O B-Tag O O O O O O O O O O O O O O B-Software O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Software O O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software I-Software I-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Software O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Software O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O B-Software I-Software I-Software

TESTING <sc>binulator</sc>+<sc>gravsphere</sc> ON MOCK DATA In Section 4.1 , we introduced an updated version of the gravsphere code (Read Steger 2017 ; Read et al. 2018 ) with a new reworked binning method, the binulator . In this Appendix, we present tests of the new code on mock data drawn from the Gaia Challenge 2 spherical and triaxial suite (Read et al. 2021 ). We focus on two mocks that were particularly challenging for the previous version of gravsphere : PlumCuspOm and PlumCoreOm. The former is a Plummer sphere embedded in a spherical, cuspy dark matter halo; the latter is the same embedded in a dark matter halo with a central constant density core. In both cases, the velocity dispersion profile is isotropic at the centre and maximally radially anisotropic at large radii. Both mocks are described in detail in Read et al. ( 2021 ). Here, we model both assuming Gaussian velocity errors on each star of 2 km s −1 for 100, 1000, and 10 000 randomly sampled kinematic tracers. We assume that the photometric light profile is in all cases well sampled with 10 000 stars, similarly to the situation with real data for nearby dsPh galaxies (e.g. Read et al. 2019 ). Previously, gravsphere struggled on these mocks. For both PlumCoreOm and PlumCuspOm with 1000 tracers, it returned a dark matter density that was systematically low for , shifting, however, to for 10 000 tracers. The velocity anisotropy was well recovered in all cases, except PlumCoreOm for which 1000 tracers were insufficient to detect the radial anisotropy at large radii (Read et al. 2021 ). In Gregory et al. ( 2019 ), gravsphere was tested on mock data for fewer tracers (20, 100, and 500 tracer stars). There, a similar bias towards low densities at large radii was reported. We show results applying the updated gravsphere with its new binulator binning module to the PlumCoreOm and PlumCuspOm mocks in Fig. A1 . In all cases, we obtain an unbiased recovery of both the dark matter density profile, , and the symmetrized stellar velocity anisotropy, . The code is no longer biased to low density at large radii. This owes to a combination of the improved data binning, the proper inclusion of the full error PDF for the virial shape parameters, and to our switch to using the coreNFW profile (recall that the non-parametric power-law-in-bins profile used previously by default in gravsphere biases models towards falling very steeply at large radii in the absence of data). Notice that now, even with just 100 tracers, we are able to detect that the PlumCuspOm is denser and falls more steeply than PlumCoreOm. For PlumCuspOm, we are also able to weakly detect that the velocity distribution is radially anisotropic at large radii. As we move to 1000 and 10 000 tracers, we obtain an increasingly high-fidelity recovery of both the density profile and the velocity anisotropy. Figure A1. Testing the updated gravsphere code and its new binulator module on spherical mock data from the Gaia Challenge suite.


O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Instrument I-Instrument B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Instrument O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O B-Instrument O O O O O O O B-Observatory O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O B-Instrument O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

of higher-Γ EEs. We also estimate P k using declination-averaged effective area for IceCube, , shown as IC () in Table 2 , which shows slightly higher for EE-opt-dist. Although the declination dependence of does not change our conclusion much, the declination-dependent analysis is important for more quantitative evaluations. Table 2 The Detection Probabilities, , for d L = 300 Mpc Note. IC: IceCube, Gen2: IceCube-Gen2, up+hor: upgoing+horizontal events, down: downgoing events, all: covering-factor-weighted average over the up+hor and down, : using the declination-averaged effective area. Using the relation , we estimate as a function of d L , which is shown in Figure 2 . Here, we ignore the effects of cosmological redshift, since we focus on the local universe at Gpc. The vertical dotted lines show d L = 300 Mpc and d L = 600 Mpc, which corresponds to the sensitivity ranges of face-on NS–NS and NS–BH mergers by aLIGO, respectively. For NS–BH mergers, since the distance is longer, is lower than those for NS–NS mergers. The detection probability of nearby events is affected by , while that of distant events is not. Figure 2. Detection probability as a function of luminosity distance d L . The upper and lower panels are with IceCube and IceCube-Gen2, respectively. The vertical thin-dotted lines show d L = 300 Mpc and d L = 600 Mpc. We estimate the detection probability within a given time interval, , which is estimated to be , where N is the number of EEs for the time interval within the covering area of neutrino detectors. The local SGRB rate is (e.g., Nakar et al. 2006 ; Wanderman Piran 2015 ), so the event rate within the sensitivity range of aLIGO (300 Mpc) is . According to the Swift results, ∼25% of SGRBs are accompanied by EEs (Sakamoto et al. 2011 ), noting that softer instruments could detect more EEs (Nakamura et al. 2014 ). Here, we simply assume that half of SGRBs have EEs, leading to N ∼ 2–5 for years. Within the sensitivity range of NS–BH mergers by aLIGO (600 Mpc), the SGRB rate is , leading to ∼9–22 EEs for a 5 year operation. The estimated values of are tabulated in Table 3 . We find that the simultaneous detection of gamma-rays, neutrinos, and GWs is possible in the era of IceCube-Gen2 and aLIGO/aVirgo/KAGRA, assuming a cosmic-ray loading factor, . This will allow us to probe the physical conditions during EEs, including the cosmic-ray loading factor and the Lorentz factor (see Section 4 ). Table 3 The Detection Probabilities within a Given Time Interval, Note. The SGRB rate is assumed to be . In the near future, KM3NeT will be in operation. While IceCube is more suitable to observe the northern sky, KM3NeT will achieve a better sensitivity for the southern sky, helping us improve the possibility of detections. In reality, not only Γ but also the other parameters for EEs (, , , α , β , , , d L ) should be distributed in certain ranges. However, their distribution functions are quite uncertain, and detailed discussion of


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ACKNOWLEDGEMENTS We thank the Gemini staffs for preparing and carrying out the observations. We thank the anonymous referees for many insightful comments. We acknowledge K. Matsuoka, Y. Matsuoka, R. Momose, T. Nagao, M. Nakamura, A. Schulze, V. Wong, X. B. Wu for useful discussions. TG acknowledges the support by the Ministry of Science and Technology of Taiwan (MoST) through grant 105-2112-M-007-003-MY3, and YO acknowledges the support by the MoST of Taiwan through grant 106-2112-M-001-008- and 107-2119-M-001-026-. CJ is supported by the Hundred Talents Program of the Chinese Academy of Sciences. CJ acknowledges the National Natural Science Foundation of China through grant 11873054. CD acknowledges the Science and Technology Facilities Council (STFC) through grant ST/P000541/1 for support. EKE acknowledges a post-doctoral fellowship from TUBITAK-BIDEB through 2218 program.


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We thank the anonymous referee for helpful suggestions. The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation. We thank Dr. Mark Miesch for comments that improve this manuscript. F.C. is supported by the Advanced Study Program postdoctoral fellowship at NCAR. This work is also supported in part by the NASA LWSCSW grant NNX13AJ04A and NASA grant NNX14AI14G. Computing resources were provided by the NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation, on Yellowstone ( http://n2t.net/ark:/85065/d7wd3xhc ).


