was performed only after evaluating each light-curve segment. These criteria are basically the same as those defined by Eqs. (3a)– (3d) of Chang et al. (2015) and are consistent with adaptations made by Davenport (2016) . When running FLATW’RM from command line, the user can change the number of flare points needed for a flare, the detection level of the flares, and the full with at half maximum (FWHM) that is used for the analytic fit of the events. Optionally, the rotation period can be given as an input to run the code faster, or to fix it to a chosen value if the rotational modulation is too weak, and the polynomial degree can also be fixed. The number of votes needed for a flare candidate to be kept, the window size (compared to the rotation period), and the step length with which the search window is shifted cannot be changed from command line, but can be easily modified if the flare-finding function is imported to another code. Fig. 2. Demonstration of the voting algorithm on a light-curve section of KIC 1722506. The top plot shows the original light curve (in blue, near a normalized flux of 1), and each light-curve segment in individual windows tested by FLATW’RM (each a different color), and the flare candidates are marked for the given run with circles. In the bottom plot , the candidates with one (light gray), two (medium gray), and at least three (black) votes are plotted. In this setup, the flares plotted in black are kept as final flare candidates. 2.4. Summary of the selection process For clarity, we explicitly state the procedure that FLATW’RM steps through in locating the flares in the light curve. A period search is first performed on the input light curve. The input light curve is divided into windows of 1.5 × P that can be effectively fit with polynomials. Each light-curve


they are not noticeably affected by the motions of individual stars within binary systems (because PMs provide a measure of the motions of stars integrated over a baseline and not an instantaneous measure of the velocity as RVs do). In the text that follows, we denote the velocity dispersions in RA and Dec. as σ α and σ δ , though technically the velocity dispersions of the PMs in RA and Dec. should be written as and . Fig. 5 shows the vector point diagram of PMs for the majority of Cyg OB2 members. The PMs of non-members of Cyg OB2 are not shown, but these have a similar distribution, implying that Cyg OB2 members cannot be kinematically separated from the field population. A number of outliers with very large relative PMs are evident in this diagram and are discussed in more detail in Section 3.5 . These outliers cause the velocity dispersion (Section 3.1 ) to come out very differently for a Gaussian dispersion compared to that calculated from an outlier-resistant method such as the interquartile range (IQR), and the use of a forward modelling approach (Section 3.2 ) reinforces this. Figure 5. Vector point diagram for members of Cyg OB2 with PMs (note that PMs are not placed on an absolute reference system but are only calculated relative to each other) with the spectroscopically known OB stars shown as red dots. The left-hand panel shows 869 of the 873 stars with PMs (four stars with very high PMs are not shown), highlighting the presence of a number of runaways or possible contaminants with high PMs. The right-hand panel (inset shown in the left-hand panel with a blue box) shows a close-up of the centre of the velocity space, with 822 of the 873 stars shown. 3.1 Calculating the velocity dispersions Fig. 6 shows the binned velocity distribution (over the range covered by the majority of stars), which has a broadly Gaussian distribution with low-amplitude, broad wings. The simplest estimate of the velocity dispersion is the standard deviation, which for our sample of 873 stars gives mas yr −1 and mas yr −1 (uncertainties calculated from a Monte Carlo simulation in which the individual PMs are varied by their estimated uncertainties). These velocity dispersions are considerably larger than the observed distribution because they are being enlarged by a number of outliers with large velocity offsets. There are 23 (17) stars with |μ| > 10 mas yr −1 in the RA (Dec.) dimension, and 1 (2) of these have |μ| > 100 mas yr −1 . These outliers could be removed by a process of ‘sigma clipping’, but this is a procedure fraught with difficulties of subjectivity and irreproducibility. Figure 6. PM velocity distributions along both axes (black histogram) showing the interquartile range velocity dispersions (green dashed lines) and the two-component Gaussian mixture model for the velocity dispersion (red dashed lines). The best-fitting velocity dispersions are listed in each case, which for the Gaussian mixture model is the dominant Cyg OB2 component.


