→ ∞. This arises from the fact that the gravitational restoring force contains an imaginary component, which acts as an anti-damping (growth) term and dominates the Chandrasekhar dynamical friction when the angular velocity is sufficiently large. Order-of-magnitude estimates for the various time-scales (damping and oscillation) were computed, and their ramifications in the context of this rotating system were explored. We also demonstrated a formal equivalence between Eddington black hole accretion and dynamical friction, thereby ensuring that both these problems can be treated in a unified manner. Through a comparison of the time-scales, it was shown that the Eddington accretion time-scale is faster in some instances, thereby constituting the more dominant effect. However, as black holes cannot accrete matter in such a fashion indefinitely, the limitations of this paradigm were also duly indicated. We have discussed some of the limitations of our formalism in Sections 1 and 5 , since some of the inherent assumptions are not accurate over the entire domain of the galaxy. However, it may be possible to use some of the results obtained herein to study the dynamics near the Galactic Centre (Genzel et al. 2010 ). For instance, recent numerical simulations of supermassive black hole binaries, with Galactic rotation taken into account, suggest that they can be significantly displaced from the Galactic Centre (Awais Mirza et al. 2017 ). Hence, the formalism developed in this paper may provide a heuristic explanation for such phenomena (although we have considered only single black holes in our analysis). Additionally, as the solutions obtained are analytical in nature, the main purpose of the paper is to arguably provide a benchmark solution against which numerical simulations can be compared. Lastly, we note that our treatment is quite general as it is Newtonian in nature, and does not invoke any of the specific features of black holes – it is equally applicable to a massive object in a sea of light particles. For instance, it may be possible to consider Saturn as our massive object, and the (moonlets that constitute) rings of Saturn as the lighter particles, analogous to the works of Griv et al. ( 2000 ) and Griv, Gedalin Yuan ( 2003 ). Moreover, it might be possible to also model axisymmetric systems via this formalism, in the regimes specified herein, such as discs with a Miyamoto–Nagai gravitational potential (Miyamoto Nagai 1975 ). By employing the same mathematical methods employed herein, we can also model the dynamics of a Reissner–Nordström (charged) black hole interacting with a constant galactic magnetic field via the Lorentz force. APPENDIX A: DYNAMICAL FRICTION IN A ROTATING ISOTROPIC CLUSTER Consider a cluster described by a potential–density pair together with an ergodic distribution function (DF) . If we introduce an overall rotation to the cluster, then it was argued in Lynden-Bell ( 1967 ) that the new DF can be obtained by the


If the synchrotron losses dominate as a radiative cooling channel, the product of the maximum attainable energy and the square root of the magnetic field strength, , can be taken as a measure of the accelerator efficiency. The extension of the electron spectrum to PeV energies in the magnetic field exceeding , tells us that in the Crab Nebula we deal with an acceleration efficiency approaching the ideal MHD limit (i.e. the strength of the accelerating electric field gets close to the strength of the magnetic field). Another important issue of the spectral modelling of the Crab Nebula is related to the so-called Crab flares – intense flashes of synchrotron radiation extending to GeV energies (Abdo et al. 2011 ; Tavani et al. 2011 ). The short variability time-scale and the distinct spectral shape of the flaring component require a magnetic field that is significantly larger than the average nebular field, , a non-ideal MHD configuration, and/or relativistic motions with a large bulk Lorentz factor (see Bühler Blandford 2014 , and references therein). Even under these extreme conditions, the Crab flares require the presence of electrons with energy exceeding a few PeV. The Crab flares are likely to be formed in a region(s) quite different from the site(s) where the steady component of radiation is produced. In both cases, the acceleration of electrons proceeds with efficiency close to or even beyond the ideal MHD limit. The tough efficiency requirement for the acceleration of the wind electrons can be significantly relaxed assuming that another component of electrons is responsible for the multi-MeV gamma-rays. This hypothesis is supported by a non-smooth transition between the spectra of the INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL ) and the Imaging Compton Telescope ( COMPTEL ). If this spectral feature is real, then it is better to reproduce the spectral structure at multi-MeV energies by invoking an additional component of electrons with a hard energy distribution (Aharonian Atoyan 1998 ). The currently available data do not exclude a significantly stronger magnetic field in the regions where this hypothetical hard distribution is localized (Aharonian Atoyan 1998 ). Therefore, the IC emission produced by electrons from the hard component could be suppressed compared with the IC radiation associated with the standard wind electron component. The synchrotron radiation alone does not allow us to infer information about the electrons and magnetic fields in this most critical – for highest energy electrons – MeV/GeV energy region. For any reasonable magnetic field, the MeV synchrotron radiation is produced by electrons of many hundreds of TeV. Therefore, the UHE gamma-rays produced by the same electrons through the IC scattering contain information that can shed light on both the electron energy distribution and the magnetic field strength. In this regard, the recently reported detection of gamma-ray fluxes above 100 TeV


We are grateful to the anonymous referee for valuable comments, which improved the analysis and the presentation of the results. We gratefully acknowledge Knut Olsen for providing the ATCA/Parkes H i data in a preferred format and for useful suggestions. We are grateful to Smitha Subramanian and C. S. Stalin for the remarks and suggestions, which improved the presentation of the paper. We thank Gurtina Besla for her comments on the paper. Thanks to Arun Surya and Rathnakumar for the valuable support in matlab programming.


(cf. Equation ( 1 )). Note that the ionization fractions derived in Ghavamian et al. ( 2002 ) are insensitive to the total preshock gas density n 0 . 2.2.2. Magellanic Supernova Remnants Ghavamian et al. ( 2003 ) study the entire remnant of DEM L71 using Fabry–Perot imaging spectroscopy, with preshock densities inferred from Chandra ACIS-S spectra modeled by Rakowski et al. ( 2003 ). The latter find a range of preshock densities along different regions of the rim of the remnant, roughly bounded by the range ≈0.5–1.5 cm −3 . In particular, n 0 ≈ 0.5 cm −3 is consistent with the majority of the eastern rim of the remnant, while in portions of the northwest rim, n 0 ≈ 1.5 cm −3 . Modeling the observed collisionally excited hydrogen-Balmer emission, Ghavamian et al. ( 2003 ) conclude that a wide range in neutral fraction may be plausible, but that would be necessary in order to produce detectable H α emission. Ghavamian et al. ( 2007 ) revisited DEM L71 in the far-UV, as well as the LMC remnants 0509-67.5, 0519-69.0, and 0548-70.4, using spectra obtained from the Far Ultraviolet Spectroscopic Explorer . The ratio of fluxes in Ly β and O VI 1032 Å depends linearly on the preshock neutral fraction; the observed ratio in DEM L71 requires a hydrogen neutral fraction of 20–40%, consistent with previous limits. No UV lines were found for the remnant 0548-70.4. For the remnants 0509-67.5 and 0519-69.0, the same method constrains the neutral hydrogen fraction in the surrounding ISM to >40%. The best-fitting ambient densities can be found by comparing the present size and ionization state of the remnant with hydrodynamical models: recently, Kosenko et al. ( 2014 ) found n 0 = 0.1–0.3 cm −3 for 0509-67.5, and n 0 = 1.0–2.0 cm −3 for 0519-69.0, although Kosenko et al. ( 2010 ) report densities as high as 2.4 cm −3 . As a conservative estimate, we adopt 0.3 cm −3 and 2.4 cm −3 as our fiducial ISM densities for 0509-67.5 and 0519-69.0, respectively. The radius of the forward shock for both remnants is ∼4 pc, for an LMC distance of 50 kpc. 3. Constraints on the Nature of the Progenitors of Nearby SNe Ia 3.1. Flash Ionization We may now investigate the extent to which the presence of neutral hydrogen at the present radii of all remnants considered above constrains the release of ionizing photons in the last τ rec ≈ 100,000 years. Chevalier Raymond ( 1978 ) were the first to consider the simplest case, a “burst” of ionizing photons from the supernova itself. For a present shock radius R and mean ambient density n , the total number of hydrogen-ionizing photons emitted in such a burst must have been fewer than 4 π R 3 n /3 ≈ (0.2–6) × 10 58 for SN 1006, 0509-67.5, 0519-69.0, and DEM L71 (see Table 1 ). Notably, this upper bound applies not only to the shock breakout from the supernova itself, but to any short-lived phase that the progenitor or its companion underwent immediately preceding or following the explosion, such as any briefly hot, luminous surviving WD


We thank Calcul Québec for computational resources. This research was partially supported by the Natural Sciences and Engineering Research Council of Canada and the Faculté des Études Supérieures et de la Recherche de l'Université de Moncton. This paper is based on: (1) observations obtained at the CFHT which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii; and (2) data obtained from the ESO Science Archive Facility under request number 72877.


blazar-like counterparts of the UGSs. 3. We describe the statistically significant correlations between the γ -ray photon index and the mid-IR colors for both the whole sample of Fermi blazars and the BZB and BZQ spectral classes separately, the basis of the IR– γ -ray connection. This correlation appears “stronger” than the well-known radio– γ -ray connection because it involves the spectral shapes of the Fermi blazars over ∼10 orders of magnitude and not only their fluxes. 4. We argue that the peculiar mid-IR colors of Fermi blazars do not depend on their γ -ray photon index. In turn, the IR– γ -ray connection is unexpected. We have also highlighted its potential use to implement the search for blazar-like counterparts of the Fermi UGSs. 5. We show that a large fraction of the BCUs listed in the 3FGL whose WISE counterpart has mid-IR colors consistent with the WISE Gamma-ray Strip have Fermi spectral index values consistent with the IR– γ -ray connection. Taking advantage of the overwhelming fraction of Fermi blazars detected in the WISE all-sky survey (i.e., ∼99%) in the first two mid-IR filters, we suggest that a comprehensive investigation of their IR properties at the light of the IR– γ -ray connection described in this paper can represent a powerful tool to reveal the real fraction of Fermi blazars hidden within the sample of UGSs. We thank the anonymous referee for useful comments that led to improvements in the paper. We also thank J. Ballet for helpful discussions. F.M. gratefully acknowledges the financial support of the Programma Giovani Ricercatori—Rita Levi Montalcini—Rientro dei Cervelli (2012) awarded by the Italian Ministry of Education, Universities and Research (MIUR). This research has made use of data obtained from the high-energy Astrophysics Science Archive Research Center (HEASARC) provided by NASA’s Goddard Space Flight Center. The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Part of this work is based on the NVSS (NRAO VLA Sky Survey). The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under contract with the National Science Foundation and on the VLA Low-frequency Sky Survey (VLSS). The Molonglo Observatory site manager, Duncan Campbell-Wilson, and the staff, Jeff Webb, Michael White, and John Barry, are responsible for the smooth operation of the Molonglo Observatory Synthesis Telescope (MOST) and the day-to-day observing program of SUMSS. SUMSS is dedicated to Michael Large, whose expertise and vision made the project possible. The MOST is operated by the School of Physics with the support of the Australian Research Council and the Science Foundation for Physics within the University of Sydney. This publication makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University