O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O B-CelestialObject I-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength B-Wavelength O O O O B-Wavelength I-Wavelength O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject O O B-Wavelength O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-Formula I-Formula I-Formula O O O O O O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O B-CelestialObject O O O O B-Wavelength O O O O O O B-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Formula I-Formula I-Formula O O O O O B-Citation I-Citation I-Citation

to the spectroscopic data. This source is less luminous than J0100+2802 and its mass is smaller, according to the estimate obtained by fitting the SED. With the same accretion disc model as before, in fact, we obtain M BH = 1.3 × 10 9 M ⊙ , L disc = 3.9 × 10 46 erg s −1 = 0.23 L Edd , L X = 0.8 L disc ∼ 3 × 10 46 erg s −1 and L X + L disc = 0.41 L Edd . As previously explained for J0100+2802, the value of the black hole mass should be taken as a lower limit. We conclude that both sources, despite the difference in black hole mass, share similar Eddington ratios and similar partition between optical–UV and X-ray luminosities. We can compare our results on ULAS J1120+0641 with those of Mortlock et al. ( 2011 ), who found M BH ∼ 2 × 10 9 M ⊙ (through the virial method) and a disc luminosity of 2.5 × 10 47 erg s −1 (applying a a fiducial bolometric correction taken from Willott et al. 2010 ). Differently from us, the results of Mortlock et al. ( 2011 ) indicate a slightly super-Eddington luminosity. 4.3 Comparison with other powerful quasars It is well-established that the X-ray-to-optical power-law slope parameter α ox of quasars correlates significantly with the ultraviolet 2500-Å monochromatic luminosity ( L 2500 Å : Steffen et al. 2006 ; Just et al. 2007 ). For J0100+2802 with rest-frame 2500-Å flux density, f 2500 Å , estimated from Wu et al. ( 2015 ) and rest-frame 2-keV flux density, f 2keV , estimated from the power-law model, we have parameter α ox with value −1.74 ± 0.01. In Fig. 6 , we show the location of J0100+2802 and the other highest-redshift quasars with z > 6, for which we take α ox and L 2500 Å from the literature (Brandt et al. 2002 ; Farrah et al. 2004 ; Shemmer et al. 2006 ; Moretti et al. 2014 ; Page et al. 2014 ; Gallerani et al. 2017 ), in the α ox – L 2500 Å relation. It is clear that the SED of the ultraluminous J0100+2802 is not abnormal among the highest-redshift quasars and all quasars at z > 6 follow the α ox – L 2500 Å relation like low- and median-redshift quasars. As discussed in Nanni et al. ( 2017 ), which presents a systematic analysis of X-ray archival data of quasars at z > 5.5, these results support the non-evolutionary scenario of SEDs of luminous quasars. For J0100+2802, the inferred value of α ox in Nanni et al. ( 2017 ) is , which is in agreement with ours considering the scatter of the α ox – L 2500 Å relation. Figure 6. Location of J0100+2802 (red star) in the X-ray-to-optical power-law slope parameter α ox versus 2500-Å monochromatic luminosity. The grey dots are quasars from the samples of Just et al. ( 2007 ), Steffen et al. ( 2006 ) and Gibson, Brandt Schneider ( 2008 ). The blue dots are weak-line quasars and PHL 1811 analogues from Luo et al. ( 2015 ). The solid line represents the α ox – L 2500 Å relation from Just et al. ( 2007 ) and the dot–dashed line from Nanni et al. ( 2017 ). The red symbols represent high-redshift quasars with z > 6.0 from the literature (squares from Shemmer et al.


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behind the Sun. Our data include 48 epochs taken before the discovery, starting on 2003 December [upper limit from the Sloan Digital Sky Survey (SDSS) DR9 4 ] up to 2012 March. These data were taken mainly by amateur astronomers. One epoch was secured using the Ultraviolet and Optical Telescope on board the Swift satellite on 2013 September 05.65. However, only upper limits were estimated for the UVW2 (>20.9 mag) and UVW1 (>20.0 mag) bands (V egamag ). Photometric observations were preprocessed following the standard recipe in iraf 5 for CCD images (trimming, overscan, bias, and flat-field corrections). For the NIR exposures, we also applied an illumination correction and background-sky subtraction. For later epochs, multiple exposures obtained in the same night and filter were combined to improve the signal-to-noise ratio (S/N). The SN magnitudes were measured using point-spread-function (PSF) fitting with SNO o P y . 6 No template subtraction was performed since no major differences were found when comparing the photometry obtained through both PSF fitting and template subtraction. The data derived with the two methods are in agreement to within 0.1 mag. In order to calibrate the instrumental magnitudes to standard photometric systems, we used the zero-points and colour terms measured through reference SDSS stars in the field of SNhunt151. The Johnson–Cousins magnitudes of these reference stars were calculated from the Sloan magnitudes following the conversions of Chonis Gaskell ( 2008 ). For the NIR photometry, we used the Two Micron All Sky Survey (2MASS) catalogue as reference for the calibration. Once the local sequence was calibrated, we proceeded to calibrate our transient, even for non-photometric nights. Unfiltered magnitudes from amateurs were scaled to Johnson–Cousins V - or R -band magnitudes, depending on the wavelength peak efficiency of the detectors. Uncertainty estimates were obtained through artificial-star experiments. This is combined (in quadrature) with the PSF fit error returned by daophot and the propagated errors from the photometric calibration. The final calibrated SN magnitudes are listed in Tables B2 and B5 for the optical bands, and in Table B4 for the NIR range. 3.2 Space-Based Observations The SNhunt151 site was also observed by the Hubble Space Telescope ( HST ) with the Ultraviolet-Visible (UVIS; ∼ 0.04 arcsec pixel −1 ) Channel of the Wide-Field Camera 3 (WFC3) in the F 555 W and F 814 W bands. These images were taken on 2016 October 23 as part of the SN snapshot survey GO-14668 (PI: A. V. Filippenko), 1113.1 d after the V -band peak of SNhunt151's Event B (see below). A source was detected at the transient position in all images with root-mean-square uncertainties 0.01 arcsec (Fig. 1 d), through comparison with ground-based, post-discovery Copernico Telescope+AFOSC, and NOT+ALFOSC images taken on 2013 August 31 (seeing 1.16 arcsec) and 2014 August 24 (seeing 0.96 arcsec). The magnitudes of the source in


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We gratefully acknowledge data provided by the NASA/Space Physics Data Facility (SPDF) and Wind /3DP Data Center. We thank K. Ogilvie, R. Lin, A. Szabo, and L. Wilson III for their support of this work. Also, we thank D. Reames, X. Shao, and the anonymous reviewer for their valuable comments.