optical copper lines are free of non-local thermodynamic equilibrium (NLTE) effects (e.g. Mishenina et al. 2002 ). The first indication that something could be wrong with this statement came from Shi et al. ( 2014 ), who noted that the important NLTE mechanism affecting the Cu i spectrum is the ultraviolet (UV) overionization. Later, Yan, Shi Zhao ( 2015 ) investigated copper abundance in 64 late-type intermediate metal-poor stars from Galactic disc and halo. They succeeded in showing that NLTE effects are important for this atom (the correction is about 0.17 dex for metallicity −1.5). The NLTE calculations enhanced the copper abundance obtained in the range of metal-poor stars, giving a flatter distribution of [Cu/H] versus [Fe/H] than was declared in previous works based on the local thermodynamic equilibrium (LTE) assumption. This conclusion was confirmed by Yan et al. ( 2016 ) who stated that NLTE effects are strong for copper in metal-poor stars. Until now, the most comprehensive study of the Galactic evolution of copper in the light of NLTE computation was performed by Andrievsky et al. ( 2018 ). They showed that for a sample of intermediate and extreme metal-poor stars ([Fe/H] from −4.2 to −1.4) the mean [Cu/Fe] value is about −0.22 dex. This is very different from the results of LTE analyses, which show significant underabundance at the early stages of Galactic evolution. Very recently, Roederer Barklem ( 2018 ) performed new work on copper abundance in late-type stars using UV Cu ii lines, which are supposedly free from the influence of the NLTE effect. The Hubble Space Telescope ( HST ) and ground-based spectra were used for this aim. They showed that the mean copper abundance in six warm metal-poor ([Fe/H] from −2.50 to −0.95) dwarfs derived from Cu i and Cu ii lines differs by 0.36 dex (Cu ii lines give higher abundance compared with Cu i lines). Generally, this difference agrees with derived NLTE corrections in metal-poor stars reported by Yan et al. ( 2015 ) and Andrievsky et al. ( 2018 ). In this paper, we examine NLTE copper abundance in a sample of the same six metal-poor stars derived from different Cu i lines (including the far-UV region) and Cu ii lines. We aim to obtain an independent estimate of the reliability of our NLTE corrections, as reported in Andrievsky et al. ( 2018 ). 2 SPECTROSCOPIC MATERIAL We employed UV stellar spectra that were secured with the help of the Space Telescope Imaging Spectrograph (STIS; Kimble et al. 1998 ; Woodgate et al. 1998 ) on board the HST . Observations were made using the E230H echelle grating, the 0.09 x 0.2 arcsec 2 slit and the NUV Multianode Microchannel Array detector.The resolved power was R = 114 000. The investigated Cu i and Cu ii lines are situated in the range 2024−2248 Å. We retrieved archive spectra from the Mikulski Archive for Space Telescopes (MAST). All spectra are centred at 2013 Å. The following lines fall in the spectral range: Cu i 2024 Å and Cu ii 2037, 2055,


experiments in Rongcheng, along with the measured median profiles, are shown in Fig. 4 . The performance for estimation by the Dewan outer scale is the worst among four models. The estimated by the Dewan model is much smaller than the measured value below 8 km, with an abrupt change occurring at 8 km, and much larger than the measured value above 8 km. For completeness, Appendix A discusses the individual profiles in Rongcheng. The HMNSP99 and Thorpe models have a similar performance for estimation below 12 km, and are consistent with the measured values in both change trend and magnitude. At high altitude, the two models deviate from the measured values by different degrees: a larger deviation above 12 km appeared for sounding experiments for the Thorpe model. The Sθ model has the best prediction results, and it is consistent with the observed median profile in variation trend and magnitude. The relative error profiles for the above four models are illustrated in Fig. 4(b) . The relative error can demonstrate the variation of the deviation between the estimated value and the measured value with altitude. The deviation between the Dewan model and the observed median turbulence is the largest, while that of the Sθ model is the smallest, for all altitudes. The HMNSP99 and Thorpe models have a similar performance in RE (relative error) below 10 km, while HMNSP99 has better results above 10 km. Figure 4. Evaluation of the estimated median profiles (Rongcheng): (a) comparison of the estimated median profiles using the Thorpe (red), HMNSP99 (blue), Dewan (purple) and Sθ (green) models, and the measured profiles (black); (b) relative error of the estimated median profiles. Table 4 presents the RMSE, R xy , and MRE for the estimations of median obtained from the considered four outer-scale models for balloon experiments. The RMSE and MRE of estimated by the Sθ model are better than those for the other three models. It is worth noting that the R xy values of Thorpe, HMNSP99 and Sθ exceed 0.9, which means that the three models may accurately reflect the variation trend of measured turbulence. For the median values, the correlation coefficient of the estimated by the Sθ scale was the highest of all four models. As shown in Table 4 , the average relative error of the median values was generally lower than 1.6%, which meets estimation accuracy requirements for . Table 4. Statistical analysis for the estimation of in Rongcheng using the four outer-scale models, given for median profile. The specific results of the integral statistics of each sounding balloon and median profiles for Rongcheng are tabulated in Table 5 . Clearly, the Sθ scale provides reliable results, close to observed values. As can be seen, our new outer-scale model gives reasonable results when calculating integrated atmospheric parameters. Table 5. Comparison of integrated atmospheric parameters obtained via values observed by meteorological balloons and estimated by the Sθ model


