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ACKNOWLEDGEMENTS The authors thank Frank van den Bosch for insightful discussions and Shun Saito for helping us estimate the fraction of satellite galaxies in our sample. We also thank Felipe Ardilla and Christopher Bradshaw for useful comments. SH thanks Feng-Shan Liu for sharing the μ ⋆ profile of the z ∼ 1 BCG from his work. This material is based upon work supported by the National Science Foundation under grant no. 1714610. The HSC collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by National Astronomical Observatory of Japan (NAOJ), Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, High Energy Accelerator Research Organization (KEK), Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from Japanese Cabinet Office, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University. Funding for SDSS-III has been provided by Alfred P. Sloan Foundation, the Participating Institutions, National Science Foundation, and U.S. Department of Energy. The SDSS-III website is http://www.sdss3.org . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration, including University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, University of Florida, the French Participation Group, the German Participation Group, 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, 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. The Pan-STARRS1 surveys (PS1) have been made possible through contributions of Institute for Astronomy; University of Hawaii; the Pan-STARRS Project Office; the Max-Planck Society and its participating institutes: the Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute for Extraterrestrial Physics, Garching; Johns Hopkins University; Durham University; University of Edinburgh; Queen’s University Belfast; Harvard-Smithsonian Center for Astrophysics; Las Cumbres Observatory Global Telescope Network Incorporated; National Central University of Taiwan; Space Telescope Science Institute; National Aeronautics and Space Administration under grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate; National Science Foundation under grant no. AST-1238877; University of Maryland, and Eotvos Lorand University. This paper makes use of software developed for the LSST. We thank the LSST project for making their code available as free software at http://dm.lsstcorp.org . This research was supported in part by National Science Foundation under grant no. NSF PHY11-25915 and grant no. NSF PHY17-48958 This research made use of STSCI_PYTHON , a general astronomical data analysis infrastructure in Python. STSCI_PYTHON is a product of the Space Telescope Science Institute, which is operated by Association of Universities for Research in Astronomy (AURA) for NASA; SciPy , an open source scientific tool for Python (Jones et al. 2001 ); NumPy , a fundamental package for scientific computing with Python (Walt, Colbert Varoquaux 2011 ); Matplotlib , a 2D plotting library for Python (Hunter 2007 ); Astropy , a community-developed core Python package for astronomy (Astropy Collaboration 2013 ); scikit-learn , a machine-learning library in Python (Pedregosa et al. 2011 ); astroML , a machine-learning library for astrophysics (Vanderplas et al. 2012 ); IPython , an interactive computing system for Python (Pérez Granger 2007 ); sep Source Extraction and Photometry in Python (Barbary 2016 ); palettable , colour palettes for Python; emcee , Seriously Kick-Ass MCMC in Python; Colossus , COsmology, haLO and large-Scale StrUcture toolS (Diemer 2015 ).


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

we assume a completeness , relative to CRTS, 7 i.e. 2.4 Models of variability The luminosity of an object in a binary system will not necessarily vary on the orbital period or at all. The premise of photometric identification of MBHBs is that the binary period is somehow imprinted into variations of the observed luminosity. In the particularly convincing example of PG 1302-102 (Graham et al. 2015b ), sinusoidal variations in the light curve can be well explained by Doppler boosting from a mildly relativistic orbital velocity (D’Orazio, Haiman Schiminovich 2015b ; but see also Liu, Gezari Miller 2018 ). Additionally, purely hydrodynamic modulations to accretion rates have been observed in simulations (e.g. Farris et al. 2014 ). Here, we describe models for both types of variability mechanisms. Throughout our analysis, each variability mechanism is considered entirely independently, i.e. we do not consider systems which may be both hydrodynamically and Doppler variable. The physical scenario is depicted schematically in Fig. 5 , assuming thin-disc geometries and a mass ratio q ≳ 10 −2 (see Section 2.4.2 ). On the left, the two MBHs, each with a circum-single disc, are shown within a cavity (‘gap’) of material evacuated by the binary orbit that separates them from the circumbinary disc. The radii of the circum-single discs are determined by the Hill radius of each MBH (see equation 6 ). Despite the presence of the gap, the circumbinary disc continues to transport angular momentum outwards, requiring material to be accreted inwards. Material from the disc overflows across the gap as accretion streams on to each circum-single disc. The orbital period at the inner edge of the circumbinary disc is longer than that of the binary, causing periodic variations in the accretion rate on to each circum-single disc (Fig. 5 , upper right). The secondary MBH is farther from the centre of mass and closer to the circumbinary disc edge, which leads to it receiving a disproportionate fraction of the accreting material [as described by equation ( 1 ) and shown in Fig. 1 ]. Each circum-single disc, in addition to the circumbinary disc (although typically to a lesser extent), will produce AGN-like emission. 2.4.1 Doppler variability Any component of the binary orbital-velocity along the observer’s line of sight will lead to both a relativistic boost and a Doppler shift in the observed spectrum of each circum-single disc. The boost is calculated using the Doppler factor, D ≡ [γ(1 − || / c )] −1 , where the Lorentz factor γ ≡ (1 − 2 / c 2 ) −1/2 . The line-of-sight velocity, || ≡ sin ( i ), depends on the binary inclination i , which we define as zero for face-on systems. The observed flux is calculated as (D’Orazio et al. 2015b ) where the observed frequency ν is related to the rest-frame frequency as, . Assuming a power law of index α ν for the section of the spectrum being observed, the Doppler variation in flux from the source will be (Charisi et al. 2018 ) where


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We thank Lisa Kewley, Renbin Yan, Shude Mao, Junqiang Ge, Jong-Hak Woo, and Chun Lyu for helpful discussions and suggestions. We thank an anonymous referee for helpful suggestions that improved the paper significantly. The research presented here is partially supported by the 973 Program of China under grants No. 2013CB834905 and No. 2009CB824800, by the National Natural Science Foundation of China under grants No. 11073040, by the Strategic Priority Research Program “The Emergence of Cosmological Structures” of Chinese Academy of Sciences, Grant No. XDB09000000, and by Shanghai Pujiang Talents Program under grant No. 10pj1411800. K.Z. acknowledge the support by the No. 53 China Post-doc general Fund under grants No. 2013M531232. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The SDSS website is http://www.sdss.org/.


