by stochastic kicks as seen by the torque fluctuating about zero, resulting in small inward and outward migration. The bottom panel is in a constant β disc, where it is clear that despite stochastic kicks being present, the torque, on average, is slightly negative, resulting in inward migration. Figure 14. Total z -component of the torque exerted by the disc material on a 1 M ⊕ planet is shown on the left-hand panels. The migration tracks are shown on the right-hand panels. The top five panels are simulations modelled with a variable β , whilst the bottom panel is one of the simulations modelled with a constant β . The migration is dominated by stochastic kicks, which results in random outward or inward motion, as seen in the torques oscillating about zero. 5.2 Comparison with previous work We compare our results to those of Baruteau et al. ( 2011 ) and Malik et al. ( 2015 ), who considered giant planet migration in self-gravitating discs. There are a couple of differences in this work. They perform their simulations using a 2D grid-based code, whereas the simulations in this work are performed using a 3D SPH code. The initial conditions of the disc are also slightly different. Their disc surface density and temperature decreased as R −2 and R −1 , respectively, whereas in this work, the disc surface density and temperature decreases as R −1 and R −0.5 , respectively. To ensure that the different initial conditions and codes used do not influence the results, we initially performed a set of simulations with a constant value of β = 15 to compare with Baruteau et al. ( 2011 ) and Malik et al. ( 2015 ). Despite the differences, we agree with their findings that using a constant β results in the giant planets rapidly migrating towards the inner edge of the disc. However, the crucial development in our work is how the disc is cooled: Whilst we also utilize the β -cooling approach, we allow β to vary with radius to mimic a more realistic disc such that our discs remain gravitationally stable in the inner regions, and the spiral structure only forms in the outer regions. The planets are able to slow down their rapid inward migration before reaching the inner disc edge. Using radiative transfer, Stamatellos Inutsuka ( 2018 ) migrate 1 M Jup planets in self-gravitating discs using a 3D SPH code. The initial conditions in their discs are more similar to ours: the same initial disc mass and surface density profile. Their usage of a realistic treatment of the disc thermodynamics meant that like in the simulations presented here, the planets are evolved in discs that are only gravitationally unstable in the outer regions. Using realistic thermodynamics to allow the gas to control its cooling/heating based on its properties, the thermodynamics of the circumstellar and circumplanetary disc is better captured. This enhances the mass growth of the planet causing the planets to grow to beyond the brown dwarf limit. This resulted in their planets opening up


feature tracking. 3. Results The polar crown prominence in the northwest limb (N63W72) had been stable for over two weeks before our observation began on 2016 June 4. Figure 1 shows the prominence of interest in the H α , AIA 131, 171, and 304 Å images. The prominence is bright in H α , but dark in the AIA images. Note that the intensity of the H α image is reversed, and that darker features in the image are actually brighter. The dark structure in the AIA images is wrapped in the bright emissive gas, indicating that the cool material is wrapped inside the hot coronal gas. The main body of the polar crown prominence lies vertical to the plane of the sky, and an arch-shape prominence newly emerged in the northern region of the polar crown prominence after 04:00 UT. The arch-shape prominence was brighter than the main prominence in the AIA images, but it was fainter in the H α images. The observed arch-shape prominence looks similar to the hedgerow prominence overlying a cavity observed by Ryutova et al. ( 2010 ) except for the horizontal flow within it. We detected a horizontal flow, which is highlighted in the next paragraph. Figure 1. Polar crown prominence observed on 2016 June 4, with the newly emerged arch-shaped prominence in the region north of it. The SDO/ AIA 131, 171, 304 Å data, and H α images (upper-left, upper-right, lower-left, and lower-right panels, respectively) show the formation of a vortex on the arch-shaped prominence. Note that the intensity of the H α image is reversed. The dashed boxes in the H α image represent the FOV of the Figure 3 (small red), Figure 4 (big red), and Figure 8 (blue). A full sequence of the images, covering from 08:09:43 to 09:31:46 UT, is provided in the animation. In the animation, 08:09:43 UT is taken to be the epoch of time t . (An animation of this figure is available.) Figure 2 shows H α images of the observed region at the moment of the rising of the arch-shape prominence and the formation of a 5′′-size vortex. The arrows plotted on the H α images represent the velocity vectors of the stream on the plane of the sky. Near the left-hand side leg of the arch-shape prominence (690′′, 680′′), the dominant direction of the plasma flow is upward along the arch. It rose up slowly (20 km s −1 ) and reached about a height of 20′′. Then it streamed to the right along the arch toward the polar crown prominence with a speed of 20–60 km s −1 . The stream can be clearly identified in both panels of Figure 2 . The measured collimated flow speed of about 20–60 km s −1 is higher than the typical speed of the prominence plasma (10–20 km s −1 ; Zirker et al. 1998 ; Ahn et al. 2010 ; Vial Engvold 2015 ). The full dynamics of the evolution can be seen better in the animation of Figure 1 . Very luckily, the flow lies parallel to the plane of the sky considering the narrow bandpass width of the filter. Figure 2. Velocity vectors superposed on H α images at the moment of the rising of the arch-shape prominence (left)


Acknowledgements Daniel Thun was funded by grant KL 650/26 of the German Research Foundation (DFG). Most of the numerical simulations were performed on the bwForCluster BinAC. The authors acknowledge support by the High Performance and Cloud Computing Group at the Zentrum für Datenverarbeitung of the University of Tübingen, the state of Baden–Württemberg through bwHPC and the German Research Foundation (DFG) through grant no INST 37/935-1 FUGG. All plots in this paper were made with the Python library matplotlib ( Hunter 2007 ).


M. Vitale is supported by the International Max-Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. This work is partly based on observations with the 100-m telescope of the MPIfR (Max-Planck-Institut für Radioastronomie) at Effelsberg. The authors would like to thank Alex Kraus for support and help during observations and data reduction. The FIRST Survey is supported in part under the auspices of the Department of Energy by Lawrence Livermore National Laboratory under contract W-7405-ENG-48 and the Institute for Geophysics and Planetary Physics. The Sloan Digital Sky Survey is a joint project of the University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Max Planck Institute for Astronomy, the Max Planck Institute for Astrophysics, New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Apache Point Observatory, site of the SDSS, is operated by the Astrophysical Research Consortium. Funding for the project has been provided by the Alfred P. Sloan Foundation, the SDSS member institutions, NASA, the NSF, the Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org . This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) via the Cologne Bonn Graduate School (BCGS), and via grant SFB 956. We had fruitful discussions with members of the European Union funded COST Action MP0905: Black Holes in a violent Universe and the COST Action MP1104: Polarization as a tool to study the Solar System and beyond. We received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement No. 312789.


) and the 321 GHz H 2 O maser line (Hirota et al. 2014a ). The brightness temperature of the 658 GHz H 2 O line, >2 × 10 4 K, would indicate that the line is emitted via maser action. In contrast, the 336 GHz H 2 O line shows a different distribution (Figure 5 (c)) and a spectral profile with symmetric double-peaks (Figure 6 ). As discussed in Alcolea Menten ( 1993 ) and Hirota et al. ( 2014a ), the 336 GHz H 2 O line could be a thermal line and trace the edge-on disk, unlike emission from the other transitions at 232, 321, and 658 GHz. We note that via Menten et al. ( 2006 ) the 336 GHz H 2 O line toward the red supergiant VY CMa also favors a thermal nature for this line’s excitation. Recently, theoretical model calculations for the excitation of the 658 GHz H 2 O line have been presented (Richards et al. 2014 ; Nesterenok 2015 ) for the red supergiant VY CMa and for asymptotic giant branch (AGB) stars. The 658 GHz H 2 O maser is predicted to be pumped efficiently for H 2 densities of 10 9 –10 10 cm −3 , a fractional H 2 O abundance of 10 −4 –10 −5 , and gas temperatures of 1000–1500 K (Nesterenok 2015 ). Although the physical and chemical properties of the 658 GHz H 2 O maser emitting region associated with Source I would be expected to be different from that of a late-type star, these parameters are roughly consistent with those for the disk-outflow system of Source I associated with SiO masers and other submillimeter H 2 O lines (Reid et al. 2007 ; Goddi et al. 2009 , 2011 ; Hirota et al. 2014a , 2015 ). 4.4. Relationship between the 22 GHz H2O Supermaser We note that our ALMA observation was done during an active phase of the 22 GHz H 2 O maser burst in Orion KL, called a “supermaser” (Hirota et al. 2011 , 2014b ). The 22 GHz supermaser is located at the phase tracking center of the ALMA observation, corresponding to the Compact Ridge region (Hirota et al. 2011 , 2014b ). While the total flux density of the 22 GHz H 2 O supermaser was decreasing on 2012 August 25, it was still Jy (Hirota et al. 2014b ). In spite of the extremely high flux density of this maser, there was no significant emission of the 658 GHz H 2 O line in the Compact Ridge region in our ALMA data with the 1 σ noise level of 2 Jy beam −1 in the relevant region. Thus, the 658 GHz H 2 O line is not related to the 22 GHz supermaser phenomenon, as has also been reported for other transitions at 321 and 336 GHz (Hirota et al. 2014b ). 4.5. Continuum Emission at ALMA Band 9 To measure the position of the 658 GHz H 2 O emission, we also made a map of the ALMA band 9 continuum by applying the self-calibration solutions. Continuum emission is detected at the position of Source I, although it is outside the primary beam of the 12 m antenna. The flux density and the peak intensity are derived from Gaussian fitting, respectively 1.04 ± 0.04 Jy and 0.77 ± 0.03 Jy beam −1 (Figure 2 (b)). If we correct the primary beam attenuation by a factor of 8.6, the absolute flux


