O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization B-Observatory I-Observatory I-Observatory O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

the impact of model errors on the performance of the PW+EFC correction loop. We consider the same errors as for PW in Sect. 3.3 : influence function size, translation and rotation of the DM. We use the assumptions of Sect. 3.1 except for the amplitude aberrations. Here they are assumed to be at 10% rms error and their PSD distribution is almost flat so that we may approach the testbed environment of the THD2. The two probes for the PW technique are considered to be the bumps of the actuators 466 and 498. We fix the loop gain at g = 0.5. We simulate 578 actuators in the pupil to calculate the matrix G and we select 550 modes after the EFC SVD. As we study the correction of both amplitude and phase aberrations by a single DM, the correction is done within a half DH spreading from 2 λ / D to 13 λ / D on the horizontal axis and −13 λ / D to 13 λ / D on the vertical axis. After the tenth iteration, the contrast level C is computed as the 1 σ azimutal standard deviation of the intensity in the coronagraphic science image divided by the maximum of the non-coronagraphic point spread function (PSF). The results are shown in Fig. 6 . In each plot, the full line is the performance with no model error. Model errors can strongly impact both the WFS (Sect. 3.3 ) and the WFC. In order to reach a 10 −7 contrast level, the size of the influence function has to be known with less than 25% error, the translation of the modeled DM relative to the true one should be less than 0.5 pitch and the orientation of the modeled DM should be better than 1°. Fig. 6. RMS contrast as a function of the angular separation for different cases of model errors when implementing PW+EFC. Model errors simulated are the size of the influence function ( left ), a lateral translation of the DM ( center ), and a rotation of the DM ( right ). 5. Lab performances: wavefront sensing and control on the THD2 bench 5.1. Bench description We compared the two wavefront sensing and control techniques described above on a HCI testbed developed at LESIA (Observatoire de Paris). The optical testbed, called THD2 for trés haute dynamique , is located in an ISO7 pressurized clean room. It is described in detail in Baudoz et al. (2018a) and its layout is shown in Fig. 7 . In this paper, we used the following components: Fig. 7. Layout of the THD2 bench presenting different optical components. – An optical single mode fiber providing a monochromatic light source of wavelength 783.25 nm with a bandwidth less than 2 nm. The focal length of the first off-axis parabola (500 mm) flattens the Gaussian output of the fiber over the pupil diameter. The resulting amplitude aberration allows to reach a contrast level below 10 −7 at 1 λ / D . – An entrance pupil of 8.23 mm diameter. – 32 × 32 Boston-Micromachine (DM3) settled in pupil plane 2. – A FQPM located at the focal plane 3 in Fig. 7 . – A Lyot-stop of 8 mm diameter in the pupil plane 3 (corresponding to a Lyot filtering of 97.2%). In this Lyot plane, a


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This work is supported by the European Research Council under the SeismoSun Research Project No. 321141 (D.J.P., V.M.N., C.R.G.), the STFC grants ST/L000733/1 (V.M.N.) and ST/L000741/1 (P.J.A.S., L.F.), the Russian Foundation of Basic Research under grants 15-02-01089-a, 15-02-03835-a, 16-32-00315-mol-a (SAA), and by the Federal Agency for Scientific Organisations under project II.16.3.2 Non-stationary and wave processes in the solar atmosphere, CITIS No 01201281650 (S.A.A.). The data is used courtesy of the SDO/AIA team. This research has made use of NASA’s Astrophysics Data System.


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

part of the diagram to the bottom-right, stable nuclear burning of hydrogen is not possible and this region should be populated with other types of soft X-ray sources. Indeed, Fig. 5 shows that in late-type galaxies (M 83, M 51, M 101 and M 81), there is a distinct group of rare soft and luminous sources located above these line. These sources have temperatures of approximately several tens of eV and seem to clearly stand out in the populations of soft sources in these galaxies. When interpreting the results shown in Fig. 5 , one should bear in mind that it shows absorbed luminosities in the 0.3−2.0 keV band and that absorption and bolometric corrections increase roughly exponentially with decreasing color temperature, and therefore the softest sources are truly luminous. For this reason, we classify sources to the left of the red line in Fig. 5 as classical SSSs. We also include those sources that are located outside the stable nuclear burning boundary but whose error bars cross this boundary. In addition, we added to this list two sources in M 101 that are located outside but close to the stable nuclear burning boundary (the two sources in the upper right panel of Fig. 5 with kT ≳ 100 eV and L X ≳ 10 37 erg s −1 ). The catalog of SSSs is presented in Table C.1 , and their numbers in galaxies from our sample are listed in Table 2 . 6.2. Specific frequency of super-soft X-ray sources across morphological types From Fig. 5 , it is evident that SSSs are considerably more abundant in late-type galaxies than in early-type galaxies. However, for a statistically sound conclusion one needs to take into consideration the completeness limits of the various data sets. To this end we used the sensitivity limit for M 51 corrected for the difference in the absorption column density as described in Sect. 5.2 to select SSSs. In each galaxy, we selected sources to the left of the thick red line and above the dashed blue line in Fig. 5 . This selection is within the 20 counts flux limit (solid black line in Fig. 5 ) in all galaxies, except for M 83 where at the low temperature end the 20 counts limit for this galaxy is higher by a factor of about two. This may result in slight underestimation of the specific frequency of super-soft sources in late-type galaxies. In Centaurus A, we used different criteria for sources located in and outside the dust lanes (cf. dotted line in Fig. 5 ), although this does not change the final result. In order to estimate specific frequencies of SSSs, we group the data separately for early- and late-type galaxies. There are 29 super-soft sources in late-type galaxies (M 83, M 51, M 81, M 101), which, for the total stellar mass of 13.9 × 10 10 M ⊙ yield the specific frequency of In computing statistical errors we used Gehrels approximation ( Gehrels 1986 ). Counting lenticular and elliptical galaxies together (Centaurus A, NGC 3115, NGC 3379, NGC 4278, NGC 4697), we find seven SSSs for the total stellar mass of 28.3 × 10 10 M ⊙ ,


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We thank the referee for constructive comments that helped improve the manuscript. This research made use of the data obtained from HEASARC provided by the NASA’s Goddard Space Flight Center. Part of this work is based on archival data, software, or online services provided by the ASI Science Data Center (ASDC). This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASDC, Italy. Use of Hydra cluster at Indian Institute of Astrophysics is acknowledged.