1843.03. Contours are spaced in 5% intervals in core mass fraction, with darker colors corresponding to high core mass fraction and lighter colors corresponding to low core mass fraction. As expected, denser planets with higher core mass fractions survive to shorter orbital periods. The limiting orbital period of a pure iron planet is approximately 3.8 hr at , 3.6 hr for , and 3.5 hr for . We note that this figure marginalizes over stellar mass because stellar mass only weakly affects the Roche-limiting minimum orbital period (Rappaport et al. 2013 ). The stellar density does, however, affect whether the planet can reach its Roche limit before colliding with the star (i.e., a = R ⋆ ) and thereby the minimum survivable orbital period for the planet. Figure 4. Composition and mass constraints on planets with KOI 1843.03's measured transit radius and host star mass. Colored contours show the values of the planet mass, which increases with decreasing orbital period and increasing core mass fraction. The boundary of the colored contours in the lower left corner corresponds to the Roche limit. The dashed gray line indicates the measured orbital period of KOI 1843.03. Figure 4 displays interpolated planet masses for a range of orbital periods and core mass fractions in systems consistent with KOI 1843.03's host star mass and transit radius. The boundary of the colored contours in the lower left corner corresponds to the Roche limit; as orbital period decreases, the core mass fraction is more tightly constrained. As anticipated, considering a fixed orbital period in Figure 4 , increasing the planet’s iron mass fraction increases the planet’s mass. Less intuitively, at fixed core mass fraction, decreasing the planet’s orbital period also leads to an increase in the inferred planet mass. This is due to the tidal distortion of the planet; at shorter orbital periods, the volume of the planet exceeds by larger and larger factors. As it orbits less than one stellar radius from the host star’s photosphere ( a / R ⋆ = 1.9), KOI 1843.03 will be significantly elongated in the direction of the star due to tidal distortion. Based on the parameters of KOI 1843.03, our models predict that it must be at least 31% longer along the star–planet line than along the perpendicular axes (aspect ratio of about 1.3), and our models support a value up to nearly twice as long along the star–planet line (aspect ratio of almost 1.8); various possibilities are illustrated in Figure 5 . For comparison, Saturn has an aspect ratio of about 1.1. Figure 5. Aspect ratio constraints on KOI 1843.03, as a function of core mass fraction. To the left of the plot, we indicate the maximum and minimum values of aspect ratio supported by the model grid and show three representative planet cross-sections (assuming ellipsoidal shapes); peach and navy represent the iron-dominated core and silicate mantle, respectively. Results are shown both at the measured transit radius 0.61 and the 1 σ limits


structure is completely determined by the conservation of rest-mass, energy, and angular momentum of the accreting gas, the Polish donut model is less constrained. It requires the relation between the fluid angular velocity and the fluid angular momentum per unit energy, Ω = Ω ( l ), as well as the fluid angular momentum per unit energy at the inner edge of the disk, l in . The simplest Polish donut model is the configuration with l = constant, which turns out to be marginally stable with respect to axisymmetric perturbations (Font Daigne 2002 ). Accretion disks in the Kerr spacetime only exist for l ms l l mb , where l ms and l mb are, respectively, the angular momentum per unit energy of the marginally stable equatorial circular orbit (or ISCO) and of the marginally bound equatorial circular orbit (Abramowicz et al. 1978 ; Bardeen et al. 1972 ; Li Bambi 2013 ). Indeed, for l l ms , the fluid angular momentum is too low and there is no stable accretion disk (the fluid directly plunges onto the black hole), while, for l > l mb , the fluid angular momentum is too high and there is no accretion (there is just a fluid rotating around the black hole). In the presence of an accretion disk, when , the inner edge of the disk, R in , is between the marginally bound orbit and the ISCO, i.e., R mb R in R ISCO (Bardeen et al. 1972 ; Abramowicz et al. 1978 ; Li Bambi 2013 ); that is, for a given black hole spin, the inner edge of a Polish donut disk is always smaller than the inner edge of a Novikov–Thorne disk. Since the exact location of the inner edge of the disk is crucial in reflection spin measurements, we can already suspect that systematic uncertainties related to the use of an incorrect disk model to fit the data of a source can be important. 3. Simulations and Fits In order to estimate the impact of the disk structure on spin measurements with the iron line method, we use the code presented in Riaz et al. ( 2020 ) to calculate the theoretical reflection spectrum of a Polish donut disk. We use the xillver model (García Kallman 2010 ; García et al. 2013 ) to calculate the nonrelativistic reflection spectrum at the emission point in the rest-frame of the gas in the disk, and we use our ray-tracing code to convolve this nonrelativistic spectrum into a relativistic spectrum of a thick disk. At this point, we need to choose the properties of our source and of our instruments to simulate the observation of a black hole with a thick accretion disk. As X-ray mission, we consider NICER (Gendreau et al. 2016 ), which has a good energy resolution near the iron line and is thus suitable for X-ray reflection spectroscopy measurements. We assume that the source has a very simple spectrum, just a power-law component and a reflection component. In XSPEC language (Arnaud 1996 ):where TBABS takes the Galactic absorption into account (Wilms et al. 2000 ), powerlw is the power-law component generated by inverse Compton scattering of thermal photons from the disk off