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suited for tracing the very inner regions of a molecular disc ( Hirota et al. 2014 ; Ginsburg et al. 2018 ). To our sensitivity and resolution limit, the H 2 O emission appears devoid of any structure and does not extend beyond the outer radius of the disc as traced by the dust continuum emission (grey contours Fig. 2 b). The peak of emission is away from the centre of the dust disc in all velocity channels, while the H 2 O emission peaks between the enhanced continuum dust ring and the central location of G17.64 at the highest blue- and red-shifted velocities. The zero-moment contours in Fig. 2 a show that the H 2 O emission might appear like a disc with a central hole or like a single wide ring ranging from approximately half of the beam (∼30 au) to 120 au in radius (e.g. like the SO emission in Yen et al. 2014 ). The cut for the PV diagram was taken at a PA of 25.9° using a width of 5 pixels to encompass one synthesised beam (grey dashed line in Figs. 2 a,b). The PA was established by fitting a line through the centres of Gaussian fits to independent zero-moment maps of the blue- (3.2−21.4 km s −1 ) and red-shifted (22.7−44.8 km s −1 ) emission and the central position of G17.64 from the dust continuum. The PV diagram depicts the clear pattern of Keplerian rotation, particularly the red-shifted emission > 30 km s −1 , where the highest velocities peak closer towards the central source. The H 2 O undoubtedly traces a rotating disc. Fig. 2. Panel a : integrated intensity (zero-moment) map of the H 2 O 5 5, 0 −6 4, 3 ν 2 = 1 (232.68670 GHz) molecular line emission. The contours trace emission at the 3, 5, 7, 9, and 11 σ levels, where 1 σ = 7.13 mJy beam −1 km s −1 . Panel b : velocity-weighted integrated intensity (first-moment) map overlaid with the contours of the continuum emission from Fig. 1 a in grey. The outer extent of the H 2 O emission matches that of the dust continuum. Panel c : PV diagram for the H 2 O emission extracted from a 5 pixel wide slice along the dashed line at PA = 25.9° as indicated in (a) and (b). The contours of the data are plotted at the 20–80% levels in steps of 10%, where 10% corresponds to ∼1 σ (0.65 mJy beam −1 ). Panel d : same as (c), but the contours indicate the best representative model using inner and outer disc radii of 30 and 120 au, respectively, a stellar mass of 45 M ⊙ , and a disc inclination angle of 40°. The spatial (28 mas) and velocity resolution (1.3 km s −1 ) are indicated by the black cross at the bottom right. 4. Discussion 4.1. Stellar mass Based on its luminosity, G17.64 is firmly positioned as an O star (e.g. Vacca et al. 1996 ). However, previous estimates of the stellar mass, which are essential for understanding the disc stability, were not well constrained because the kinematics were poorly resolved ( Maud et al. 2018 ). Building from our previous representative models presented in Maud et al. (2018) , we matched the H 2 O PV diagram with only very minor changes. We used


O O B-Survey I-Survey I-Survey O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Mission O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion O O O O O O O O O O O B-Mission O O O O O O O O O O O B-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Mission O O O O O B-Instrument B-Instrument B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion B-CelestialRegion O O O O O O O O O O B-Instrument O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Instrument O B-Instrument O O

2. 2019 MMS Turbulence Campaign In the special MMS Solar Wind Turbulence Campaign, in 2019 February, the four MMS spacecraft were rearranged into a “beads on a string” configuration instead of the standard tetrahedron formation. The four spacecraft were positioned in a collinear configuration with log-spaced separation. Interspacecraft separations ranged from 30 to 200 km. Additionally, the spin axis was tilted to obtain improved electric field measurements. In this phase of the MMS orbital parameters, the formation spent a substantial period of time during each orbit in the solar wind, well beyond the bow shock. As such, the project was able to obtain a number of useful burst resolution measurements in the solar wind. The longest of those was a continuous interval of burst data lasting 5 hr, and which is analyzed in this paper, as well as in Bandyopadhyay et al. ( 2020 ). For orientation, the configuration of the four MMS spacecraft, while in the solar wind during the Turbulence Campaign, is illustrated in Figure 1 . Figure 1. Diagram of the configuration of the four MMS spacecraft near apogee, during the turbulence campaign. Note that close to apogee, when the spacecraft are in the pristine solar wind, they are aligned on the GSE Y – Z plane perpendicular to the solar wind flow. 3. MMS Data We employ 5 hr of magnetic field data from the Fluxgate Magnetometer (FGM; Russell et al. 2016 ) on board each each of the four MMS spacecraft. These are designated as MMS1, MMS2, MMS3, and MMS4. The magnetic field data are accumulated at a resolution of 128 Hz and synchronized across the formation. The orbital context is illustrated in the top panel of Figure 2 . The middle panel of Figure 2 shows the three Geocentric Solar Ecliptic (GSE) components of magnetic field recorded in this period by the MMS1 spacecraft. Figure 2. Top: location of the MMS spacecraft during this interval in bold red, along with the orbit in black. The magnetopause and bow shock are shown in light green and light blue, respectively, as estimated from OMNI data. Bottom: time series of magnetic field and PVI as defined in Equation ( 1 ), for the 5 hr interval in the solar wind. Several structures at MHD and kinetic scales (flux tubes, current sheets) can be seen. To visualize and quantify the roughness or intermittency of the magnetic field signal, we compute the partial variance of increments (PVI) of the magnetic field for this interval. The PVI, which can be computed either with two spacecraft or with a single spacecraft and the Taylor hypothesis (Chasapis et al. 2015 ; Greco et al. 2018 ) is defined aswhere here, for the multispacecraft case, the spatial lag , for the position of MMS spacecraft number I given by r I , so that that the vector increment is . The lower panel of Figure 2 shows the time series of the values of PVI computed in this way (Chhiber et al. 2018 ; Greco et al. 2018 ), namely, the two-point PVI value using spacecraft MMS2 and MMS3. The separation