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ACKNOWLEDGEMENTS This work was supported in part by the NWO DRIFT project (contract 628.002.002). The authors would like to thank Ahmad Mouri Sardarabadi for discussions on an initial idea captured in Naghibzadeh et al. ( 2016b ) which evolved into this paper, Patrick Dewilde for in-depth discussions and comments regarding the algorithm and the paper, Martin van Gijzen for discussions regarding the iteratively reweighted algorithms and Stefan Wijnholds for providing the lofar station data.


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The author thanks F. Vincenzo, and V. Grieco for several fruitful discussions, and F. Matteucci for many useful suggestions and for reading the manuscript. The author also thanks an anonymous referee whose comments noticeably improved the paper. The work was supported by PRIN MIUR 2010-2011, project ‘The Chemical and dynamical Evolution of the Milky Way and Local Group Galaxies’, prot. 2010LY5N2T.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. The open circles, crosses and open squares show the average value for clusters with D = 1.6, 2.0 and 3.0, respectively. The red and black symbols show the results for the inner orbit and the outer orbit, respectively. Middle panel: half-mass radius at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. Symbols and colours as in the left-hand panel. Right-hand panel: velocity dispersion of the cluster members at t check as a function of the initial virial ratio vir for clusters with different initial fractal degrees. Symbols and colours as in the left-hand panel. We found that the initially virialized clusters experience a smaller mass-loss rate than both supervirial and subvirial clusters of the order of 10percent (see left-hand panel of Fig. 6 ). This result is evident also in the left-hand panel of Fig. 7 , in which we show the mass evolution of three realizations of clusters on the outer orbit as a function of their initial virial state for the first 1Gyr of evolution. Once again, such a trend mirrors the value of the relaxation time at t check . We found that initially sub/supervirial clusters evolve with systematically smaller relaxation times from the very early stages. A collapsing system will then exhibit a shorter crossing time, inducing faster relaxation of the system. On the other hand, in a tidally limited system such as a star cluster in a galaxy it is possible that if the cluster is initially expanding the number of escapers in the early stages can be enhanced, once again reducing the number of cluster members and hence the relaxation time of the system. Figure 7. Evolution of the mass (left-hand panel), half-mass radius (middle panel) and velocity dispersion (right-hand panel) of initially spherical clusters ( D = 3.0) on the outer orbit with different initial virial ratios. The dark blue, red and light blue lines show the results of the simulations of clusters with initial virial ratio D 0.2, 0.5 and 0.8, respectively. The vertical black dashed line indicates the time t check at which the properties have been evaluated in Fig. 6 . This trend is also reflected in the size of the clusters. Initially virialized clusters evolve with slightly bigger half-mass radii. However, we also note that such a variation is of the order of only a few percent and is of the order of the variations associated with the random realizations of the clusters (see the middle panels of Figs 6 and 7 ). Similar to the effect of the initial fractal dimension, the initial virial state of the clusters also does not significantly affect the evolution of the velocity dispersion of the cluster members. Finally, we note that also in this case, the discussed trends are quite well reproduced for both the inner and outer orbits. 3.3 Impact of the initial degree of mass segregation on the long-term


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ACKNOWLEDGEMENTS The authors acknowledge the support from the Program of target financing of the Ministry of Education and science of the Republic of Kazakhstan, Grant No. BR05236730.


B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation

Hirschmann et al. 2010 ; Jahnke Macciò 2011 ). A closely related issue involves the connection between BH accretion and star formation in the host galaxy. Here, too, no consensus has yet emerged. While some contend that star formation rate (SFR) correlates strongly with AGN luminosity across a wide range of redshifts, implying the simultaneous growth of the BH and its host (e.g., Bonfield et al. 2011 ; Rosario et al. 2012 ; Xu et al. 2015 ; Lanzuisi et al. 2017 ; Dai et al. 2018 ; Stemo et al. 2020 ), others find only moderate or no correlation (Rosario et al. 2013 ; Azadi et al. 2015 ; Stanley et al. 2015 , 2017 ). The disagreement is partly explained by the different timescales of the measured SFR and AGN variability (Hickox et al. 2014 ). At high redshifts (e.g., z > 1), many works do not find a significant correlation between SFR and AGN luminosity (e.g., Shao et al. 2010 ; Rosario et al. 2012 ; Schulze et al. 2019 ; but see Stemo et al. 2020 ). For low redshifts, the correlation is moderate in weak AGNs (e.g., Shimizu et al. 2017 ) but strong in more powerful systems (e.g., Netzer 2009 ; Imanishi et al. 2011 ; Xia et al. 2012 ; Lani et al. 2017 ; Zhuang Ho 2020 ). It has also been argued that the relationship between SFR and AGN luminosity is not intrinsic but instead arises indirectly from the the mutual correlation of both quantities to the host galaxy stellar mass (e.g., Xu et al. 2015 ; Yang et al. 2017 ; Suh et al. 2019 ; Stemo et al. 2020 ), stellar mass surface density (Ni et al. 2020 ), or BH mass (e.g., Stanley et al. 2017 ). Using a hierarchical Bayesian model, Grimmett et al. ( 2020 ) recently demonstrated that AGNs of higher X-ray luminosity more tightly correlate with higher SFRs than lower luminosity AGNs. In any event, when present, the association between star formation and BH accretion seems to occur preferentially on nuclear scales, both in moderately luminous AGNs (Davies et al. 2007 ; Watabe et al. 2008 ; Diamond-Stanic Rieke 2012 ; Esquej et al. 2014 ; Zhuang Ho 2020 ) and in more powerful quasars (Imanishi et al. 2011 ; Canalizo Stockton 2013 ; Bessiere et al. 2014 , 2017 ; Lutz et al. 2016; Kim Ho 2019 ; Zhao et al. 2019 ). This is not unexpected, as cold gas on small scales naturally fuels nuclear star formation and feeds the BH (Hopkins Quataert 2010 ; Volonteri et al. 2015 ; Gan et al. 2019 ). Observations of nearby galactic nuclei offer useful clues. For example, the molecular gas in the central regions of many galaxies (e.g., Scoville et al. 1994 ; Smith Harvey 1996 ; Rubin et al. 1997 ; García-Burillo et al. 2005 , 2019 ; Hicks et al. 2009 ; Izumi et al. 2018 ; Salak et al. 2018 ; Treister et al. 2018 ; Boizelle et al. 2019 ), including the Milky Way (e.g., Ho et al. 1991 ; Hsieh et al. 2017 ), resides in the form of a circumnuclear disk. Theoretical works suggest that the star formation in the circumnuclear disk may control the gas fueling BH accretion (Shlosman et al. 1989 ; Goodman 2003 ; Thompson et al.