broadly consistent with the predictions of Fairhurst ( 2011a ). While the inclusion of LIGO-India was not examined in Fairhurst ( 2011a ), we recover a median localization of 9.3 deg 2 for the HIKLV network. 4.3. Comparison with Previous Studies We can compare our result to several studies of advanced network sky localization that have already been performed. We compared our results to those from analytic expectations of Wen Chen ( 2010 ) and Fairhurst ( 2011a ) throughout Sections 4.1 and 4.2 , respectively. The expression used to calculate the expected error regions from Wen Chen ( 2010 ) produces values that are consistent with both Fairhurst ( 2011a ) and our studies. In addition, our study remains broadly consistent with the analytic results of Vitale Zanolin ( 2011 ), recovering similar scalings in localization improvement for successive detector networks for a canonical BNS to our results in Table 2 . Studies such as Singer et al. ( 2014 ) have examined the sky localization capabilities of two- and three-interferometer networks of LIGO and LIGO–Virgo, using more realistic assumptions. In particular, they carried out an end-to-end study of the localizations from the outputs of one compact binary search pipeline used in the first two observing runs (Messick et al. 2017 ). They use a stream of data with colored, but Gaussian, noise and apply a minimum network S/N cut of 12 for each event. Singer et al. ( 2014 ) projected that Virgo would join the LIGO instruments during the second observation run at the sensitivity indicated in Abbott et al. ( 2016b ). They examine a population of BNSs in the HLV configuration, obtaining a median sky localization of 235 deg 2 at the 90% credible level. For our study of NSBH localization, we obtain a median sky localization of 193 deg 2 , seemingly contrary to the expectation that BNS sources are better localized than NSBHs. However, the fiducial networks in our study are have better sensitivities over a given frequency range compared to Singer et al. ( 2014 ), leading to improvements in the effective bandwidth measured by a given instrument. So, our improved localization from that predicted by Singer et al. ( 2014 ) can be attributed to our use of 2018-era instruments as opposed to the less-sensitive 2016 configuration used in Singer et al. ( 2014 ). Rodriguez et al. ( 2014 ) resolve sky localization for a BNS population in which each event realizes a network S/N of 20. On the contrary, our NSBH study samples a wide distribution of network S/Ns, meeting a minimum S/N threshold. 6 6 We require an S/N of at least 5.5 in the second-loudest detector. Therefore, our study probes the S/N regime at which detections are most likely to occur, while Rodriguez et al. ( 2014 ) ignores this low network S/N range. Nevertheless, our Figure 1 is qualitatively comparable to Figures 6 and 7 in Rodriguez et al. ( 2014 ). In particular, the increased isotropy of a three- to four-instrument network and the subsequent,


, H β and H α , and narrow [O iii ] λλ 4959, 5007, and Balmer lines. The absorption features around 5450 Å are telluric. The arc spectrum shows some narrow emission lines, such as [O ii ] λ 3728, H β , [O iii ] λ 5007, H α , and [N ii ] λ 6583, and some weak absorption lines, such as Ca ii K λ 3933 and Ca ii H λ 3968. The arc spectrum is contaminated by the QSO, showing broad H α and Mg ii lines (see Section 2.2.2 for details). The redshift of the QSO is measured to be 0.3954 ± 0.0001 from the [O iii ] λλ 4959, 5007 emission lines. The redshift of the arc, using the QSO-contamination-subtracted spectrum, is measured to be 0.3970 ± 0.0001 via [O ii ] and H β emission lines, and consistent with the value of 0.3968 ± 0.0003 measured via the Ca ii K λ 3933 and Ca ii H λ 3968 absorption lines. The arc is likely located nearer than the QSO and moving toward it with a line-of-sight velocity of roughly 340 km s −1 . Figure 4. VLT FORS2 spectrum of the QSO PHL 6625 with model components. We fitted the spectrum from 2750 to 7100 Å, where the S/N is high. The windows used to fit the continuum are marked in black bars, and pixels with telluric absorptions around 5450 Å were excluded in the fitting. The dereddened spectrum is shifted to the rest frame of the QSO at z = 0.3954. Purple: power law; yellow: pseudo-continuum = power law + Fe ii templates; red: summed line model; blue: narrow-line components; green: broad-line components. Figure 5. VLT FORS2 dereddened spectrum (black) of the arc galaxy with the QSO contamination (blue), the galaxy population synthesis model (green), and the total model (red). All emission lines and telluric absorptions are masked during the population synthesis fit. The dereddened spectrum is shifted to the rest frame of the arc at z = 0.3970. 2.2.1. Decomposition of the QSO Spectrum The QSO spectrum is decomposed into multiple emission components following Shen et al. ( 2008 ). The fitting is performed in the rest-frame wavelength range of 2750–7100 Å, where the S/N is sufficiently high. First, a pseudo-continuum was fitted to the spectrum in some continuum windows 12 12 2925–3500 Å, 4200–4230 Å, 4435–4700 Å, 5100–5535 Å, 6000–6250 Å, and 6800–6900 Å at the rest frame. , consisting of a power-law component and Fe ii templates in both the Mg ii region (Salviander et al. 2007 ) and the H β region (Boroson Green 1992 ). The continuum-subtracted line spectrum was then fitted with multiple Gaussian components: three Gaussians for each of the H α , H β , and Mg ii broad components; five Gaussians for narrow lines in the H α region; 13 13 Two for [S ii ], two for [N ii ], and one for narrow H α . three near H β; 14 14 Two for [O iii ] and one for narrow H β . and one for narrow Mg ii . All of the narrow lines are imposed to have the same shift and width. The monochromatic continuum luminosity λL λ of the power-law component at the rest frame 3000 and 5100 Å, the power-law spectral index, and the broad-line width derived from the