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

form from that obtained for the fundamental frequencies of crustal torsional oscillations in the phases of spherical and cylindrical nuclei (Sotani et al. 2018 ). We also remark that the fundamental frequency in the tube and bubble phases can be smaller than that in the phases of spherical and cylindrical nuclei and that the fundamental frequencies with general values of l can also be well fitted in the same functional form: with a different set of the adjustable parameters , , and . Hereafter, we will thus attempt to identify the observed QPO frequencies using the fitting formula ( 10 ) for the tube–bubble layer, in addition to the formula given in Sotani et al. ( 2018 ) for the sphere–cylinder layer. Figure 2. (Colour online) Fundamental frequencies of the l = 2 torsional oscillations in the tube and bubble phases, as obtained for the neutron star models with M = 1.4M ⊙ and R = 12 km as well as with various sets of L and K 0 . Here, the left-hand and right-hand panels correspond to the results for the maximum and minimum enthalpies that participate in the oscillations, i.e. and 0, respectively (see the text for details). The solid line denotes the fitting given by equation ( 9 ). Note that the obtained fundamental frequencies in the tube–bubble layer are generally lower than those obtained in our earlier analysis by assuming that only the bubble phase is oscillating (Sotani et al. 2017a ). This tendency is more significant for larger values of L . This is partly because for larger L , the bubble phase is less likely to appear, as shown in Table 1 , and partly because the shear modulus and hence the shear velocity is relatively small in the tube phase, as shown in Fig. 1 . As we will see later, therefore the 26 Hz QPO observed from SGR 1806-20 is identified as the l = 4 fundamental torsional oscillation in the tube–bubble layer, in contrast to our earlier analysis (Sotani et al. 2017a ) in which it was identified as the l = 2 fundamental torsional oscillation. Up to now, we have already done many trials to identify the QPOs observed in SGR 1806-20 and SGR 1900+14 as the crustal torsional oscillations. As long as we adopt the QPO frequencies derived in the conventional non-Bayesian analyses of RXTE data for the X-ray afterglows of the giant flares and the recurrent X-ray outbursts, such identification has worked out relatively well (Sotani et al. 2012 , 2013a , b , 2016 , 2017a , 2018 ). In fact, the observed QPOs, except for the 26 Hz QPO in SGR 1806-20, can be identified as the torsional oscillations inside the phases of spherical and cylindrical nuclei in such a way that the QPOs of frequencies lower than ∼200 Hz correspond to the fundamental oscillations with various values of l, while the higher QPOs observed in SGR 1806-20 correspond to the overtones (Sotani et al. 2018 ). In this case, since it is still uncertain how much fraction of dripped neutrons in the phase of cylindrical nuclei would be locked to the motion of protons in 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 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 B-Wavelength 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Wavelength O O O O B-Citation I-Citation I-Citation O 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 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 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 B-CelestialObject 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 O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation 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 O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O 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 B-Wavelength O O B-Instrument O O O O O O O O O O O O O O

We thus expect an homogeneous envelope to become transparent after a timewhich is frustratingly well above the duration of the Eddington luminosity phase. Here we assume κ ≈ 0.1 cm 2 g −1 , which is a reasonable value for ordinary supernova material. At lower X-ray energies ( x ≲ 3 keV), photoionization may delay the time at which the envelope becomes transparent by an additional factor of . Despite this, the youngest neutron star we have uncovered has an age of about 340 yr (Fesen et al. 2006 ). In a few instances, a surviving binary companion has been detected in postexplosion deep optical imaging of extragalactic supernova (Maund Smartt 2009 ; Folatelli et al. 2014 ). In the case of 1993J, for example, the brightness of the transient dimmed sufficiently after about a decade so that its spectrum showed the features of a massive star superimposed on the supernova (Maund et al. 2004 ). It is perhaps a stinging fact that despite the expected manifestations of neo-neutron stars, one of the main issues in the field has been that most Galactic supernova remnants have no detectable central source. Figure 11 shows the current detections and upper limits of thermal emission in nearby neutron stars with model predictions. Observational selection effects are clearly at play when uncovering young objects yet there is the possibility that a sizable fraction of massive star collapses might produce black holes rather than neutron stars, with the clearest example being W49B (Lopez et al. 2013 ) and the other four examples, from Kaplan et al. ( 2004 , 2006 ), all plotted in Figure 11 . Figure 11. Plot of luminosity as a function of the age of the remnant for nearby neutron stars together with the predictions from neutron star cooling models. The (green) dots are measurements and the (blue) squares are upper limits from detected neutron stars (data taken from Beznogov Yakovlev 2015 ) while the (red) dotted error bars are upper limits on the compact objects, black holes or neutron stars, expected to be presents in five core-collapse supernova remnants. These remnants are, in order of increasing age: G043.3–0.2 (a.k.a. W49B, marked by a diamond) from Lopez et al. ( 2013 ), and G127.1+0.5, G084.2+0.8, G074.0–8.5, and G065.3+5.7 from Kaplan et al. ( 2004 , 2006 ). Shaded areas show model predictions of Page et al. ( 2004 , 2009 ) for the minimal cooling of neutron stars that cover uncertainties on the chemical composition of the envelope and nucleon pairing at high densities. In contradistinction, the dashed-pentadotted curve, Z , exemplifies the effect of fast neutrino emission from the direct Urca process expected to occur in massive neutron stars (Boguta 1981 ; Lattimer et al. 1991 ) resulting in very cold stars (Page Applegate 1992 ). Also plotted are the three different models (A, C, D) shown in Figure 9 . 6.2. Neutron Star Mergers, Short Gamma-Ray Bursts, and LIGO Events The merger of binary neutron stars and the subsequent production of a beamed,


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

We thank an anonymous referee for insightful comments. We are grateful to B. Burkhart, A. Lazarian and Z. Manchester for insightful comments on the manuscript. T.H. thanks B.T. Draine for stimulating discussions on spacecraft charging. This work was supported in part by a grant from the Breakthrough Prize Foundation.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

NLRs and in the NLRs, effects of the dusts on the observed values (marked by the suffix of obs) should be where D (BLRsextNLRs) , D (extNLRs) and D NLRs represent effects of dusts in all regions, effects of dusts in the regions from the BLRs to the observer and the effects of dusts in the NLRs, respectively. Effects of dust extinctions can be considered as the role factor to determine the scatters of the correlations shown in Fig. 5 . There are more similar dust extinctions on L (5100 ,obs) and on , but more different dust extinctions on the L (5100 ,obs) and on the . Therefore, there are tighter correlations between L (5100 ,obs) and than the correlation between L (5100 ,obs) and . Moreover, with considerations of dependence of Balmer decrements (which can be used to trace the dust extinctions) on [O iii ]luminosity, the steeper correlation of L (5100 ,obs) and can also be simply explained as follows. Based on the observed and the Balmer decrements from common NLRs BD obs, NLRs for our objects with both narrow H and narrow H, we can find that there is a moderately negative correlation shown in Fig. 7 , with Spearman rank correlation coefficient of about 0.32 with P null 510 8 . And the anticorrelation can be simply described by with narrow 0.045. Then, combining with the empirical equation to estimate colour excess with 3.1 as the intrinsic flux ratio of narrow H to narrow H, the intrinsic luminosity can be estimated by where k and E ( B V ) represent the reddening curve and colour excess, respectively, and narrow 0.8 k narrow . Meanwhile, similar equations to estimate L (5100 ,int)) and can be described by where ext 0.8 k ext and have probably different values of ext and 5100 from the value of narrow , because of different dust obscurations for observed continuum luminosity and for observed luminosity from the extended components of [O iii ]lines. And, the values of must be smaller than 1, otherwise an unreasonable result can be expected that intrinsic luminosity after considerations of dust extinctions could be smaller than the observed luminosity. Then, we have the following sub-equations Based on the third sub-equation in equation ( 10 ) combining with the shown results in the top panel of Fig. 6 , we can find that . Therefore, the correlation of L (5100 ,obs) versus is steeper, because of its larger slope of being about 1.2times larger than the slope of for the correlation of L (5100 ,obs) versus . Certainly, the results above are highly idealized, and seriously depend on physical properties of dusts in central regions of AGN; however, the results can be applied to find qualitative explanations to the results shown in Fig. 5 . Figure 7. Correlation between observed Balmer decrements(flux ratio of narrow H to narrow H) and the luminosities of the core components of the [O iii ]emission lines. Before the end of this section, we show our simple discussions on which component is well applied to trace central AGN intrinsic luminosity in type-2