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including SNe II). We have found a good agreement between the L X – M ⋆ relation of the models and that of observed ETGs, over the whole M ⋆ range. In particular, the largely different observed L X values at the same M ⋆ are reproduced by the sensitivity of the gas flow to many properties characterizing ETGs, as galaxy shape, presence of rotation, presence of star formation, and AGN feedback. The models also show an overall agreement with the observed L X – relation, though of the models is slightly larger than that derived by F17 , for ETGs of the same M ⋆ . The agreement between models and observations holds with and without radiative and mechanical (from AGN winds) AGN feedback. These results imply that the mass input from the stellar population is able to account for a large part of the observed L X , and that—under the assumptions of this work—AGN feedback does not have a significant role in determining the present epoch L X . This is an important conclusion about the fate of recycled stellar material in the presence of AGN feedback, since an outcome of the simulations could have been, for example, a major degassing of the galaxies. Such a different outcome would have implied the necessity to assume other sources of mass (as gas accretion from outside). F17 noticed a good agreement between their results and the predictions of cosmological SPH simulations, where the hot gas mostly originates from a cosmological reservoir from which gas falls into the dark matter halos, is shock-heated, and is then further significantly heated by mechanical feedback due to AGN winds (Choi et al. 2015 ). If this mechanical feedback is not included, the simulations predict an L X far larger than that observed; thus, it is concluded that the AGN plays an important role in determining L X (in addition to M t ). This conclusion is not in contradiction with the results of the present work, which starts after z ≃ 2, and indicates that the AGN has not shaped dramatically the value of L X observed today. In fact the cosmological simulations of Choi et al. ( 2015 ) as of many others (see, e.g., Section 1 ), start from the galaxy formation epoch, and obtain at early times AGN-driven powerful outflows that remove nearly all the gas, and stop star formation. In this sense, the role of the AGN is certainly very important. Our simulations ( N14 , N15 , C17 ) start from these “initial conditions” created at the epoch of quenching, and find that at later epochs the energy injected by the AGN is not crucial in determining L X of the recycled material (while fundamental to stop the recurrent cooling flow and keep the MBH mass low). The conclusions of the two approaches, one including and the other excluding the epoch of galaxy formation and the presence of cosmological gas, then agree, provided that AGN feedback in the first approach is stronger than that found here. In fact, if AGN-driven outflows are to clear the gas out of massive ETGs at early epochs and/or prevent a


O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Model O O O O O O O O B-Model O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database O O O O O O O B-Instrument O B-Instrument O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O B-Location O O O B-Telescope I-Telescope I-Telescope I-Telescope O O B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O B-Instrument O O O O O O O O O O O B-Telescope I-Telescope O B-Observatory I-Observatory I-Observatory B-Observatory B-Citation I-Citation I-Citation I-Citation O O B-Instrument O

for stars hotter than 5500 K ( Ryabchikova et al. 2015 ). The Balmer lines in B to F stars are in general well matched by LTE computations, and they are practically identical to the non-LTE predictions ( Przybilla Butler 2004 ). The region around H was chosen because it harbours several iron lines with accurate atomic parameters. The Balmer lines provide an excellent diagnostic of for stars cooler than 8000 K ( Gray 1992 ; Heiter et al. 2002 ). For stars hotter than 8000 K, Balmer line profiles, in particular their wings, are sensitive to both temperature and gravity ( Gray 1992 ; Smalley 2005 ). Metal line diagnostics are also good indicators of , , and [Fe/H] as the best-fit synthetic spectrum corresponds to the spectrum that yields the same abundance for different ionization stages of the same element (ionization balance) and in the same abundance for all excitation potentials of the same element in a given ionization stage (excitation potential). On the other hand, lines such as the Mg ii triplet around 4481 Å and the Fe ii lines between 4500 and 4530 Å are excellent indicators of (see for example Royer et al. 2014 ). For all the above mentioned reasons, we applied the global spectral fitting technique to the whole spectral range from 4400 and 5000 Å. The derived parameters are obviously model dependent, but the models that we are using (Sect. 2.2 ) are well suited to describe the atmospheres and spectra of “normal” A and Am stars. The selection of the observed spectra and construction of the learning databases are detailed in Sect. 2 . The PCA and the derivation of the eigenvectors and coefficients are recalled in Sect. 3 . Radial velocity correction and re-normalization of the spectra are discussed in Sect. 4 . The results of the inversion are presented in Sect. 5 . A few outliers have been analysed in detail in Sect. 6 . Discussion and conclusion are gathered in Sect. 7 . 2. Observations and learning database 2.1. Target selection The PolarBase contains reduced stellar spectra collected with the NARVAL and ESPaDOnS high-resolution spectropolarimeters. These two spectropolarimeters are mounted on the 2 m aperture Télescope Bernard Lyot (TBL) in France and on the 3.6 m aperture CFHT telescope in Hawaii, respectively. Both instruments have a spectral resolving power of 65 000 in polarimetric mode and 76 000 when used for classical spectroscopy. As a first step, we have selected all high-resolution Echelle spectra of stars whose spectral type ranges from F0 up to B9 from the database at two different resolutions and in spectroscopy mode only. Fifty spectra were thus retrieved. We have also retrieved A-type stars spectra from the ELODIE and SOPHIE archives. These archives are on-line databases of high-resolution Echelle spectra and radial velocities. The ELODIE is a fiber-fed, cross-dispersed Echelle spectrograph that was attached to the 1.93-m telescope at Observatoire de Haute-Provence (OHP; Baranne et al. 1996 ). The ELODIE recorded


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We thank the IRAM PdBI staff for excellent support. This research was supported by J.E.L.’s appointment to the NASA Postdoctoral Program at the NASA Goddard Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA. S.A. thanks the Swedish National Science Council for grant support. We also thank the referee Chiara Feruglio for comments and suggestions which significantly contributed to improving the quality of the manuscript.


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The authors dedicate this work to Stanislav (Stan) Štefl (1955–2014) in whose honor the Štefl frequencies are named. A. C. C. acknowledges support from CNPq (grant 307594/2015-7) and FAPESP (grant 2015/17967-7). The authors are very grateful to an anonymous referee for comments serving to clarify the results. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. Partly based on observations obtained at the Canada-France-Hawaii Telescope (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 Scientique of France, and the University of Hawaii. This research has made use of NASA’s Astrophysics Data System Service, as well as of the SIMBAD database, operated at CDS, Strasbourg, France.


O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Mission I-Mission B-Instrument O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Mission B-Instrument O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