O O O O O B-Person I-Person O O B-Organization B-Location I-Location O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O B-Person B-Person O B-Person O O O O O B-Person O B-Person O O O O B-Person O B-Person O O O O O O O O O O O B-Person O B-Person

ACKNOWLEDGEMENTS We are grateful to Miklós Slíz (software engineer, Graphisoft, Budapest, Hungary) for the development of the computer simulation software. We thank Tatiana Salnikova for her valuable comments on an earlier version of our manuscript. Author contributions . Substantial contributions to conception and design: JSB, AB and GH. Performing experiments and data acquisition: JSB and AB. Data analysis and interpretation: JSB and GH. Drafting the article or revising it critically for important intellectual content: JSB and GH.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

their subsequent dynamical mass-loss. This range represents an order of magnitude departure from the commonly adopted initial enriched fractions in MBL models. Figure 4. Required initial fraction of enriched stars as a function of the present cluster mass. Data points correspond to old () clusters born in high-pressure environments (), coloured by their gas pressure at birth. The grey area corresponds to the commonly assumed initial enriched fraction range of 5–10 per cent (Bastian Lardo 2018 ). The disparity between the commonly used range and our results indicates that either different polluters have to be considered (i.e. that produce greater amounts of ejected material per unit cluster mass, e.g. SMSs, see Gieles et al. 2018 ) or some yet-to-be-understood physical processes in stellar evolution and/or star formation lead to the large (>0.4) enriched fractions. 5 DISCUSSION We investigate whether dynamical mass-loss from GCs under realistic conditions satisfies the requirements from current multiple population models for reproducing the observed fractions of enriched stars in GCs. To do so, we use all surviving clusters present in the 25 present-day Milky Way mass galaxy simulations from the e-mosaics project (Kruijssen et al. 2018 ; Pfeffer et al. 2018 ). We determine the initial-to-present cluster mass ratios and study their dependence on cluster properties in Fig. 1 . We find a steep decrease of the amount of mass lost with present cluster mass. For intermediate mass (10 3 – M ⊙ ) clusters, we also find significant trends of increasing mass-loss towards smaller galactocentric radii, higher gas pressures at birth, and higher cluster metallicities. More massive clusters show no dependence between their median mass ratio and these quantities due to their small amount of mass lost. Assuming all dynamical mass-loss is in the form of unenriched stars, as posited by current multiple population models, we determine the enriched fraction of our stellar clusters. We study its dependence on cluster mass, metallicity, and galactocentric radius and compare it to observed enriched fractions from Milone et al. ( 2017 ) in Fig. 2 . These mirror the dependencies found for the amount of mass-loss and fall below the observed fractions by a factor of 2–20, with an opposite dependence on GC mass. These severe discrepancies rule out cluster mass-loss as the driving mechanism behind the high observed enriched fractions. In order to reconcile our results with observations, we consider what can be changed in models to match the observed enriched fractions. The addition of stellar evolution-driven expansion mass-loss, which is the preferred disruption mechanism suggested in the literature to solve the mass budget problem, predicts an even steeper trend between the numerical enriched fractions and galactocentric radius, in clear contrast with observations. These can only be reproduced if we consider an unphysically steep cluster mass-size relation, which


O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-CelestialObject O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O

least three distinct components, when stars are grouped by their spectral types and kinematics (e.g. Genzel et al. 2010 , section II). We choose to examine the limiting case of a Bahcall–Wolf cusp with γ = 0, which is analytically tractable and roughly matches the observed, slightly flatter density profile of the entire visible stellar population (e.g. Genzel et al. 2003 ; Bartko et al. 2010 ), as well as the observed distribution of diffuse light (e.g. Schödel et al. 2017 ), emanating from stars that could plausibly be old enough to be dynamically relaxed. Figure 3. The on-sky trajectories of the stars S1, S2, S9, and S13 over the time of simulated observations (solid and dashed lines), starting in the year 2000 and covering exactly one orbital period of S2 [approx. 16 yr, see Gillessen et al. ( 2017 ) for measurements of the orbital elements], overlaid on a snapshot of a sample realization of the distribution of background stars (shown as points) and their average light distribution (shown in colour). In the inner region of the nuclear cluster, stars move to good approximation like test particles in a point mass potential Φ( r ) = − GM 0 / r created by the central supermassive black hole, which has a canonical mass of M 0 ≈ 4 × 10 6 M ⊙ , and is located at a distance of R 0 ≈ 8 kpc from the Sun. To be in a stable configuration, these stars must be on bound, effectively Keplerian orbits, which can be defined by six orbital elements. The required distribution of the semi-major axes a = GM 0 /2ε of the background stars, to generate a realization of a Keplerian Bahcall–Wolf cusp, is (Schödel et al. 2003 ; Alexander 2005 ) The corresponding number density profile is . To ensure numerically that in our simulations the correct surface density profile is reproduced within the central square arcsecond, an upper cut-off of this distribution at a = 2 arcsec is sufficient. Any stars with larger semi-major axes are unlikely to be found very close to the central black hole, even in projection. We do not impose a strict lower cut-off, but exclude very few stars with a minimum (pericentre) distance r p = a (1 − e ) r t from the black hole, where r t is the approximate tidal radius of a typical observed B-type star in the Galactic Centre (e.g. Habibi et al. 2017 ): The required distributions of the eccentricity e , the inclination of the orbital plane i , the angle of the ascending node Ω, and the argument of pericentre ω, the specific forms of which encode the assumption of isotropy for the stellar velocities and positions, are the following: The time of pericentre has to be sampled uniformly over the duration of one orbital period, which, in turn, depends on the semi-major axis: The reference epoch t 0 = 2000 is arbitrary, but chosen to coincide roughly with the beginning of Galactic Centre observations using advanced high-resolution observing techniques, specifically adaptive optics imaging and integral field spectroscopy. Magnitudes are assigned to the