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

We highly appreciate the referee for his/her valuable comments and suggestions that significantly improved our work. J.F.Z. thanks support from the National Natural Science Foundation of China (grant Nos. 11233006 and 11363003). A.L. acknowledges the NSF grant AST 1212096 and the Center for Magnetic Self Organization (CMSO). H.L. and J.C. acknowledge support by the National R D Program through the National Research Foundation of Korea, funded by the Ministry of Education (NRF-2013R1A1A2064475).


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 B-Model 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 O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Model 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 B-Citation I-Citation I-Citation O O O O O O O O B-Wavelength I-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 B-Tag O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O B-Wavelength 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 B-Formula I-Formula I-Formula 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 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 B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength I-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O

show the rest of the sources detected; in the case of sources 32, 35, and 38 the K = 0, 1 lines were detected, but no valid solution was found for the simultaneous Gaussian fitting of all four components. Integrated line fluxes obtained from the Gaussian fitting are reported in Table 1 and were used to compute Boltzmann plots (i.e., the rotational diagram) relating the column density of the emitters normalized by the level degeneracy and the energy of the levels. Using standard procedures (e.g., Fontani et al. 2002 ), assuming LTE and optically thin conditions that are appropriate for this line and class of sources (e.g., Bergin et al. 1994 ) the temperature and total column density of CH 3 C 2 H can be derived from a linear fit to the rotational diagram (Goldsmith Langer 1999 ). Because our observations are single-pointed toward the 70 μ m peak of the sources, we could only derive beam-averaged column densities and we chose to focus on the analysis of the CH 3 C 2 H rotational temperatures (see Table 1 ). 3. RESULTS 3.1. CH3C2H Detection Statistics The sources listed in Table 1 are ordered according to their L/M value computed from the Herschel fluxes, augmented with ancillary data at mid-IR wavelengths (D. Elia et al. 2016, in preparation), and it can be immediately seen that the detection rate in CH 3 C 2 H( J = 12–11) is strongly dependent on the L/M values. We can distinguish three ranges of L/M : the rate is 0 (none out of 23 sources) for the sources with L/M 1, 58% (seven out of 12) for sources with 1 L/M 10 and 90% (16 out of 18 sources) for sources with L/M > 10. In Table 1, in sources # 32, 35, and 38, at least the K = 0 line is detected, but the four-component Gaussian fit to the four lines did not converge and so no further analysis could be carried out for these sources. This finding is preliminary confirmation of the working hypothesis that higher values of L/M should be related with a more advanced evolutionary stage. As CH 3 C 2 H is a temperature probe for gas with densities in excess of 10 5 cm −3 (Bergin et al. 1994 ), its values are influenced more by the inner clump regions and relatively less by the outer envelope. Looking at Figure 3 , the range of L/M ≲ 1 is characteristic of “pre-stellar” clumps (in which, contrary to the sources of the present study, 70 μ m emission is not detected); the internal input energy producing the detectable 70 μ m flux would not seem sufficient to drive up considerably the bolometric luminosity as well as the internal clump temperature, resulting in non-detections in CH 3 C 2 H( J = 12–11) for any of the sources with L/M 1. This suggests that in these clumps intermediate or high-mass star formation has not yet started. Above the L/M = 1 threshold, corresponding to the upper envelope of the “pre-stellar” clumps distribution in Figure 3 , the CH 3 C 2 H( J = 12–11) detection rate increases sharply, implying that the internal energy produced by star formation is rising to


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

the power-law slope α , the dust temperature , and the spectral slope of the dust emissivity as fitting parameters, using the observed-frame 500 μ m flux density as a normalization factor. We also fit “general” models that allow for wavelength-dependent changes in optical depth, adding the wavelength , where the optical depth reaches unity as an additional fitting parameter. The optically thin fitting procedure yields statistical mean values of K, , and . 19 19 α is only poorly constrained by the data. The general fit yields mean values of μ m, K, , and . The fit also implies rest-frame infrared (8–1000 μ m) and FIR (42.5–122.5 μ m) luminosities of L ⊙ and L ⊙ , respectively. 20 20 The measured agrees to within ∼2% with independent estimates based on integrating a normalized MAGPHYS-based SED template based on the z = 6.34 starburst HFLS3 (Cooray et al. 2014 ), showing that the adopted power-law approximation of the short wavelength emission has a minor impact on the measured quantities. Assuming a dust absorption coefficient of m 2 kg −1 at 125 μ m (e.g., Dunne et al. 2003 ), we also find a dust mass of M ⊙ . 21 21 Given the limited photometry, the uncertainties may be somewhat underestimated. Assuming a Chabrier ( 2003 ) stellar initial mass function, these parameters suggest a total SFR of ∼2400 M ⊙ yr −1 . Given the limited SED constraints in the rest-frame optical, we obtain an estimate for the stellar mass M ⋆ of ADFS-27 by normalizing the MAGPHYS-based SED template of HFLS3 in Figure 4 to the observed-frame 4.5 μ m limit. This yields M ⋆ 1.2 × 10 11 M ⊙ . 4.2. Molecular Gas Mass, Gas-to-dust Ratio, and Gas Depletion Time The value of ADFS-27 (based on the adopted r 51 = 0.39) implies a total molecular gas mass of M ⊙ . 22 22 We here adopt a conversion factor of M ⊙ (K km s −1 pc 2 ) −1 for nearby ultra-luminous infrared galaxies and SMGs (e.g., Downes Solomon 1998 ; Tacconi et al. 2008 ). Taken at face value, this yields a gas-to-dust ratio of /, which is comparable to that in the z = 6.34 starburst HFLS3 and within the range of values found for nearby infrared-luminous galaxies (Wilson et al. 2008 ; Riechers et al. 2013 ), but ∼4× lower than that for the z = 5.30 starburst AzTEC-3 (Riechers et al. 2014 ). At its current SFR, this implies a gas depletion time of /SFR ≃ 100 Myr, consistent with the general SMG population (e.g., Carilli Walter 2013 ). 4.3. SFR and Gas Surface Densities, Gas Dynamics, and Conversion Factor The apparent 870 μ m continuum sizes of ADFS-27N (mal) and ADFS-27S (yong) imply physical sizes of (1.83 ± 0.18) × (1.28 ± 0.16) and (2.05 ± 0.18) × (0.87 ± 0.15) kpc 2 at z = 5.655, which are comparable to the ∼2.5 kpc diameters found for other z > 4 dusty starbursts like AzTEC-3, HFLS3, and SGP-38326 at similar wavelengths (Riechers et al. 2013 , 2014 ; Oteo et al. 2016 ). Assuming that their flux ratios at 870 μ m are representative at the peak of the SED, this implies surface densities of and 7.5 × 10 12 L ⊙ kpc −2