peak temperature that we have previously reported (Jennings et al. 2011 , 2016 ) continued through late northern spring to the solstice. The latitude of maximum temperature (center of north–south symmetry) closely tracked the subsolar point from 13 S in 2005 to 24 N in 2017. We find a non-zero phase offset that corresponds to a small seasonal lag at equinox, about 0.1 Titan months. Figure 1 shows that a small lag is consistent with the non-uniform GCM case, although it is not as clear that there is a lag in the uniform case (see also Tokano 2019 , Figure 3). Our seasonal lag agrees with that reported by Janssen et al. ( 2016 ) and is also in line with the observations of Voyager 1 IRIS near the previous equinox in 1980 November (Flasar et al. 1981 ; Courtin Kim 2002 ). A small lag is consistent with the low thermal inertia required of the surface for diurnal variations (Cottini et al. 2012 ). Our equatorial temperature of 93.5 ± 0.4 K at equinox ( L s = 0°) agrees with the Voyager IRIS measurement, 93 ± 1 K (Courtin Kim 2002 ). From early to late in the mission the maximum amplitude of the cosine dropped by about 1 K, from 93.9 to 92.8 K. The time-dependent width in formula (1) signifies a “flattening” of the temperature distribution as the peak moved north, i.e., a more gradual fall-off toward the poles. An examination of the measurements and of the fitted cosines suggests that, although the peak temperature decreased, the average of north and south pole temperatures in each period remained approximately the same throughout all seven periods. Our formula can be used to inspect the change in surface temperature at any particular latitude over the two-season mission. For example, at the Huygens landing site, 10 S, the temperature ranged from 93.9 to 92.5 K between 2005 and 2017. Because the peak temperature decreased as it shifted northward, the semi-annual temperature variation was strongly dependent on latitude. The temperature variation was greatest at 40 S (93.6–91.7 K), where the surface was relatively dry, and was smallest at 40 N (92.6–92.7 K), where surface temperatures were moderated by the wetter north (Lora et al. 2015 ; Tokano 2019 ). Changes in surface condensation must be much less at mid-northern than at mid-southern latitudes. At 40 S between winter and summer, vapor pressures would have increased by a factor of 1.26 for methane and 1.61 for ethane while at 40 N they would have varied by only factors of 1.01 and 1.03. Any northward migration of volatiles while the south is warmer will not be fully undone later in the yearly cycle because the northern temperatures never get as warm as in the south. The temperature ranges at the poles were virtually identical: 91.9–89.8 K at 80 S and 89.9–91.9 K at 80 N. Both poles, at their coldest, reached the triple points for methane (90.7 K) and ethane (90.3 K). The poles may at times harbor both liquid and solid phases. Overall our results indicate that the northern hemisphere presents a


O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject O B-CelestialObject O B-CelestialObject O B-CelestialObject O B-CelestialObject O B-CelestialObject O O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation O B-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database

Figures 2 (a)–(f) show compressed spectra from 85 to 101 GHz toward CO Peak 1, NQC2, N79, N44C, N11B, N113, and N159W, respectively. In the preparation of these data, we corrected slight intensity variations among the subscans for 1.5 hr by using the intensity of the strongest line of the observing band. For the compressed spectra, we subtracted the baseline by using the fifth-order polynomial over the 2.2 GHz region. Although the standing waves caused by the telescope system are still visible, we were readily able to identify emission lines, because the typical line width observed toward the target sources (5 km s −1 ) is narrower than the period of the standing waves. Lines are identified with the aid of the spectral line database CDMS (Müller et al. 2001 , 2005 ). We used the 13 CO line velocity ( V LSR ) of 229, 266, 285, 282, 232, 235, and 238 km s −1 for CO Peak 1, NQC2, N11B, N44C, N79, N113, and N159W, respectively, to identify the molecular lines. We detected eight molecules (CO, 13 CO, CS, SO, CCH, HCO + , HCN, and HNC) in the seven sources, c -C 3 H 2 in N79, N44C, N11B, N113, and N159W, and CN in N79, N44C, and N113 (Table 4 ). N 2 H + is marginally detected in N113 and N159W. The detection criterion is that the line is detected at the expected velocity with the significance of 5 σ or higher in the integrated intensity. Note that the c -C 3 H 2 line was not covered with the frequency setting for CO Peak 1. Since line intensities in CO Peak 1 and NQC2 are typically weaker by a factor of 2 than the other sources, fewer lines were detected in these sources. The signal-to-noise ratio is rather poor for N113 and N159W in comparison with the previous studies (Chin et al. 1997 ; Heikkilä et al. 1999 ; Wang et al. 2009 ), and hence, only strong lines were detected in this study. Figure 2. Compressed spectra observed toward CO Peak 1 (a), NQC2 (b), N79 (c), N44C (d), N11B (e), N113 (f), N159W (g). The spectrum of the spiral arm of M51 is taken from Watanabe et al. ( 2014 ) (h). The composite spectrum of a translucent cloud is prepared by averaging the intensities of HCN, HCO + , HNC, CS, and SO observed toward 38 translucent clouds by Turner ( 1995a , 1995b , 1996 ), and Turner et al. ( 1997 ) (i). The spectrum of Orion KL (j) and NGC 2264 CMM3 (k) are taken from Watanabe et al. ( 2015 ). Note that the vertical scale is different from source to source. Table 4 Observed Line Parameters Notes. The errors are 1 σ . The upper limits are 3 σ . a Assumed. The spectral profile of each molecular line is shown in Figures 3 and 4 . For Figures 3 and 4 and Table 4 , the baselines are subtracted in a narrow range (typically 100 MHz) by using the fifth-order polynomials to remove the base line ripples. We conducted Gaussian fitting to each base-line-subtracted spectral line to obtain the V LSR , Δ v , and the peak T MB , where the observed frequencies are converted to the LSR velocities based on the rest frequency of each transition given in CDMS.


O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O B-Citation I-Citation I-Citation O O O B-Telescope O O O O O O O O O O O O O B-Wavelength O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength O O O O O B-Telescope O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

confidently identify these periodic variations. Price-Whelan et al. ( 2020b ) identified 19 635 candidate binaries in the APOGEE survey based on radial velocity variations between multiple observations. Of these, 53 are in our giant star data set, including 15 of our RC stars – one of which is Li-rich. It has only three observations with APOGEE, indicating an RV range of . In terms of photometric signatures of binarity in the form of transits, assuming random orbital inclinations and observed orbital period distributions (e.g. Raghavan et al. 2010 ), 2.5 ± 0.5 per cent of our Li-rich RC stars should be in eclipsing binary systems. The secondary star will block about 1 per cent of the disc of the primary with an eclipse period of ∼3 d. This does not require a very high cadence in photometric monitoring, but none of our Li-rich RC stars have so far had light curves in ASAS-SN (Kochanek et al. 2017 ) or TESS (Ricker et al. 2014 ) that show evidence for eclipses. The astrometry from Gaia is precise enough to measure the motion of the photocentre of some binary systems (depending on heliocentric distance and the binary properties). The model assumption underlying the data processing for Gaia DR2 is that sources are single objects, and if there are photocentre shifts in binary systems these are interpreted as larger than expected astrometric errors. Work by Penoyre et al. ( 2020 ) and Belokurov et al. ( 2020 ) have used large values of the Renormalized Unit Weight Error ( RUWE ), an astrometric error metric reported by Gaia , to identify possible binaries. Our data set excludes stars with large RUWE by construction (it is part of flag_sp ), because parallax is an important prior in our stellar parameter determination. 3.5 Infrared excess A fraction of Li-rich RGB stars have been reported to have excess flux in their spectral energy distribution in the IR, which has been postulated as a sign of a physical connection between lithium production and mass-loss. This can be seen in photometry from the IRAS satellite (e.g. Fekel Watson 1998 ) and from WISE , although the latter’s wavelength coverage does not reach as far into the IR. A close investigation by Rebull et al. ( 2015 ) found that the majority of lithium-rich giants in the literature with reported IR excesses were artefacts in the WISE catalogue or cases of source confusion. However, they do confirm some as real cases of IR excess, and they do find that the stars with the largest IR excess are lithium-rich K giants. Within our data set, there are only 1862 giants with clean WISE detections; that is, they have the cc_flags confusion flag set to 0000 and the ph_qual photometric quality flag set to A for W 1 and W 4 . Fig. 9 shows an IR colour–magnitude diagram for these stars, divided in the same way as Fig. 7 with RC stars in the upper panels, RGB stars in the lower panels, all stars in the left-hand panels, and the lithium-rich stars highlighted in the right-hand panels. There are 549 RC stars