O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Model O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

much shorter or much longer than the Galactic orbital timescales, the distributions of element abundances at any orbital phase should not be affected by these subtleties. We therefore expect this to be inconsequential. Finally, we have assumed all along that there are measurable gradients in stellar abundances with respect to kinematics in the Galaxy or stellar population of interest. In the Milky Way, these are readily observed with existing spectroscopic surveys, and our measurements of individual element abundances will only become more numerous and precise in the coming years. 7.4. Extensions of Orbital Torus Imaging The implementation of Orbital Torus Imaging used in this paper falls into the category of classical (frequentist) statistics. However, the concepts introduced here also lead naturally to probabilistic generative model (Bayesian) versions of Orbital Torus Imaging. Bayesian implementations of this method at first look very different: instead of trying to minimize the dependence of abundance-ratio statistics on the conjugate angles (as we do here), Bayesian formulations would instead involve building a flexible forward model for the element-abundance distribution as a function of the actions alone. A non-intuitive aspect of this is that the angles would never explicitly appear in the probabilistic model. The Bayesian implementations would therefore look conceptually like extended DFs (Sanders Binney 2015 ), but while also varying the mass models, or forward models of the DF (e.g., Magorrian 2014 ), where element abundances or stellar labels are treated as additional invariants. In the implementation presented here, we use an abundance deviation that is based on a nearest-neighbor interpolation in action space (see Section 6 and Appendix ). That is a blunt tool; in principle, our results would improve if we instead explicitly modeled the abundance distribution moments as functions of the actions. One option for this modeling would be to use a generative, physical model for the star formation history of the Galaxy (or sample), including the products of nucleosynthesis and effects of chemical enrichment and stellar migration (similar to what is done in Sanders Binney 2015 ). Another option would be to use a flexible machine-learning method, such as a Gaussian process. We have parameterized the Milky Way mass model with a very simple, few-component mass model. Another option would be to instead parameterize the torus foliation of phase space directly. The representation of this foliation could be very general: any foliation of phase space with closed 3-tori is, in principle, allowed by dynamics. A direct reconstruction of the foliation could then be interpreted in terms of the force law, and hence the potential or mass model. That would be a more data-driven approach—with far fewer assumptions—than what has been executed here. We used the means of a set of hand-chosen abundance-ratio deviations as our invariants for the inferences.


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This scientific work makes use of the Murchison Radio-astronomy Observatory, operated by CSIRO. We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. Support for the operation of the MWA is provided by the Australian Government (NCRIS), under a contract to Curtin University administered by Astronomy Australia Limited. We acknowledge the Pawsey Supercomputing Centre, which is supported by the Western Australian and Australian Governments. A.S. would like to thank Atul Mohan (graduate student at the National Centre for Radio Astrophysics—Tata Institute of Fundamental Research (NCRA-TIFR), Pune, India) for thought-provoking discussions and providing timely, constructive criticisms. A.S. would also like to thank NCRA-TIFR for the computation and infrastructure support, and the Kishore Vaigyanik Protsahan Yojana scheme under the Department of Science and Technology, Government of India for the financial support provided during the period of this work. Facility: MWA. Software: Python ( http://www.python.org ), NumPy (van der Walt et al. 2011 ), Scipy (van der Walt et al. 2011 ), Matplotlib (Hunter 2007 ), Scikit-Learn (Pedregosa et al. 2012 ) and Scikit-Image (van der Walt et al. 2014 ).


O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O B-Model O O O B-Citation I-Citation O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

in a close-up of the Bridge region, shown in the right-hand panel, and the range of [Fe/H] becomes wider, as indicated by the two near horizontal arrows for the younger stars in the Bridge region. 3.2 Chemo-kinematical analysis To connect the observed stellar chemical properties to kinematic properties, we compute the vertical action and the mean orbital radius for our sample of stars using galpy in the fixed MWPotential2014 configuration (version 1.5; Bovy 2015 ). Although MWPotential2014 is time-independent and axisymmetric and cannot capture disequilibrium effects present in the real disc, it is none the less a good and useful approximation for the purpose of this work. Fig. 7 shows the distribution of [α/Fe] and [Fe/H] as a function of age and vertical action J z . The general trend is that J z is decreasing with age, with the older population being significantly hotter than the younger population. As also inferred from Fig. 6 , Fig. 7 clearly shows that the Bridge region starts appearing at age 13 Gyr and it spreads to lower [α/Fe] and to a wider range of [Fe/H] with decreasing age as seen in the triangle features at [α/Fe] 0.12 dex in the panels of 10 τ 12 Gyr. The lower panels of age lower than 10 Gyr show the dominant population of the low-[α/Fe] and kinematically colder thin disc stars. The lower panels also reveal a small population of kinematically hot, young stars, and as high [α/Fe] as the thick disc population in Fig. 6 . To understand their origin, we compare this population of stars with the thick disc stars (high [α/Fe] and old), and we discuss the results in Section 3.3 . Figure 7. The distribution of [α/Fe] and [Fe/H] coloured by the square root of the vertical action, , for the samples of stars within eight different age bins. The top four panels show [Fe/H]–[α/Fe] relationship for the older stars (10 τ 16 Gyr), and the lower four panels present those for the younger stars (τ 10 Gyr). There is a kinematically hot population of young high-[α/Fe] stars seen in the lower panels. To further examine whether or not there is a clear distinction between the high and metal-rich, low-[α/Fe] sequence, we select the high-metallicity ridge shown in the left-hand panel of Fig. 8 . The ridge is considered to represent the most advanced chemical evolution path of the stars born in the inner disc, R 6 kpc (e.g. Schönrich Binney 2009 ), and in fact, as shown in the left-hand panel of Fig. 9 , their mean orbital radius is always smallest among the same [α/Fe] population. For the stars within this high-metallicity ridge, we divided the samples according to their [α/Fe]. We measure the scale height using a Markov chain Monte Carlo approach, where we fit the J z distribution in each [α/Fe] bin with an isothermal profile, i.e. (Binney 2010 ; Binney McMillan 2011 ; Ting Rix 2019 ). We compute the scale height, , and its uncertainty in 13 selected bins using [α/Fe]. The results, shown in the right-hand panel of Fig. 8 , reveal a smooth decrease