complex structure within the overall galaxy mass functions. For instance, in increasingly higher halo mass regimes, we observe high-mass drop-offs that occur at higher galaxy mass. These drop-offs mark the natural boundary in the largest central galaxy mass for a given halo mass, as seen in Figure 5 (b). Figure 13. Breakdown of RESOLVE-B (top row), L r ,tot -limited RESOLVE-B (middle row), and ECO (bottom row) SMF and BMF into different group halo mass regimes. The four group halo mass regimes are M halo 10 11.4 M ⊙ (low-mass groups, often solo centrals, blue), M halo between 10 11.4 and 10 12 M ⊙ (intermediate-mass groups, green), M halo between 10 12 and 10 13.5 M ⊙ (large group, orange), and M halo > 10 13.5 M ⊙ (cluster, red, ECO only). The dark gray marks the overall SMF or BMF for each data set, and the gray hash-marked region denotes the incomplete regions for each mass function. The conditional mass functions are much more complex than the overall mass function, with pronounced bumps and dips. In both the RESOLVE-B and ECO intermediate (green) and large (orange) group halo mass regimes, we observe a peak in the SMF and BMF. For intermediate group halos, this peak occurs at ∼10 10.2 M ⊙ , right between the gas-richness threshold and bimodality mass scales. For large group halos, the peak occurs at ∼10 10.8 M ⊙ , above the bimodality mass scale and also near the knee of the overall mass functions. The peak in the large group halo regime appears to be causing the pronounced “bump” seen in the overall RESOLVE-B SMF and BMF. While the ECO data set also has this characteristic peak in its large group halo regime mass functions, the more gradual decline in the overall SMF and BMF for large galaxy masses seems to be due to the cluster galaxy population in ECO. The cluster population makes up 17% of galaxies with M star > 10 10.5 M ⊙ and 31% of galaxies with M star > 10 11 M ⊙ for ECO. The RESOLVE-B “bump,” meanwhile, may be emphasized by the lack of a cluster galaxy population and the overabundance of halos in this large group halo regime, as shown in Figure 5 (a). It is clear that the low-mass slopes of the SMF and BMF in these different halo mass regimes are very different. In the cluster halo mass regime, the rise is quite smooth, although the slope appears to flatten out at lower masses, at least in part due to incompleteness in galaxy counts around the clusters caused by high fiber collision rates and by missing ultradiffuse galaxies like those recently found in the Coma and Virgo clusters (Mihos et al. 2015 ; van Dokkum et al. 2015 ). We note that Yamanoi et al. ( 2012 ) found a fairly flat slope for the Coma cluster LF down to galaxy magnitudes of M R = −14.0, with a steep upturn for galaxies below our luminosity limit. Also, not all previous studies of cluster LFs have found steep slopes, and many cluster LF studies have relied on using statistical counts to remove background galaxies (e.g., Dressler 1978 and Goto et al. 2002 ).


effects of binary disruption and binary segregation resulting in a significant delay of complete mixing compared to the inert binary case. In order to further describe the overall effect of the different dynamical processes affecting the survival and evolution of binaries on the FG and SG binary mixing, we present in Fig. 3 the time evolution of the cumulative radial distribution of FG and SG binaries for four different models with different values of the initial hardness parameter of the binary population. Figure 3. Cumulative radial distribution of FG (red lines) and SG (blue lines) binaries. From left to right, each panel shows the evolution of radial distribution. Three different models with x g,0 = 3, 3-20, 50, and 800 are presented (top to bottom). The cumulative radial distribution of inert binaries are shown as dashed lines for comparison. The last panel for the model with x g,0 = 800, the distribution at t ∼ 40τ rh, 0 is shown to illustrate a complete spatial mixing of very compact binaries. The cumulative radial distribution of FG and SG inert binaries in the MPr5f1m2 are also shown in order to illustrate the spatial mixing of stars with the same mass of binaries but not affected by other processes such as ionization and ejection due to the recoil velocity acquired during interactions with other stars. At t = 0, FG and SG binaries in all models have the same cumulative distribution. For the MPr5f1x3 model, the rapid disruption of SG binaries significantly depletes the inner binary population as illustrated by the shift of the SG binary cumulative radial distribution towards the outer regions. For the MPr5f1x3-20 model, the evolution of the distribution of FG binaries is similar to that for the MPr5f1x3 model. However, the presence of harder binaries implies that the effects of ionization are not as strong as in the previous case and the evolution of the SG cumulative radial distribution is more similar to that of inert binaries. It is interesting to note the development of an approximately flat portion in the cumulative radial distribution of SG binaries in the MPr5f1x3 and x3-20 simulations. The formation of this shell depleted in SG binaries is due to the combined effect of binary segregation and disruption; binaries are rapidly disrupted in the inner regions but as the segregation time-scale increases with the distance from the cluster’s centre. Therefore, there is no replenishment of binaries beyond the gap because the segregation time-scale is longer than the cluster’s age (see also the fig. 7 in Paper I ). The development of this gap is also responsible for the rapid variation in R h,SG and R h,FG / R h,SG around t ∼ 23τ rh, 0 in Figs 1 and 2 for the MPr5f1x3-20. For the MPr5f1x800 model, the cumulative distributions for FG and SG binaries are, in general, very similar to those in the inert binary model. Eventually, the spatial mixing of FG and SG binaries is achieved at t ∼ 40τ rh, 0 . Fig. 4 shows the time evolution of the


we sample 10,000 parameter combinations and generate one random light curve with the time sampling of the observed Keck data (∼30 nights of historical data and four nights of 2019 data) for each parameter set. We present the complementary cumulative distribution function (CCDF, or 1—CDF) of these 10,000 light curves in Figure 5 in the form of the median CDF and 1, 2, and 3 σ credible intervals. Figure 5. Top panel: comparison of the complementary cumulative distribution function (CCDF) of the observed data (historical data and 2019 data; black) and the median CCDF (dashed blue line) and the 1, 2, and 3 σ contours calculated from 10,000 simulations. The simulations were drawn from the posterior in Witzel et al. ( 2018 ). The dashed section of the observed CCDF represents flux densities that occurred only during the brightest flux excursion on 2019 May 13. These simulations show that if we repeated the entire experiment with the time sampling of 30 historical nights of Keck observations 10,000 times, then the probability of observing a single night with flux levels as high as 6 mJy is less than 0.3%. Bottom panel: the same as for the top panel but contours determined from simulations based only on the time sampling of the four nights in 2019. Because three of the four nights have elevated Sgr A* flux levels, if an experiment with four nights of observations were repeated 10,000 times, the probability of observing Sgr A* flux levels similar to the nights in 2019 would be less than 0.05%. Based on simulations drawn from the Sgr A* flux model, we can compute the probability of observing the light curves presented here. The simulations show that if we repeated our experiment 10,000 times with the time sampling of the 30 nights of historical Keck observations (from 2005 to 2013) of Sgr A*, and including the 2019 nights, there is a 0.3% probability that we observe a single night with flux levels as high as seen on 2019 May 13. These simulations are the most consistent with our current observations because they have very similar noise properties, observed duration, and timing. If we also include VLT nights for a total of over 130 nights, then the probability is less than 1.5% to observe flux values higher than 6.18 mJy on a single night. We can also consider the probability of randomly drawing 4 light curves similar to the observations in 2019. This probability is considerably lower at less than 0.05%. We also note that we have only observed the decay of the light curve on 2019 May 13, which suggests the actual maximum was likely even higher (Figure 3 ). Here we examine two possibilities for explaining the very unusual brightness and variation of Sgr A* observed this year: (1) the statistical models need to be changed or updated, and (2) there is a physical change in the accretion activity of Sgr A*. Based on the statistical model of Witzel et al. ( 2018 ), with the four nights of observations, there is a probability of less than 0.05% to


1 . While ID11 and notably also A4.1 fall in the transition region between HII galaxies and giant HII regions, the rest of the lensed systems are among the most luminous star-forming systems and occupy a region of the diagram corresponding to the most luminous HII galaxies. The Lynx arc result from Fosbury et al. (2003) is shown with two different values of velocity dispersion; the lower value corresponds to the semi-forbidden lines and the higher value corresponds to the fit to the permitted CIV 1550 Å line. There is more scatter in the lensed systems, but on the whole the results tend to support the lensing model estimates of the magnification apart from the Lynx arc result when using semi-forbidden lines. There is a crucial general point that we need to make regarding this exercise: The luminosity in these young bursts of star formation evolves quickly in timescales of few megayears, which moves their position away from the correlation to lower luminosities and smaller equivalent widths (EW) of H or H ( Melnick et al. 2000 ; Bordalo Telles 2011 ). This fact may be related to the scatter of the Richard et al. (2011) points below the relation (Fig. 1 ). It is therefore highly recommended to obtain and publish the EW of H or H of star-forming systems to allow for an evolution correction to be performed. 4. Conclusions Regarding the intrinsic properties of ID11, Fig. 1 implies that it is either a luminous giant HII region, such as 30 Doradus in the Large Magellanic Cloud or those found in spiral galaxies like M101, or a low luminosity HII galaxy. Given that the deep HST images of ID11 show no indication of an underlying galaxy, we confirm the Vanzella et al. (2016) conclusion that ID11 is a low luminosity HII galaxy at . The relation spans more than three orders of magnitude in luminosity, which allows us to observe a significant number of objects at large redshifts without recourse to gravitational telescopes; hence this accounts for the power of the relation as a cosmological probe ( Plionis et al. 2011 ; Terlevich et al. 2015 ; Chávez et al. 2016 ). But, of course, only the most luminous HII galaxies can be observed at higher redshifts with the current generation of 810 m telescopes, so gravitationally amplified objects such as ID11 provide us with the unique chance to verify that at high redshift the correlation holds also for low luminosity and possibly low metallicity HII galaxies. We used an independent method, which is based on the standard candle provided by the relation that is valid for HII galaxies and giant HII regions, to measure the amplification affecting the star-forming system ID11 by the Abell cluster S0163 as ; this coincides with the value of 17 obtained by Vanzella et al. (2016) from the strong lensing model of Caminha et al. (2015) . Our result suggests that we can use giant HII regions in high- lensed galaxies as instruments for studying gravitational lenses and that the combination of the standard candle plus detailed


We acknowledge the support of the staff of the Li-Jiang 2.4 m telescope (LJT), Xing-Long 2.16 m telescope, and Tsinghua-NAOC 0.8 m telescope (TNT). Funding for the LJT has been provided by the Chinese Academy of Sciences (CAS) and the People’s Government of Yunnan Province. The TNT is owned by Tsinghua University and jointly operated by the National Astronomical Observatory (NAOC) of the CAS. Financial support for this work has been provided by the National Science Foundation of China (NSFC, grants 11403096, 11178003, 11325313, 11133006, 11361140347, 11203034, 11473063, 11322327, 11103072, 11203078, 11303085, 11203070 and 11103078); the Major State Basic Research Development Program (2013CB834903); the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the CAS (grant No. XDB09000000); the Key Research Program of the CAS (Grant NO. KJZD-EW-M06); the Western Light Youth Project; the Youth Innovation Promotion Association of the CAS; the Open Project Program of the Key Laboratory of Optical Astronomy, NAOC, CAS; and the key Laboratory for Research in Galaxies and Cosmology of the CAS.