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a very different architecture, PCA-Davies-nominal performs very similarly with scatter just below : . The increased sample size of the training sample, better purity, and improved intrinsic continuum recovery compared to PCA-Davies-smaller make a clear difference, as the latter has . Finally, using only wavelengths that would be observed in the optical at 5.5 z 6.2, PCA-optical only predictably performs worse than new PCAs and stacks of neighbours with access to longer wavelengths, but still better than both older PCAs and power-law reconstructions, with . Over the Ly β forest [972 λ(Å) 1000], the distinction in performance between methods is similar, with the Power-Law method doing the worst with at 1σ (2σ). Again, both larger-sample PCAs are more accurate with for PCA-Davies-smaller . The improved training sample improved the bias and reduced scatter below to for PCA-Davies-nominal , overtaking Neighbours stacking that has an accuracy of . PCANN-QSANNdRA performs very similarly to PCA-Davies-nominal , with an accuracy of . Finally, the optical wavelengths-only PCA performs significantly worse than IR PCAs but still better than power-law extrapolation, with . Beyond mean biases, the residuals from the different methods show very different wavelength dependences (Fig. 4 ). Residuals at the location of broad emission lines can be seen in the Power-Law, PCA-Pâris-10 , and PCA-Pâris-5 methods, while the Neighbours technique and PCA methods trained on larger samples ( PCA-Davies-smaller, PCA-Davies-nominal ) do not show residuals at the locations of the N ii 1085 Å, Fe iii 1125 Å, and C iii 1175 Å broad emission lines. This indicates that correlations between blue-side emission lines and red-side properties are, unsurprisingly, adequately captured by stacks of quasars with similar red-side properties. The more recent PCA decompositions also capture broad-line correlations. An important addition in the PCA-Davies-smaller and PCA-Davies-nominal was an independent fitting parameter |δ z | 0.05 to account for redshift uncertainties in the testing sample. Indeed, small residuals visible around the O vi line in PCANN-QSANNdRA are likely due to the lack of redshift correction as a fitting parameter, which is mitigated by the larger number of components (53/42 for the red/blue sides compared to 10/6). The absence of a redshift shift parameter in the other models might disadvantage them if the quasar redshifts in eBOSS are more inaccurate than in z > 5.5 quasars. Indeed, the systemic redshifts of high- z quasars are often known to be within |δ z | 0.0005 from detections of sub-millimetre emission lines in quasar hosts (Willott, Bergeron Omont 2015 ; Decarli et al. 2017 ; Eilers et al. 2020 ). The n > 5 components of the Pâris-10 PCA introduce shape perturbations at the edges of broad emission lines that account for some of these redshift uncertainties. We find that these high-order components give continua unphysical shapes (see e.g. Kakiichi et al. 2018


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points also remain almost unchanged. Further investigation of stabilizing effects due to increasing magnetic field strength will be discussed in Section 6. Let us compare the stability of relativistic magnetized jets with their non-relativistic counterparts. Fig. 8 shows the non-relativistic stability analysis of the strongly magnetized jet. Fig. 8 of this paper is borrowed from Kim etal. (2015) , where it was labelled Fig. 5 . We can directly compare Fig. 6 with Fig. 8 (a). We see that the fundamental pinch mode in Fig. 6 (a) for the mildly relativistic ( 0 2) case is slightly more stable than the fundamental pinch mode in Fig. 8 (a). The growth rate of the fundamental pinch mode even for the mildly relativistic jet is now below the stability criterion. For the first reflection pinch instability mode, the growth rate at resonance (the wavenumber where its growth rate is a maximum) has a slightly lower value. However, the difference is not significant. Figure 8. The dispersion relation of the non-relativistic magnetized jets with 0.1 and M 4. The velocity profile in the jet is top-hat. The plasma of the jet is 1/2. This is obtained in the non-relativistic linear stability analysis that appears in Kim etal. (2015) . Panel (a) shows the pinch mode ( m 0) instabilities, while panel (b) shows the kink mode ( m 1) instabilities. The red and blue lines represent the fundamental and the first reflection mode. The real and imaginary part of are shown as the solid and dashed lines. The dotted curves refer to the stability criterion for each of the unstable modes. Similarly, let us also compare our relativistic results with non-relativistic results for the kink ( m 1) modes. Please compare Fig. 7 with Fig. 8 (b). Actually there are only minor improvements in the stability for the fundamental kink mode of the mildly relativistic jet. For the first reflection mode, there is only a very tiny range of unstable wavelengths in the non-relativistic jet. However, the range is relatively wider in the relativistic jet. 5.2 Scaling property of the strongly magnetized jets Analogously to Section 4.3 , we study the stability of magnetized jets with increasing Lorentz factors. In this section, we use the strongly magnetized jets ( 1/2) to verify that there still exists a scaling law even in the magnetized case. Fig. 9 is analogous to Fig. 5 but for the strongly magnetized jet case. Fig. 9 (a) shows the pinch mode ( m 0) instabilities. In Fig. 9 (a), we can see the same trend that is shown in Fig. 5 (a). The temporal growth rate of the fundamental pinch instability mode is inversely proportional to the square of the Lorentz factor ( I 1/ 0 2 ). The growth rate of the first reflection pinch instability mode, however, is just proportional to 1/ 0 . Figure 9. The scaling property of the strongly magnetized jets ( 1/2) with increasing Lorentz factor. Panel (a) shows the pinch mode ( m 0) instabilities, while panel (b) shows the kink mode ( m 1) instabilities. The red


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The authors are grateful to ISRO-RESPOND Programme for providing the financial assistance under grant no. ISRO/RES/2/370 for carrying out this work. Three of us (BM, NI and NA) are also highly thankful to IUCAA, Pune for providing the necessary facilities in completing this work.


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We thank Paul Duffell, Chris Matzner, and Frank Timmes for useful discussions. This research was funded by the Gordon and Betty Moore Foundation through grant GBMF5076. E.R.C. acknowledges support from NASA through the Einstein Fellowship Program, grant PF6-170170. E.Q. thanks the theoretical astrophysics group and the Moore Distinguished Scholar program at Caltech for their hospitality and support. This work was supported in part by a Simons Investigator Award from the Simons Foundation. The software used in this work was developed in part by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. Software: FLASH (Fryxell et al. 2000 ).