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

obliquity and angular velocity (Rubincam 2000 ; Vokrouhlický Capek 2002 ; Scheeres 2007 ), and even causing the tumbling motion (Vokrouhlický et al. 2007 ). Combined with the effect of internal energy dissipation, the YORP effect may lead to a new asymptotic tumbling state of asteroids (Breiter Murawiecka 2015 ). In Section 2 , the main equations and the shape model in the simulation are introduced. Highly elongated and disk-like irregular shapes are generated as pseudo ‘Oumuamua. In Section 3 , the description of the torque curve and statistic results are shown. The origin of tumbling motion of the interstellar asteroid ‘Oumuamua is discussed. A comparison is made between the ISM collision effect and the YORP effect for distant asteroids in the solar system. 2. Simulation 2.1. Equations In this study, the kinetic approach is used to analyze the collisions between the interstellar asteroid and gas, as first proposed by Hoang et al. ( 2018 ). For a surface element dS , The mass of particles colliding with the surface within a time interval dt isHere I set v as the translational velocity vector of the asteroid relative to surrounding interstellar gas. Although the asteroid is rotating, the rotational velocity is too small compared to the translational velocity. Here, n is the outward unit normal vector of the surface element dS . Several assumptions are made in the following derivation: (1) mirror reflection of particles and no sputtering on the surface, (2) the strongly supersonic regime of the body, and (3) the convexity of the surface. After colliding with the surface element, gas particles are reflected, with the velocity component perpendicular to the surface reversed. In this process, the momentum transferred from the particles to the asteroid is is the reflection coefficient, with γ r = 1 representing a mirror reflection. Plugging ( 6 ) into ( 7 ), we can obtain In this paper γ r is set to 1 because of the assumption (1). Note that the process of “sputtering” also produces a torque, which is calculated to be smaller by one order of magnitude than the ISM collision torque, which is shown in Appendix B . We should take caution in further research when neglecting this “sputtering” effect since the variation by just one order of magnitude could be removed by the uncertainty of the parameters. Assumption (2) discards the effect of the gas particles’ thermal motion. Let us consider interstellar gas in the warm phase with the temperature of 5000 K. Applying Maxwell’s velocity distribution, the averaged speed of the gas is , less than the assumed speed of the asteroid. The asteroid can be considered to be supersonic. In the hot region (e.g., above 20,000 K), the above equations are certainly invalid. Assumption (3) avoids the shadowing and secondary collisions of particles. But we could expect Equation ( 8 ) is still valid for moderately concave shapes. According to Golubov et al. ( 2016 ), for the YORP effect, the formulas proposed under the


O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O

that the ejected metals are preferentially reincorporated back into galaxies from the circumgalactic medium (CGM). Li et al. ( 2010 ) essentially adopt this type of idea in their SAM by adopting a route to recycle most of the metals produced in newly formed stars through the hot phase. In their model, 95% of newly produced metals are deposited directly into the hot gas for galaxies with a dark-matter halo virial mass less than 5 × 10 10 M ⊙ . The metals then eventually fall back to the galaxy and fuel the next episode of star formation, resulting in a shallow metallicity−luminosity relation. Furthermore, the ejective feedback has other uncertainties that can affect predictions for low-mass galaxies. Henriques et al. ( 2013 , 2015 ) showed that when the outflowed mass has a long delay before being reincorporated into low-mass halos, the model can match the evolution of the field galaxy luminosity function remarkably well. Hou et al. ( 2016 ) demonstrated a model where the mass-loading factor decreases with time, as suggested by a recent hydrodynamic simulation (Muratov et al. 2015 ). Together with saturated outflows at the low-mass end and a strong local reionization, which are effectively similar to our extended model, the model (named “EvoFb-LR” in Hou et al. 2016 ) can achieve a reasonable fit to both the SMF and MZR of MW dwarf galaxies. While these prescriptions for outflow and reincorporation have been tested by recent hydrodynamical simulations, the actual behavior of the outflow is still a matter of active debate (e.g., Anglés-Alcázar et al. 2016 ; Christensen et al. 2016 ). We note the important caveat that tidal effects from the MW-mass stellar disk can reduce the number of surviving subhalos (e.g., Zolotov et al. 2012 ; Wetzel et al. 2016 ; Zhu et al. 2016 ), which can affect how the ejective model fits the stellar mass function. We stress, however, that the MZR is independent from the satellite abundance. Therefore, the requirement for weaker outflow implied by this relation is robust, even if a fraction of subhalos are destroyed by the MW disk. Still, it is clear that there is some degeneracy between the preventive feedback and the destruction of subhalos. To break this degeneracy, detailed modeling of these processes and quantitative inferences from dwarf galaxies both within and outside the MW will be essential. Although the model presented here with the addition of preventive feedback can match the data, the physical mechanisms that produce the prevention remain unclear. We have taken an extreme model where baryons are prevented from collapsing into low-mass halos, but the assumption has not been fully tested against observation. At the current stage, other alternative hypotheses, where baryons still make it into the galaxy but are prevented from forming stars by large turbulent pressure or photoheating (e.g., Forbes et al. 2016 ), can produce similar effects in galaxy formation models. The data constraints adopted in this


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low-Mg accreted population is Si-poor relative to the high-Mg population—but this trend starts to blur at metallicities below −1.5. In Figure 9 , we show the APOGEE-2 Jhelum giant and the GES candidates as well as both in situ and accreted GCs (Horta et al. 2020 ), along with all of the 1495 Jhelum pointing stars (light gray points). As seen in Figure 9 , the APOGEE-2 Jhelum giant star falls into the high-Si and high-Mg region that both accreted and in situ GCs occupy, as well as accreted dwarf satellite stars (e.g., Sculptor and Carina) and Milky Way field stars. Thus, based on currently available abundances, we cannot narrow down the origin of the Jhelum stream based on chemistry alone. Figure 9. The [Si/Fe] vs. [Mg/Fe] distributions for all Jhelum pointing stars (small gray points), the APOGEE-2 Jhelum RGB star (blue triangle), high- e metal-rich stars (cyan circles), high- e metal-rich stars with [Al/Fe] 0 (magenta circles), accreted MW GCs (orange circles) and in situ MW disk GCs (gray circles). The accreted GCs (orange) are associated with the GES merger and the H99 streams (see Horta et al. 2020 for details on the accreted/in situ classifications for the GCs). 5. Summary In this study, we looked in detail at stars in the direction of the Jhelum stellar stream, taken from the APOGEE-2 database. By isolating stars that have the proper-motion signal detected for Jhelum stream stars by Bonaca et al. ( 2019 ) and Shipp et al. ( 2019 ) and then fitting this proper-motion-selected sample to an isochrone for a 12 Gyr population with [Fe/H] = −1.4 and [ α /Fe] = 0.4, we identified one member of the Jhelum stellar stream. This Jhelum star is a bright red giant, near the tip of the RGB for the Jhelum population. By looking at the azimuthal and radial components of motion for stars in the six APOGEE-2 fields targeting the Jhelum stream, we identified a group of metal-rich ([Fe/H] > −1.7), high-eccentricity ( e > 0.8) stars that are likely to be part of the debris from the GES merger. We divided this GES-sample into high-Al and low-Al groups to help distinguish stars likely belonging to merger debris, as stars from accreted populations tend to have low [Al/Fe] values. While the errors for the distances to the Jhelum giants are large, and these propagate into derived quantities like energy and angular momentum, we compare the total energy as a function of angular momentum ( L z ) for the Jhelum giants to the GES giants and find that, while both populations have similar angular momenta (both are prograde), the Jhelum giants tend to have higher total energies than the GES giants. The orbit for the APOGEE-2 Jhelum giant and the APOGEE-2 GES giants were integrated forward for 5 Gyr and compared, and their respective orbits do not seem consistent with stars derived from same population. In particular, the orbits for the GES giants are highly radial and tend to stay more confined to the plane than does Jhelum. Unfortunately, at the low metallicities