5 5 TYC 1323-1592-1 (=LS 36; Stephenson Sanduleak 1971 ) is an O8 Vz star newly identified here. It has the narrowest line profiles among the LAMOST medium-resolution spectra of O dwarfs, hence, we assume ≃ 0; the exact value is of little consequence, as long as it is small (which is clearly the case). to estimate P ( λ ), which is the rectified intrinsic line profile without rotation. 2. For an assumed , we fitted the functionto S ( λ ), which is the observed He i λ 5016 profile for each ON star. Here, ⨂ is the convolution operator; is the rotational broadening function (Gray 2005 ); and are fit parameters. 3. A figure of merit, , was calculated for trial values from 180 to 400 at steps of 7 . A refined best-fit was finally obtained by fitting a third-order polynomial to the 11 ξ values about the smallest one for each star. To estimate (internal) uncertainties on the velocities, we assumed the best-fit model to be representative of the true profile, added Gaussian noise matching the observed spectra, and measured v R and v e sin i as above, repeating the process 10 4 times. Our final results for and are: (LS I +61 28) and (HDE 236672). The He i λ 5016 rectified observations and adopted models are shown in Figure 2 . If macroturbulence were more important in the target stars than in TYC 1323-1592-1, our values may be upper limits (Howarth et al. 1997 ; Simón-Díaz Herrero 2007 ), although rotational broadening clearly dominates for the rapid rotators. Figure 2. He i λ 5016 profiles of LS I +61 28 and HDE 236672. The red lines are the best-fit rotationally broadened models. We also measured the radial velocity of He i λ 5016, along with other lines of hydrogen and helium, in the low-resolution spectra at our disposal, and find no evidence for radial-velocity variability in excess of ∼20 (i.e., ∼0.1 of the resolution element). 3. Kinematics of Galactic ON Stars Gaia DR2 provides parallaxes and proper motions with unprecedented precision for more than a billion stars (Gaia Collaboration et al. 2018 ). By combining this information with radial velocities, we can determine the kinematics of ON stars in the Galaxy. In addition to the two new ONn stars reported here, we investigate all those ON stars satisfying the following criteria: (i) not classified as a supergiant, (ii) parallax accuracy of , and (iii) a radial velocity reported in Table 2 of Walborn et al. ( 2011 ). This sample is summarized in Table 2 . Other than for their rotation velocities, the dozen sample stars have similar spectral characteristics and similar effective temperatures (and thus may have arisen through similar processes). Table 2 Kinematic Parameters for the ON-star Sample Note. Spectral types (column 3) and binary indicators (column 10) adopted from Walborn et al. ( 2011 ), except HDE 236672 and LS I +61 28 (this paper). Projected rotational velocities are from Martins et al. ( 2015b ), Howarth et al. ( 1997 ), and this paper. In column 9, . We used Markov Chain Monte


to calculate the percentage retention of Si and C by the mantle. Upon simulating the sputtering yield for two cases, one with a 0.02 μ m thick ice mantle and another without an ice mantle, we observe a higher number of recoils in the grain with an ice mantle. This shows that having an ice mantle accelerates the sputtering process and increases the collision cascade inside the grain. Due to the limitations of using Monte Carlo simulations, it is hard to arrive at the exact change in collision cascade due to the ice mantle. Nonetheless, the central point of this result is to emphasize the destructive nature of the ice mantle along with its protective nature when it retains the ejected atoms from the core. This increase might not affect the absolute value of sputtering; however, it makes the grain more amorphous. Also, for relatively slow-moving projectiles such as shock-wave-accelerated particles, there would be even higher amorphization. Most of the presolar SiC grains analyzed in the laboratory have been reported to be crystalline and even spectroscopically detected as a 11 μ m feature. The absence of amorphous SiC in both the laboratory and spectroscopically has been under discussion for the past two decades, mainly because the majority of presolar silicate grains studied in the laboratory have amorphous structure (Vollmer et al. 2009 ). Both amorphous and crystalline (10%) silicates have been observed around AGB stars and young main-sequence stars (Demyk et al. 2000 ). To understand the grain shape and size dependence on infrared spectra, Speck et al. ( 2005 ) compared IR spectra from various polytypes of SiC in the laboratory. This study indicated the possibility of a 9 μ m feature being related to amorphous SiC. As for the laboratory measurements, this difference between presolar silicates and SiC mainly arises due to the different identification/separation methods. Presolar silicates have been identified based on in situ measurement, whereas SiCs are chemically separated. The in situ measurements within the meteorite sections have much less of an effect on the morphology of the grains, and hence the amorphous grains remain unaltered/intact. On the other hand, harsh chemicals used in chemical separation method could lead to the destruction of presolar grains, especially amorphous grains (disordered structure) in comparison to crystalline ones (ordered crystals). Limited efforts have been put into an in situ search of SiC within meteorite sections, and no morphological studies exist for them as of yet. Nonetheless, simulation in the present study indicates amorphization of ice-mantle SiC through GCR interactions, and hunting for these amorphous grains through in situ searches in future would be desirable. As the ice thickness or the density increases, the GCR loses more energy and increases the capacity of destruction. Introduction of Si and C from the core in this ice mantle may also increase the density of the ice mantle; however, this


that ongoing accretion is occurring at such a slow rate that it is not detectable and that we caught H α in emission when the accretion was barely high enough to detect. Despite the evidence for some gas in the disk and its young age, the disk fractional luminosity and low dust mass of T 43 is consistent with what is seen in debris disks. We conclude that T 54 has ended its primordial disk lifetime and is crossing over the bridge to the debris disks stage. The fact that this is a binary system hastens its evolution, allowing us a rare glimpse of this bridge in a young star-forming region. Future observations of this object will help us understand this short-lived stage. Appendix T 54 has a nearby FIR source that contaminates the observed FIR emission (left, Figure 9 ; Matrà et al. 2012 ). Here we show that this unidentified FIR source should have no significant contribution to most of the data that we study in this paper. The unidentified FIR source is 6′′ away from T 54. Assuming it is in Cha I (at 160 pc), it is located 1040 au away from T 54 at a position angle of 196°. To the best of our knowledge, this FIR source does not overlap with previously reported objects. Figure 9. Left: PACS 70 μ m image from the HSA archive with T 54 and a nearby 2MASS source labeled with red triangles (top and lower, respectively). The FIR source identified by Matrà et al. ( 2012 ) is denoted with a black ellipse. Center: Spitzer IRS spectral footprint overlaid on the PACS 70 μ m image. We show the short-low (yellow) and long-low (black) slits as well as the two nods of the short-high observations (red). Right: Herschel PACS spectral footprint (red boxes) corresponding to the [O i ] observations discussed in Section 4.1.4 overlaid on the PACS 70 μ m image. Note that T 54 is in the central spaxel, which was used to extract the spectrum, and the unidentified FIR source is not covered by the central spaxel. Matrà et al. ( 2012 ) find that the unidentified FIR source is not detected in JHK -band photometry, IRAC photometry, or MIPS data taken at 24 μ m. However, it is detected in PACS 70 and 100 μ m data as well as in SPIRE photometry taken at 160, 250, and 350 μ m. The flux of this unidentified FIR source is comparable to or greater than the flux of T 54 at 100 μ m and beyond (Matrà et al. 2012 ). Therefore we show in Figure 8 the fluxes reported by Matrà et al. ( 2012 ) as upper limits since these data include emission from both the T 54 system and the nearby unidentified FIR source. It is unlikely that the unidentified FIR source is contributing to the Spitzer IRS spectra of T 54. As reported by Matrà et al. ( 2012 ), the unidentified FIR source is not detected in NIR, MIR IRAC, or MIPS images. To explore this further, we overlaid the IRS slit positions on a PACS 70 μ m image of T 54 (center panel, Figure 9 ). Low- and high-resolution IRS spectral observations of T 54 are available in CASSIS. In the low-resolution observations (2005 April 24 10:57:08), the


We thank the referee for an encouraging and incisive report which improved the quality of this paper. We gratefully thank Thierry Foglizzo for fruitful exchanges and the mpi-amrvac development team, in particular Oliver Porth, Rony Keppens and Zakaria Meliani, for useful assistance. We acknowledge the financial support from the UnivEarthS Labex programme of Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). IEM acknowledges financial support from the ENS of Cachan through a contrat doctoral spécifique pour normaliens and from the University Paris 7 Diderot. The numerical simulations were run on the François Arago Centre facilities in Paris 7 and using the HPC resources from GENCI-CINES (Grant c2015047469).


We would like to thank Kevin France for discussions concerning the MUSCLES database and Sukrit Ranjan for discussions concerning DNA action specta. This work has made use of the MUSCLES M dwarf UV radiation field database. We would also like to acknowledge support from DFG funding ENP KA 3142/1-1 and the Simons Foundation (290357, Kaltenegger and 290360, Sasselov).