Acknowledgments DK and DP thank the Institut Lagrange de Paris, a LABEX funded by the ANR (under reference ANR-10-LABX-63) within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, where this work was started. AL acknowledges the NSF grant AST 1212096 and Center for Magnetic Self Organization (CMSO). He also acknowledges Institut D'Astrophysique de Paris and Institut Lagrange de Paris for hospitality during his visit.


also shows a U-shaped cavity wall encompassing the E1 and E2 lobes, extending to ∼17 from the source. The emission is from the swept-up material in the dense core, which has a radius of 1500 au (∼17). Unlike the observation, however, no emission is seen extending over ∼17 from the source to ∼4′′ to the northeast. In our model, that region is within the AGB halo. Thus, in order to produce detectable emission there, the AGB halo could be denser than currently assumed in our model. Figure 6 shows the comparison of HV CO J = 3–2 emissions between the observation and the model. Both panels are also plotted over the HST images of CRL 618. In the observation (Figure 6 (a)), HV (−183.2 to −114.1 km s −1 ) emission is observed at the tips of lobes E1, E3, E4, and E5, but not observed at the tip of lobe E2. In the model, HV emission, with a similar velocity range to that in the observation, is predicted to be seen at the tips of all the lobes. The velocity of the emission increases with distance, similar to that seen in the observation. Notice that the emission intensity in our model is about half of that observed, and thus more bullet mass may be needed to produce more HV CO emission. The reason for no HV emission being detected at the tip of and along the southern edge of lobe E2 is unknown. Figure 6. (a) Observed HV CO J = 3–2 emission (contours) plotted on the H α image of CRL 618 (from Figure 2 of Lee et al. 2013a ). The velocity ranges of the contours are −183.2 to −160.6 km s −1 (blue), −157.8 to −132.5 km s −1 (cyan), and −132.5 to −114.1 km s −1 (green). The contours start at 1 Jy beam −1 km s −1 , with a step of 2 Jy beam −1 km s −1 . The synthesized beam is ∼053 × 035 at a position angle of ∼83°. (b) Simulated HV CO J = 3–2 emission (contours) in Model 2, with similar velocity ranges to those in (a). HV CO emissions are seen at the tips of the E1 to E5 lobes. The contours start at 0.5 Jy beam −1 km s −1 , with a step of 1 Jy beam −1 km s −1 . The synthesized beam is the same as that in (a). Figures 7 (a) and (b) show the PV diagrams of the observed outflows in CO, cut along the axis of lobes E1 and E2. Figures 7 (c) and (d) show the same PV diagrams but calculated from the model. In these diagrams, lobes E4 and E5 can also been seen. In Figures 7 (c) and (d), the bullets are seen at the tips of the outflows and thus are traced by the fast molecular outflows. The diagrams also show that the velocities of the molecular outflows decrease linearly with the distance to the central source, as seen in the observations. The slope of the PV structure is roughly equal to , where p is the projected distance from the center and t is the time after ejection. Therefore, different slopes are seen for the outflows in different ejection episodes. Notice that since no molecular emission is detected for lobe E2, no PV structure is detected for lobe E2 in the observation, as shown in Figure 7 (b). Figure 7. (a and b) PV diagrams of CO J = 3–2 emission of CRL


This work was supported by NSF grants AST-1211995, AST-1616598, and AST-1616710. A.W. gratefully acknowledges the assistance of Vincenzo Pota in prototyping the modeling code. A.J.R. is a Research Corporation for Science Advancement Cottrell Scholar. A.V. is supported by the NSF Graduate Research Fellowship Program. D.F. thanks the ARC for financial support. J.S. acknowledges support from a Packard Fellowship. S.B. acknowledges the support of the AAO PhD Topup Scholarship. We thank the anonymous referee for useful suggestions. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. This research has made use of NASA’s Astrophysics Data System and the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Funding for the DEEP2/DEIMOS pipelines (Cooper et al. 2012 ; Newman et al. 2013c ) has been provided by NSF grant AST-0071048. The DEIMOS spectrograph (Faber et al. 2003 ) was funded by grants from CARA (Keck Observatory) and UCO/Lick Observatory, a NSF Facilities and Infrastructure grant (ARI92-14621), the Center for Particle Astrophysics, and by gifts from Sun Microsystems and the Quantum Corporation. This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013 ). We acknowledge the use of other open source Python packages, including Numpy (Walt et al. 2011 ), Scipy (Jones et al. 2001 ), Matplotlib (Hunter 2007 ), Pandas (McKinney 2010 ), IPython (Pérez Granger 2007 ), and Scikit-learn (Pedregosa et al. 2011 ). The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Facility: Keck:II (DEIMOS).


other hand, in more extended BCDs the observed CO emission corresponds only to the most luminous regions of the starbursts, so it may be considered as a lower limit to the total CO emission. For all the observed galaxies our CO observations cover at least 50% of the projected size of starburst (, see Sect. 3), while for three objects this fraction, , is 100%. Table 3 Multiwavelength properties of galaxies from the literature. Notes. Columns: (2) radius at the mag arcsec isophote; (3) radius of the star-forming region from 2D surface photometry ( Amorín et al. 2009 ); (4) inclination; (5) H i gas mass; (6) logarithm of H i gas surface density; (7) stellar mass; (8) logarithm of star-formation rate density; (9) gas-phase metallicity; (10) logarithm of H surface density assuming a Galactic CO-to-H conversion factor. Reference. For metallicity: References for : (a) Shi et al. (2006) ; (b) Cairós et al. (2007) ; (c) García-Lorenzo et al. (2008) ; (d) López-Sánchez Esteban (2010) ; (e) Zhao et al. (2010) ; (f) Pérez-Montero Díaz (2003) ; (g) Gil de Paz et al. (2003) . (h) Frayer et al. (1998) ; (i) Leroy et al. (2005) ; (j) Barone et al. (2000) ; (k) Albrecht et al. (2004) ; (l) Leon et al. (1998) ; (m) Verdes-Montenegro et al. (1998) ; (n) Taylor et al. (1998) ; (o) Tacconi Young (1987) ; (p) Wei et al. (2010) . A wobbler switching mode was used at a frequency of 0.5 Hz with a beam throw up to 240 in azimuth. Two independent SIS receivers at each frequency (A100, B100 at 3 mm and A230, B230 at 1.3mm) were used to observe both polarizations of the CO 10 and 21 transitions simultaneously. The receivers were tuned in single side band, using only the lower band (LSB), which improves the calibration procedure and avoids contamination by other spectral lines in the image band, especially in observations of the calibration sources. The SIS receivers were connected to two filter-banks with resolutions of 1 MHz and 4 MHz at 115 GHz and 230 GHz, respectively, which yields velocity resolutions, , of 2.6 km s and 5.2 km s, respectively. These backends have 512 channels each, covering a total instantaneous velocity range of 1300 and 2600 km s. Pointing and focus were checked before each integration on continuum sources and planets. The pointing accuracy was better than 2.5 on average. Calibrations were done using the chopper wheel method, by observing strong radio sources (Orion A, CW Leo, and W51d). System temperatures at both frequencies varied between 290–470 K, the higher values being due to bad weather conditions. Thus, we obtained a range for the antenna temperature sensitivity of –15 mK. The CO spectra was reduced using CLASS 2 ( Buisson et al. 1997 ). To increase the signal-to-noise ratio (S/N), averaged spectra for each pointing were obtained by weighting multiple scans by a factor of , where is the integration time and is the system temperature. In all cases, baselines of zeroth order were subtracted. The spectra was then scaled to a main-beam


; Pierrehumbert et al. 2011 ; Rose 2015 ). The substellar point in our simulations was located over the pacific ocean. We also tried aquaplanet simulations and achieved similar results. It would be interesting to test whether locating the substellar point over a large land mass such as Asia would significantly affects our results. 5. Conclusions The main conclusions of this paper are as follows. 1. Tidally locked planets will not necessarily exhibit a snowball bifurcation. This is in contrast with planets with Earth-like rotation and orbit, which are required to exhibit a snowball bifurcation except in unrealistic edge cases. 2. The reason tidally locked planets are not required to exhibit a snowball bifurcation is that the insolation increases strongly as the substellar point is approached. 3. Whether a tidally locked planet actually does exhibit a snowball bifurcation depends on the heat transport and ice/ocean albedo contrast. Higher heat transport and a higher ice/ocean albedo contrast both favor a snowball bifurcation. 4. We performed GCM simulations that suggest that realistic tidally locked planets will not exhibit a snowball bifurcation. Although they should tend to have stronger heat transport, the top-of-atmosphere ice/ocean albedo contrast should tend to be smaller. 5. This work suggests that we will not find habitable tidally locked exoplanets with an active carbon cycle in a snowball state. This should be verified with a model incorporating an active carbon cycle. Appendix Artifact of Sea Ice Scheme Interestingly, and in contrast with Lucarini et al. ( 2013 ), we find a small separation between equilibrated states that were initialized from Warm and Cold Starts. The most likely reason Lucarini et al. ( 2013 ) did not observe this separation is that they started their Cold Start simulations from a significantly warmer climate state that was not globally glaciated. To further investigate this issue, we show global mean sea ice concentration for a series of simulations with a stellar flux of 1200 W m −2 and initial conditions representing equilibrated climate states with different amounts of sea ice (Figure 9 ). We find that states started within the apparent separation band are stable, rather than approaching separate stable warm and cold states at the upper and lower ends of the separation band. This means that the separation band actually represents a smeared state, which we can consider a continuum of states rather than two distinct “fixed points” with separate basins of attraction. This is clearly unrelated to a snowball bifurcation and does not alter our interpretation that there is no snowball bifurcation in PlaSim in the tidally locked configuration. Figure 9. Time series of global mean sea ice concentration for a series of simulations at a stellar flux of 1200 W m −2 with different initial conditions. This plot demonstrates that the solution is a continuum of states rather than two distinct fixed points. By further