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

high L 2–10 and powerful outflows. Assuming the material scattering X-rays has an outflowing component, we can also calculate its maximum kinetic energy power using the n e estimates of the warm scattering region. We assume the same velocities v ≈ 3000 km s −1 seen in Alexandroff et al. ( 2018 ) launched at scale height h = 10 pc: which makes up a small fraction of the bolometric output. Thus, the phase of gas responsible for producing the scattered X-rays is not an energetically important component of the quasar ouput. 4.4 Comparing with other observations While there are X-ray studies of highly obscured quasars, most have been limited to low-redshift samples. Another class of reddened quasars are the HotDOGs, which have properties similar to those of ERQs in terms of spectral energy distribution, luminosity, and redshift (Eisenhardt et al. 2012 ; Assef et al. 2015 ). Despite these similarities, there are some interesting differences stemming from somewhat different selection methods. One such difference is that HotDOGs are well below the Stern ( 2015 ) and Chen et al. ( 2017 ) relationships (Ricci et al. 2017 ; Vito et al. 2018 ), while also showing Compton-thick obscurations (Piconcelli et al. 2015 ), in contrast to ERQs explored in Goulding et al. ( 2018 ) and in this paper. We compare their L 6 μm – L 2–10 properties in Fig. 5 . A recent NuSTAR observation of a z = 2.298 HotDOG (W1835+4355) showed Compton-thick obscuration, N H ≈ 0.9 × 10 24 cm −2 , and absorption-corrected luminosity of L 2–10 = 1.6 × 10 45 erg s −1 (Zappacosta et al. 2018 ) similar to those of SDSSJ1652 presented here. Compared to other HotDOGs, this target also exhibited higher X-ray luminosity, nearly consistent with the Stern ( 2015 ) and Chen et al. ( 2017 ) relations, shown in Fig. 5 . In contrast to SDSSJ1652, their target was modelled with θ i = 70° and a larger model-dependent . This suggest remarkable similarities between ERQs and HotDOGs with the only differences in the obscuration properties: θ i and f sc . This indicates a variety in HotDOG properties with some that have overlapping L 6 μm – L 2–10 properties to ERQs. 5 CONCLUSION We report on deep ∼ 130-ks XMM–Newton and ∼ 218-ks NuSTAR observations of SDSSJ1652, an obscured, extremely red quasar at z = 2.94. We characterize the intrinsic X-ray properties and obscuration geometry using XMM–Newton , which is sensitive to the absorbing column, and NuSTAR , which probes the intrinsically unobscured X-rays. We determine the accretion luminosity and the obscuration properties of SDSSJ1652 to provide verification for severely photon-limited studies of the high-redshift, obscured quasar population. We extracted spectra from the XMM–Newton MOS and PN and the NuSTAR FPMA detectors. Unfortunately, we could only place a 3 σ upper limit for the NuSTAR FPMB. We fit 0.5–10 keV XMM–Newton and 6–79 keV NuSTAR spectra with a physically motivated MYTorus model that models the zeroth-order continuum reprocessing due to the


O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person I-Person O O O O O O O O O O O O O B-Grant O O O B-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant O O O O O O O O B-Telescope O B-URL O O B-Organization O O O O O O O O O B-Organization O O B-Organization O B-Location O O O O O O B-Database I-Database O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Organization O B-Organization O O O B-Survey O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization I-Organization B-Telescope B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization

The authors thank Natalya Lyskova and Florian Sarron for sharing data and providing useful insight during the preparation of this manuscript, as well as Andrea Biviano, Clotilde Laigle, and Miguel A. Aragón-Calvo for fruitful discussions. This research has been supported by the funding for the ByoPiC project from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement ERC-2015-AdG 695561. This work makes use of observations obtained with Planck ( http://www.esa.int/Planck ), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada. It also made use of the SZ-Cluster Database ( http://szcluster-db.ias.u-psud.fr ) operated by the Integrated Data and Operation Centre (IDOC) at the Institut de Astrophysique Spatiale (IAS) under contract with CNES and CNRS. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.


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S.A. dedicates this work to the memory of his father Duilio. We thank Adam Mantz for discussion on his papers.


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The SAMI Galaxy Survey is based on observations made at the Anglo-Australian Telescope. The Sydney-AAO Multi-object Integral field spectrograph (SAMI) was developed jointly by the University of Sydney and the Australian Astronomical Observatory. The SAMI input catalog is based on data taken from the Sloan Digital Sky Survey, the GAMA Survey and the VST ATLAS Survey. The SAMI Galaxy Survey is funded by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020, and other participating institutions. The SAMI Galaxy Survey website is http://sami-survey.org/ . S.O. thanks D.W.L. for his continued support. SKY acknowledges support from the Korean National Research Foundation (NRF-2014R1A2A1A01003730). S.M.C. acknowledges the support of an Australian Research Council Future Fellowship (FT100100457). J.T.A. acknowledges the award of a SIEF John Stocker Fellowship. M.S.O. acknowledges the funding support from the Australian Research Council through a Future Fellowship Fellowship (FT140100255). JvdS is funded under Bland-Hawthorn’s ARC Laureate Fellowship (FL140100278). S.B. acknowledges the funding support from the Australian Research Council through a Future Fellowship (FT140101166). Mahajan acknowledges the funding support from the INSPIRE Faculty award (DST/INSPIRE/04/2015/002311) and the Fast track fellowship (SB/FTP/PS-054/2013) from the Department of Science and Technology (DST) and the Science Education and Research Board (SERB), respectively. NS acknowledges support of a University of Sydney Postdoctoral Research Fellowship. H.J. acknowledges support from the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2013R1A6A3A04064993). Support for A.M.M. is provided by NASA through Hubble Fellowship grant # HST -HF2-51377 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This work has been supported by the Yonsei University Future-leading Research Initiative of 2015 (RMS2 2015-22-0064).