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Acknowledgements The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. Swift /BAT transient monitor results are provided by the Swift /BAT team. This research has made use of MAXI data provided by RIKEN, JAXA, and the MAXI team. TSA acknowledges support through the Russian Government Program of Competitive Growth of Kazan Federal University. We thank Sebastian Heinz and Chris Fragile for useful discussions.


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This work required the use and integration of a number of Python software packages for science, including AstroPy (Astropy Collaboration et al. 2013 ), 5 5 http://www.astropy.org Matplotlib (Hunter 2007 ), 6 6 http://matplotlib.org NumPy, 7 7 http://www.numpy.org SciPy, 8 8 http://www.scipy.org/scipylib/ and yt (Turk et al. 2011 ). 9 9 http://yt-project.org We are thankful to the developers of these packages. We also thank Volker Springel for the use of the AREPO code. J.A.Z. thanks David Barnes, Rahul Kannan, Federico Marinacci, and Hui Li for useful discussions. He also thanks Grant Tremblay for assistance with a last-minute fix to a figure. J.A.Z. acknowledges support through Chandra Award Number G04-15088X issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. J.Z. acknowledges support by a Grant of Excellence from the Icelandic Research Fund (grant No. 173929−051). The numerical simulations were performed using the computational resources of the Advanced Supercomputing Division at NASA/Ames Research Center.


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It is a pleasure to thank Eve Ostriker for stimulating discussions and insightful suggestions, Anne Decourchelle and Jean Ballet for enlightening elements regarding the observations of supernovae remnants and Matthieu Gounelle for triggering our interest in supernova explosions. We thank the anonymous referee for a careful reading of the manuscript which has significantly improved the paper. This work was granted access to HPC resources of CINES under the allocation x2014047023 made by GENCI (Grand Equipement National de Calcul Intensif). P.H. acknowledges the financial support of the Agence Nationale pour la Recherche through the COSMIS project. This research has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 306483 and No. 291294).


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

; Taddia et al. 2018 ; Prentice et al. 2019 ). Indeed, the previous studies on 56 Ni mixing in stripped-envelope SNe indicate that 56 Ni mixing can affect the photospheric velocity evolution in stripped-envelope SNe (e.g. Dessart et al. 2012 ). In this paper, we perform a systematic study of the effect of 56 Ni mixing on the photospheric velocity evolution in stripped-envelope SNe. The rest of this paper is organized as follows. We summarize how we get progenitor models, how we mix 56 Ni, and how we conduct radiation transfer simulations in Section 2 . Our results are presented in Section 3 . We discuss the results and conclude this paper in Section 4 . 2 METHODS 2.1 Progenitor models We obtain hydrogen-free progenitor models by using the public stellar evolution code mesa (Paxton et al. 2011 , 2013 , 2015 , 2018 , 2019 ). We assume a metallicity of Z = 0.02. We adopt the standard mixing-length theory for convection with a mixing-length parameter of 2.0 with the Schwarzschild criteria. Our focus in this paper is on hydrogen-free SNe. There are many mechanisms to remove the hydrogen-rich envelope from SN progenitors and the mass-loss mechanisms themselves are a well investigated field of research (Smith 2014 ). In this work, we artificially remove hydrogen-rich envelopes to obtain hydrogen-free SN progenitors. We first evolve massive stars from zero-age main sequence (ZAMS) to the end of helium burning without mass loss. The helium core mass does not change much after the helium burning. At this point, we stop the stellar evolution calculation and gradually reduce the mass from the surface through wind by using the relax_mass option in mesa . The maximum mass-loss rate allowed in this process is 10 −4 M ⊙ yr −1 ( lg_max_abs_mdot = -4 in mesa ). When the stellar mass reaches the desired mass, we resume the stellar evolution calculation without mass loss. The stellar evolution calculations are performed at least until the end of oxygen burning. The subsequent evolution would not affect the envelope structure of the progenitors significantly. Using the method described above, we obtain three hydrogen-free progenitor models: He3.85, CO3.85, and He4.90 (Table 1 ). The density structure of the progenitors is shown in Fig. 1 . He3.85 and CO3.85 have the same mass (3.85 M ⊙ ), but He3.85 is a helium star while CO3.85 is a carbon+oxygen star without helium. The ZAMS masses of He3.85 and CO3.85 are 14 M ⊙ and 20 M ⊙ , respectively. He4.90 is a 4.90 M ⊙ helium star progenitor with a ZAMS mass of 17 M ⊙ . These masses are determined to have the typical ejecta mass (≃2 M ⊙ ) in stripped-envelope SNe (e.g. Lyman et al. 2016 ). Figure 1. Density structure of the progenitor models in the mass coordinate (top) and radius coordinate (bottom). Table 1. Progenitor properties. When we explode these progenitors, we set a mass cut M cut below which is assumed to form a compact remnant that is not ejected. The mass cut is set at 1.35 M ⊙ (He3.85 and CO3.85) and 1.40


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The author wishes to thank Derek Ward-Thompson for valuable discussions, the anonymous referee for a detailed and constructive review which greatly improved the content of this paper, and Chris Powles for proof-reading the derivations. The author wishes to thank the Science and Technology Facilities Council for studentship support under grant number ST/K501943/1 and post-doctoral support under grant number ST/K002023/1 while this research was carried out. This research has made use of the NASA Astrophysics Data System.