can be asymmetric both in position (i.e. different distances from disc centre) and brightness (e.g. Baptista, Harlaftis Steeghs 2000b ; Baptista et al. 2005 ). Aside of the transient spiral structures seen during dwarf nova outbursts, spiral shocks were also observed in nova-like systems – where they presumably are persistent, tidally induced effects in permanently large and hot accretion discs (Baptista Bortoletto 2008 ; Saito et al. 2010 ). V348 Puppis is the optical counterpart of the faint HEAO X-ray source 1H0709-36, identified by Tuohy et al. ( 1990 ) as an eclipsing CV inside the period gap ( P orb = 2.44 h, Baptista et al. 1996b ; Rolfe, Haswell Patterson 2000 ). Its light curve, which shows the gradual eclipse of an extended source, and the observed rotational disturbance in its emission lines during eclipse indicate the presence of a bright, high mass accretion rate disc outshining the contributions from the WD at disc centre and the bright spot at disc rim. The detection as a hard X-ray source, the presence of a strong He ii λ4686 emission line in the spectrum and the possible existence of a second periodicity close to the orbital period led to the suggestion that V348 Pup might be a magnetic CV of the DQ Her type close to synchronize (Tuohy et al. 1990 ; Rosen et al. 1994 ). However, its spectrum exhibits strong single-peaked Balmer and He i emission lines that remain largely unobscured during disc eclipse (indicating significant contribution from above the orbital plane) and displays absorption components at phases opposite to the disc eclipse (φ = 0.4–0.5). This spectroscopic behaviour led Rodríguez-Gil et al. ( 2001 ) to classify V348 Pup as a nova-like variable of the SW Sex type. Moreover, the nature of the second periodicity became clear with the discovery of long-lasting, positive superhumps (with a period 6 per cent longer than P orb ), resulting from the gravitational interaction between a slowly precessing non-axisymmetric accretion disc and the mass-donor star (Rolfe et al. 2000 ). Its eclipsing nature and the location within the period gap make V348 Pup an obvious target for an investigation of its accretion disc properties with eclipse mapping techniques (Horne 1985 ). For this purpose, time series of UV and optical spectroscopy of V348 Pup were collected with the Hubble Space Telescope ( HST ). A first analysis of this data set were reported by Froning, Long Baptista ( 2003 ). They found that the HST out-of-eclipse spectrum is characterized by a blue continuum with strong emission lines and a broad dip in the spectral range λ2000–3000 Å (attributed to a blend of Fe ii absorption lines known as the ‘Fe ii curtain’; Horne et al. 1994 ), but the Balmer jump is shallow or absent. The eclipses are remarkably shallow across the observed spectral range (≃40–50 per cent of the out-of-eclipse light remains visible at mid-eclipse in the continuum, and up to 80 per cent in the emission lines) indicating that a significant


that the progenitor was enshrouded in a dusty cocoon of material that was lost close to the explosion. If the SN was not an electron capture SN it would have been the explosion of a 11 M ⊙ red supergiant. However 2008S has little in common with other such SN from progenitors in this mass range (Smartt 2015 ; Davies Beasor 2018 ). In conclusion using the new distance to determine the luminosity of the progenitor we find it more likely than before that SN 2008S was an electron capture event. It also was likely to have been the result of a binary interaction which was suggested by Podsiadlowski et al. ( 2004 ) to be the most likely channel for such core-collapse events. While SN 2008S is at the minimum mass for a core-collapse SNe, N6946-BH1 is at the maximum mass for a core-collapse of a red supergiant. This star was observed to rapidly fade with a light curve that was in agreement with a source powered by a feeding black hole (Adams et al. 2017 ). When the nature of the progenitor was examined this study assumed a distance of 5.95 Mpc. Therefore again this increases the suggested progenitor luminosity from log ( L/L ⊙ ) = 5.3 to 5.5. As shown in Fig. 1 this increase in the luminosity implied a mass for the progenitor star or 24 M ⊙ that is above the predicted mass limit for the formation of a black hole. This is also consistent with the mass estimated from the surrounding stellar population by Murphy et al. ( 2018 ). Again while it is only one event tension between the mass estimates for black hole formation and the luminosity of the observed progenitor stars are reduced by this study. We note that this result is in agreement with the work of Murphy et al. ( 2018 ). 4 CONCLUSIONS We have re-evaluated the distance to NGC 6946. The value of 5.9 Mpc is incorrect and should not be used in future studies. We used the observed SN rate to estimate the star formation rate and thus the FUV luminosity of the galaxy. Using the standard candel method we derive a distance of 7.9 ± 4.0 Mpc. This is consistent with the more recent distances estimated by Anand et al. ( 2018 ) and Murphy et al. ( 2018 ) of 7.72 ± 0.32 Mpc and 7.83 ± 0.29 Mpc, respectively. We strongly recommend that all future studies concerning NGC 6946 use the updated distance of 7.72 ± 0.32 Mpc from Anand et al. ( 2018 ). Their distance is consistent with the distance of Murphy et al. ( 2018 ) but Anand et al. ( 2018 ) took additional steps to reduce contamination and is therefore preferred. We re-evaluated the nature of the five progenitors of observed core collapse events in NGC 6946 using the distance of 7.72 ± 0.32 Mpc. We found that the mass constraints change significantly. The two most significant changes are: first, that the observed progenitor of SN 2008S is now more consistent with predictions for the progenitors of electron capture SNe. We suggest that SN 2008S was an electron capture SN with the progenitor having experienced a binary interaction before explosion. Second, the


the microlensing detection (e.g. Alcock et al. 2000 ), halo white dwarfs have been suggested as natural candidates to contribute to the dark matter content of the Galaxy (e.g. Oppenheimer et al. 2001 ). An intense debate arose on this issue, although later studies demonstrated that the white dwarf contribution to dark matter was rather limited (e.g. Torres et al. 2002 ; Flynn, Holopainen Holmberg 2003 ; García-Berro et al. 2004 ; Kilic et al. 2004 ; Bergeron et al. 2005 ). In any case, the search for white dwarfs in the Galactic halo has proven to be a difficult endeavour. In this sense, the intrinsic faintness and the low space density of halo white dwarfs, along with their high surface gravity, which erases any trace on metal content from their atmospheres and disables accurate radial velocity measurements due to the broadening of the Balmer lines, are some of the main factors that have hindered the discovery of suitable candidates. Consequently, during decades, the identification of halo members has relied on the search of cool objects in high proper motion surveys (e.g. Monet et al. 2000 ; Nelson et al. 2002 ; Hall et al. 2008 ; Catalán et al. 2012 ; Munn et al. 2016 ). It was not until the ESO SNIa Progenitor surveY project (see Napiwotzki et al. 2020 , and references therein) that radial velocities were measured for the first time with enough precision to recover the 3D kinematics of white dwarfs. That permitted to identify high eccentric retrograde orbits as strongly indicators of their belonging to the halo population (Pauli et al. 2006 ). Although the number of halo members was sparse, an estimate of the age of the inner halo has been possible ( Gyr; Kalirai 2012 ). A key ingredient of these studies is the white dwarf luminosity function. Defined as the number of white dwarfs per bolometric magnitude unit and cubic parsec, the white dwarf luminosity function is a valuable tool to derive the age, history, and evolution of the components of our Galaxy. Moreover, the luminosity function holds all the information about the cooling process of the white dwarfs, being then an excellent tool for testing the physics of evolutionary models (see García-Berro Oswalt 2016 , for a comprehensive review about these issues). However, the effectiveness of the white dwarf luminosity function requires the existence of a complete, well-defined volume sample. In this sense, the lack of accurate distances previous to the Gaia era, joint to the selection biases inherited from magnitude-limited samples, have hampered the achievement of more conclusive results in such an elusive sample as the halo white dwarf population. The first observational halo white dwarf luminosity function (Liebert et al. 1989 ) contained only five objects, and no more than 20 were proposed as halo candidates through a neural network artificial intelligent classification algorithm (Torres, García-Berro Isern 1998 ). Based on the SuperCOSMOS Sky Survey observations towards the southern


We thank Paz Beniamini, Petar Mimica, Enrico Ramirez-Ruiz, Lorenzo Sironi, and Alexander van der Horst for useful comments on the manuscript. We acknowledge support from NASA grant no. NNX13AP13G.


15 Myr. This excess in BH number can be partially explained by an increase in binary interaction rates in these models. Specifically, model 2a has a higher number of binary mergers involving stars with zero-age main sequence (ZAMS) masses between 10 and 25 M ⊙ that would not have otherwise been BH progenitors (at 0.1 Z ⊙ , the minimum ZAMS mass that will form a BH is roughly 20 M ⊙ ). However, these merger products do evolve into BHs with masses roughly in the range of M BH ≈ 5–15 M ⊙ . For models 2e and 2k , the higher number of BHs can be partially attributed to mass transfer in a binary increasing the mass of one of the components past the threshold of BH formation. Naturally, some of these differences are clearly due to stochastic fluctuations in the initial evolution of the model, leading to divergent paths in the dynamical evolution of the system. The main takeaway is that binary evolution processes, coupled with dynamics, can greatly influence BH growth. We leave a detailed study of the extent to which binary evolution processes affect the long-term cluster evolution and dynamics for a future study. It is important to note that many (roughly 55%) of these “excess” BHs formed with masses less than 15 M ⊙ are ejected promptly from their host cluster through natal kicks. Low-mass BHs are expected to form with less mass fallback and thus receive larger natal kicks (e.g., Fryer et al. 2012 ). Thus, this excess of BHs formed is unlikely to have a significant effect on the long-term cluster dynamics. 4. Discussion and Conclusions Our results show that high binary fractions for massive stars lead to an increase in binary-mediated dynamical interactions, which in turn have an important effect on massive BH formation. We have demonstrated that increasing the high-mass binary fraction, consistent with observations, while keeping all other cluster parameters (e.g., cluster masses, virial radii, metallicity) fixed at the values used in Kremer et al. ( 2020b ), may significantly change the early evolution of YMCs. In particular, high-mass binaries facilitate high rates of massive star collisions (occurring through both dynamical encounters and binary-evolution-driven mergers) that can lead to the formation of massive BHs, both within and above the pair-instability mass gap. With the exception of the high-mass binary fraction, the parameters for the models calculated in this Letter are identical to those in Kremer et al. ( 2020b ), which were shown to lead to present-day properties matching well those of Milky Way GCs. If indeed the majority of high-mass stars have binary companions at birth, massive BH formation may therefore be a common occurrence in the early phases of GC evolution. As shown in Figure 2 , the formation of massive BHs is sensitive to small changes in initial virial radius. This is in agreement with previous works on the topic of IMBH formation that have shown that the onset of a collisional runaway occurs abruptly under small