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

is inconsistent with a single Rayleigh distribution of inclinations ( i ). Its vertical distribution was better reproduced with two dynamical populations with typical inclination dispersions ( i rms ) of 1° and 9°. Such a scenario is analogous to the classical Kuiper belt, which also has a bimodal inclination distribution (e.g. Brown 2001 ). Similarly, ALMA observations of AU Mic marginally resolved its vertical extent (Daley et al. 2019 ) and constrained as well the distribution of inclinations to i rms ∼ 3°. For moderately inclined and narrow discs, the vertical extent can be constrained by comparing the surface brightness as a function of azimuth if the resolution is comparable or smaller than the disc width (Marino et al. 2016 ). This is because the non-zero vertical thickness of a disc widens the surface brightness distribution near the minor axis, hence reducing slightly its surface brightness compared to a flat disc. This principle has helped to marginally constrain the vertical thickness of HR 4796’s debris ring (Kennedy et al. 2018 ), finding i rms ∼ 3°. Similarly, it is also possible to determine the height of a wide disc if it contains narrow features such as a gap, as done by Marino et al. ( 2019 ) for HD 92945’s disc, finding i rms ∼ 4°. Note that the latter case is very similar to modelling done in protoplanetary discs with gaps to measure the degree of dust settling (e.g. Pinte et al. 2016 ). The width of debris discs provides as well a direct upper limit on the eccentricity levels. This is because for a uniform distribution of longitudes of pericentres, the difference between pericentre and apocentre distance must be equal or smaller than the disc width. This is particularly interesting when applied to narrow debris discs interacting with an eccentric planet since the final width of the disc strongly depends on the forced eccentricity induced by the planet (e.g. Pearce Wyatt 2014 ). Kennedy ( 2020 ) used these arguments to show that the narrowness of the debris disc around Fomalhaut (MacGregor et al. 2017 ) and HD 202628 (Faramaz et al. 2019 ) is inconsistent with the standard secular evolution theory. The dispersion of eccentricities in those discs, constrained by the disc widths, is smaller than expected under the presence of an eccentric planet. This inconsistency could be due to planetesimals being born on eccentric and aligned orbits or their relative velocities being damped reducing the proper eccentricities (e.g. through collisions; Nesvold et al. 2013 ). The multiwavelength analysis of disc sizes can also constrain stirring levels. By combining far-infrared (FIR) and mm spatial information with collisional evolution models, Geiler et al. ( 2019 ) found that the FIR emission of HR8799’s debris disc cannot be reproduced by a dynamically cold wide belt that best matches the mm data. They concluded that to fit both the large extension of the FIR emission and high mm flux, their model required the presence of two


O O O O O B-Wavelength O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O

between W (CH) and A v than those between W (OH), W (CO) and A v . To better examine these relationships, we adopt the usual definition of “ X -factor”,where N H2 is the column density of H 2 and W is the integrated intensity of the molecular tracers CH, OH, CO. We plot the correlation of “ X -factor” of CH, OH and CO versus the visual extinction in Figure 8 . When the visual extinction A v is in the range between 0.8 and 2.1 mag, the X CH -factor is almost a constant (1.0 ± 0.06) × 10 22 cm −2 K −1 km −1 s. The dispersion of CH X -factor is visibly less than those of OH and CO at 0.8 ≤ A v ≤ 2.1 mag. CH appears to be a better tracer of molecular gas than CO and OH in the transition zone (0.8 ≤ A v ≤ 2.1 mag). Where extinction drops below 1 mag in TBR, the integrated intensities W of the three molecules lie above the overall fitting lines, indicating a stronger intensity of these spectra, which is likely the result of C-shock in the TBR-O (Section 5 ). Figure 8. Correlation plot of the integrated intensity W of CH, OH and CO vs. the visual extinction A v , and the correlation of the “ X -factor” of CH, OH and CO vs. the visual extinction A v . “ r ” means Pearson correlation coefficient. 5. CH ABUNDANCE AND C-SHOCK MODEL We have calculated the column density of CH in Section 3.2 . The column density of CH across the TBR is shown in Figure 7 . Mattila ( 1986 ) found a good correlation between the CH column density and visual extinction for diffuse, dark molecular cloud N (CH) = 3.4 × 10 13 ( A v − 03) cm −2 as the dashed line shows in Figure 7 . This correlation is reasonable considering the CH formation threshold, which requires substantial H 2 (Black Dalgarno 1973 ). The derived column density of CH below 1 mag extinction (blue shade in Figure 7 ) in TBR obviously lies above the typical value observed by Mattila ( 1986 ). Furthermore, considering the correction factor for excitation temperature and optical depth (as discussed in Section 3.2 ), the actual column density of CH in TBR-O is likely to be even larger by an additional factor of 3. The true CH column density in TBR-O can thus be one order of magnitude higher than the simple extension from the X -factor for higher extinctions. We compared the CH column density with the prediction of C-shock models. Flower Pineau des Forets ( 1998 ) made a prediction that CH column density would increase from 10 13 to 10 14 cm −2 when extinction increases from 0.1 to 1 mag at a C-shock front, which matches exactly the measured values here. Xu et al. ( 2016 ) also found an overabundance of OH below 1 mag extinction (by a factor of 80). The overabundance of CH and OH suggests that there may be an additional channel of CH and OH production, possibly due to the shock (e.g., Draine Katz 1986a ) produced by the colliding streams (Xu et al. 2016 , Figure 4). When shock waves propagate through the molecular ISM, the gas is compressed, heated, and accelerated. CH can be produced during CH + synthesis


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P.G. and K.H. acknowledge NSF grants AST-1010039 and AST-1412648. This work was also supported by NASA grant HST -GO-12055. K.H. was supported by a NSF Graduate Research Fellowship. D.R.W. is supported by NASA through Hubble Fellowship grant HST-HF-51331.01 awarded by the Space Telescope Science Institute. We thank Bernhard Aringer, Zachary Jennings, and Alex Rudy for helpful conversations. We appreciate the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most grateful to have had the opportunity to conduct observations from this mountain.