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ACKNOWLEDGEMENTS I appreciate discussions with Hanno Rein, Dan Tamayo, Scott Tremaine, Ed Bertschinger, Walter Dehnen, Matt Payne, and Marie-Claude Arnaud. I appreciate feedback from the anonymous referee.


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

et al. 2014 )—have positions on the IR CMD consistent with the field locus (e.g., Figure 14 ). Finally, the AB Dor member SDSS J1110+0116 (T5.5; Gagné et al. 2015a ) also coincides with the field locus. Thus, for L/T objects as young as ≈100 Myr, while the temperatures for a given spectral type may be age dependent, the IR absolute magnitudes across the L/T transition do not seem to strongly depend on age. Figure 25. Absolute magnitudes vs. spectral type for our sample with an expanded range of spectral types, in order to highlight the latest-type objects. The L/T objects are shown as green squares, with the measurement errors comparable to the symbol size. Normal field objects (small gray triangles) are the same as in Figure 12 . The thick black lines are the polynomial fits from Dupuy Liu ( 2012 ), and the gray region shows the rms about the fits. See Figure 6 caption for further details. The two latest-type red objects in our sample, WISE J0206+2640 (L9 (red)) and WISE J0754+7909 (T2p (red)), may be illuminating landmarks for the transition. Their spectra are unusual compared to most field objects of similar type, especially WISE J0754+7909 (see details in Appendix ). And yet their absolute magnitudes are largely consistent with field objects, with the largest discrepancy being WISE J0206+2640 having ≈0.5 mag fainter magnitudes at Y and J bands compared to the field. Even given its very peculiar spectrum, WISE J0754+7909 has absolute magnitudes and color–magnitude positions in accord with the field. Thus, while the spectral peculiarities of these two objects may not be due to low gravity (indeed both have old field kinematics; Table 15 ), their consistency with field objects may be circumstantial evidence that the IR magnitudes of the L/T transition are robust over a range of physical properties. One interesting question that we can address is whether the J -band flux reversal that is a hallmark of L/T transition binaries in the field population (e.g., Liu et al. 2006 ) would appear different at lower gravities. The most extreme such flux-reversal binaries known are 2MASS J1404−3159AB (Δ J = −0.54 ± 0.08 mag, Δ K = 1.33 ± 0.05 mag; Looper et al. 2008a ) and SDSS J1052+4422AB (Δ J = −0.45 ± 0.09 mag, Δ K = 0.52 ± 0.05 mag; Dupuy et al. 2015 ). SDSS J1052+4422AB has a very precise evolutionary-model-based age derived from its dynamical masses and luminosities, clearly demonstrating that it is field age and gravity ( Gyr and = 5.0–5.2 dex; Dupuy et al. 2015 ). Now that we have parallaxes for members of YMGs that span the L/T transition, we can imagine hypothetical L/T transition binaries composed of these coeval objects. For example, if the AB Dor members WISEP J0047+6803 (L7 int-g ) and SDSS J1110+0116 (T5.5) were paired together in a binary, they would have Δ J = −0.37 ± 0.11 mag, Δ K = 2.04 ± 0.09 mag. If the primary were instead 2MASS J2244+2043 (L6 vl-g ), the flux ratios would be Δ J = −0.47 ± 0.09 mag, Δ K = 1.89 ±0.09 mag. Thus, it


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ACKNOWLEDGEMENTS This work has been funded by a French Doctoral Contract. The authors are also grateful to Google for the unrestricted gift given to the University of Santa Cruz to carry out the project: “Deep Learning for Galaxies”.


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We thank Seshadri Nadathur, Shaun Hotchkiss, David Alonso, Airam Marcos-Caballero, Fabio Finelli, Francesco Paci, István Szapudi, and the anonymous referee for useful comments that improved the paper. We also thank Krishna Naidoo, Ofer Lahav, and Aurelien Benoit-Lévy for informative discussions. AK thanks Márton Vargyas, and JGB the Theory Division at CERN, for their hospitality, where the main ideas of the project were discussed. Funding for this project was provided by the Spanish Ministerio de Economía y Competitividad (MINECO) under projects FPA2012-39684, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234 and SEV-2012-0249.


O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject 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 B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O B-Model O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O B-Model I-Model I-Model O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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 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

model assumes a temperature of 10 K for the gas, whichis up to 40% higher than the values found for the central parts of the cores (6–7 K). However, further calculations have shown that lowering the temperature by 2–3 K does not produce significant differences in the results (Roueff, priv. comm.). Visser et al. (2018) highlighted how isotope-selective photodissociation is a key mechanism to understand the nitrogen isotopic chemistry in protoplanetary disks. We can speculate that different levels of selective photodissociation in different environments could reproduce the variety of N-isotopic ratios that are observed. Further investigation of this point from both an observational and a theoretical point of view is merited. From the L1544 and L694-2 results, there seems to be tentative evidence that N 15 NH + is more abundant than 15 NNH + . This can be explained by the theory according to which the proton transfer reaction, tends to shift the relative abundance of the two isotopologues, slightly favouring N 15 NH + due to the fact that N 15 NH + zero-point energy is lower than that of 15 NNH + by 8.1 K (see reaction RF2 in Wirström Charnley 2018 ). It is interesting that the same trend is found also in a very different environment such as OMC-2 FIR4, a young protocluster hosting several protostellar objects. In this source, Kahane et al. (2018) measured lower values for the isotopic ratio, but in agreement with our result found that 15 NNH + is less abundant than N 15 NH + . However, we emphasise that higher-quality observations and those with better statistics are needed to confirm this point. 6. Conclusions We have analysed the diazenylium isotopologues’ spectra in three prestellar cores, L183, L429 and L694-2 in order to derive nitrogen isotopic ratios. Since LTE conditions are not fulfilled, especially for the N 2 H + (1–0) transition, we have used a fully non-LTE radiative transfer approach, implemented in the numerical code MOLLIE. We have carefully derived the physical models of the sources, computing their volume density and dust temperature profiles. With these, we were able to produce synthetic spectra to be compared with our observations, in order to derive the best-fit values for the molecular abundances and column densities. Using the same method, we have also recomputed the isotopic ratio of L1544. The difference with the literature value of Bizzocchi et al. (2013) , due to changes in the molecular collisional rates, is well within the uncertainties. In our sample of four cores, we derived 14 N/ 15 N values in the range 580–1000. Within the confidence range given by our uncertainties estimation, all our results are inconsistent with the value ≈400, predicted by the current theoretical models. L1544 still presents higher depletion levels than the other sources, but in general all the cores are anti-fractionated. The theoretical bases of such a trend are at the moment not understood. A deep revision of our knowledge of 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O 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 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O