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We thank our referee for valuable comments. JL is supported by NSFC grant 11203032, and LG is supported by the Strategic Priority Research Program ‘The Emergence of Cosmological Structures’ of CAS grant XDB09000000, NSFC grant 11333005, and NAOC grant Y234031001. This research is based on data obtained from the Chandra Data Archive and uses data from NuSTAR mission.


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G.D. would like to warmly thank Alessandro Romeo, Kirsten Knudsen, and Clive Tadhunter for the useful discussions that contributed to improve this paper. The authors also thank the referee for detailed suggestions and a thorough report that helped to clarify this paper. G.D. also thanks Nina Hatch for providing HST fluxes for the Spiderweb galaxy and A. Galametz for providing images for part of the sample. G.D. thanks Philip Best for providing the 3C 368 and 3C 470 data. N.S. is the recipient of an ARC Future Fellowship. The work of DS was carried out at Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). GD acknowledges the support from the ESO scientific visitor programme.


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Acknowledgments I thank the anonymous referee for useful comments and guides on how to improve this work. This work was supported by Sharif University of Technology's Office of Vice President for Research under Grant No. G950214.


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The authors would like to thank Sonny Harman and Yuka Fujii for useful discussions regarding this work. E.V.Q. and M.J.W. are grateful for support from GSFC Sellers Exoplanet Environments Collaboration (SEEC). This research has made use of the Habitable Zone Gallery at hzgallery.org . The results reported herein benefited from collaborations and/or information exchange within NASA’s Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA’s Science Mission Directorate.


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Acknowledgements MB, GPS and SLM acknowledge support from the Science and Technology Facilities Council through grant number ST/N000633/1. CPH acknowledges financial support from PRIN INAF 2014.


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ACKNOWLEDGEMENTS I acknowledge funding from the Swiss National Science Foundation. I am very grateful to Dan Fabrycky for thoughtful comments on drafts of this manuscript, and to Moe Maxwell for insight regarding the surveys of binary mass ratios. I also appreciate discussions with Anastasios Fragkos, Georges Meynets, Diego Muñoz, Marc Pinsonneault, Lisa Prato, Mads Sørensen, and Amaury Triaud which helped motivate some ideas. Finally, I acknowledge the referee, Hagai Perets, who provided a thorough review, which undoubtedly significantly improved the quality of the paper.


O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Instrument B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

their rotation profiles did not commence until later. A sample of ETGs were observed to be elongated (Sandage, Freeman Stokes 1970 ), which was expected to be due to rotation (Larson 1975 ). Early measurements of rotation profiles in lenticular (S0) galaxies confirmed the expectation of strong rotation (Williams 1975 ). Astronomers were then surprised by data suggesting that there was little rotation in some elliptical (E) galaxies (e.g. Bertola Capaccioli 1975 , who measured significantly less rotation in the flattened elliptical NGC 4697 than present in spiral galaxies). This unexpected finding led to much research regarding the nature of rotation versus anisotropic velocity dispersion (e.g. Illingworth 1977 ; Binney 1978 ; Schechter Gunn 1979 ; Davies 1981 ; Kormendy Illingworth 1982 ; Davies et al. 1983 ). One of the early manners in which information about rotational support was condensed was the so-called Binney ( 1978 ) diagram. This diagram presented the ratio of the maximum rotational velocity to the central velocity dispersion v /σ against the ellipticity ε for individual galaxies. In particular, this diagram was used by Binney ( 1978 ) to address the question of how galaxies that are not rotationally supported can be elongated by anisotropy. Davies et al. ( 1983 ) later used this diagram and noted that fainter ellipticals ( M B > −20.5 mag) tended to be rotationally supported, whereas brighter ellipticals ( M B −20.5 mag) were pressure supported by near-isotropic velocity dispersion. The use of this diagram was ideal for longslit data, in which a maximum rotation value along the major axis and a central velocity dispersion could be measured. With the increasing use of two-dimensional spectroscopy, in particular via integral field units (IFUs), much more information was available with which to characterize the kinematics of galaxies. In order to utilize 2D measurements of both velocity and velocity dispersion within a specified aperture, an observationally measureable, luminosity-weighted spin parameter, denoted by λ R , was developed by the SAURON team (Emsellem et al. 2007 ). The use of spatial weighting allowed this parameter to better indicate the rotation of galaxies with non-conventional kinematics (whose properties could not simply be summarized by major-axis measurements, such as galaxies with kinematic twists and misalignments as was later discussed by Krajnović et al. 2011 ). The main outcome of the use of the λ R parameter by the SAURON (de Zeeuw et al. 2002 ) and ATLAS 3D (Cappellari et al. 2011a ) teams was to plot this parameter in conjunction with the ellipticity ε in a spin-ellipticity diagram to identify two classes of early-type galaxies according to their kinematics: fast and slow central rotators. Despite the use of high-quality 2D kinematic data, the final results are still typically reduced to a single measurement for each galaxy. The breadth of information which can be gained from this diagram is further


O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O B-Citation O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O B-Survey O O O O O B-Citation O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O B-Model O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O B-Software O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O B-Software B-Identifier I-Identifier B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Software I-Software O O O B-Software I-Software I-Software I-Software I-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O

observations presented in Prochaska et al. ( 2017 ; hereafter P17 ). These data were previously analyzed using PIE models, which, as stated, are usually able to reproduce the low and intermediate ions but have trouble matching O vi (Lehner et al. 2013 ) without invoking very-low densities (Stern et al. 2016 ). The structure of this work is as follows. In Section 2 we discuss the observational data, and in Section 3 we give a brief description of MAIHEM as well as the MCMC code used to conduct our analysis. In Section 4 we show the main results of our analysis, followed by a discussion in Section 5 . 2. Data The data used for this analysis are a compilation of absorption-line systems probing the CGM of low-redshift galaxies from the COS–Halos survey. Specifically, we model the observations presented in P17 , which were previously analyzed using PIE models. These data consist of several ions for multiple absorbers along quasar sightlines that probe M ⊙ galaxies out to an impact parameter b ≈ 150 kpc (Tumlinson et al. 2013 ). The reader is encouraged to refer to previous work by the COS–Halos survey for additional details on the data collection and processing. Here, we study the same COS–Halos sightlines that were analyzed in P17 , for a total of 44 low-redshift ( z ≲ 0.5) systems. These sightlines exhibit absorption from a mixture of ionization states that include C ii , C iii , Fe ii , Fe iii , Mg ii , N ii , O i , O vi , Si ii , Si iii , Si iv , and S iii . As we now have the ability to model a multiphase medium, we also include Si iv and O vi , the column density for which were not incorporated into the analysis of P17 . We apply the MCMC analysis to the entire sample, finding, however, that only 32/44 systems converge on solutions with the MAIHEM model. Systems that are unable to find solutions have either all upper or lower limits, or only have accurate column density measurements for a single ion. When drawing comparisons with P17 , we thus limit our sample to only include the 32 systems with a converged solution. 3. Methods 3.1. MAIHEM Models We use the MAIHEM code to model ionic fractions in an isotropic turbulent medium. This cooling and chemistry package is a modified version of the open-source hydrodynamics code FLASH (Version 4.4) (Fryxell et al. 2000 ), which explicitly tracks the reaction network of 65 ions, including: hydrogen (H i and H ii ), helium (He i –He iii ), carbon (C i –C vi ), nitrogen (N i –N vii ), oxygen (O i –O viii ), neon (Ne i –Ne x ), sodium (Na i –Na iii ), magnesium (Mg i –Mg iv ), silicon (Si i –Si vi ), sulfur (S i –S v ), calcium (Ca i –Ca v ), iron (Fe i –Fe v ), and electrons from an initial non-equilibrium state to a steady state. Modifications for solving the hydrodynamic equations include using an unsplit solver based on Lee ( 2013 ), as well as a hybrid Riemann solver that utilizes the Harten Lax and van Leer solver (Einfeldt et al. 1991 ) to ensure stability in regions of strong shocks, and