O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant B-Person O B-Person O O O O B-Organization I-Organization I-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization B-Organization B-Person O O O B-Organization B-Grant I-Grant I-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Fellowship B-Person O O O O B-Location I-Location B-Grant O O B-Organization O O B-Grant B-Person O O O O B-Organization I-Organization O B-Location O O B-Grant B-Person O O O O B-Location O B-Organization O O B-Grant O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization O B-Grant O B-Organization O O O B-Grant I-Grant I-Grant I-Grant O O B-Grant O B-Grant I-Grant B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant O O O O O O O O O O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O O O B-Grant B-Person O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O O B-Grant O B-Organization O B-Grant O B-Grant B-Person O B-Person O O O O B-Organization I-Organization I-Organization O O B-Grant O B-Grant O O O O O O O O B-Person I-Person O O B-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location O O O B-Survey O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Observatory O O B-Grant O O B-Person I-Person O B-Person I-Person I-Person O O O O O O B-Person I-Person O O O O O B-CelestialObject I-CelestialObject O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O B-Location I-Location O O O O O O B-Location O O O O O O O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive B-Archive O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Archive I-Archive I-Archive I-Archive B-Archive

This research was conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. BPS and IRS acknowledge support from the Australian Research Council Laureate Fellowship Grant FL0992131. ST acknowledges support by TRR33 ‘The Dark Universe’ of the German Research Foundation (DFG). DJH acknowledges support from NASA theory grant NNX14AB41G. KM is supported by a Marie Curie Intra-European Fellowship, within the 7th European Community Framework Programme (FP7). NER acknowledges the support from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 267251 ‘Astronomy Fellowships in Italy’ (AstroFIt). MF acknowledges support from the European Union FP7 programme through ERC grant number 320360. MS acknowledges support from the Royal Society and EU/FP7-ERC grant no. [615929]. AGY is supported by the EU/FP7 via ERC grant no. 307260, the Quantum Universe I-Core programme by the Israeli Committee for planning and budgeting and the ISF, by Minerva and ISF grants, by the Weizmann-UK ‘making connections’ programme, and by Kimmel and ARCHES awards. AMG acknowledges financial support by the Spanish Ministerio de Economía y Competitividad (MINECO) grant ESP2013-41268-R. The research leading to these results has received funding from the European Union's Seventh Framework Programme [FP7/2007-2013] under grant agreement no. 264895. SJS 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. SWJ and YC acknowledge support from the National Science Foundation through grants AST-0847157 and PHY-1263280, respectively. Part of this research was conducted while John Hillier was a Distinguished Visitor at the Research School of Astronomy and Astrophysics at the Australian National University. This research is based 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 ID 188.D-3003. We thank Stefano Benetti and Massimo Della Valle for helpful comments. We also thank Ben Shappee for kindly providing spectra of SN 2011fe. We thank the referee Jeff Silverman for a careful review of this work with many insightful comments that greatly improved the paper. 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. We 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. This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration. 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. This research has also made use of NASA's Astrophysics Data System (ADS).


B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Model I-Model

et al. ( 1996 ) and Giri Chakrabarti ( 2013 ): the cooling rate is ∝ρ 2 T β , where β > 0 is the cooling index. For β = 0.5, the process is bremsstrahlung. In order to ensure the formation of a cold Keplerian disc, we must use higher β in order for the cooling time-scale to be reduced compared with the infall time-scale. Thus we increase cooling gradually inside the would-be Keplerian component. When the region with Keplerian distribution becomes optically thick, the index is raised to 0.6 as used in earlier simulations. This saves the prohibitive time required for Monte Carlo simulations, in order that normal bremsstrahlung radiation may be emitted as blackbody radiation in the optically thick region. Giri et al. ( 2015 ) found that the result is insensitive to the exact cooling process, since blackbody cooling also produced the expected standard disc in the equatorial plane in their simulation. In Fig. 2 (a) and (b), we show the density, velocity and specific angular momentum distribution at t = 19.8 s just before viscosity is turned on. As can be seen clearly, a standing shock at a distance of about 40 r g is formed, with a sudden rise of density and pressure. The colour (online) scale is on the right. The outflow starts in the region between the centrifugal barrier and the funnel wall (Molteni et al. 1996 ). Specific angular momentum remains at its initial value of 1.7. Figure 2. (a) Density, velocity and (b) specific angular momentum distribution at t = 19.8 s just before viscosity is turned on ( t 0 in Fig. 1 a). Here, a standing shock has formed at a distance of about 40 r g , with a sudden rise of density and pressure, and outflow has started between the centrifugal barrier and funnel wall region. Density ρ is chosen to be unity in dimensionless units at the injection radius. In (b), the specific angular momentum distribution is represented by the solid curve for comparison with the Keplerian distribution (dot–dashed curve). At t 0 , the specific angular momentum remains at its initial injected value of 1.7. After viscosity is turned on, as matter accretes, initially the viscous stress near the inner edge remains close to zero. As α increases with time, −α P becomes significant close to the inner edge, due to high pressure, and angular momentum transport starts efficiently. On the equatorial plane, this result is similar to what was seen in Chakrabarti Molteni ( 1995 ). However, at the outer edge, though α itself is high, pressure being very low, the stress is not high enough and thus angular momentum transport remains slower. 4.1 Results using viscosity description of Case I In this case, we use . We chose α 0 = 0.12, which is above the critical value of 0.074 required for a Keplerian disc to form with the used injected parameters. In Fig. 3 (a)–(b), we show the distributions at t = 41.58 s of (a) the density and velocity vector and (b) the angular momentum distribution (solid). To compare, we also plot the Keplerian distribution