index Γ and the inner disc temperature are consistent with the results of previous studies of M33 X-8, where a similar spectral model and data from Swift /XRT (La Parola et al. 2015 ), XMM–Newton (Foschini et al. 2004 ), or Suzaku (Isobe et al. 2012 ) were used. The innermost disc radius, R in , can be directly estimated from the normalization of the diskbb component: , where D is the distance to the source in units of 10 kpc and i is the inclination of the disc. The estimated inner disc radius, R in = (37 ± 2)cos −1/2 i km, is in good agreement with the results of previous studies (e.g. Middleton et al. 2011 ). Associating this size with the radius of the innermost stable orbit of a standard accretion disc suggests that the relativistic compact object has a mass of at least ∼4 M ⊙ , with the exact value depending on the (unknown) inclination of the disc. More accurate estimation should take into account the inner boundary condition, the spectral hardening and relativistic corrections, which in turn would depend on the structure of the accretion disc (whether it is thin or slim). Nevertheless, the above crude estimate is consistent with the compact object being a stellar-mass black hole. Replacing the power-law component by its modification with an exponential cut-off (Model 5) further improves the fit statistics to χ 2 /d.o.f. =891/900, indicating the presence of a high-energy cut-off in the spectrum (the F -test probability is 10 −14 for the null-hypothesis Model 4). We conclude that the broad-band 0.3–20 keV spectrum of M33 X-8 cannot be described by a single accretion disc model diskpbb , which was previously used to successfully fit some narrow-band spectra of this source (e.g. La Parola et al. 2015 ). The broad-band spectrum strongly requires an additional power-law component with a possible high-energy cut-off. 3.3 Physically motivated models We have demonstrated that the broad-band spectrum of M33 X-8 certainly contains two components: the first one is well approximated by a multicolour disc with the inner temperature of kT ∼ 1 keV, and the second one is a power-law-like high-energy tail detected up to 20 keV. As often discussed in the literature (e.g. Gierliński et al. 1999 ; Steiner et al. 2009 ), the combination of a low-energy blackbody-like component with a high-energy power law does not allow one to properly model the spectrum at low energies, because a steep power law extending to the soft part of the spectrum requires the introduction of an artificially high absorption column density and can result in erroneous determination of the disc properties. This problem can be solved by using a self-consistent Comptonization model that has a low-energy cut-off in the otherwise power-law-like spectrum, such as the convolution model simpl (Steiner et al. 2009 ), which provides a description of Comptonization based on the non-relativistic theory developed by Sunyaev Titarchuk ( 1980 ). In this model, a fraction of the photons from an


images are for the HST bands and for the Spitzer bands. We adopt a -CDM cosmological model with km s Mpc, , and . We assume a Salpeter IMF ( Salpeter 1955 ). All magnitudes are expressed in the AB system ( Oke Gunn 1983 ). 2. Data 2.1. Spectroscopy The available low-resolution (LR, ) and medium-resolution (MR, ) VLT/VIMOS spectroscopy covering the spectral ranges 3400–7000 Å and 4800–10 000 Å were obtained during 2005, with 4hr exposure time for both LR and MR spectra. The LR spectrum continuum sensitivity is at 3700 Å with 4 h and assuming seeing and airmass 1.2. It is calculated over one pixel along dispersion and (full width half maximum) along spatial direction. ( Popesso et al. 2009 ; Balestra et al. 2010 ). Slit widths of were adopted and the median seeing during observations was . We have newly reduced both configurations, in particular focusing on the Lyman continuum emission (LR-spectrum) and the ultraviolet spectral properties in the non-ionizing domain (MR-spectrum). Reduction was done in two ways: as described in Balestra et al. (2010) and the AB–BA method as described in Vanzella et al. (2011 , 2014b) . Both methods produce consistent results. Recently, a near infrared spectrum of Ion2 was obtained with Keck/MOSFIRE in March 2015 (PI: Günther Hasinger). Integration time of 32, 32, and 36 min were obtained in the -, -, and -bands, respectively, with the AB–BA dithering pattern of 2.9. The adopted slit width was 0.7 producing a dispersion of 1.30 Å, 1.63 Å, and 2.17 Å per pixel, in the -, -, and -bands, respectively; the pixels scale along the spatial direction was 0.18/pixel. Ion2 was inserted in a mask aimed to target low- objects as well. The -band is useful for monitoring low- emission lines. Reduction was performed using the standard pipeline 1 . Briefly, two-dimensional sky-subtracted spectra, rectified and wavelength calibrated, are produced from which the one-dimensional variance weighted spectrum is extracted with a top-hat aperture. The wavelength solution was computed from sky emission lines (e.g., Rousselot et al. 2000 ) in the three bands reaching an rms accuracy better than 1/20, 1/30, and 1/40 of the pixel size in -, -, and -bands, respectively (typical rms 0.05 Å). Table 1 Emission line properties. Notes. (a) Observed emission line flux and error corrected for slit losses (50%) in units of erg s cm. In parenthesis, the [O iii ] flux adopting the theoretical ratio ( Storey Zeippen 2000 ). (b) The emission line dust correction method is described in Appendix A . (c) FWHM (instrumental corrected) and error in units of km s. (d) Equivalent width and error in units of Å. (e) Sum of the two components. (f) Main component. (g) Marginal detections (Fig. 6 ): , , and . (h) FWHM is the contribution of the two blended components, 1907–1909 Å. (i) The error is large because the line is on the top of a sky line (Fig. 4 ). Flux calibration was performed by observing the standard star A0V HIP 26577. Given the slit width () and the


to calculate N H values for all targets studied. For 1ES 0229+200, the calculated value of N is (13.00 ± 0.37) × 10 20 cm −2 . This value is larger than the one from the LAB survey (8.06 × 10 20 cm −2 ) and consistent with the one provided by Willingale et al. ( 2013 ,10.80 × 10 20 cm −2 ). The value is also higher than free N H = (10.6–10.8) × 10 20 cm −2 , calculated by Kaufmann et al. ( 2011 ). For PKS 0548−322, the calculated value of N is (3.10 ± 0.10) × 10 20 cm −2 . This value is larger than the one from the LAB survey (2.58 × 10 20 cm −2 ) and consistent with the one provided by Willingale et al. ( 2013 , 2.87 × 10 20 cm −2 ). However, Sambruna Mushotzky ( 1998 ) have found a significantly higher value of N H of 1.03 × 10 21 cm −2 , which is needed to explain X-ray properties of PKS 0548−322. For 1ES 1741+196, the calculated value of N is (10.47 ± 0.41) × 10 20 cm −2 . This value is larger than the one from the LAB survey (7.32 × 10 20 cm −2 ) and consistent with the one provided by Willingale et al. ( 2013 , 9.58 × 10 20 cm −2 ). For 1ES 2344+514, the calculated value of N is (17.34 ± 0.15) × 10 20 cm −2 . This value is larger than the one from the LAB survey (15.10 × 10 20 cm −2 ); however, it is smaller than the one provided by Willingale et al. ( 2013 , 24.60 × 10 20 cm −2 ). We note here that the reddening E ( B − V ) and the atomic hydrogen column density ( N H ) are related. According to recent work, Liszt ( 2014 ) has described this dependence by the following formula N H = 8.3 × 10 21 E ( B − V ). The formula gives N H values of 9.7 × 10 20 , 2.5 × 10 20 , 0.6 × 10 20 , 6.3 × 10 20 , and 15 × 10 20 for 1ES 0229+200, PKS 0548−322, RX J 1136+6737, 1ES 1741+196, and 1ES 2344+514, respectively. The quoted values are consistent with the ones from the LAB survey and do not indicate a need for an additional absorption. All values of N H values, including the catalogue ones, are collected in Table 5 . Table 5. Summary of Galactic column densities values. Notes . (1) Source name; (2)–(4) N H as provided by Kalberla et al. ( 2005 ), Dickey Lockman ( 1990 ), and Willingale et al. ( 2013 ), respectively; (6) N H value calculated as a result of this work. All values are given in 10 20 cm −2 . 4.2 Constrains on the model parameters The model used to describe the IR to X-ray emission of the blazars is characterized by the host galaxy, curvature seen in the X-ray spectrum, total absorption (which includes both Galactic component and possibly additional ones), and UV excess. The host galaxy, understood as the entire component described with the template by Silva ( 1999 ), is well constrained with the model used. Still, the remaining three parameters cannot be disentangled only using information from the X-ray spectral fitting. The limitations on three entangled parameters are as follows: β : For all of the blazars studied, the convex curvature of the X-ray spectrum is assumed. This implies that negative values of β are not accepted.


between 10 10 and 10 11 M ⊙ . McCarthy et al. ( 2020 ) also use an analytic model, but paired with SDSS observations to explore the host galaxy mass function along with other host observables. For the host galaxy mass function, our results are consistent with theirs. However, our larger range of DTDs presented in Figure 2 reveals the large spread between different assumed DTDs and the stable peak near 10 10.5 M ⊙ . Adhikari et al. ( 2020 ) also find that other host observables paired with stellar mass are necessary to obtain a better understanding where BNSs merge. Overall, we find that future explorations of this topic will need to consider a wide range of DTDs and the full range of the observable in question. While the work we present here continues our understanding of what we can learn from observations of BNS host galaxies, further investigations are necessary to fully understand how BNSs form and evolve. One example of such an investigation is to expand the set of DTDs examined using the methods in this paper. The set of DTDs we examine is broad, covering those most commonly referenced (e.g., Eldridge Stanway 2016 ; Safarzadeh Berger 2019 ), but we do not exhaustively search the full range of DTDs proposed (e.g., Dominik et al. 2012 ; Simonetti et al. 2019 ). Also, our convolution of IllustrisTNG’s SFRH with our DTDs does not include any form of natal kicks. If these kicks are strong enough to dislodge the binary from smaller galaxies, it is possible that their addition would weight the host mass functions toward higher-mass galaxies. With a greater range of DTDs examined and a more detailed convolution, we will gain a clearer picture of where BNS mergers are located, which delay times can be distinguished using the host galaxy mass function, and the most likely places they will be observed. Another way to incorporate a more complete set of DTDs would be to use a varied set of population synthesis models that cover a wide range of binary separations, kick velocities, initial mass functions, etc. Including other star formation histories could also provide a more detailed look at the spread in possible host galaxy mass functions. While IllustrisTNG is broadly consistent with the cosmic SFR density and redshift-dependent galaxy stellar mass functions (Pillepich et al. 2018a ), its accuracy should not be overinterpreted, and different simulations will surely produce somewhat varied star formation histories that could impact our results. However, we can say that up to their mass cutoff our results align with those of Artale et al. ( 2019 ), who found no significant difference when comparing results from Illustris and Eagle. The lack of variation in Artale et al. ( 2019 ) most likely indicates that—while there is some variation—the SFRHs in Illustris and EAGLE are sufficiently similar to not significantly impact the results. Thus, by adopting the SFRHs from galaxy formation simulations and assumptions about the functional form of the DTD,


ACKNOWLEDGEMENTS Our research was supported by the Joint Research Fund in Astronomy (No.11963002; U1631236 and U1431114) under a cooperative agreement between NSFC and CAS. We also want to thank Dr Frank Levinson for his generous financial support that enabled Butler University to join the SARA telescope consortium and upgrade its Holcomb Observatory telescope. This work was also supported by the Natural Science Foundation of Guizhou Province Office of Education (Grant No. 2014298). We also thank Professor Prabhakar Misra for revising the language of our paper. We acknowledge the support of the staff of the Xinglong 60-cm telescope and Cultivation Project for LAMOST Scientific Payoff and Research Achievement of CAMS–CAS.