acceleration. Our inference above is qualitatively different from these models in the sense that it is independent of SNe event in a star cluster. We also note that LOFAR observations show PeV CRs to be enriched in low-Z nuclei (Buitink et al. 2016 ), consistent with their being accelerated from CNO enriched wind material in SBs (Thoudam et al. 2016 ). It is also possible that the hard component of CRs due to WTS is the one inferred to be present in molecular clouds (de Boer et al. 2017 ). Therefore, WTSs are potential PeVatrons and they should be studied in detail in this regard. 5.5 Decoupling of grammage from ISM Our proposed scenario can also provide the astrophysical framework for the phenomenologically motivated models of CR propagation in which the grammage traversed by CRs are mostly near the source (Blasi Serpico 2009 ; Cowsik Madziwa-Nussinov 2016 ; Eichler 2017 ; Biermann et al. 2018 ). In these models, the diffusion property of CR particles is assumed to be different inside the ‘cocoons’ surrounding the CR acceleration sites than elsewhere in the ISM in order to alleviate problems associated with secondary production. The scenario of CR acceleration in SBs satisfies the basic premises of these models, since most of the CR collisions occur in the outer shell of shocked ISM, whereas CRs are advected by the wind in the inner regions. The grammage suffered by CRs in the shocked ISM region is ∼10 g cm −2 , comparable to the total grammage of GCR (Gabici et al. 2019 ), since the typical residence time is t r ∼ 1 Myr (∼κ/ v 2 , for a diffusion coefficient κ ∼ 10 27 cm 2 s −1 and v ∼ 50 km s −1 , the typical outer shock speed), and typical density in this region is ∼10 cm −3 . Therefore, CR grammage can be decoupled from Galactic residence time, alleviating a number of outstanding problems (Butt 2009 ; Gabici et al. 2019 ). Instead of listing them all, we mention one of the problems here, that of the observed scaling of light elements with metallicity in halo stars (Parizot Drury 1999 ). In the case of isolated SNRs (which accelerates ISM particles), the Li/Be/B abundance is expected to scale as Z 2 , since both CR and the target gas share the same metallicity. In the case of WTS, the metallicity of CRs is independent of that of the ambient ISM, the abundance of spallation products should scale as Z , as observed (Parizot Drury 1999 ). 5.6 Caveats and future directions In this study, we show the first calculations for estimating the energetics of the wind and SN shocks in isolated stars/star clusters. We have used a shock detection algorithm and three different tracers to quantify the fraction of shock energy processed by wind, SN ejecta, and ambient material. Although in the above sections, we have shown that this study has succeeded in revealing answers to various problems in GCRs, below we highlight some of the limitations of our models and future directions. Non-radiative strong shocks: We have considered the Rankine–Hugoniot


effect saturates in the DML, so MOND can provide only a limited amount of additional stability even for a galaxy with arbitrarily low surface density. This might explain why low surface brightness disk galaxies often have spiral features (McGaugh et al. 1995 ), usually taken as a sign that disk self-gravity is important (Lin Shu 1964 ; Das et al. 2020 ). The global stability of disks thus offers a promising way to break the CDM-modified gravity degeneracy in galaxies. M33 is one of the nearest galaxies with a rather low surface brightness. S19 recently conducted isolated N -body and hydrodynamical (hydro) simulations of M33 in the CDM context. As with many other galaxies, its observed RC required them to use a cored DM profile. They found it rather difficult to explain the weak observed bar together with the two-armed spiral (Corbelli Walterbos 2007 ) in the presence of a live CDM halo. Weak bars are also observed in many other galaxies (Cuomo et al. 2019 ). They are problematic in the CDM picture because a bar in the baryons creates a response in the live DM halo, which would cause a resonant effect (Athanassoula 2002 ). This was demonstrated explicitly by S19 , who compared their live halo simulations to a “frozen halo” simulation in which the DM particles provide a fixed gravitational potential. 7 7 This can be thought of as the DM particles providing gravity but not moving. S19 showed that M33 would be more stable in a frozen halo, leading to a weak bar similar to that in the observed M33. Such a model is of course unphysical in the ΛCDM context, but useful to better understand the dynamics. Interestingly, a frozen halo is somewhat similar to gravity theories like MOND where galaxies lack hypothetical DM. This is because features in the disk very rapidly become irrelevant to the potential as one moves away from its plane. Consequently, perturbations in the disk have very little effect on the Milgromian “phantom DM” (PDM) halo because its density depends only on the local potential. 8 8 PDM is the DM density distribution that would be needed for the Newtonian gravitational field to equal the MOND one of the baryons alone. The PDM distribution of thin exponential disks was visualized in, e.g., Lüghausen et al. ( 2013 , 2015 ). Indeed, this is why a bare disk can be stable in MOND. The lack of an actual DM halo automatically removes the possibility of bar–halo angular momentum exchange. However, disk self-gravity is enhanced in MOND compared to the case of a frozen DM halo. The presence of an EFE would slightly decrease this enhancement, but would also decrease the spheroidal potential support from the PDM. In general, it would also break the axisymmetry and up–down symmetry of the problem. Clearly, numerical simulations are needed to properly understand how disk stability is influenced by a fundamental modification to the gravity law. Several MOND N -body simulations have considered isolated disks, starting with the seminal work of Brada