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

on a relatively short timescale. The surface velocity is divided by a factor of 10 in 200 Myr, until the star spins down enough to enter the unsaturated-dynamo regime and further decreases by another factor of 10 for the following 4.3 Gyr. For clusters older than the Hyades (beyond 700 Myr), the observed distributions of rotation periods strongly narrow. By the time the models reach 1 Gyr, the torque has become much less efficient and the angular velocity profile of the fast rotator is similar to that of the median and slow rotators. The three models later follow the same evolution, which is dictated by the meridional circulation and shear turbulence until the age of the Sun. The surface angular velocity and the total angular momentum content of the slow, medium, and fast rotators are similar beyond 1 Gyr. The angular velocity profiles also share a similar shape and evolution in all three cases. Fig. 4 Angular momentum fluxes carried by meridional circulation (dashed red), shear (dotted blue), and the total flux (solid black) in the fast and slowly rotating models ( top and bottom , respectively). Hatched areas in all plots indicate the convective regions. 4.3. Transport of AM Here we examine the processes that drive the internal transport of AM in our reference models. To do so, we followed the diagnostic procedure proposed by Decressin et al. (2009) , which relies on the analysis of the AM fluxes associated with each transport process that is accounted for. The transport of angular momentum is mainly driven by the meridional circulation as long as the star is rotating relatively fast (above the saturation value), as shown in the left panels of Fig. 4 , and this independently of the initial velocity. After the ZAMS (60 Myr), in all cases meridional circulation weakens because the star does not contract any longer and the surface velocity has already decreased. Angular velocity gradient increases at the base of the convective envelope, leading to a predominance of the shear turbulence over the meridional circulation in this region. For the slower rotators, the shear turbulence takes over the transport of AM in the outer radiative zone below the envelope and efficiently extracts (acting along the angular velocity gradient) the angular momentum, ensuring a continuous decrease of the surface angular velocity from the ZAMS until the age of the Hyades (700 Myr; see lower panel in Fig. 4 ). On the other hand, in the fast rotator, the meridional circulation is very efficient as long as the star contracts (2 orders of magnitude larger than in the slow rotator) and efficiently couples the interior to the convective envelope up to the ZAMS. Beyond this age, its efficiency decreases rapidly, and the shear generated by the torque dominates below the convective envelope, although it is not sufficient to maintain an efficient transfer of AM from the core to the envelope. The overall transport of AM by these processes tends to become less efficient as the


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

that BSF galaxies both in the cocoon and in the supercluster have significantly lower stellar masses than galaxies from other populations. This is what could be expected from galaxies which are still forming their stellar content and increasing their stellar mass. Small differences in stellar masses of galaxies from other populations are not statistically significant and we can conclude that galaxies from these populations in our sample have statistically similar stellar masses, in a range of M * ≈ 3 × 10 9 h −1 M ⊙ − 3 × 10 11 h −1 M ⊙ . Figure 10 (upper left panel) shows that BSF galaxies have the highest values of the concentration index, C , and VO galaxies have the lowest C values among our galaxy populations, and they are similar in the supercluster and in the cocoon. In this respect, RQ galaxies differ from others. In the supercluster they have lower values of C than in the cocoon, these differences are statistically significant at a very high level, with a p -value of p ≤ 0.01 (Table 4 ). The distribution of probabilities for galaxies to be of late-type, P late , are plotted in Fig. 10 (upper right panel). This probability is the highest for BSF galaxies and for RQ galaxies in the cocoon, and the lowest for VO galaxies (in both environments). However, KS test shows that these differences are not statistically significant (Table 4 ). BSF galaxies also have the lowest values of stellar velocity dispersions and VO galaxies have the highest (Fig. 10 , lower left panel). This agrees with earlier results which have shown that galaxies with young stellar populations have lower stellar velocity dispersions than galaxies with old stellar populations ( Shankar et al. 2009 ; Bezanson et al. 2012 ; Einasto et al. 2018b ). The stellar velocity dispersions of RQ galaxies are similar in the supercluster and in the cocoon, indicating, in accordance with the results for P late , that the overall morphological type of RQ and RSF galaxies is the same in both environments. As the stellar mass distribution for VO, RQ, and RSF samples are similar, this suggests that VO galaxies are mainly non-rotating early-type galaxies, but RQ and RSF galaxies (and BSF galaxies) may have also a significant rotation component corresponding to the dynamics of disky galaxies. The metallicities Z of BSF, RQ, and RSF galaxies (Fig. 10 , lower right panel) are statistically similar in both environments, BSF and RQ galaxies having the lowest metallicity values. VO galaxies in the supercluster have higher metallicities than galaxies from other populations in our study. In the cocoon, they are similar to the metallicities for galaxies from other populations. We additionally checked whether the galaxy content of long filaments with length ≥20 h −1 Mpc depends on the distance of filament member galaxies from the supercluster centre, D c . The values of D n (4000) index versus D c for galaxies in long filaments are plotted in Fig. 11 . In this figure, background colours show the


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properties across luminosity and redshift indicates very similar underlying physical mechanisms that can be understood in terms of Eigenvector 1 ( Boroson Green 1992 ; Francis et al. 1992 ) where the Eddington ratio drives the relative strength of the lines, and orientation effects influences the observed kinematics of the lines ( Shen Ho 2014 ). The specific local physical conditions that regulate the accretion rate then account for the majority of the inter-quasar variation. In this section, we will investigate whether the targets selected are simply scaled-up version of average quasars, or remarkable in some sense. 6.1. Comparison to global population The QSOs selected for this study lie amongst the brightest values of compared to the spectroscopically confirmed SDSS QSOs ( Shen et al. 2011 ), which are uniformly selected to 90 percent completeness ( Richards et al. 2002a ; Vanden Berk et al. 2005 ). It is clear that the sample presented here represents some of the brightest quasars existing between redshift 1 and 2. It is therefore potentially a biased subset of the global quasar population. Quasars have previously been shown to exhibit a high degree of homogeneity over many orders of magnitude ( Dietrich et al. 2002 ), but this is only true for quasars resembling average quasars and not exotic sub-types. To ensure that the targets selected for this sample are not outliers in color, the spectrophotometric colors are compared to those of the quasar population presented in Pâris et al. (2014) 3 . We show the comparison in Fig. . From the magnitudes, we first confirm that the quasars selected here are among the intrinsically brightest visible in -band with a 2.7 sigma magnitude distance from the mean absolute -band magnitude, normalized at redshift 2, of the full SDSS quasar catalog for DR10. Despite their luminosities the colors are representative of the subset fulfilling the selection criteria. As a consistency check, the composite generated in this work is used to fit for the dust content of quasars with varying degree of extinction and consistent results were obtained as compared with composites generated from other subsamples of the parent population. For a comparison between SDSS and quasars detected in GALEX, UKIDSS, WISE, 2MASS and Spitzer , see Krawczyk et al. (2013) . Fig. 6 Quasar color, , as a function of redshift, . The full quasar sample from SDSS DR10 ( Pâris et al. 2014 ) is shown in gray color. Bounding contours show the 0.5, 1, 1.5, 2 contours of the density of points. The olive points are individual quasars from the SDSS sample which satisfy . Overplotted in pink are the quasars contributing to the composite presented here. The quasar colors have been marginalized over in the right side where the tall pink lines are at the position of the composite quasars and the olive shaded area is the kernel density estimation of the distribution of quasars fulfilling the selection criteria. The gray-shaded area is the projection of the