only the two-point statistic is insufficient to probe all the effects of different cosmological parameters on the evolution of the overall cosmological field. This motivates the need for considering other summary statistics in the analysis of clustering on smaller scales. Since the total information available in a survey scales with the number of independent modes (Tegmark 1997 ), and given that there are many more independent modes on small scales, it is important to develop these new statistical methods, that better extract information from small scales, to make optimal use of data from ongoing and future cosmological surveys. Various approaches towards harnessing information beyond that contained in the two-point statistics have been explored in the literature. One method is consider the higher N -point functions in the analysis – the three-point function and its Fourier transform, the bispectrum (e.g. Scoccimarro et al. 1998 ; Takada Jain 2004 ; Sefusatti et al. 2006 ), or the four-point function and its Fourier transform, the trispectrum (e.g. Verde Heavens 2001 ). While these additional statistics can be highly informative about small-scale clustering, and promise to yield significantly tighter constraints on some cosmological parameters (Coulton et al. 2019 ; Hahn et al. 2020 ), one drawback is that they generally entail much higher computational costs to measure either from simulations, or from data. The computational complexity rises with N – the order of the highest connected correlation function considered, while keeping the data size fixed. Further, the noise properties for these higher order estimators often make it difficult to obtain good signal-to-noise ratio (SNR) over a wide range of scales. In spite of these issues, analyses including higher order correlations, especially the bispectrum, have successfully been applied to certain cosmological data sets (Gil-Marín et al. 2015 ; Slepian et al. 2017 ; Gualdi et al. 2019 ). In this context, there also exist approaches which attempt to undo the non-linear effects of gravitational clustering on various cosmological fields. Once this procedure is applied, the analysis proceeds with the measurement of the two-point function of the linearized field. This approach has already been applied specifically to the reconstruction of the Baryon Acoustic Oscillation (BAO) signal (Eisenstein et al. 2007 ; Padmanabhan, White Cohn 2009 ; Padmanabhan et al. 2012 ). Schmittfull et al. ( 2015 ) showed that the reconstruction process can be interpreted as the transfer of information from the higher connected N -point functions in the observed field into the reconstructed two-point function. More recently, methods have been proposed for the full reconstruction of the initial linear modes from non-linear observables at low redshift (Baldauf et al. 2010 ; Seljak et al. 2017 ; Modi, Feng Seljak 2018 ; Horowitz, Seljak Aslanyan 2019 ). There is also a large body of literature investigating the one point


O B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization B-Person O B-Person O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Observatory B-Observatory B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant B-Person O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Citation O O O O B-ComputingFacility I-ComputingFacility B-ComputingFacility O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Observatory O O B-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O B-Fellowship I-Fellowship O O O O O O B-Archive I-Archive I-Archive I-Archive

ACKNOWLEDGEMENTS EZ and AV acknowledge funding from the Swedish National Space Board. AKI and TH acknowledge the financial support from the National Astronomical Observatory of Japan (NAOJ) ALMA Scientific Research Grant number 2016-01 A. AKI also acknowledges the support from the Japan Society for the Promotion of Science (JSPS) KAKENHI 17H01114. TH acknowledges the JSPS Grant-inAid for Scientific Research 19J01620. Numerical simulations of S16 have been performed with Cray XC30, XC50 at the Center for Computational Astrophysics at NAOJ and with Cray XC40 at the Yukawa Institute for Theoretical Physics at Kyoto University. DC is a DAWN fellow. This research has made use of NASAs Astrophysics Data System.


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

We gratefully acknowledge support by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics (MAS), by Fondecyt Regular 1150345 and by the BASAL-CATA Center for Astrophysics and Associated Technologies PFB-06. This work was finalized at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1066293. M.Z. and D.M. were partially supported by a grant from the Simons Foundation, during their stay in Aspen.


O O O O O O O O O O B-Organization I-Organization I-Organization O O O B-Grant O O O O O O O O O B-Organization O O B-Grant B-Person O O O O B-Grant I-Grant B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant O O O B-Person I-Person I-Person O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization O O O O O O O O O O O B-Telescope I-Telescope O O O O B-Archive O O O O O B-Organization I-Organization I-Organization B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O O O B-Telescope I-Telescope I-Telescope O 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 O O O O B-Telescope O O O O B-Organization O O O O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Observatory I-Observatory I-Observatory O O O O O O O B-Telescope O O O O B-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location O O O O O O O O O O O B-Instrument O O O O B-Telescope B-Location B-Location B-Location B-Location O O B-Telescope I-Telescope O O O O O B-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O B-Archive I-Archive I-Archive O O O O O O O O O B-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 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 O O O O O O O O O O O O O

ACKNOWLEDGEMENTS This material is based upon work supported by the National Science Foundation under Grant No. 1411943. Part of the work presented herein is supported by NASA Grant No. NNX15AK92G. P.F.W. acknowledges funding through the Horizon 2020 European Research Council Consolidator Grant No. 683184. We thank the Stanislav S. Shabala as the referee for a constructive report that greatly improved the paper. This study is based on data taken with the Karl G. Jansky VLA that is operated by the National Radio Astronomy Observatory. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work is based, in part, on data collected at the Subaru Telescope and obtained from the SMOKA, which is operated by the Astronomy Data centre, National Astronomical Observatory of Japan; observations made with the Spitzer Space Telescope , which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA; and data collected at UKIRT that is supported by NASA and operated under an agreement among the University of Hawaii, the University of Arizona, and Lockheed Martin Advanced Technology centre; operations are enabled through the cooperation of the East Asian Observatory. When the data reported here were acquired, UKIRT was operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the UK. This study is also based, in part, on observations obtained with WIRCam, a joint project of CFHT, Taiwan, Korea, Canada, France, and the Canada–France–Hawaii Telescope that is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawai’i. The scientific results reported in this article are based in part on observations made by the Chandra X-ray Observatory and data obtained from the Chandra Data Archive. The spectrographic 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 thank the indigenous Hawaiian community for allowing us to be guests on their sacred mountain, a privilege, without with, this work would not have been possible. We are most fortunate to be able to conduct observations from this site.