by magenta, green, and orange lines, respectively, with solid (dashed) lines indicating results for the northern (southern) hemisphere. The SSN is shown for each hemisphere. 6. Discussion Taken at face value, the results as illustrated by Figures 10 and 11 are unexpected in that the shallow return flow present in the northern hemisphere appears to be inconsistent with most prior determinations of the meridional circulation that employ multiyear observations and attempt to remove the effects of center-to-limb related artifacts. Specifically, most analyses involving modeling time–distance travel-time perturbations show a poleward flow in both hemispheres that persists from the surface down to approximately 0.9 R ⊙ (i.e., about 70 Mm below the surface). This includes the analyses of Zhao et al. ( 2013 ), Jackiewicz et al. ( 2015 ), Rajaguru Antia ( 2015 ), and Chen Zhao ( 2017 ). A notable exception is the recent analysis of Gizon et al. ( 2020 ), which is discussed below. In general, uncertainties in the inference of the flow increase with the depth of those inferences. This makes the discrepancy with other helioseismic analyses at a relatively shallow depth all the more puzzling. If we assume that the results for at least the northern hemisphere are spurious, then the challenge is to understand the cause of what appears to be an uncorrected artifact. Of course, real hemispheric differences in the meridional circulation may very well exist, but it is worth considering the possible nature of pseudoflows, which are themselves asymmetric. The comparison of the time variation of the frequency shifts with the sunspot numbers for both hemispheres (Figure 12 ) indicates that the observed hemispheric differences in the 88 month interval persist regardless of the level of solar activity or its preference for one hemisphere over the other. While this does not rule out the presence of real solar-cycle variations in flows (e.g., Chou Dai 2001 ; Zhao Kosovichev 2004 ; González Hernández et al. 2008 ; Hathaway Rightmire 2010 ) or potential pseudoflow artifacts related to magnetic regions (e.g., Liang Chou 2015 ), there is no direct correlation between hemispheric differences in solar activity and the differences in the frequency shifts. Errors in the control measurements due to uncertainties of the leakage discussed in Appendix B appear to be too small to account for the hemispheric differences observed in Figure 9 . In particular, we note that likely errors in the leakage factor amounting to 20% of the selected value of 0.84 (see Appendix B ) cause uncertainties in the scaled frequency shifts of the deepest modes of around 1 m s −1 . These are smaller than the standard errors of the observations shown in Figure 9 and substantially smaller than the 4 m s −1 discrepancy observed at the highest phase speeds. It is plausible that the results may be compromised by incorrect assumptions regarding the azimuthal invariance of the center-to-limb correction. At


SLS thanks STFC for her studentship and the Australian National University for hospitality. CAT thanks Churchill College for his fellowship, the Australian National University for a visiting fellowship and the Monash University for support as a Kelvin Watford distinguished visitor. LF and DTW thank the Institute of Astronomy for supporting visits.


This work was supported by the European Research Council under ERC grant agreement no. 337705 (CHASM) and by a Consolidated Grant from the UK STFC (ST/J001627/1). Some of the calculations for this paper were performed on the DiRAC Complexity machine, jointly funded by STFC and the Large Facilities Capital Fund of BIS, and the University of Exeter supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS, and the University of Exeter. We thank Isabelle Baraffe for providing the 1D stellar structure model used in this paper and for offering comments on an earlier version of this manuscript. We also thank the referee for a thorough reading of our paper and providing many helpful comments, improving the clarity of our paper.


Acknowledgements We thank the referee for useful suggestions; Sebastian Hönig for many illuminating discussions; Claudio Ricci for careful reading and comments on the manuscript. MS acknowledges support by the Ministry of Education, Science and Technological Development of the Republic of Serbia through the projects Astrophysical Spectroscopy of Extragalactic Objects (176001) and Gravitation and the Large Scale Structure of the Universe (176003); by FONDECYT through grant no. 3140518; by the Center of Excellence in Astrophysics and Associated Technologies. This research made use of Astropy, a community-developed core python package for Astronomy (Astropy Collaboration et al. 2013 ). Based on European Southern Observatory (ESO) observing programmes 60.A-9629, 076.B-0599, 078.B-0255, 087.B-0746, 088.B-0159, 089.B-0070, 385.B-0896 and 386.B-0026.


Acknowledgements We thank David Bühler and Jayant Joshi for acquiring the quiet-Sun data. The Swedish 1-m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of Stockholm University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North at Umeå University and the PDC Centre for High Performance Computing (PDC-HPC) at the Royal Institute of Technology in Stockholm. JdlCR is supported by grants from the Swedish Research Council (2015-03994), the Swedish National Space Board (128/15) and the Swedish Civil Contingencies Agency (MSB). This research was supported by the CHROMOBS and CHROMATIC grants of the Knut och Alice Wallenberg foundation and by the Research Council of Norway through the grant “Solar Atmospheric Modelling” and through grants of computing time from the Programme for Supercomputing.


ACKNOWLEDGEMENTS SJC would like to acknowledge the support of the Lau Endowment as part of the Undergraduate Research Scholars Program of the UCLA Undergraduate Research Center – Sciences, the Undergraduate Research Fellows Program, and the Maggie Gilbert Research Award through UCLA College Honors. SN thanks Howard and Astrid Preston for their generous support. We would like to thank Professor Stassun, Professor Gómez Maqueo Chew, Professor Heller, and Dr Hamers for their thoughtful comments and suggestions.


or less blended and we saw only one to three components. Next, we used the least-squares deconvolution (LSD; Donati et al. 1997 ) technique and calculated LSD profiles with the LSD code by Tkachenko et al. ( 2013 ), based on the same line mask as we used for our previously mentioned synthetic spectrum. Figure 1 shows the LSD profiles vertically arranged according to the JD of observation. The resolution is distinctly better than that of the CCFs; four components are now seen in the majority of the LSD profiles. The measured RVs are marked, and the calculated orbital curves plotted in Figure 1 show that we could assign all components in all LSD profiles to four different stars located in two different binary systems, S 1,2 and S 3,4 . Figure 1. LSD profiles calculated from the 29 spectra, vertically arranged according to the JD (2,457,000+) of observation. Measured RVs are marked by open circles and crosses, in the left panel for components C 1 and C 2 and in the right panel for C 3 and C 4 , respectively. The red and green curves illustrate the corresponding, calculated orbital solutions. The RVs of the four components, C 1 to C 4 , were determined by fitting the LSD profiles with multiple Gaussians. The mean (internal) errors of the fit were 0.25, 0.36, 0.28, and 0.37 km s −1 for the RVs of C 1 to C 4 , respectively. We used the method of differential corrections (Schlesinger 1910 ) to determine the orbits from the RVs. Because of the short time span of the observations, this could be done for the two systems separately, without accounting for any interaction between them or for light-travel-time effects. In the case of S 1,2 , we fixed the orbital period to the value known from the Kepler light-curve analysis. The RVs of the four components of KIC 7177553 determined from the multi-Gaussian fit to the LSD profiles are listed in Table 5 in Appendix B . Figure 2 shows the RVs and orbital curves folded with the orbital periods. Table 1 lists the derived orbital parameters. The times of observation of all spectra are based on UTC. To be consistent with the Kepler DCT time scale and the results listed in Table 3 , we added 68 s to the calculated times of periastron passage T . Figure 2. RVs and calculated orbital curves folded with the orbital periods. Left: C 1 (open circles) and C 2 (open squares). Right: C 3 (open circles) and C 4 (open squares). Phase zero corresponds to the time of periastron passage. Table 1 Orbital Solutions Obtained from Multi-Gaussian Fits of the LSD Profiles and with KOREL Note. The table lists period P and orbital elements (eccentricity e , argument of periastron ω , time of periastron passage T , and mass ratio q ) of the two systems, and the RV semiamplitudes K and individual systemic velocities γ . Errors are given in units of the last two digits in parentheses. The last two rows list the rms of the residuals after subtracting the orbital solution from the RVs and the projected masses calculated from the spectroscopic


The work of R. B. is supported by the Deutsche Forschungsgemeinschaft (DFG) under grant BU 3115/2-1. We thank R. J. MacDowall for providing the Wind/WAVES data and acknowledge the use of the Wind/3DP data. Work at JPL was supported by NASA. Work at APL ( ACE /ULEIS and STEREO /SIT) was supported by NASA grant NNX13AR20G/115828 and NASA subcontract SA4889-26309 from the University of California Berkeley.


We thank I. Smail for his detailed comments and suggestions that help improve this manuscript; J. M. Simpson for providing the SCUBA2 data; C. Y. Peng and G. Barro for their advice on GALFIT ; S. Zibetti for his support with ADAPTSMOOTH ; C. M. Casey for providing the DSFG comparison data plotted in Figure 4 ; and D. Watson, J. Hjorth, I. Davidzon, H. Rhodin, K. K. Knudsen, P. Laursen, D. B. Sanders, M. P. Haynes, R. Pavesi, T. K. D. Leung, and S. Martín-Álvarez for helpful comments and suggestions. We are grateful to the anonymous referee, whose comments have been very useful to improving our work. C.G.G. and S.T. acknowledge support from the European Research Council (ERC) Consolidator Grant funding scheme (project ConTExt, grant number 648179). A.K., E.J.A., and F.B. acknowledge support by the Collaborative Research Centre 956, subproject A1, funded by the Deutsche Forschungsgemeinschaft (DFG). Support for B.M. was provided by the DFG priority program 1573, “The physics of the interstellar medium.” D.R. acknowledges support from the National Science Foundation under grant number AST-1614213. V.S. acknowledges support from the European Union’s Seventh Framework program under grant agreement 337595 (ERC Starting Grant, “CoSMass”). M.A. acknowledges partial support from FONDECYT through grant 1140099. ERD also acknowledge support by the Collaborative Research Centre 956, subproject C4, funded by the DFG. M.J.M. acknowledges the support of the National Science Centre, Poland, through POLONEZ grant 2015/19/P/ST9/04010; this project has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement No. 665778. Based on observations made with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program #13294. Support for program #13294 was provided by NASA through a grant from the Space Telescope Science Institute. This research made use of the following ALMA data: ADS/JAO.ALMA#2012.1.00978.S. ALMA is a partnership of the ESO (representing its member states), NSF (USA), and NINS (Japan), together with the NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by the ESO, AUI/NRAO, and NAOJ. This paper employed Astropy , a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013 ); APLpy , an open-source plotting package for Python (Robitaille Bressert 2012 ); CASA (McMullin et al. 2007 ); Matplotlib (Hunter 2007 ); Numpy ; Photutils (Bradley et al. 2016 ); PyBDSF ; and R, a language and environment for statistical computing.