little variation of A e with rotation. The peak values are also quite different: 150 per cent for HD 37776, 50 per cent for HD 189775, and only 10 per cent for HD 175362. Stars with highly variable A e likely exhibit greater surface abundance anisotropies than stars in which A e is less variable. In order to obtain a single number with which to characterize the average strength of deviations between the magnetic curves derived for different elements for a given star, we used the idl curvefit routine to generate second-or third-order harmonic best fits, which were then integrated as functions of rotational phase. The significance of this integrated value is then A e /σ e , which is given for each star in the second-last column of Table 2 , where σ e is the mean uncertainty in the individual A e measurements. If A e /σ e 1, it can be concluded that differences in 〈 B z 〉 between different elements are a consequence of noise rather than real variations. It is this significance in which we are interested, as it will help to decide whether accurate measurements are available using metallic lines, or whether H lines should be used instead. Fig. 9 shows the histogram of A e /σ e for all stars. For the full sample (top panel), the median significance is 2.7σ. For the sub-sample of He-weak and He-strong Bp stars, the median of the distribution is at 2.9σ (second panel from the top). Amongst pulsating β Cep and SPB stars (third panel from the top) and the remainder of the sample with no apparent peculiarities (bottom panel), only one star, HD 96446, has A e /σ e ≥ 3: as HD 96446 is also a He-strong star, this likely reflects the star's chemical peculiarities. The medians of these distributions are 1.4σ and 1σ, respectively. While there are only eight non-chemically peculiar stars for which A e could be measured, these results are consistent with an origin of the effect in distortion due to chemical spots, and confirm that when chemical peculiarities are not present, there is no significant difference in 〈 B z 〉 when measured using different chemical elements. Even amongst the Bp stars, although there are several stars for which A e /σ e ≫ 3, differences in 〈 B z 〉 measured from different elements are negligible for many of the stars. Figure 9. Significance histogram for A e for (top–bottom) all stars in the sample for which A e could be measured, Bp stars, pulsating stars, and chemically normal, non-pulsating stars. The dashed line marks 3σ significance. Approximately half the sample shows at least a 3σ spread in 〈 B z 〉 measurements conducted with different elements. All of these are Bp stars: the only pulsator with A e /σ e ≥ 3 is HD 96446, which is also a He-strong star. It should be noted that while the mathematical treatment of A e is based upon random uncertainties, these variations are in fact systematic . Unfortunately, it is not obvious what simple mathematical tools might be utilized in order to capture the systematic variations between


5.2. Comparison with the IRSF monitoring data in the SMC The NIR monitoring data for three stars has recently been published by Ita et al. (2018) using the InfraRed Survey Facility (IRSF, Kato et al. 2007 ). These data were not used in our LC analysis and can therefore serve as an independent test. The K -band data ( H band for 12.627600 −72.858307) were analysed in the same way as the VMC data and literature data. Table 2 compares the periods and amplitudes. For the first two stars the agreement is good. In the last case the periods do not agree within their mutual error bars, but this is a faint source for the IRSF survey ( K ∼ 15.5 mag), while our analysis might be hampered by the relatively small number of data points (18 in total). Table 2. Comparison with three sources in the IRSF survey. Notes. (a) In the K band. 5.3. LPVs with periods over 1000 days Of the likely AGB stars, 34 stars have periods longer than 1000 days 6 . The longest period we find is 3108 d, but this object has alternative periods that are much shorter. Six other stars also have shorter possible periods, and therefore the periods beyond 1000 days are only tentative in these cases. It will be interesting to analyse the IRSF data for the LMC objects when they become available (cf. the SMC data presented in Ita et al. 2018 ). Nine stars with periods over 1000 days in the MCs were previously reported by Wood et al. (1992) and Whitelock et al. (2003) based on NIR observations. Recently, Menzies et al. (2019) presented a compilation of Miras with periods over 1000 days in the Milky Way (17), SMC (3), and LMC (18), while Karambelkar et al. (2019) published a list of 417 luminous IR variables, of which 86 have periods over 1000 days, located in seven galaxies (the majority in M 83 (49 objects), and M 81 (11 objects)). The compilation by Menzies et al. (2019) was based on Wood et al. (1992) and Whitelock et al. (2003) , OGLE data in the SMC and LMC ( Soszyński et al. 2011 , 2009a ), and GS18 (which is partly based on a preliminary analysis of VMC data). Of the 21 MC objects, 18 are confirmed with updated periods. Three objects are not in our list. One object (IRAS 05506−7053) is too red; the period in GS18 is based on WISE data. The two others (HV 888 and HV 11417) are too blue to have passed the selection criteria, and both have been classified as RSGs (GS18, Kraemer et al. 2017 ). The longest period in the study of GS18 of almost 400 AGB stars with Spitzer IRS spectra is 1810 d based on a re-analysis of OGLE-III data for MSX SMC 055 (also known as OGLE-SMC-LPV-08137 and IRAS 00483−7347). No errors on the period are given in GS18 because they are very hard to reliably estimate for these long periods. The period in the OGLE-III release is 1859 d, which gives some indication of the uncertainty. In Groenewegen et al. (2009) such a long-period has been recognised based on OGLE-II data and, it was suggested that the object may be a candidate super-AGB star, based on its