O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Instrument O O O O B-Wavelength I-Wavelength O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Instrument O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument I-Instrument I-Instrument B-Instrument O B-Telescope I-Telescope I-Telescope O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O B-Archive I-Archive I-Archive O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Model I-Model O O O O O O O O O O O O O O B-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 B-Telescope B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation O O O B-Model I-Model I-Model I-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation I-Citation O B-Model I-Model I-Model B-Model O O O O B-Dataset I-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O B-Software I-Software 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 B-Model I-Model O O O O O O O O B-CelestialObjectRegion O O B-CelestialObject I-CelestialObject O O O O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation I-Citation O O O

thick discs. We observed (see Table 1 ) the mid-plane of NGC 4111 with the SCORPIO in the wavelength range 4800–5600 Å with the spectral resolution ∼2.2 Å =55 km s −1 . The remaining five data sets were obtained using SCORPIO-2 at slightly lower spectral resolution (∼3.8 Å =95 km s −1 at 5100 Å) at the broader wavelength range (3600–7070 Å). Table 1. Long-slit spectroscopy of the sample galaxies. We reduced our spectroscopic observations with our own idl -based reduction pipeline. We estimated the night sky background from outer slit regions not covered by our target galaxies and an optimized sky subtraction technique that takes into account spectral resolution variations along the slit (Katkov Chilingarian 2011 ; Katkov, Sil'chenko Afanasiev 2014 ). All three galaxies were observed with the Infrared Array Camera (IRAC) at Spitzer Space Telescope in the imaging mode at wavelengths 3.6 μm and 4.5 μm. We fetched fully reduced 3.6 μm images from the Spitzer Heritage Archive. 1 2.3 Data analysis Van der Kruit Searle ( 1981 ) have shown that in case an isothermal disc in the equilibrium state the vertical disc density profiles are described by the law I = I 0 sech 2 ( z / z 0 ), where I 0 is the central intensity and z 0 is the disc scale-height. We fitted vertical profiles obtained by averaging Spitzer IRAC images along the radius using models including one and two components. We set central positions of both components to be the same in the case of two-component fitting but left the position itself a free parameter. Our results for NGC 4111 and NGC 5422 quantitatively agree with those presented in the S4G survey (Salo et al. 2015 ), however the results for NGC 4710 decomposition were not presented there. To derive internal kinematics and stellar population properties (mean ages and metallicities [Fe/H]) of thick and thin discs we first binned our long slit spectra in the spatial direction with the adaptive binning algorithm in order to reach the minimal signal-to-noise ratio S / N = 30 per bin per spectral pixel in the middle of the wavelength range. Then, in every bin we applied the nbursts full spectral fitting technique (Chilingarian et al. 2007a , b ) with a grid of high resolution stellar pegase.hr (Le Borgne et al. 2004 ) simple stellar population (SSP) models based on the ELODIE3.1 empirical stellar library (Prugniel et al. 2007 ). The nbursts technique implements a pixel space χ 2 minimization algorithm where observed spectrum is approximated by a stellar population model broadened with parametric line-of-sight velocity distribution (LOSVD) and multiplied by polynomial continuum (10th degree in our case) to take into account dust attenuation and/or possible flux calibration imperfections in both observations and models. We used Gaussian parametrization of the stellar LOSVD, except our higher resolution mid-plane spectra of NGC 4111 where we exploited the standard Gaussian–Hermite parametrization (van der Marel Franx 1993 ). The [Mg/Fe]


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with high stellar mass surface densities (see next section). Figure 5. Comparison of circularized half-light radii at ALMA/870 μ m (red circles) with those at HST / H 160 band (cyan squares) for our sample of 12 galaxies with size measurements at 870 μ m. Gray circles indicate the rest-optical sizes for star-forming galaxies around the main sequence at z = 1.9–2.7, which are drawn from the 3D- HST survey. A dashed line shows their fitting function, . Table 2 Galaxy Properties for 12 SFGs with 870 μ m Size Measurements Notes. a Sérsic indices and half-light radii at 1.6 μ m. We do not use U4-16795 because the best-fit Sérsic index reaches the constrained limit of n = 8. b Half-light radii at 870 μ m. c Stellar mass surface density within a central 1 kpc calculated in stellar mass maps. d SFR surface density within a central 1 kpc calculated from the best-fit exponential models at 870 μ m and total SFRs. e Bulge formation timescales to reach the stellar mass surface density of log(Σ M bulge / M ⊙ kpc −2 ) = 10 (Equation ( 3 )). f Gas depletion timescales by star formation and outflows (Equation ( 4 )). In the analysis of size measurements, we do not include two massive star-forming galaxies with log( M * / M ⊙ ) > 11 in the parent sample of galaxies identified by the narrowband survey. One is not observed with ALMA, and the other one (U4-36568) is not detected in the high-resolution map (Figure 1 ). Given the high completeness of 86% (12/14) in the stellar mass range, our results are not significantly affected by the sample selection. Therefore, we find massive galaxies to commonly form stars in the extremely compact central region as at least 64% (9/14) have small 870 μ m sizes of R 1/2,870 μ m 1.5 kpc. This result is in excellent agreement with similar and independent evidence coming from an ALMA/870 μ m study of six massive star-forming galaxies at z ∼ 2 (Barro et al. 2016 ). Barro et al. ( 2016 ) find that the mean half-SFR radius is ∼30% smaller than the mean half-mass radius. The main difference between our work and Barro et al. ( 2016 ) is that they preselect only optically compact star-forming galaxies while our study almost completely selects main-sequence galaxies. 4. BULGE FORMATION IN EXTENDED, ROTATING DISKS Given that our ALMA sample is already massive, , they are likely to soon thereafter quench the active star formation and to be observed as quiescent galaxies in the local universe. Quiescent galaxies are always smaller than star-forming galaxies at any redshift and any stellar mass and have a cusp profile ( n > 2) unlike star-forming galaxies with exponential disks (Wuyts et al. 2011b ; van der Wel et al. 2014b ). A spatial distribution of stars within galaxies would not be changed unless a violent process like major mergers happens. However, centrally concentrated star formation reduces the half-light or half-stellar-mass radii of galaxies, and their Sérsic index would increase by central bulge formation. We quantitatively


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We would like to thank John O’Meara for providing HIRES spectra and Nigel Mathes for reducing UVES spectra. We thank Nicolas Lehner for discussions on the UV ionizing background. We also thank Neil Crighton for the MCMC analysis software and Cloudy ionization training. Support for this research was provided by NASA through grants HST GO-13398 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. S.K.P. acknowledges support through the Australian Government Research Training Program Scholarship. G.G.K., N.M.N., and M.T.M. acknowledge the support of the Australian Research Council through the Discovery Project DP170103470. C.W.C. and J.C.C. acknowledge support by the National Science Foundation under grant No. AST-1517816. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100012. 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. Observations were supported by Swinburne Keck programs 2014A_W178E, 2014B_W018E, 2015_W018E and 2016A_W056E. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programs listed in Table 2 .