We thank the referee for the very helpful suggestions that have significantly improved our manuscript. We acknowledge financial support from the 973 Program of China under grant 2013CB837000, the National Natural Science Foundation of China (No. 11573060), the Key Laboratory of Astroparticle Physics of Yunnan Province (No. 2016DG006), the Strategic Priority Research Program, and the Emergence of Cosmological Structure of the Chinese Academy of Sciences, Grant No. XDB09000000. The work of D.H.Y. is supported by CAS “Light of West China” Program.


for studies of the host galaxies of AGN ( Kauffmann et al. 2003 ). When using the Vanden Berk et al. (2001) template, it is important to know that it contains significant host galaxy contamination, in particular at redder wavelengths (e.g., Fynbo et al. 2013 , their Fig. 5). In this paper, we use data from the X-Shooter spectrograph to build a new QSO template that covers the full range from rest-frame Ly to 11 350 Å based on bright SDSS QSOs and observed with a single instrument over this spectral range. In Sect. 3 we describe the sample selection and provide details of the observations. Section 4 describes the construction of the composite spectrum, and Sect. 5 presents the resulting composite. In Sect. 6 we perform a comparison with existing composites and in Sect. 7 offer our conclusion. We use the cosmological parameters from Planck Collaboration XVI (2014) with km s Mpc, , and throughout the entire paper. 2. Issues with the currently most used template The currently most widely used QSO template is the SDSS template of Vanden Berk et al. (2001) . As described very clearly in that paper, the SDSS composite spectrum shows a significant change to a shallower spectral slope around 5000 Å. This is mainly attributed to contaminating light from the underlying host galaxies. Other effects also contribute, such as the emission from a hot dust component, but the dominating factor is probably the host contamination. Our main motivation for building a QSO template without this problem is the following: a search for dust-reddened QSOs using near-IR (NIR) selection of QSOs has been initiated ( Fynbo et al. 2013 ; Krogager et al. 2015 ). In the central southern SDSS footprint, Stripe 82 ( Annis et al. 2014 ), about 50 such candidate QSOs have been studied using the New Technology Telescope (NTT). Although the search was for QSOs reddened by foreground absorber galaxies, most systems turned out to be QSOs reddened by dust in their host galaxies. The optical spectra can be matched well by the SDSS template spectrum reddened by SMC-like extinction curve, but the NIR (rest frame optical) photometry from the UKIRT Infrared Deep Sky Survey (UKIDSS) cannot be simultaneously fitted. The problem is illustrated in Fig. 6 in Fynbo et al. (2013) , where they attempt to model the EFOSC2 spectrum of a dust-reddened QSO at observed in that survey. As seen, the SDSS spectrum and photometry can be matched well with the Vanden Berk template, but the photometry from UKIDSS is much too blue for even the unreddened template. This is not a unique case, but a problem that is seen for all the dust-reddened QSOs found in their search. In the SDSS composite, the QSOs which contribute to the spectrum at 5000 Å have to be at fairly low redshifts (). These QSOs have absolute magnitudes that are three to four magnitudes fainter than bright QSOs (e.g., Vanden Berk et al. 2001 , their Fig. 1). They are also likely to have the brightest rest frame optical host galaxies, so host


by Proshina et al. (2020) . 2. Observations and the data involved Our long-slit spectral observations were made with a multi-mode focal reducer SCORPIO-2 ( Afanasiev Moiseev 2011 ) at the prime focus of the Russian 6 m telescope of the Special Astrophysical Observatory, Russian Academy of Sciences. UGC 5936 was observed on February 28, 2014. In these observations, the 1′′ slit was aligned with the major axis, PA(slit) = 83deg, and the total exposure time was 75 min; also the target was exposed in the orientation through the neighbouring dwarf galaxy, PA(slit) = 135deg, with the exposure time of 45 min. The seeing during these observations was mediocre, F W H M = 3′′. We used the VPHG1200@540 grism providing an intermediate spectral resolution F W H M ≈ 5 Å in the wavelength region from 3700 Å to 7200 Å. This spectral range includes a set of strong absorption and emission lines making it suitable to analyse both stellar and gaseous kinematics of the galaxy as well as the gas excitation and chemistry and properties of the stellar populations. The slit is 6′ in length, which allowed us to use the edge spectra for subtraction of the sky background. The CCD E2V CCD42-90, with a format of 2048 × 4600, using in the 1 × 2 binning mode provided a spatial scale of 0.357 ′′/px and a spectral sampling of 0.86 Å/px. The data reduction as well as kinematics and stellar population characteristics derivation were standard for our SCORPIO-2 data; see for example Sil’chenko et al. (2019) or Proshina et al. (2020) . We used the g r -band images from the SDSS/DR9 archive ( Ahn et al. 2012 ) to study the large-scale structure of the galaxy. 3. Photometric and dynamical structure of UGC 5936 The smooth lenticular galaxy UGC 5936 (see 2MASS J -band image, Fig. 1 , lower middle) possesses a large pseudo-ring which looks unclosed in the optical continuum bands (Fig. 1 , upper left). However Fig. 1 (lower right), which shows the WISE/W3 data in the 12 μ m band delineates a perfect closed ring; in this figure hot dust heated by star formation reveals its organisation in a typical S0 outer ring structure. The colour map (Fig. 1 , upper right), demonstrates the blue colour of the ring, which is narrow to the east and splits into two arcs to the west, as well as the red colour of the arc connecting the core and the western part of the ring. The western blue-ring structures correspond to the ring in the unsharp-masked image (Fig. 1 , upper middle). Interestingly, the GALEX near-ultraviolet (NUV) map (Fig. 1 , lower left), which also refers to young star concentration, shows UV flux excesses beyond the borders of the continuum-band pseudo-ring; the offset is seen especially well at the major axis. To the south-east from UGC 5936, a small satellite, SDSS J105009.10+362009.9 , is observed at 15 kpc projected onto the sky plane; this satellite is observed at 19 kpc if we suggest that it lies in the plane of the UGC 5936 disc. This small satellite is very blue. According to


ACKNOWLEDGEMENTS We are grateful to Peter Camps for code support, interesting discussion, and the development of skirt . We thank Ricardo Amorin, Ilse De Looze, Hiroyuki Hirashita, Roberto Maiolino for helpful discussion, and Nicolas Laporte for providing data. AF acknowledges support from the ERC Advanced Grant INTERSTELLAR H2020/740120. We acknowledge the use of the python programming language (Van Rossum de Boer 1991 ), and use of the numpy (van der Walt, Colbert Varoquaux 2011 ), ipython (Perez Granger 2007 ), jupyter (Kluyver et al. 2016 ), matplotlib (Hunter 2007 ), and pymses (Labadens et al. 2012 ) packages. This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration et al. 2013 ).


map maximum. The variability period is illustrated by the red dashed line in the global spectra. A possible aliasing period is displayed in blue. Lower panel: Lomb–Scargle periodogram for the same LC. The main peak labelled ‘A’ corresponds to the period of 18.86 d, whereas ‘B’ indicates the 39 d period. 3.3 KIC 4829241, KIC 10420021 and KIC 11822535 The stars KIC 4829241, KIC 10420021 and KIC 11822535 were classified as non-periodic by Maoz et al. ( 2015 ). Instead, our study suggests a periodic or quasi-periodic modulation well describing a variability signature in the wavelet representations. We attribute to this variability periodicities ranging between 11 and 16 d, which is reasonable for WDs (e.g. Kawaler 2015 ; Valeev et al. 2017 ; Braker et al. 2017 ). In fact, these periodicities are more persistent in KIC 4829241 and KIC 10420021 than in KIC 11822535, even though also noticeable in the latter star. We do not expect to find magnetic cool-spot signatures for KIC 4829241 and KIC 11822535 considering their high T eff and their log g values (Tremblay et al. 2015 ). However, a transient signature for KIC 10420021 is conceivable in view of its T eff and log g being close to the limit value (Tremblay et al. 2015 ), so the presence of a convection zone at the WD surface can still be envisaged. Combining the surface gravities and the effective temperatures, derived spectroscopically by Hallakoun et al. ( 2018 ), with evolutionary grids (Benvenuto Althaus 1999 ), we are able to estimate the mass of these three WDs. KIC 4829241 is a WD of mass . The Lomb–Scargle periodogram for this WD shows a period of 16.68 d with an amplitude of 286 ppm, as indicated by the letter A in the upper-right panel of Fig. 5 . Following Maoz et al. ( 2015 ), given its mass, rotation combined with an accretion of gas from the interstellar medium (ISM) and the material carried on the magnetic poles generating hotspots, with an accretion luminosity of Δ L acc ∼ 1.4 × 10 29 erg s −1 , could explain the periodic modulation. Fig. 5 (upper-left panel) displays the wavelet analysis, from which we noticed a long-lasting periodicity of 16.04 d over the time observation. With a lower amplitude, we also found a 40-d period that could be considered as a possible aliasing period. The 16-d period characterizes the WD photometric modulation since it is the main period obtained in both Fourier- and wavelet-based techniques. Based on a rough FAP estimation (see Section 2 ), these periods likely lie above the confidence level. Figure 5. Left: light curves with additional treatment, wavelet local and global spectra of Kepler WDs (from top to bottom) KIC 4829241, KIC 10420021, and KIC 11822535. Contour levels are 90 , 80 , 70 , ..., 20 , and 10 of the map maximum. The variability periods are illustrated by the red dashed lines in the global spectra. Possible aliasing periods are displayed in blue. Right: respective Lomb–Scargle periodogram for the same WD. The main peak labelled 'A'


We thank Peter Stetson for a copy of DAOPHOT as well as his helpful engagement on its usage. Support for this work was provided by NASA through Hubble Fellowship grant #51386.01 awarded to R.L.B. by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. M.G.L. and I.S.J. were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) No. 2017R1A2B4004632. Support for program #13691 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Facility: HST (ACS/WFC). Software: DAOPHOT (Stetson 1987 ), ALLFRAME (Stetson 1994 ), TinyTim (Krist et al. 2011 ).