the 12 CO line profiles are dominated by infall and outflow motions and we find no significant evidence of rotation in the outflow. As mentioned in Sect. 3.2 , however, CH 3 OH and SO 2 do show clear evidence for rotation within ~16 au ( Fig. 8 ). This emission originates in the central region, where it appears that material is infalling and rotating simultaneously. Even so, the velocity gradients measured from the CH 3 OH and SO 2 lines are consistent with one another, and thus one might expect that the outflow should rotate in the same sense. A 12 CO moment 1 map ( Fig. A.3 ) and line profiles at different positions ( Fig. 4 ), meanwhile, do not show any significant difference in the velocities between northern and southern outflow cavity walls. In the redshifted outflow, however, there is a blueshifted component at small separations (≲30 au) south-west of the protostar ( Fig. 3 ), consistent with the inferred rotation seen in SO 2 and CH 3 OH. Likewise, a redshifted component is observed in the blueshifted outflow on comparable scales, but this component is seen along the jet axis and not the north-western side as would be expected if this component was due to rotation in the outflow. Attributing the inner features to rotation is in any case difficult since the outflow is nearly in the plane of the sky, and expansion of the outflow, deviations of the outflow axis from axisymmetry, or internal shocks (e.g. Fendt 2011 ) can produce similar features. Hints of expansion are indeed seen in the lowermost PV diagram of Fig. 9 , where an extended U-shaped structure is observed at blueshifted velocities. Although this emission structure barely exceeds the 3 σ threshold, itis clear that the velocity is increasing towards the outflow axis. A similar feature is found on the redshifted side at slightly lower S/N, and lower velocities. While an onion-layered velocity structure (whereby velocities close to the outflow axis are high and then fall off with distance) is expected for a rotating, magnetically-launched wind (e.g. Bacciotti et al. 2002 ; Pudritz et al. 2006 ), the symmetry of the PV diagram w.r.t. the zero position offset in the lowermost panel of Fig. 9 is not consistent with this picture. It is, however, consistent with expanding cavity walls. The rotation and expansion velocity at different offsets from the protostar can be estimated using the method presented in Lee et al. (2018) , assuming that only two velocity components are present. While this is an oversimplification of reality, assuming the outflow velocity does not change significantly over the considered distances, it does provide a useful method to deduce any trends in rotation and expansion. We fit 2D Gaussians to several PV diagrams with cuts perpendicular to the outflow axis but with different offsets. One example of such a fit (at zero offset from the continuum peak) is presented in the uppermost panel of Fig. 9 ). We only consider pixels where the emission is above 3 σ ,


2009 ), which assumes that all LyC flux converts to unbinding the atmosphere. The LyC flux corresponds to the energy-limited mass-loss rate . In this case, the adiabatic cooling rate is and still has a less than 15% effect in the region of main concern. 8.2. Comparing with Other Hot Jupiter Upper Atmosphere Models Christie et al. ( 2013 ).—The present study agrees with the conclusion in Christie et al. ( 2013 ) that the 2 p occupation is set by radiative excitation and de-excitation, and as an improvement, we include an Ly α radiation transfer inside the atmosphere instead of applying a constant solar Ly α intensity. Because of the ∼30 times stronger stellar Ly α intensity of HD 189733 compared to the Sun and considering the Ly α photons generated inside the atmosphere owing to collisional excitation and recombination cascades, the Ly α mean intensity should be ∼100 times larger for the majority of the atomic layer. In addition, because Christie et al. ( 2013 ) underestimate n 2 p by a factor of 20 owing to a math error, n 2 p should be significantly larger in the whole simulation domain, and thus the atmosphere is optically thick to H α mainly owing to the absorption of H(2 p ). The observed H α absorption width agrees well with an optically thick atmosphere model. Because of the much larger , the photoionization of H(2 l ) is larger compared to photoionization of the ground state in the atomic layer. Hence, n e and n p in this work are ∼10 times larger. Considering the proton collisional l -mixing process with a rate ∼10 times larger than the electron collisional process, as well as the large H(2 p ) population, the creation of 2 s hydrogen is dominated by l -mixing rather than collisional excitation considered in Christie et al. ( 2013 ). As a result, 2 s and 2 p reach collisional equilibrium. In addition, it is shown that the metal lines are crucial in cooling the atmosphere. Assuming solar abundance, lines of Mg and Na can cool the atomic layer by ≃2000–3000 K. Menager et al. ( 2013 ).—Menager et al. ( 2013 ) investigate the Ly α emission and reflection by the atmosphere of HD 189733b. The temperature and electron, hydrogen, and helium number density profiles of HD 189733b from the Koskinen et al. ( 2011 ) unpublished model were applied. The temperature, n e , n p , and are in broad agreement with the profiles presented in this paper in the corresponding pressure range. According to a similar model of HD 209458b presented in Koskinen et al. ( 2013a ), it should be a one-dimensional hydrodynamic model of the upper atmosphere considering hydrogen and helium constructed on top of a full photochemical model of the lower atmosphere. They chose the average solar flux as their stellar spectrum, which is ∼10 times smaller than the synthetic spectrum from MUSCLES. Different from the photoelectron heating efficiency calculated at the fixed ionization fraction x e = 0.1 throughout the model, or a constant η applied in Koskinen et al. ( 2013a ), a