O O O B-CelestialObject O O O O O B-Wavelength O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O B-CelestialObject O O O O O B-Survey O O O O O O O O B-Telescope O O O O O O O B-Wavelength O O B-CelestialObject O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O B-CelestialObject O O O O O O O O B-CelestialObject O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O B-CelestialObject O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O

currently say whether IC10 is an example of the radioFIR conspiracy as the sample size used to determine the radioSFR relation is small with a large scatter. Future studies with a larger sample would reveal the true significance of the deviation. 5 CONCLUSIONS We present high-resolution e-MERLIN observations of the nearby dwarf irregular galaxy IC10 as a part of the LeMMINGs project. Our main conclusions are as follows. Our e-MERLIN observations reveal 11 compact radio sources at 1.5GHz coincident with IC10s star-forming disc, five of which also have detections at 5GHz. Although we cannot conclusively classify all sources on the basis of their spectral index due to differences in sampling the uv plane, we gain insight into the nature of each source through the use of low-resolution multiwavelength data, the positional coincidence with features at other wavelengths such as H and 70m, and an estimate of their brightness temperature. Based on our analysis of the expected background source counts, the number of detected sources is consistent with them all being background sources. However, as some sources closely trace compact emission in maps at other wavelengths, giving us confidence that some of these sources do in fact belong to IC10. We find that of the 11 sources, three likely reside in IC10 (sources 1, 2 and 4), all of which are H ii regions; five are background sources (sources 3, 5, 6, 9, 10) and three are yet to be conclusively classified (sources 7, 8, 11). Based on the time-scale over which SNR are typically observable and the resolution limitations of these high-resolution interferometry observations, we expect that we will not be able to detect any SNR with the present e-MERLIN observations. The only SNe we would expect to be able to detect are very young RSNe, but it is unlikely that we would observe any due to a combination of their short observable time-scales and low SFR observed in IC10. We explore other possible factors that could affect SNR detectability in dwarf irregular galaxies and conclude that e-MERLIN alone is well suited to study SNR in galaxies located at distances greater than 4Mpc due to the spatial frequencies covered by the array. For galaxies closer than 4Mpc, additional VLA observations are required to fully cover the spatial scales that SNR candidates occupy. The same reasons as mentioned above explain why we see no compact sources within the NTSB in IC10 and that the detected sources that belong to IC10 are likely to be compact H ii regions. Based on starburst99 models, we determine lower limits for the stellar cluster masses required to produce these observed compact H ii regions; the largest one is about half the size of 30Doradus in the LMC. We present updated integrated flux densities for IC10, where we subtract the contribution from background sources from literature data. We find a 4percent reduction in the measured flux at 1.5GHz and a 2percent reduction at 4.85GHz. With this updated measurement, we


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ACKNOWLEDGEMENTS SB thanks Martin Millon and Aymeric Galan to help identifying the issue with astrometry while working on the Time-delay Lens Modelling Challenge (Ding etal. 2018 ). We thank Adriano Agnello, Anowar Shajib, Chih-Fan Chen, Dominique Sluse, Patrick Kelly, Xuheng Ding, and Jenny Wagner for useful feedback on the manuscript. We thank the anonymous referee for useful suggestions and comments that improved the presentation of this work. Support for this work was provided by NASA through grant numbers HST -G0-14254 and HST -G0-15320 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. TT acknowledges support by the NSF through grant AST-1714953 and by the Packard Foundation through a Packard Research Fellowship.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O B-CelestialObject I-CelestialObject O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Observatory O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O

a spherical explosion triggered inside a rotationally supported torus (presumed to be formed by preceding binary interaction), which results in a collimation of ejecta toward the system’s poles. Frank et al. ( 2018 ), García-Segura et al. ( 2018 ), and Reichardt et al. ( 2018 ) recently discussed the interaction of stellar winds with the debris of a common-envelope episode and how this process might contribute to observed bipolar planetary nebulae. Here we expand on this line of work to show that bipolar morphologies can, instead, arise from the interaction of successive components of equatorial mass loss from the coalescing binary. We analyze numerical simulations of coalescing binaries transitioning from Roche lobe overflow toward the onset of the common-envelope phase. We show that early outflows, contrary to previous theoretical predictions, are bound to the binary system and form a circumbinary torus. Later ejecta, generated just as the secondary object plunges within the envelope of the donor, have larger radial velocities and are unbound. The interaction of unbound ejecta with the bound torus redirects ejecta toward the poles, laying the foundation for the generation of bipolar remnants of stellar coalescence recently reported by Kaminski et al. ( 2018 ). 2. Bipolar Remnants of Stellar Coalescence and Binary Interaction 2.1. Remnants of Galactic Red Novae There is growing evidence that the remnants of galactic luminous red nova outbursts, believed to originate from stellar coalescence, can exhibit bipolar structures. There is strong evidence for a bipolar morphology of V4332 Sgr. We also review the less extensive evidence related to the two other galactic transients that have been studied, V1309 Sco and V838 Mon. Some of the first evidence for bipolar morphologies came from V - and R -band linear polarization measurements of the remnant of V4332 Sgr, which flared in 1994 (Kamiński Tylenda 2011 ). Correcting for the effect of significant unpolarized line emission, Kamiński Tylenda ( 2011 ) estimated continuum polarizations of approximately 40% and 20% for the V and R bands, respectively, and suggested that dust scattering in a bipolar outflow is one of the only morphologies that can produce such high linear polarization in an unresolved source. Spectropolarimetric observations by Kamiński Tylenda ( 2013 ) confirmed Kamiński Tylenda’s ( 2011 ) suggested continuum polarization. Earlier conclusions regarding morphology have recently been strengthened by submillimeter observations, which have offered an opportunity to spatially resolve galactic remnants of stellar-coalescence transients (Kaminski et al. 2018 ). Spatially resolved observations using the ALMA of V4332 Sgr produce a position–velocity diagram that is best modeled with a bipolar molecular outflow with a 60° opening angle (see Figures 5 and 6 of Kaminski et al. 2018 ). The merger of V1309 Sco has been extremely useful in decoding observations of luminous red novae in general.