We thank the anonymous referee for his/her constructive comments that helped improve the paper. P.T. acknowledges support from NASA grant 80NSSC18K0408 (solicitation NNH17ZDA001N-ADAP). This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory and funded by the National Aeronautics and Space Administration. This research made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). This research has made use of data obtained from the Suzaku satellite, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA). Facilities: Suzaku , NuSTAR .


ACKNOWLEDGEMENTS This research has used the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


We thank the referee for useful comments that helped to improve the manuscript. We also thank Prof. R. A. Chevalier and Dr D. Caprioli for critically reading the manuscript. MP acknowledges support for this work by NASA through Einstein Post-doctoral Fellowship grant number PF3 140113 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.


that the outburst ejecta are comprising small and bright particles. The decrease of the colour temperature and colour shortly after the peak brightness suggests an increase of the mean particle size with time for the particles crossing VIRTIS FOV. The presence of silicatic grains devoid of organic material could be explained by the high grain temperatures causing sublimation of the organics. Quantitatively, the September 13 outburst data are consistent with the silicatic grain hypothesis. However, large colour temperatures (>600 K) are measured at the peak brightness of the September 14 outburst, whereas computed temperatures are 530 K for olivine grains. Several explanations are possible. First, we did not consider grains smaller than 100 nm in radius, whereas we cannot exclude their presence. These grains might reach higher temperatures than 100 nm grains, though this is not expected from model calculations (Lasue et al. 2007 ). In our model, 100 nm grains are compact ( P = 0). Considering instead that these grains are aggregates, their temperature would be higher than the temperature of the equivalent sphere (Xing Hanner 1997 ). Another possibility is that the spectral indices of amorphous olivine differ significantly from those of the refractory material of cometary grains. We performed Mie calculations with inclusions of FeS within an olivine matrix. For a volume fraction of 6 per cent of FeS consistent with the suggestion of Fulle et al. ( 2016a ) for 67P grains, the colour temperature reaches 575 K (Fig. 12 ), which is not far from the extremum values measured during the September 14 outburst. Could fractal agglomerates explain the outburst spectra? For carbon/amorphous olivine mixtures, the colour and colour temperature of their infrared spectrum match the measurement, but this is not the case for the bolometric albedo (Fig. 10 ). Calculations made for units of amorphous olivine provide a bolometric albedo 0.4, i.e. a factor of 2 below the measured values. During 67P outbursts, MIDAS collected a high amount of micrometric grains (Bentley, personal communication), in agreement with an ejecta population dominated by compact grains rather than aggregates. We performed calculations setting the maximum size of the fractal aggregates to a max = 1 μm, and the bolometric albedo is still 0.4. Finally, the main contributors to the scattered and thermal parts of the spectrum could be distinct populations of grains. Cold and bright grains would essentially contribute to scattered light, whereas this is the opposite for warm and dark grains made of strongly absorbing material. These two populations of grains were found in the outburst ejecta of the extraordinary outburst of comet 17P/Holmes in 2007 October ( r h = 2.45 au) (Yang et al. 2009 ). The near-IR spectra of the outburst ejectas showed strong absorption bands at 2 and 3 μm related to water ice (Yang et al. 2009 ). Infrared signatures of ice are not detected in the VIRTIS-H outburst


NS thanks J. S. Gallagher for discussions regarding binary evolution and LBVs, and in particular for drawing our attention to previous work by N. King. We benefitted from discussion about SN host environments with P. Crowther, J. Anderson, and P. Kelly, and from further discussions concerning binary evolution with S. de Mink. We also thank the referee (J. Eldridge) for a careful reading and thoughtful comments that improved the paper. Partial support was provided by NSF award AST-1312221. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France.


We are very grateful for the warm reception and skillful help we have received from the staff of the Dominion Radio Astrophysical Observatory, which is operated by the National Research Council Canada. The CHIME/FRB Project is funded by a grant from the Canada Foundation for Innovation 2015 Innovation Fund (Project 33213), as well as by the Provinces of British Columbia and Quebec. Additional support was provided by the Canadian Institute for Advanced Research (CIFAR) Gravity Extreme Universe Program, McGill University and the McGill Space Institute, University of British Columbia, and University of Toronto Dunlap Institute. The Dunlap Institute is funded by an endowment established by the David Dunlap family and the University of Toronto. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research Innovation. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. J.C. was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Undergraduate Student Research Award. P.C. is supported by a Mitacs Globalink Graduate Fellowship. M.D. is supported by an NSERC Discovery Grant, CIFAR, and Fonds de Recherche du Québec—Nature et technologies Centre de Recherche en Astrophysique du Québec (FRQNT/CRAQ). B.M.G. is supported by an NSERC Discovery Grant and the Canada Research Chairs program. M.H. and G.H. are supported by CIFAR. V.M.K. is supported by a Lorne Trottier Chair in Astrophysics Cosmology, a Canada Research Chair, CIFAR, an NSERC Discovery Grant and Herzberg Award, and FRQNT/CRAQ. U.-L.P. is supported by CIFAR. K.W.M. is supported by the Canadian Institute for Theoretical Astrophysics National Fellows program. S.M.R. is supported by CIFAR and the NSF Physics Frontiers Center award 1430284. I.H.S. is supported by CIFAR and an NSERC Discovery Grant. P.S. is supported by a DRAO Covington Fellowship from the National Research Council Canada. Software: CHIME/FRB pipeline, alpenhorn (Hincks et al. 2015 ), bonsai (K. M. Smith et al. 2018, in preparation), Grafana ( grafana.com ), Prometheus ( prometheus.io ), RRATTrap (Karako-Argaman et al. 2015 ), PRESTO ( github.com/scottransom/presto ).


Acknowledgements The authors thank the anonymous referee for his or her thorough review and comments, which contributed to improving the manuscript. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement No. 291058. This research was supported by the Research Council of Norway through the grant “Solar Atmospheric Modelling”. This research was supported in part with computational resources at NTNU provided by NOTUR, http://www.sigma2.no . Some 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. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA) and the University of Cambridge (UK).


occupy distinct regions of NUV– r space, and all share some overlap with SPOGs, suggesting that SPOGs are a heterogeneous group comprised of galaxies with different mechanisms for UV emission. In FUV–NUV (bottom panel of Figure 6 ), we find a similar trend, with SPOGs displaying a larger range in FUV–NUV colors compared to the star-forming sample. Once again the E + A, AGN, and interacting samples all share a similar color distribution as SPOGs, but seem to occupy distinct subregions. These plots suggest that UV emission in SPOGs may be an amalgam of the mechanisms that the comparison samples represent in different proportions. Future multiwavelength and high-resolution morphological analyses will clarify which individual SPOGs exhibit similar UV emission mechanisms to each comparison group. Figure 6. Top: k -corrected NUV– r color vs. SDSS i -band absolute magnitude ( M i ) of SPOGS (gray contours) and all comparison samples. Bottom: k -corrected FUV–NUV color vs. SDSS i -band absolute magnitude ( M i ) of SPOGS (gray contours) and all comparison samples. In both plots, the black stars are SPOGs that fall outside the outer contour. While most of the comparison samples fall within the color–magnitude space occupied by SPOGs, no single sample fully covers the SPOGs parameter space, suggesting that SPOGs may be composed of a combination of these samples. All contours are in increments of 10 percentiles of the maximum density. Figure 7 shows the cumulative distribution of FUV–NUV colors for SPOGs compared to each of the comparison samples. We used AD tests to compare the shapes of these 1D UV color distributions. For samples in the full range of masses, all samples, except the AGN sample, have statistically distinct color distributions from SPOGs with greater than 99% significance. The AGN sample is distinct from SPOGs at the 78% significance level. When restricting the comparison to a specific range of masses (−23 M i −21), all samples, except the interacting sample, have statistically distinct color distributions from SPOGs with greater than 99% significance. The interacting sample is distinct from SPOGs at the 85% significance level. This test shows that the differences in UV colors are not attributable to differences in stellar mass distribution. Figure 7. Cumulative distributions of GALEX FUV–NUV color for SPOGs and each of our comparison samples. With Anderson–Darling tests, we show that SPOGs are a distinct distribution from all other comparison samples, except AGN (see Section 3.1 ). 3.2. Mixture Models To further test which of the comparison samples contribute to the FUV–NUV colors of SPOGs and in what fractions, we used the method of Gaussian mixture models (GMMs) 20 20 We provide an example of our code and method at https://github.com/f-ardila/SPOGs-GMMs . . GMM models some underlying distribution whose true probability density function is unknown as the sum multiple Gaussian distributions (Ivezic et al. 2014 ). Here, we first


spectroscopic analysis. Results for 11 SB1 are shown as open circles. The atmospheric parameters we determined for 402 GK stars are presented in Table 1 (Cols. 69), where the numerical values of , , , and [Fe/H] are presented together with their intrinsic uncertainties. The values of resulting atmospheric parameters generally remain within the range of the TGVIT model grids. Figure 5 shows the relations between the atmospheric parameters presented in Table 1. We note that the results obtained for single-line spectroscopic binaries (SB1) agree very well with those for apparently single stars. The effective temperature lies between 4398 K and 6394 K with a median value of 5167 K. The distribution of , presented in Fig. 6 a, shows two maxima, one for giants (cooler) and one for subgiants (warmer), which are the two most numerous groups of stars in our sample. The intrinsic uncertainty distribution in is presented in Fig. 6 e. The gravitational accelerations for our sample range between 1.49 and 4.72 with a median of 3.65. The distribution of is presented in Fig. 6 b. We found that 5 stars have , 60 have , 277 have and 60 stars have . Most of our stars (194) have of which means that generally they are subgiants. The uncertainty distribution in is presented in Fig. 6 f. The microturbulence velocity, , reaches values from to and has a median at . Most of our stars have between and (Fig. 6 c). The uncertainty distribution in is presented in Fig. 6 g. The metallicity of the stars in our sample, [Fe/H], remains within the limit of to with a median value at . Most of our objects have [Fe/H] in the range of to . Figure 6 d presents the distribution, which clearly shows that our stars are mostly less metal abundant than the Sun. The uncertainty distribution in [Fe/H] is presented in Fig. 6 h. Fig. 6 Histograms of of , , , and [Fe/H] obtained for 402 stars with complete spectroscopic analysis. Results for 11 SB1 are shown in black. 3.6. Uncertainy estimates of the atmospheric parameters The mean intrinsic uncertainties of our determinations, that is, those delivered by TGVIT, are K, , , and [Fe/H] . Figure 7 shows the intrinsic uncertainties of these three parameters as a function of . No correlation exists between the uncertainties and the obtained parameter values for any of the atmospheric parameters in the wide range of between 4500 K6000 K. The scatter of the uncertainties is uniformly distributed over the whole range of resulting parameters. We note, however, that for stars with below 4500 K or above 6000 K the uncertainties are slightly higher, especially in and [Fe/H]. To test the effect of the shift in EWs between DAOSPEC and ARES measurements presented in Sect. 3.4 , we calculated stellar atmospheric parameters for the same five stars using DAOSPEC and ARES EWs separately. We obtained agreement within 1 intrinsic in all parameters except for the microturbulence velocity, in which the results differ by 23 intrinsic . We therefore assume that