This completes the presentation of the Galaxy model potential. Appendix C Implementation Notes In this section, we sketch a brief technical resume of the GalMod platform contents (ver. 16.2). Nevertheless, we warn the reader that the platform “GalMod” is continuously updated and the Web page (the tutorial page: www.galmod.org/gal/tutorial ) is the most up-to-date place to search for the latest refinements, bug corrections, and tested implementations that might differ from what is presented in this section. A cycle of 12 upgrades per year is planned. We organized GalMod in modules, i.e., independent sub-units of the source code that interact through interfaces (e.g., the Poisson solver modules, the CMD generator modules, the extinction integrator modules, and so forth). This approach facilitates the use of multiple language codes/libraries with different types of licenses. A rough scheme of the GalMod infrastructure is shown in Figure 17 . We presented each of these modules in dedicated papers. The technique to generate the photometry and chemistry of the stars is introduced in Pasetto et al. ( 2012b ) and references therein, the kinematics and potential solver in Pasetto et al. ( 2016b ) and references therein, and the extinction based on DART-Ray in Natale et al. ( 2017a ). The Web-interface system and cloud computing service is realized and maintained by Clover-lab TM . These references collect the results of several years of work performed by several researchers and programmers. They are not meant to be an exhaustive list. Figure 17. The superstructure of GalMod. Each square box represents a series of modules of GalMod where some computation is performed (either in serial or parallel mode). The numbered blue arrows represent the ideal flux from the input parameters to the delivery of the mock catalog (or the output) . The modules are the Poisson-solver modules that, once the density/potential parameters have been adopted, provide Φ, its gradients and Laplacian, and a series of kinematics indicators (rotation curve, total mass, etc.) relative to . are the modules computing the maximum number of stars for the galaxy considering and the input parameters . can be simply an input parameter depending on the type of simulation. M are the modules assigning the star-like particle mass in the case GalMod is used to generate N -body i.c.. N is the number of stars generated so far. are the modules distributing the stars according to the density profiles, , their number N , and the input condition . The age/metallicity/velocity dispersion modules compute the distribution of the stars or star-like particles in the age τ , metallicity Z , and velocity space. They include the mass generation of the star and the extinction modules in the case of mock stellar catalogs only, while a separate module provides the same information with a preassigned stellar particle mass in the case of i.c. generation. GalMod produces a stochastic realization (i.e., stellar


This work was supported in part by the Collaborative Research Center TR 33 “The Dark Universe” of the Deutsche Forschungsgemeinschaft. This work is based on data collected at the ESO VLT (prog. ID 186.A-0798).


M.Š. acknowledges the support of the Czech Science Foundation (grant 14-04338S) and of the institute research project RVO:67985815 to Astronomical Institute of Czech Academy of Sciences. A.S.B. acknowledges financial support by CNES Solar Orbiter grant, CNRS/INSU Programme National Soleil-Terre, ERC STARS2 207430 and SolarPredict 640997 grants and wishes to thank M. DeRosa for useful discussions.


by Werner, Rauch Kruk ( 2018 ) in the hot white dwarf in the peculiar binary nucleus of the planetary nebula EGB 6. Ar vii λ = 1065.55 spectral line is observed in ultraviolet spectra of hot PG 1159 and extremely hot helium rich white dwarfs (Werner, Rauch Kruk 2016 , 2017 ). Ar iii and Ar ii spectral lines are used in the determination of argon abundance in B-type star and subdwarf atmospheres (Heber Edelmann 2004 ; Blanchette et al. 2008 ; Lanz et al. 2008 ; Fossati et al. 2009 ). In our recent works, Hamdi et al. ( 2017 ) and Hamdi et al. ( 2018 ), we have reported Stark widths for 300 spectral lines of singly charged argon (Ar ii ). Our Stark widths were compared with experimental results and good agreements were found for most spectral lines. In order to complete the set of Stark broadening parameters of Ar ii spectral lines, we report here Stark shifts. Stark shifts are calculated using semiclassical perturbation approach (SCP) (Sahal-Bréchot 1969a , b ) and a set of atomic data is calculated using Hartree–Fock method with relativistic corrections (Cowan 1981 ). Our results are compared with experimental results for 100 spectral lines. Shifts by collisions with ionic perturbers are also taken into account. We also present results as a function of temperature for 161 spectral lines for collisions with electrons, protons, singly charged helium, and singly charged argon. In previous works (Hamdi et al. 2011 , 2013 , 2014 ), the same method was used and we have determined Stark broadening parameters for 114 spectral lines of Pb IV and 32 spectral lines of Ar iii . 2 THE IMPACT SEMICLASSICAL PERTURBATION METHOD A detailed description of this formalism with all the innovations is given in Sahal-Bréchot ( 1969a , b , 1974 , 1991 ), Fleurier, Sahal-Bréchot Chapelle ( 1977 ), Dimitrijević, Sahal-Bréchot Bommier ( 1991 ), Dimitrijević Sahal-Bréchot ( 1996 ), Sahal-Bréchot, Dimitrijević Ben Nessib ( 2014 ), and earlier papers. The profile F (ω) is Lorentzian for isolated lines: where i and f denote the initial and final states and E i and E f their corresponding energies and w is the half width. The shift ( d ) (in angular frequency units) of an electron-impact shifted spectral line can be expressed as: where N is the electron density, the Maxwellian velocity distribution function for electrons, denotes the impact parameter of the incoming electron. The phase shift due to the polarization potential ( r −4 ), is given in section 3 of chapter 2 in Sahal-Bréchot ( 1969a ) and R D is the Debye radius. The cut-off R 3 is described in section 1 of chapter 3 in Sahal-Bréchot ( 1969b ). Energy levels and oscillator strengths needed for SCP calculations of Stark shifts are obtained using Hartree–Fock method with relativistic corrections (HFR) (Cowan 1981 ). We use as for the width calculations an atomic model including 24 configurations: 3s 2 3p 5 ; 3s 2 3p 4 nl ( nl = 4p, 4f, 5p, 5f, 6p, 6f, 6h, 7p, 7f, 7h) (odd parity) and 3s 3p 6 ; 3s 2 3p 4 n ′ l ′ ( n


The authors would like to acknowledge Rainer Beck for helpful discussions. J.T.L. and J.N.B. acknowledge the financial support from NASA through grants NNX15AM93G, NAS2-97001, 80NSSC18K0536, and GO7-18073X.


the two objects could also exhaust helium shell burning and simply cool into double degenerates. Upon merger, they would likely form a rapidly rotating CO WD, potentially preceded by an R CrB phase if substantial He remains, as expected for hybrid WDs (Perets et al. 2019 ). For further details on these systems, please see Kupfer et al. ( 2020a , 2020b ). 6. Conclusion Using data from the ZTF, we have significantly increased the number of known binary systems with an orbital period of less than one hour. Using high-speed photometric follow-up in combination with spectroscopic follow-up, we have characterized the physical parameters of the systems using model-dependent techniques invoking WD mass–radius relations. In future work, we hope to obtain more model-independent measurements such as orbital decay rates to more robustly characterize the physical parameters of these systems. We will continue to analyze ZTF data as it accumulates more epochs and discovers more such objects. At the current stage of the survey, the sample we have discovered exhibits a remarkably high fraction of pairs of He WDs, likely due to selection effects. As we continue the survey, we anticipate discovering more systems and that our discoveries will begin to include other classes of sources, such as pairs of CO WDs. All of the detached systems in our sample should be undergoing rapid orbital decay due to general relativity, and we expect to detect this orbital decay in every detached system with high significance before LISA launches. The algorithms and analysis techniques we are developing will be applicable to upcoming surveys such as the one that will be conducted by the Vera Rubin Observatory (LSST Science Collaboration et al. 2009 ). These data sets will be accompanied by their own challenges (in particular, lower cadence, split across many filters). Given the clear promise demonstrated by the discoveries emerging from ZTF, we are optimistic that optical time-domain surveys will continue to revolutionize our understanding of binaries in the millihertz regime. These surveys will set the stage for LISA, having discovered dozens, if not hundreds, of sources by the time the instrument begins to operate (Korol et al. 2017 ). In future work, we will characterize our recovery efficiency in greater detail using synthetic lightcurves, in order to better characterize ZTF’s sensitivity to detecting the population of DWDs in the galaxy. Efforts are currently underway to increase sensitivity to the shortest-period binary systems by accounting for their orbital period evolution, which requires algorithms that can accommodate acceleration searches (Katz et al. 2020 ). Binaries with compact object components are transitioning into a golden age, as we enter an era when time-domain surveys such as ZTF enable detection via periodic features. Massively multiplexed spectroscopic surveys acquiring multiple epochs such as SDSS-V (Kollmeier et al. 2017 ) and LAMOST (Cui et al. 2012 )


We thank the ESO Paranal team for supporting our SPHERE and AMBER observations. We are also grateful to the referee Susanne Höfner for her valuable comments, particularly on the interpretation of the extended H emission. This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. K.O. acknowledges a grant from Universidad Católical del Norte.


source at its given velocity (within 15 km s −1 ), position (within 5 arcmin), and derived a velocity width and size within our cuts used in Section 2.2 . We recovered every injected source at high velocities, where Galactic emission is the weakest, and nearly every source at low velocities and Leo T velocities (97% and 82%, respectively), the latter of which is lower because Leo T’s velocity is often within the region of average Galactic emission >1 K which we purposely ignored. Nevertheless, we can confidently say that SoFiA would successfully detect Leo T at its actual distance in the vast majority of our search area. We next wanted to determine how accurate our detection limit of Leo T-like objects was, based on our observed flux distribution. To do this, we performed the same procedure as before with two alterations; we scaled the peak flux of the injected source to a larger distance (from 0.5 to 1 Mpc), and we reduced the size of the injected source to better correspond to a more distant galaxy. At high velocities, the detection fraction dropped to its lowest value of 86% at 1 Mpc, but the difference at low and Leo T velocities is much more drastic, as shown in the first three rows of Table 3 (with Mass = 1 Leo T). Note, however, that a typical local group galaxy that is 1 Mpc away has a velocity closer to our high-velocity case than either of the lower-velocity cases. In other words, the region of distance-velocity space where our detection fraction is lowest also probably contains the smallest number of dwarf galaxies. We also tried reducing the injected sources’ size, which results in a ∼10% drop in the detection fraction at lower velocities compared to the same test without changing the size, meaning the dominant reason for the overall drop is the reduction in flux caused by increasing distance. In the bottom three rows of Table 3 we inject sources with successively larger multiples of Leo T’s mass to determine how complete we are out to 1 Mpc. We note that we would detect ≈50% of galaxies at lower velocities with only 2 times Leo T’s mass, and ≈66% of those with 3 times Leo T’s mass. 6 6 At 4 times Leo T’s mass we naturally recover the same detection fractions as the first row of Table 3 , because multiplying the mass of the third row by 4 is equivalent to halving the third row’s distance in terms of H i flux. Table 3 Detection Fraction of Sources Injected at or beyond a Distance of 500 Note. The H i mass of Leo T is . The last row of 10 times Leo T’s mass is an exception to the previous rows in that the size and w 50 cuts we apply are the dominant cause for reduction in recovered sources in regions significantly contaminated by Galactic emission at low velocities. Without the size and w 50 cuts, the detection fractions are all >92%. The higher level of background noise at low latitude causes SoFiA to chop off the outer regions of the object in its size calculation. Therefore our size cut may lead us to miss some dwarf galaxies