spectrum (Figs. 2 and 3 of Ho et al. 2003 ), while atomic hydrogen transitions may produce additional features. That may explain some of the observed multiple lines. In view of the limited significance of the line detections it appears difficult to make specific assignments. Another way to explain multiple lines is to invoke – beyond the radiation from the hot cap at the magnetic dipole – separate hot spots on the stellar surface having higher multipolar magnetic fields. The first strong evidence for this comes from the discovery of strongly phase-variable absorption lines which are visible only for about 20% of the neutron star rotation. The lines were detected in the X-ray spectra of RX J0720.4−3125 and RX J1308.6+2127 ( Borghese et al. 2015 , 2017 , respectively) and have energies a factor of ∼2.5 higher than the broad lines (Table 3 ). Such multipole fields must be quite young compared to the age of the NS. They may be formed by extracting magnetic energy from the toroidal field that resides in deep crustal layers, via Hall drift (e.g., Geppert Viganò 2014 ). We conclude that proton cyclotron lines produced in strong magnetic fields of isolated neutron stars can explain the absorption-type features observed in the soft X-ray spectra of young isolated neutron stars of the M7 class. More accurate measurements in the future in combination with further theoretical work on magnetized atmospheres and the magneto-thermal evolution of neutron stars are required to make further progress in this exciting field. 9. Summary With this contribution we attempt to provide a review on the current state of our knowledge about X-ray sources that show cyclotron line features in their spectra – both for electron cyclotron lines (this is by far the larger part) and for proton cyclotron lines. We concentrate on the observational aspects, providing a number of Tables that contain detailed informations on all sources that we consider reasonably well secured regarding the existence of cyclotron lines. In the case of electron cyclotron lines – observed from binary X-ray pulsars, highly magnetized accreting neutron stars in binaries – we also give a Table with candidate sources, mostly objects for which a detection of a cyclotron line was claimed some time ago, but had not been confirmed in subsequent observations, or sources that were observed rather recently, but only once and with somewhat peculiar properties. On the other hand: for some of the objects listed in the main Tables, the existence of a cyclotron line still needs confirmation (or not) through re-measurements (with a finite probability that they have to be moved into the candidates category). We try to address the basic physics underlying the cyclotron line phenomenon, including a large number of references to theoretical work, with some coverage of specific theoretical modeling. Since the discovery of the first CRSF in Her X-1 in 1976, a new field of Cyclotron Line Research has evolved. With the rather


multilayer system. In general, unlike the symmetric case studied, e.g., by Roberts ( 1981b ), the dispersion relation Equation ( 15 ) cannot be decoupled into two equations that correspond to the well-known sausage (oscillations at the slab boundaries in antiphase, that correspond mathematically to the equation containing ) and kink (perturbations of the slab boundaries oscillating in-phase that correspond to the equation with ) MHD waves. Solutions to Equation ( 15 ) will provide modes modified by the density difference at the sides of the magnetic slab similar to a single asymmetric slab investigated by Allcock Erdélyi ( 2017 ). We adopt the notions of quasi-sausage and quasi-kink to describe these eigenmodes, because they have mixed characters. The slab cross-sectional width, that is constant for symmetric kink modes, is affected for asymmetric kink modes and the line of zero perturbation is shifted for asymmetric sausage modes when compared to the symmetric case, namely, the center of the slab. Furthermore, both the sausage and kink modes can be further categorized as body and surface modes. Surface waves exist when , which corresponds to evanescent solutions of Equation ( 5 ), while body waves exist when , which corresponds to spatially oscillatory solutions. This nomenclature for wave classification was introduced by Roberts ( 1981b ) for symmetric and Allcock Erdélyi ( 2017 ) for asymmetric equilibria. Let us now consider some specific cases of an asymmetric multilayered plasma slab structure that are analytically solvable and have potential for solar application. First, by setting p = q = 0, we verify that the dispersion relation reduces to that which governs the asymmetric slab configuration of Allcock Erdélyi ( 2017 ), namely,We will now focus on cases of two layers (one magnetic and one nonmagnetic), and three (a magnetic layer sandwiched between two nonmagnetic) slabs, respectively, and investigate how the multilayered structure affects the eigenmodes and their eigenfunctions. 2.1 Two-slab Case Let us first consider the case of two slabs, represented by p = 1 and q = 0, which is illustrated by Figure 2 . The width of the nonmagnetic and magnetic slabs are denoted as and d 0 , respectively. Such a model could be useful for modeling MHD waves in MBPs of the solar photosphere (as shown on Figure 3 ). MBPs are approximately vertical magnetic structures between supergranule convection cells of different densities and temperatures. Since neighboring granular cells affect the MBP, we can apply a two-slab description to analyze what will change when comparing eigenmodes to MHD waves in a single slab case. Figure 2. Equilibrium configuration for a two-slab case: a magnetic slab, , and a nonmagnetic slab, . Figure 3. Asymmetric multislab approximation for an elongated MBP, based on Figure 11 of Liu et al. ( 2018 ), observed by the New Vacuum Solar Telescope in TiO 7058 Å. From condition ( 15 ), we obtain the dispersion relationNote, that the