in changing our results. We stop our pure infall models earlier than , as these runs require much more computing time than our standard runs. However, this should not greatly affect our analysis, as the behaviour of these runs is clear and is unlikely to change significantly in the period between t final and 1000 yr. In the pure infall realizations only one sink forms and grows rapidly via accretion, reaching a mass of over in only ∼100 yr. In contrast, all of the other runs show considerable fragmentation within the first 1000 yr, forming anywhere between 15 and ∼120 sinks. The total mass in sinks (M tot ) and the total number of sinks (N tot ) in each realization at the final output time is listed in Table 3, and time evolution of these quantities is shown in Figs 2 and 3 , respectively. In addition, Fig. 4 shows some illustrative examples of the evolution of some of our realizations. The difference in behaviour that we see between the pure infall runs and the other runs occurs because the pure infall runs are the only ones in which no disc forms over the course of the simulations. Some non-zero angular momentum arises during the gravitational collapse but is too small to trigger the formation of a disc. In all of the other runs 3 a dense, gravitationally unstable accretion disc forms which soon fragments. Figure 2. Total mass in sinks as a function of time after the first sink is created. Each panel shows the results for the five different realizations of each setup. Increasing the initial turbulent or rotational energy tends to systematically decrease the total mass in sinks at any given time. We also see that there is significant variation from simulation to simulation for all of the setups with non-zero initial turbulence, but not for the setups with non-initial turbulence. Figure 3. Total number of sinks as a function of the time elapsed after the formation of the first sink. The colour scheme is the same as in Fig. 2 . We see that the number of sinks that form varies substantially from simulation to simulation for all of the setups. A colour version is available online. Figure 4. Column density plots (two top rows: x – y plane of the simulation box; two bottom rows: x – z plane of the simulation box) of the evolution of realization β01 – 1, α005 – 5, and α025β001 – 3. In the purely rotational runs, the protostellar disc lies in the geometrical x – y plane of our simulation box during the whole of the simulation, as demonstrated here for run β01 – 1. In all runs including turbulence, however, the orientation of the disc varies strongly over time. The projections are centred on the centre of mass of both sink particles and gas within a 500 AU radius around the most massive sink particle at the time of the snapshot considered. The projection thickness is about half the size of our simulation box (), the distance between the position of the first sink and the edge of the simulation box. In our plots of the evolution of the total mass


ACKNOWLEDGEMENTS This work is based on observations obtained with the Southern African Large Telescope (SALT), programmes 2010-1-RSA-OTH-001 and 2018-1-MLT-008, and supported by the Russian Foundation for Basic Research grant 19-02-00779. AYK acknowledges support from the National Research Foundation (NRF) of South Africa. LMO acknowledges partial support by the Russian Government Program of Competitive Growth of Kazan Federal University. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.


for the sample of velocity-selected clusters. As in Fig. 5 , θ is the acute angle between the projected major axis of each galaxy and that of the cluster in which it resides. Cluster position angles were determined from moments of inertia of the projected galaxy distribution. The Kuiper V, Rao, and binomial statistical tests all indicate a probability that the observed distribution of angles is consistent with random BCG orientations. Figure 9. BCG alignments as a function of peculiar velocity. Here, Δ V BCG /σ is the absolute difference between the BCG’s velocity and the mean cluster velocity, and σ is the cluster velocity dispersion. 4 DISCUSSION The main findings of this paper are: A significant fraction of BCGs have spatial offsets of a few tens of kpc or more from the centroid of the X-ray light distribution that presumably traces the centre of the DM halo and reflects the cluster’s dynamical state. Compared with theoretical models, these offsets are much larger than the expected ‘wobble’ around the centre of a standard CDM halo (2 kpc versus a few tens of kpc) as in the simulations of Kim, Peter Wittman 2017 ; Harvey et al. 2017 ). However, the X-ray gas may not trace the DM halo distribution (e.g. by gas sloshing, etc.) A significant number of BCGs also have significant line-of-sight peculiar velocities relative to the cluster. These observations suggest that many BCGs are not currently at rest in the potential well of their host cluster. Despite the prevalence of BCG displacements, these galaxies still show a strong tendency to share the same orientation as the cluster in which they reside (cf. Tempel, Stoica Saar 2013 , a remarkably robust coherence of structures over scales from tens to thousands of kpc, as suggested by the simulations of Rhee et al. 2017 ). 4.1 Comparison of observations with simulations The computation of the cluster and BCG elongation axes is done as in Ragone-Figueroa et al. ( 2020 ). They are obtained from the principal axes of the ellipsoids that best describe the corresponding distribution of matter. For the purposes of this work cluster principal axes and centre of mass are obtained using DM particles within r 200 . While for obtaining BCG principal axes we use star particles inside 0.1 r 500 . Fig. 10 shows the distributions of BCG offsets in position and velocity as well as their correlations with the BCG–cluster alignment angle, in full 3D space (four left-hand panels) and in projection and radial velocity (four right-hand panels). We find in simulations galaxies with significant offsets, in projected space the mean(median) offset is ∼53 kpc(78 kpc), which is larger that the mean found in the observational data (∼15 kpc). Conversely, the mean(median) normalized 1D BCG velocity | V BCG /σ| (with respect to the cluster mean) is ∼0.09(0.07), which is lesser than in the data (0.26). The maximum Δ V /σ in these simulations is lower than that observed because of the smaller number of simulated cluster samples.


Acknowledgments We thank the reviewer for their valuable and constructive feedback which greatly contributed to the quality of this paper. We thank Greg Snyder for useful discussions and input. PT acknowledges support for Program number HST-HF2-51384.001-A that was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. This research made use of a University of Victoria computing facility funded by grants from the Canadian Foundation for Innovation and the British Columbia Knowledge and Development Fund. We thank the system administrators of this facility for their gracious support. Funding for the SDSS IV has been provided by the Alfred P. Sloan Foundation, the US Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofsica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut fr Astrophysik Potsdam (AIP), Max-Planck-Institut fr Astronomie (MPIA Heidelberg), Max-Planck-Institut fr Astrophysik (MPA Garching), Max-Planck-Institut fr Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatrio Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autnoma de Mxico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University and Yale University.


We thank M.M. Romanova for valuable discussions and an anonymous referee for valuable comments. This work was supported in part by NASA grants NNX11AF33G and NSF grant AST-1211318.


ACKNOWLEDGEMENTS The authors would like to thank Jim Hinton for useful discussions and help during the production of the paper. The authors would also like to thank the HAWC collaboration for useful discussions. The research of GG was supported by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development.


Again we note that has a small constant component, , in the direction of the body frame and a big one of modulus describing a circle in the plane of the body frame. The angular velocity in the body frame is given by It follows from Eqs. ( 3 )and ( 5 )that . Since the main axis, , of the ellipsoid is much greater than the other axes, and , we find that . Moreover, for low values of , , and therefore is also small. Finally let us note that when , then and both, angular momentum and the angular velocity are aligned on the axis. Since the angular momentum, , is preserved in an inertial reference frame, we take the inertial system so that the axis is aligned with . The major axis of the bar has to keep an angle with respect to , and then also measures the angle between the main axis of the bar and the plane of the inertial reference system. For this reason, from now on, it will be referred to as the tilt angle of the motion of the bar (see bottom panel of Fig. 2 ). In the inertial frame the major axis of the bar describes a cone about the axis, while and are slightly misaligned since the bar is also rotating about its major axis. When , the major axis of the bar rotates inside the plane, there is no rotation of the bar about its major axis, and and are again aligned. We define now a new non-inertial reference frame henceforth called the precessing reference system. In this reference frame, the axis is aligned with the major axis of the bar, but the bar is not fixed as in the body frame but rotating around the axis. In the body reference system, the angular momentum and angular velocity vectors rotate around the main axis of the bar ( axis in the body frame) with angular speed . The precessing reference frame rotates with respect to the body frame about the axis they share. This is, these frames are related by means of a time-dependent rotation of axis and angular velocity , in such a way that and are constant in the precessing reference system, with values of We are interested in the equations of motion of our galactic model in the precessing reference frame. To compute them, we need the angular velocity of the precessing frame with respect to the inertial one. This angular velocity, , is the sum of the angular velocity of the body, , and the angular velocity of the body axes in the precessing frame. Therefore, and taking the value of into account, we obtain where (see Chapter 2 of Sánchez-Martín 2015 for more details about the rotations). Finally, as a complement, we briefly discuss the motion of the bar in the inertial frame. According to Poinsot’s theorem (see Arnold 1989 ), the bar, which is described by an ellipsoid, rolls without slipping on a fixed plane normal to the angular momentum . If the ellipsoid has axial symmetry, as in our case, this motion is the superposition of a rotation of the ellipsoid along its symmetry axis with constant angular velocity, , and a precession with constant pattern speed around the axis of the angular momentum.