background magnetic field than those observed in the synthetic observations (slight preference of perpendicular alignment; Fig. 6 ), which were generated from a trans- to super-Alfvénic simulation. Combined with other polarimetric properties, we suggest that the relative alignment between dense cores and pc-scale magnetic fields depends on the magnetic properties of the cloud, and could potentially provide an alternative approach than the traditional Zeeman observations on investigating the magnetization level of the cloud. APPENDIX A: CORES IDENTIFIED IN GAS DATA AND THEIR RELATIVE ALIGNMENTS Figs A1 – A3 show all subregions observed by GAS overlapped with the core boundaries identified by astrodendro . The relative alignment between cores and background magnetic field (i.e. the angle between core major axis and background magnetic field direction) in each subregion is plotted in Fig. A4 . Figure A1. Cores (red contours) identified in each individual region in the Ophiuchus cloud using NH 3 integrated emission (colour maps, in K km s −1 ) observed by GAS. Note that cores that are more rounded (with minor/major ratio >0.8) are removed from the analysis and not shown here. Dendrogram leaves without obvious central peak emission are also excluded. Figure A2. Same as Fig. A1 , but for the Perseus cloud. Figure A3. Same as Fig. A1 , but for the Taurus cloud. Figure A4. The cumulative distributions of the core–background magnetic field alignment for the subregions within the three clouds: Ophiuchus (left), Perseus (middle), and Taurus (right). APPENDIX B: RELATIVE ANGLES IN 2D AND 3D Here, we briefly describe the difference between measuring relative angle between two random vectors in 3D and 2D spaces. Without loss of generality, we assume both vectors are unit vectors and one is pointing straight up (+ z for 3D case and + y for 2D case). The probability for the second vector to have an angle θ with respect to the first one is therefore proportional to the surface area of the stripe of constant latitude θ on the 3D sphere (), or the arc length at θ of the unit circle ( R dθ). For unit vectors, R = 1, and since we only consider angles within [0, 90] deg, the cumulative probability of the relative angle to be smaller than θ is therefore Note that the probability is normalized by the total surface area of the sphere (in 3D) or the circumference of the whole circle (in 2D). This explains why a set of 3D random vectors will show a linear distribution in cos α instead of α, where α is the relative angle between any two vectors from the set. Equations ( B1 ) and ( B2 ) are illustrated in Fig. B1 as black dotted lines, which also shows that two vectors in 3D are more likely to be perpendicular than parallel if measured in degrees. Figure B1. Comparing the relative angles in 3D (top) and 2D (bottom), for both analytic solutions of equations ( B1 ) and ( B2 ) (black dotted lines) and between two sets of random vectors (solid lines), showing the angle in


We thank the anonymous referee for constructive criticism, particularly regarding estimates of the gas density from the observations. This work was supported by NASA Origins of Solar Systems grant NNX10AH37G.


We thank the staff at the Nobeyama Radio Observatory and the National Radio Astronomy Observatory for help with the observations. We thank Dr. David Frayer for his help in the observations at the GBT. M.A. thanks the Grant-in-Aid for Scientific Research on Innovative Areas (Grant No. 25108002), Grant-in-Aid for Scientific Research (C) (Grant No. 15K05395), and the Institute for Quantum Chemical Exploration.


H i Ly α (lower left), low-TZ Si iii 1206 Å (upper left), low-TZ C iii 1175 Å (lower right), and coronal soft X-rays (upper right). These flux–flux diagrams are more populated given the better FUV coverage of the two stars, although the C iii comparison for B is still missing points for epochs when E140H exposures were taken: these cut off just below Si iii 1206 Å, so C iii 1175 Å was excluded. As tentatively seen in the Mg ii panels previously, the A correlations line up nicely with the solar equivalents, although A’s X-rays still are shifted downward, and noisier than the others perhaps partly because of non-simultaneous coverage. Again, there is somewhat disjoint behavior in several of the panels between the A and B relations. Notice also that A’s Ly α slope closely matches that of the solar correlation, but B’s trend is somewhat shallower. Similarly, the Si iii correlation against C ii is noticeably shallower for B, and curiously shifted downward, compared to A or the Sun. At the same time, the C iii behavior of B appears to be steeper. Finally, A’s X-rays (though scattered) seem to show a steeper rise with increasing C ii , as in the lower branch of the Sun’s bent power law, whereas B displays a flatter relation (although still with α ∼ 2). Figure 16 (c) displays correlations between low-TZ Si iii 1206 Å and low-TZ C iii 1175 Å (lower left), mid-TZ Si iv 1400 Å (upper left), mid-TZ C iv 1550 Å (lower right), and mid-TZ N v 1240 Å (upper right). Again, the C iii comparison is lacking a few points for α Cen B, most conspicuously on the low-flux side. Despite that, all four panels have the same general appearance: the A points closely track the translated solar power laws, while B shows universally steeper slopes. Curiously, the B trends have “retreated” backward to the extent that the A and B origins of the four correlations are similar (again taking into account the abbreviated C iii series for B). This is a consequence of the behavior seen in the upper left panel of Figure 16 (b), wherein B’s Si iii points are seen to parallel those of A, but also approach a similar minimum. This behavior is unlike the other diagnostics shown earlier, for which the minimum B value generally was comparable to, or exceeded, that of A’s maximum. The contrary behavior emphasizes the unique position of Si iii 1206 Å in both the Sun and α Cen A, as a “super-active” species, showing the steepest power laws relative to the other FUV features, even including hot N v . In α Cen B, in contrast, the Si iii feature has declined in strength, and shows the expected “stellar” behavior, namely Si iv , C iv , and especially N v all exhibit power laws comparable or steeper than unity against Si iii . The final figure, Figure 16 (d), illustrates a number of miscellaneous, but nonetheless illuminating, comparisons. The lower left panel compares the two Mg ii resonance lines, which are both affected by ISM absorptions, but the k-line more so than the weaker


GMO acknowledges support of the Research Foundation – Flanders under contract G075916N and under grant number V434818N. HvW acknowledges support from the Research Council of the KU Leuven under grant number C14/17/082. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. We thank the anonymous referee for the useful comments that improved the manuscript.


We thank the referee Durgesh Tripathi for useful suggestions. We also thank Linhua Deng for providing us with the NVST data, Rui Liu for helpful discussions, and the ISSI workshop on “Decoding the Pre-Eruptive Magnetic Configuration of Coronal Mass Ejections” led by S. Patsourakos and A. Vourlidas. SDO is a mission of NASAs Living With a Star Program. X.C. and M.D.D. are supported by NSFC under grants 11722325, 11733003, and 11790303 and by Jiangsu NSF under grant BK20170011. X.C. is also supported by the “Dengfeng B” program of Nanjing University. B.K. acknowledges support by NASA under Grants NNX16AH87G and 80NSSC17K0016, the NSFC, and the DFG.


The authors acknowledge Chuck Horowitz, Evan O’Connor, and Todd Thompson for productive conversations, concerning insight into and help with the microphysics, and Ernazar Abdikamalov, Sean M. Couch, Luke F. Roberts, and Christian D. Ott for fruitful discussions on the nature of core-collapse supernovae. Support was provided by the Max-Planck/Princeton Center (MPPC) for Plasma Physics (NSF PHY-1523261). D.R. gratefully acknowledges support from the Schmidt Fellowship. A.B. acknowledges support from the NSF under award number AST-1714267. J.D. acknowledges support from a Laboratory Directed Research and Development Early Career Research award at LANL. The authors employed computational resources provided by the TIGRESS high performance computer center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology and by the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy (DOE) under contract DE-AC03-76SF00098. The authors express their gratitude to Ted Barnes of the DOE Office of Nuclear Physics for facilitating their use of NERSC. This paper has been assigned a LANL preprint # LA-UR-17-20973.


Acknowledgements We thank the referee for many useful comments and suggestions that helped to improve the paper. We would like to thank all those who are, or have been, associated with BiSON. BiSON is funded by the Science and Technology Facilities Council (STFC). MNL acknowledges the support of The Danish Council for Independent Research | Natural Science (Grant DFF-4181-00415). WJC, SJH, GRD, YPE and RH acknowledge the support of the UK Science and Technology Facilities Council (STFC). Funding for the Stellar Astrophysics Centre (SAC) is provided by The Danish National Research Foundation (Grant DNRF106).


of ε Cet are mostly not able to be individually separated, and the use of assumptions are required to untangle them (Docobo Andrade 2013 ). The angular separation of the components was 0.1 arcsec in 2015 (Mason et al. 2001 ). We obtained sixteen polarized spectra for ε Cet over a 6.0 h interval on 2016 September 21, corresponding to 2.5 per cent of the estimated rotational period of 10.2 d. The mean LSD profile (Fig. B4 ) combined 6693 lines, and a magnetic detection was obtained from the mean LSD Stokes V profile. We are unable to determine whether the magnetic detection was on the F5V or F6V components because the two stars could not be separated spectroscopically. We estimated B l at +0.6 ± 0.1 G. Our radial velocity determination +15.81 ± 0.26 km s −1 (Table 5 ) is similar to the value of +15.49 ± 0.19 km s −1 in Anderson Francis ( 2012 ), and our S-index 0.186 ± 0.003 (Table 5 ) was less than 0.219 in Pace ( 2013 ). A4 α Com α Com (HIP 64241) is a triple star consisting of a double-lined spectroscopic binary (Duquennoy, Mayor Halbwachs 1991 ) of F5V and F6V components (Edwards 1976 ; Soubiran et al. 2018 ), and a V magnitude 10.2 component with an angular separation of 85 arcsec in 2014 based on data from the continuously updated Washington Double Star Catalogue (WDS) (Mason et al. 2001 ). The system was first observed by Struve ( 1875 ) who reported that occultations were observed (Muterspaugh et al. 2015 ). Roman ( 1950 ) describes α Com as a close visual binary, with equal F5 components, and showing weak lines. Hartkopf et al. ( 1989 ) describes α Com as a ‘lovely edge-on system’ with an orbital inclination close to 90 deg, and suggested a partial eclipse was possibly missed in early 1990. The eclipsing binary has the third longest period known ( P = 25.85 yr) (Lipunov et al. 2016 ), with only eight eclipsing stars having periods longer than 10 yr. We obtained twenty-seven polarized spectra for α Com over a 3.8 h interval on 2017 February 16, corresponding to 5.3 per cent of the estimated rotational period of 3.0 d. The mean LSD profile (Fig. B5 ) combined 7628 lines, and a magnetic detection is visible in the Stokes V profile. We are unable to determine whether the magnetic detection was on the F5V or F6V components because the two stars could not be separated spectroscopically. We estimated B l at +3.1 ± 0.3 G. Our radial velocity determination −18.02 ± 0.27 km s −1 (Table 5 ) is larger the value of −16.05 ± 0.21 km s −1 in Anderson Francis ( 2012 ), and our S-index 0.272 ± 0.008 (Table 5 ) is smaller than the 0.308 in Pace ( 2013 ). A5 ω Dra ω Dra (HIP 86201) is a triple star system consisting of double-lined spectroscopic binary (Abt Levy 1976 ; Konacki et al. 2010 ), and a V magnitude 13.2 common proper motion companion with an angular separation of 70 arcsec (Abt Levy 1976 ; Fekel, Tomkin Williamson 2009 ). The mases of the primary component are 1.46 M ⊙ and secondary 1.18 M ⊙ (Konacki et al. 2010 ), which corresponds to