It is our pleasure to thank Rich Plotkin, Eric Bell, Kayhan Gültekin, and Jenny Greene for very helpful discussions. We also thank the anonymous referee for useful comments and suggestions. Support for AER was provided by NASA through Hubble Fellowship grant HST-HF2-51347.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. M.V. acknowledges funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 grant agreement No. 614199, project “BLACK”).


Since the Monte Carlo simulations described in step (2) are time consuming, we first constrained the parameter space of interest by testing a wide range of (⟨ β ⟩, rms( β )) values on a coarse sampling of the ranges ⟨ β ⟩ = − 2.2, − 1.0 and rms( β ) = 0.1, 1.5. We then accurately constrained their best-fit and confidence range through the analysis of a 35 × 35 grid in the range ⟨ β ⟩ = − 2.0, −1.4 for both the Gaussian and log-normal distributions, and rms ( β ) = 0.4, 0.8 (for the Gaussian distribution) and rms( β ) = 0.4, 1.0 (log-normal). For each position in the grid and for each magnitude bin, we extracted 25 000 objects from the CB07 library and perturbed magnitudes in all bands as described in 3). We note that the estimate of L in step (4) requires the observed and simulated UV slopes distributions to be binned: the choice of the bin widths was tailored to ensure that the extended but poorly populated tails in the observed distributions are efficiently sampled by the simulations. As shown in Fig. 5 , different bin widths were thus set depending on the 1, 2, 3 σ ranges of the observed distribution so as to reduce numerical noise in our procedure. The best-fit parameters of the Gaussian and log-normal PDF( β ) in each magnitude bin are reported in Table 2 . Confidence regions for the PDF( β ) are shown in Fig. 6 , together with observed and best-fit distributions. It is also highlighted how the latter (blue lines) are reshaped by observational effects (red): only a full modelling approach such as presented in C12 and adopted in this work allows us to recover the intrinsic slope distributions from observations. Table 2. UV slope distribution: best-fit parameters and 68% c.l. uncertainties. Fig. 6. Simulation results for the Gaussian ( left panel ) and log-normal ( right panel ) fit in the two different magnitude bins. In the leftmost column , we show maximum likelihood contours at 68%, 95%, and 99% c.l. in green, blue, and red, respectively; the red cross indicates the position of the best fit parameters. The rightmost column shows the histogram of the observed data and the relevant best-fit distribution. The red continuous line is the intrinsic PDF( β ), which is transformed into the blue continuous line by observational effects. We find that L > L * objects at z ∼ 3 have typical, average UV slopes ∼ − 1.7. No significant variation with UV magnitude is found in the Gaussian case. The log-normal best-fit distributions point to a slightly redder average (∼ − 1.5) in the fainter bin, although with large correlated uncertainties between the parameters. The absence of a strong correlation between UV slope and magnitude is in agreement with what was found by C12 at z ∼ 4, but it disagress with the previous analysis of z ∼ 3 objects by Bouwens et al. (2009) . While it is not possible to determine whether the best assumption is the Gaussian or the log-normal shapes, we note that the latter does not seem to accurately recover objects in the (poorly


that an analytic continuation of B ( c ) to the lower half-plane c , apart from poles of Landau quasi-modes, contains also a pole due to the damped mode c = c − , and near this pole B ( c ) has the form: where For real c , expression ( 23 ) can be decomposed, with the aid of equation ( 21 ), as follows: where Now analytic continuation is obvious, since ε ± ( c ) can be replaced by off the real axis, and g ± are replaced by where, depending on signs ‘’ or ‘’, integration contour passes below or above the singularity at u = c . Note that i.e. this is a decomposition of function g (). Since has one zero in the lower half-plane c = c − , B − ( c ) has a pole at this point leading to ∝exp (− γ k t ) contribution to density decay. Expansion near c = c − gives Finally, substitution to leads to the desired result ( 35 ), if we choose the integration contour along the real u -axis. The input from this pole gives a density decay slower that the Landau damping for k > k * ≈ 0.437, as is seen in Fig. 8 . Note that decomposition ( 37 ) is not unique. Moreover, it is possible to decompose B ( c ) so that parts of new decomposition have no singularities in the upper/lower half-planes (Appendix B ). Gaussian in time density decay occurred for Maxwell B ( c ) (Fig. 6 ) is simply a reflection of the fact that B ( c ) has no singularities in the lower half-plane. 4.3 Power-law decay To understand an appearance of the power-law term (Fig. 7 ), we should re-examine derivation of equations ( 7 ) and ( 8 ). They are obtained as a result of analytic continuation of the integrals over the real u -axis by deformation of the integration contour to the lower half-plane. Since g () is zero for || > * , the cut in the complex plane is finite (Fig. 10 ), and deformation of the contour is not needed for this integral. On the either side of the cut The cut leads to an additional input to density ( 6 ): Integrating by parts, assuming g () is even and real, one obtains for large t : Expression in the square brackets gives sinusoidal oscillations with some phase shift due to the presence of in the denominator. If g ( * ) is small, the power-law decay reveals itself only after a while. Figure 10. Integration contour in ( 6 ) in the complex -plane (blue dashes). ‘+’ signs mark the Landau-damped quasi-modes obtained as zeros of . A wavy line marks the cut on real axis c : − * c * . 5 IMPLICATIONS In this article, we analysed numerical solutions of equations describing perturbations of the homogeneous stellar medium. Although the equilibrium state is problematic in the infinite media and invokes a so-called Jeans swindle (e.g. BT ), it is a good testing ground for many phenomena in stellar dynamics (see Bisnovatyi-Kogan Zel’dovich 1971 , for example of a more realistic set-up). The unexpected behaviour of damped solutions in the unstable domain is associated with the presence of a genuine damped mode, which is complex conjugate to the unstable Jeans mode. The damped mode cannot


ACKNOWLEDGEMENTS We would like to thank the anonymous referee for a constructive report that helped to improve the paper. The authors would like to thank the Klaus Tschira Foundation. SJ acknowledges funding by the graduate college Astrophysics of cosmological probes of gravity by Landesgraduiertenakademie Baden-Württemberg. SJ also acknowledges support by the IMPRS for Astronomy and Cosmic Physics at the University of Heidelberg. RP, CMS and VS acknowledge support through the European Research Council under ERCStG grant EXAGAL-308037. VS also acknowledges support through subproject EXAMAG of the Priority Programme 1648 ‘Software for Exascale Computing’ of the German Science Foundation. CP acknowledges support through the European Research Council under ERC-CoG CRAGSMAN-646955.


of the AM CVn (= SDSS J120841.91+355024.8), two polars (AR UMa in a low state and AP CrB in a high state), and three dwarf novae of the sub-types U Gem, SU UMa, and WZ Sge (= GY Cnc, BZ UMa, and EZ Lyn, respectively) were obtained from SDSS DR16 (Ahumada et al. 2020 ). CV subtypes : The CV Gold Sample contains examples of all six major different sub-types, their respective numbers are listed in Table 4 . The different sub-types form clearly distinct clusters in the Gaia HR diagram (Fig. 8 , left-hand panel); 6 and the location of these clusters closely links to the spectro-photometric properties of each sub-type (Fig. 8 , right-hand panel). Table 4. The number of each type in the CV Gold Sample together with the range of their orbital periods. The novalike variables are characterized by stable high mass transfer rates and hot accretion discs that dominate the optical emission of these systems. Correspondingly, their cluster is located at small absolute magnitudes and blue colours. Two AM CVn stars, HP Lib and the prototype AM CVn itself (Faulkner, Flannery Warner 1972 ) are novalike variables with stable, hot helium discs that are somewhat bluer and fainter than their cousins with hydrogen-rich discs. The three sub-classes of dwarf novae exhibit clear trends in their location within the HR Diagram. The U Gem type dwarf novae have lower mass transfer rates than the novalike variables, their quiescent discs are therefore less luminous and their donor stars can contribute noticeably to the optical flux of the systems, which is reflected in the number of these systems being located close to the main sequence. The donors and accretion discs in the SU UMa systems are less luminous than those in U Gem-type dwarf novae, hence they are concentrated closer to the white dwarf cooling sequence. Finally, the WZ Sge type dwarf novae have the dimmest accretion discs and donor stars; in fact, some of them contain brown dwarf companions (GD552 Unda-Sanzana et al. 2008 ; QZ Lib (Pala et al. 2018 ), 1RXS J105010.3–140431 (Mennickent et al. 2001 ), SDSS J102905.21+485515.2 (Thorstensen, Alper Weil 2016 ), SDSS J143317.78+101123.3 (Hernández Santisteban et al. 2016 ), and SSS J122221.7–311525 (Neustroev et al. 2017 )). WZ Sge are therefore inherently the faintest CVs and merge into the white dwarf cooling sequence. A noticeable outlier among the dwarf novae is V1129 Cen, a long-period (≃21.4 h) CV that exhibits low-amplitude (≃0.6 mag) outbursts about once per year, but no emission lines are detected in its spectrum (Bruch 2017 ). The donor is a luminous F-type+ star, explaining the location in the HR diagram. Magnetic CVs have a larger spread due to their more varied spectral appearances. During states of low mass transfer they resemble the detached WD+M binaries whilst during high states, their optical spectra can contain cyclotron emission lines (Wickramasinghe 1988 ) that will affect their colour and absolute magnitude. Overall, the CV Gold Sample contains a


R.K. acknowledges support from STFC via ST/L000709/1. J.P. and R.K. acknowledge comments from J. Anderson and C. Gutiérrez on an earlier version. L.D. acknowledges financial support from “Agence Nationale de la Recherche” grant ANR-2011-Blanc-SIMI-5-6-007-01. This work was partly supported by the EU/FP7 programme via ERC grant number 320360 awarded to G. Gilmore. AG-Y’s team is supported by the EU/FP7 via ERC grant no. 307260, the Quantum Universe I-Core program by the Israeli Committee for planning and budgeting and the ISF; by Minerva and ISF grants; by the Weizmann-UK “making connections” program; and by Kimmel and ARCHES awards. S.J.S. acknowledges funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no [291222] and STFC grants ST/I001123/1 and ST/L000709/1. S.B. is partially supported by the PRIN-INAF 2014 project Transient Universe: unveiling new types of stellar explosions with PESSTO. Support for L.G. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. L.G. acknowledges support by CONICYT through FONDECYT grant 3140566. M.S. acknowledges support from the Royal Society and EU/FP7-ERC grant number 615929, and STFC via ST/L000679/1. K.T. was supported by CONICYT through the FONDECYT grant 3150473, and by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC12009, awarded to the Millennium Institute of Astrophysics, MAS. This work is based (in part) on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile as part of PESSTO, (the Public ESO Spectroscopic Survey for Transient Objects) ESO programme 188.D-3003/191.D-0935, and as part of programme 092.D-0586. This work utilises data from the 40-inch ESO Schmidt Telescope at the La Silla Observatory in Chile with the large area QUEST camera built at Yale University and Indiana University. The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council (proposal ID: PL12B05, P.I. R. Kotak). The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias (programme W/2013A/20). This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


I thank M. Debruyne for many years of technical support at the Elginfield Observatory where the observations were taken and also thank the student observers who took some of the observations. I am grateful to the Natural Sciences and Engineering Research Council of Canada for financial support.


example, Ganeshaiah Veena et al. ( 2021 ) have shown that massive haloes whose spin is perpendicular to the filament spine rotate on average faster (i.e. have higher spins) than haloes with spins along the filament spine. A similar effect has been pointed out by López et al. ( 2019 ), who have shown that the haloes which experienced the largest amount of spin growth are also more likely to have spin orientations perpendicular to the filaments surrounding them. 5.1 Net angular momentum growth of haloes Here, we follow the López et al. ( 2019 ) approach and define the net spin growth as the ratio between the present-day spin, , and the proto-halo spin, , in the initial conditions, which we take as the matter distribution at redshift z = 80. This definition is motivated by the TTT framework, in which the angular momentum at some time is the initial spin times a time-dependent growth factor (see equation 1 ). Thus, within the TTT approach, the net spin growth is basically the above growth factor. López et al. have shown that haloes with high ratios for their mass are more likely to have collapsed later and thus followed the TTT predictions for longer. This observation holds for the population as a whole, however not necessarily for individual haloes which could have a high ratio due to non-linear effects boosting their late-time spin growth. To keep the analysis simple, we follow the López et al. classification and for each narrow bin in mass we divide the halo population into three subsamples corresponding to the haloes with: highest, medium, and lowest net spin growth. We abbreviate these subsamples as H, M, and L, respectively. Each category corresponds to exactly a third of the haloes in each halo mass bin. This nomenclature is slightly different from the one used in López et al. ( 2019 ), where the same categories are referred as winner (W), median (M), and loser (L). Here, we decide to change the names of the samples (and the abbreviation of the one with the highest net spin growth, W→H) in order to better highlight their properties and the motivation of the classification. This analysis is illustrated in Fig. 8 , where the top panel show the net spin growth, , for individual haloes as a function of their mass. It shows that the ratio increases systematically with halo mass and illustrates why the H, M, and L subsamples need to be selected using narrow mass bins. The selection is further depicted in the bottom left-hand panel in Fig. 8 , which shows the distribution of net spin growth for a narrow mass bin. While most haloes have a narrow range in values, which for the given mass bin cluster around , the distribution has extended wings with a considerable fraction of haloes with ratios an order of magnitude higher or lower. The three subsamples, each containing a third of the haloes, are shown in the panel by the three shaded regions. Figure 8. Top panel: the halo net angular momentum growth (i.e. the present-day angular momentum divided by


also provide viable explanations. In any case, the transit of a more extended cloud of material, whether associated with a planet or not, might be more easily detectable. About 20 ks into the XMM-Newton observation (Fig. 2 ), the soft-band count rate drops by ≈35% for ≈800 s, i.e., two data points. This timescale is consistent with the occultation of a point-like source by the hypothesized planetary body of CVSO 30 b. However, the lack of an associated depression in the hard-band light curve makes an eclipse by a solid planetary disk unlikely. A temporary elevation in the absorption column by 10 21 cm −2 (e.g., caused by the transit of an extended planetary atmosphere) produces a count rate drop of 60% in the soft band with only a 10% drop in the hard band. Such a scenario would thus be compatible with the observation. By means of a Student’s t-test, we find that the mean of the two data points in question differs from that of the sample consisting of the two preceding and following points at the 2% significance level. As the ephemerides are uncertain, however, we count about ten similar opportunities during the flare where such an occultation may have happened and be interpreted in the same way. Therefore, the chance to obtain such a result by chance is about 20%, and we conclude that the data remain insufficient to produce a significant result. The hard-band light curve shows an apparent depression about 25 ks into the XMM-Newton observation (Fig. 2 ). This variation has no counterpart in the soft-band light curve, however, and might be more easily explained by the superposition of two flares or secondary heating rather than absorption or occultation of flaring material. 3.4. Planetary irradiation and mass loss Having measured the stellar X-ray flux, we now estimate the expected mass-loss rate of the candidate hot Jupiter CVSO 30 b to see whether such a configuration is physically plausible. A number of values have been proposed for the mass of CVSO 30 b (e.g., Barnes et al. 2013 ; Ciardi et al. 2015 , or Johns-Krull et al. 2016 ). These range from approximately one to seven Jovian masses. We assume here a stellar mass of 0.44 M ⊙ , a planetary mass of 3.9 M J , and a planetary radius of 1.61 R J . These values are based on those given in Table 1 . To remain on the conservative side regarding the planetary mass-loss rate, we increased the nominal mass estimate in Table 1 by its uncertainty and decreased the radius likewise. Both choices increase the assumed planetary density and inhibit mass loss. Kepler’s third law then demands a semimajor axis, a , of 0.00874 AU. The resulting Roche-lobe geometry is shown in Fig. 4 . The shape of the planetary candidate CVSO 30 b is determined by an equipotential surface, the level of which is given by the radius derived from transit modeling. The result clearly demonstrates the expected deviation from spherical geometry. Fig. 4. Roche lobe (solid line) and extent (blue shade) of planetary candidate CVSO


first mechanism does not necessarily lead to an immediate terminal SN explosion, it may explain the three-decade-long eruptive phase of SN 2000ch ( Pastorello et al. 2010 ). The second mechanism is promising as it may reproduce the sequence of events leading to SN 2009ip and its subsequent evolution (e.g. Graham et al. 2017 , and references therein). Alternatively, mass loss, driven by waves generated in the convective core during the late nuclear burnings, has also been proposed for moderate-mass ( M ZAMS ∼ 20 M ⊙ ) stars and for very massive stars at low-metallicity regime. This would explain the violent mass ejections observed in some SNe IIn from a decade to a few months prior to core-collapse ( Quataert Shiode 2012 ; Shiode Quataert 2014 ). The modern strategy of SN searches and the availability of big data archives have increased the discoveries of pre-SN outbursts, but the number of events is still of the order of a few tens, and is limited in volume. Future SN searches with big telescopes, in particular the Large Synoptic Survey Telescope ( LSST Science Collaboration 2009 ), will enormously increase the discovery rates, and will provide us with valuable datasets of light curves with coverage of many years. Appendix A: Optical photometry of SN 2018cnf Table A.1. Optical photometry of SN 2018cnf: Johnson-Bessell B , V (Vega mag), Sloan u , g , r , i , z and PanSTARRS y (AB mag). Notes. PS1 = 1.8 m Pan-STARRS Telescope + GPC1 camera (Haleakala, Hawaii Islands, USA); ATLAS = 0.5 m ATLAS-1 Telescope + STA-1600 CCD (Haleakala, Hawaii Islands, USA); ASAS-SN-5 = 0.16 m Payne-Gaposchkin Telescope + FLI ProLine PL230 CCD (Las Cumbres Observatory – South African Astronomical Observatory); ASAS-SN-3 = 0.16 m Paczyński Telescope + FLI ProLine PL230 CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); GTC = 10.4 m Gran Telescopio Canarias + OSIRIS (La Palma, Canary Islands, Spain); LT = 2.0 m Liverpool Telescope + IO:O (La Palma, Canary Islands, Spain); fl11 = 1.0 m Telescope (Dome 3) + Sinistro CCD (Las Cumbres Observatory – Siding Spring Observatory, Australia); fl16 = 1.0 m Telescope (Dome 5) + Sinistro CCD (Las Cumbres Observatory – South African Astronomical Observatory); fl03 = 1.0 m Telescope (Dome 4) + Sinistro CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); fl15 = 1.0 m Telescope (Dome 2) + Sinistro CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); fl06 = 1.0 m Telescope (Dome 7) + Sinistro CCD (Las Cumbres Observatory – South African Astronomical Observatory); fl12 = 1.0 m Telescope (Dome 8) + Sinistro CCD (Las Cumbres Observatory – Siding Spring Observatory, Australia); Copernico = 1.82 m Copernico Telescope + AFOSC (Mt. Ekar, Asiago Observatory, Italy); NTT = 3.58 m New Technology Telescope + EFOSC2 (ESO-La Silla, Chile); NOT = 2.56 m Nordic Optical telescope + ALFOSC (La Palma, Canary Islands, Spain). ( ‡ ) PanSTARRS w band converted to Sloan r ,


MVCD thanks his scholarship from FAPESP (process number 2014/18632-6). LSJ acknowledges the support of FAPESP (2012/00800-4) and CNPq to his work. This work was supported in part by the Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), Secretaría de Ciencia y Tecnología de la Universidad de Córdoba and Secretaría de Ciencia y Tecnologíca de la Universidad Nacional de San Juan. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. This work has made use of the computing facilities of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (grant 2009/54006-4) and the INCT-A.


We thank the referee for very helpful comments to improve the presentation of the paper. Y.P.L., H.L., and S.L. gratefully acknowledge the support by LANL/CSES and NASA/ATP. Simulations of this work were performed with LANL Institutional Computing resources. H.L. gratefully acknowledges useful discussions with S. Ida, R. Miranda, and R. Rafikov. Software: Astropy (Astropy Collaboration et al. 2013 ), LA-COMPASS (Li et al. 2005 , 2009a ), Matplotlib (Hunter 2007 ), Numpy (van der Walt et al. 2011 ), RADMC-3D (Dullemond et al. 2012 ).