ACKNOWLEDGEMENTS We have used NASA’s ADS Bibliographic Services. Most of the computations that made possible this work were performed with NASA NAIF SPICE Software (Acton 1996 and Jon D. Giorgini), Python 2.7 , and their related tools and libraries, iPython (Pérez Granger 2007 ), Matplotlib (Hunter et al. 2007 ), scipy , and numpy (Van Der Walt, Colbert Varoquaux 2011 ). Special thanks to the reviewers that through their criticism significantly contributed to improve the paper. In particular, we thank Steve Chesley for his in-depth initial review of this work; his comments and observations contributed to improve significantly the quality of the manuscript with respect to its initial versions. We appreciate the assistance of Jon D. Giorgini, senior analyst of the JPL Solar system Dynamics Group. We also thank Professor Ignacio Ferrin and Professor David Asher for useful comments and insightful discussions about this topic. We also thank the organizers of Meteoroid 2016 conference for allowing us to present the initial versions of this work to the meteor and asteroid scientific community. This work is supported by Vicerrectoria de Docencia-UdeA and the Estrategia de Sostenibilidad 2014-2015 de la Universidad de Antioquia . MS is supported by Colciencias, Doctorado Nacional - 647 programme. We thank Universidad Pontificia Bolivariana (UPB-Medellin) and DELL for allowing us to run most of our simulations in their data centres.


Acknowledgments We gratefully acknowledge the fine support at the MMT Observatory, and the Local Group Galaxy Survey conducted at NOAO by Phil Massey and collaborators. This research has made use of the VizieR catalogue access tool, operated at CDS, Strasbourg, France. This study has been supported in part by the Polish National Science Centre grant DEC-2013/10/M/ST9/00086. KI has been also financed by the Polish Ministry of Science and Higher Education Diamond Grant Programme via grant 0136/DIA/2014/43.


I thank Miles for significantly delaying this publication (by being born and so completely disrupting my life). I would not have it any other way. I thank the anonymous referee for constructive comments that helped to improve and clarify this manuscript. This research was supported by NASA Astrophysics Theory Program grant NNX17AG25G and made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.


This work is based on observations with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias on the island of La Palma. This work has been funded by the Spanish Ministry of Economy and Competitiveness (MINECO) under the grant AYA2011-22614 and also received partial support from the DGAPA-UNAM, Mexico under grant PAPIIT IN109614. We thank the referee, G. Stasińska, for her valuable comments that helped to improve the quality of the paper. JGR acknowledges support from the Severo Ochoa excellence programme (SEV-2011-0187) postdoctoral fellowship. We are very grateful to Dr. P. Ventura for providing the tables with the surface abundances of his AGB models, and to Dr. C. Morisset for his invaluable help and comments related to the 3Mdb. We also are grateful to A. Karakas from providing the detailed numbers of the models by Fishlock et al. (2014) . We acknowledge fruitful discussions with D. A. García-Hernández, A. Karakas, and M. Lugaro.


in green, candidate members in light grey, members in red, and members with measured radial velocity in black. Figure 4. Differences between structural parameters obtained from Sérsic fits and isophotal ones. (a) Difference between r e calculated by Calderón et al. ( 2015 ) fitting a Sérsic model and the ‘isophotal’ ∼27 mag arcsec −2 ones, versus absolute and apparent T 1 magnitudes (top and bottom axes), respectively. (b) Same as plot (a) but for the difference in effective surface brightness. It is important to remark that for the two brightest galaxies ( mag), the effective radius results underestimated when using a single component profile (for NGC 3268 the difference is even larger than 1 kpc). A similar (although milder) tendency is present for S0s and cEs. It can be seen that, as expected, the confirmed dEs show mostly positive differences, while the new galaxies (mainly candidates) are the ones showing more negative differences. This effect is less noticeable if we consider a similar difference but for the effective surface brightness (Fig. 4b ). In this case, the confirmed dEs are evenly distributed about zero. 6.2 Geometrical parameters at different galactocentric radii In this section, we analyse the geometrical parameters obtained from the ellipse output for the whole sample, considering the four radial ranges (regions 1 to 4) defined in Section 4 . Fig. 5 shows the distribution of the intensity-weighted average ellipticity 〈ε〉 for the four regions, with a cross-hatched (red) histogram for faint galaxies (dEs and dSph) and an open one for the whole sample. We note that the morphological classification was done by visual inspection of each galaxy, following the criteria used in FS90. That is why we do not establish a magnitude limit (usually set around M B = −18 mag); an overlap in luminosity between bright and dwarf ellipticals can thus be seen. Figure 5. Histograms of the mean weighted ellipticity distributions, cross-hatched in red for dE and dSph and open for the whole sample. Number of galaxies in each region is indicated in parentheses. The histograms of mean ellipticity show flatter (although slightly less extended) distributions, as compared to those obtained by Chaware et al. ( 2014 ) and Hao et al. ( 2006 ), where a main peak at 〈ε〉 ∼0.1 → 0.16 is evident in regions 1 to 4, implying a dominant fraction of nearly round galaxies. Besides a similar low 〈ε〉 peak, a second peak at 〈ε〉 ≈0.3 is also evident in region 1 of our sample. This reflects the fact that most of the brighter galaxies in Antlia are lenticulars (S0), while dwarfs also tend to exhibit relatively large flattenings, despite most of them being classified as dE (dS0s are found only among the brighter dwarfs.). Figs 6 and 7 show the distributions of the weighted mean values of the Fourier coefficients 〈 a 3 / a 〉 and 〈 a 4 / a 〉. As usual, they are reasonably fitted with a single Gaussian centred at zero, except in the outermost region, where the


We are grateful to Javier Manzano-Santamaría for his support on the experiments. Special thanks go to Marcelino Agúndez for useful discussions. This research was financed by the Spanish MINECO under projects AYA2011-29375 and AYA2014-60585-P. R.M.D. benefited from a FPI grant from Spanish MINECO.


We are grateful to F. Paresce for carefully reading the paper and useful comments, which improved the final version. We thank the referee for constructive comments and suggestions on the manuscript. This research made use of the NASA/IPAC Infrared Science Archive and Extragalactic Database, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Part of this work is based on archival data, software or online services provided by the Scientific Data Center of the Italian Space Agency.


This work is part of the VIALACTEA Project, a Collaborative Project under Framework Programme 7 of the European Union, funded under Contract # 607380 that is hereby acknowledged.


in November 2014 (red; Snodgrass et al. 2016 ). 3.2 Dust coma morphology and activity For each cube in our dataset, we extracted maps over the bandpasses of the V , R , and I Johnson-Cousins filters. All maps in the same bandpass were re-centred and then co-added. The resulting co-added maps are displayed in the top part of Fig. 2 . The dust coma morphology is the same for all three bandpasses. It is asymmetrical, likely due to the presence of dust jets. To investigate the presence of jets further, we divided the dust maps by an azimuthal median profile ( Samarasinha et al. 2013 ). Enhanced maps are displayed on the bottom part of Fig. 2 . Here, we can clearly see two jets, which are most likely the cause of the apparent asymmetry of the dust coma. The first jet is located close to the anti-sunward direction, towards the south-west. The second jet is located about 90° away, towards the south-east. Finally, we see a faint feature towards the sunward direction. Those jets are consistent with what was observed on previous passages and what is reported by Knight et al. (2017) and Snodgrass et al. (2017a ) from observations at the same epoch. They are also consistent with the modelling of the pole orientation and active region location done by Vincent et al. (2013) prior to the Rosetta mission. In addition to the two jets mentioned above, we see an enhancement towards the North-West. This corresponds to the dust trail that was reported to be at least two degrees long at that epoch ( Snodgrass et al. 2017a ; Boehnhardt et al. 2016 ; Knight et al. 2017 ). We do not see changes of the coma morphology over the five nights of our observations, nor over a single night. To constrain the comet activity at that time, we compute the Af ρ value, which is a proxy for dust production, as defined by A’Hearn et al. (1984) . We compute the Af ρ for the V , R , and I bands over a 2500 km physical aperture. We use a 2500 km aperture instead of the more commonly used 10 000 km aperture because the comet signal drops significantly at 10 000 km. We obtain values of 65 ± 4 cm, 75 ± 4 cm, and 82 ± 4 cm in the V , R , and I bands, respectively. Those values have not been corrected for the phase angle effect and are consistent with those reported by Boehnhardt et al. (2016) at the same epoch, and they are comparable (even though slightly lower) to those reported by Knight et al. (2017) once the phase angle effect is taken into account. Using the Af ρ values in the different bands, we can also compute the dust reflectivity gradient defined as ( Jewitt Meech 1986 ): where Af ρ x and the corresponding wavelength λ x are expressed in cm and nm, respectively. For the I – V combination, this gives a reflectivity gradient of 7 ± 1%∕100 nm, while it is of 11 ± 2%∕100 nm for the R – V and 7 ± 1%∕100 nm for the I – R combination. This confirms the trend outlined in Sect. 3.1 of higher reflectivity gradient at lower wavelengths. To check for trends with the aperture size, we