O O O O O O B-Organization B-Organization I-Organization I-Organization O B-Organization B-Organization I-Organization I-Organization O O B-Instrument B-Organization I-Organization I-Organization B-Organization O O O O O O O O O O O O O O O B-Person I-Person O O O O B-Software O 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 I-Organization I-Organization I-Organization I-Organization

We thank the staffs of the ESA Herschel Science Centre and NASA Herschel Science Center, and the HIFI, Instrument Control Centre (ICC) for their help with the data reduction routines. In addition, we owe special thanks to David Teyssier for clarifications regarding the hebCorrection tool. This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


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ACKNOWLEDGEMENTS This work is partly supported by Ministry of Economy and Competitiveness (MINECO) (Spain), FIS2016-76363-P, by COST Action PHAROS (CA16214), by project 2017 SGR247 Agency for Management of University and Research Grants (AGAUR, Catalonia) (SDO). AVA thanks the Program 5–100 Immanuel Kant Baltic Federal University (IKBFU, Russia).


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 B-Formula I-Formula I-Formula 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 O O O O B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O B-Wavelength O O O B-Survey 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-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength B-Wavelength I-Wavelength O O O B-Formula I-Formula I-Formula O O O O B-Model 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 O O O O O O O O O O O B-Model O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Dataset I-Dataset O O B-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Survey B-Survey O B-Telescope O B-Formula I-Formula I-Formula 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 O O B-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula 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 B-Formula I-Formula I-Formula 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 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 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 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 B-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model O

= 5 in the top panel of Fig. 5 . The result using the Tiamat halo merger trees is shown for comparison and to indicate the convergence of the quasar luminosity function at z ∼ 5. The model is in agreement with observations at the bright end (Shen Kelly 2012 ; McGreer et al. 2013 ). We indicate the quasar luminosities of the three analogues in the top panel of Fig. 5 and find that the progenitors of ZF-1, ZF-2 and ZF-3 are bright quasars in the range that optical surveys such as SDSS are able to detect. This suggests that ZF-COSMOS-20115 is likely the descendent of a high-redshift quasar and illustrates the possible connection between MQGs and high-redshift quasars (Maiolino et al. 2012 ). Figure 5. Top panel: quasar UV 1450 Å luminosity function at z ∼ 5. The results using the Tiamat-125-HR and Tiamat halo merger trees are shown with solid and dashed lines, respectively. The shaded regions represent the 95 per cent confidence intervals around the mean using 100 000 bootstrap re-samples for the Tiamat-125-HR result. The observational data is shown with different symbols: Shen Kelly ( 2012 ) using SDSS DR7 data at z ∼ 4.75 () and McGreer et al. ( 2013 ) using SDSS, UKIDSS and MMT at z ∼ 4.7–5.1 (▵). From left to right, the vertical lines indicate the quasar UV magnitudes of ZF-1, ZF-2 and ZF-3, respectively. Bottom panel: correlation between high-redshift black hole mass ( z = 5) and low-redshift SFR ( z = 3.7). The size of the empty circle represents different stellar masses and ZF-3 is indicated with the filled circle. In order to better demonstrate this, for each massive galaxy selected at z = 5.3, we present the correlation between black hole mass and subsequent SFR at z = 3.7 in the bottom panel of Fig. 5 . ZF-3 is indicated with a filled circle. We see that galaxies with less massive black holes ( M BH 10 7.5 M ⊙ ) can have a range of subsequent star formation levels. This is due to self-regulated stellar feedback being the dominant mechanism in these galaxies. However, due to persistent AGN feedback, galaxies with more massive black holes do not have intense subsequent star formation. This indicates that a high-redshift bright quasar will likely become a MQG at later times, when its accretion disc has been completely consumed. 5.3 The reionization history The three ZF-COSMOS-20115 analogues are hosted by massive haloes, which provide deep gravitational potentials that efficiently accrete baryons. The high baryon accretion efficiency induces intense star formation at high redshift, providing a significant number of ionizing photons that reionize surrounding hydrogen at a very early time. In this section, we discuss the reionization history of ZF-COSMOS-20115 . In Fig. 6 , we show the evolution of the average neutral hydrogen fraction within boxes with different sizes around the three analogues. The neutral hydrogen fraction is calculated using 21 cmFAST (Mesinger, Furlanetto Cen 2011 ) with the galaxy catalogue provided by Meraxes (see


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from (numerical) frequency runs. In that case, reorganization energies (e.g. ) computed from single-point calculations were utilized to get the adiabatic values. APPENDIX A2: ADDITIONAL DETAILS ON THE CALCULATION OF ROVIBRATIONAL PROPERTIES Deceptive as it may sound for a theoretical chemist, like in the case of other carbon chains (e.g. Bâldea 2020b ), the DFT approach appears to perform better in quantifying rovibrational spectra for MgC 4 H species than much more computationally demanding ab initio methods: For MgC 4 H 0 neutral, our very tight optimization at B3LYP/aug-cc-pVTZ level yielded MHz. The relative deviation from the experimental value MHz (Cernicharo et al. 2019 ) is per cent, which is significantly better than both 0.3 per cent at CCSD(T)-F12/cc-pCVTZ-F12 (Cernicharo et al. 2019 ) and 1.7 per cent at CCSD(T)/aug-cc-pVTZ (Cernicharo et al. 2019 ). Likewise, our value D DFT = 0.0641 kHz obtained at the B3LYP/aug-cc-pVTZ level is only 13 per cent smaller than the experimental value D exp = 0.074 ± 0.002 kHz (Cernicharo et al. 2019 ). This is better than 17 per cent, the deviation of CCSD(T)-value (Cernicharo et al. 2019 , and Table A2 ), which, in turn, is somewhat better than 18 per cent, which is the deviation of the CCSD(T)-F12-based value (Cernicharo et al. 2019 ). Noteworthily, the best estimate D Kratzer = 0.0741 kHz (cf. Table 4 and A3 ) is that based on the Kratzer formula (equation 1 ) used in conjunction with the B3LYP/aug-cc-pVTZ B and ω MgC . This Kratzer-based value cannot be distinguished from the experimental value D exp = 0.074 ± 0.002 kHz (Cernicharo et al. 2019 ). Table A3. Calculated centrifugal distortion constants D (kHz) presented along with estimates deduced via Kratzer approximation (equation 1 ) using harmonic frequencies ω MgC of the MgC stretching mode. a CCSD(T)/cc-pVTZ. b CCSD(T)/aug-cc-pVTZ. c B3LYP/6-311++G(3DF, 3PD). d B3LYP/aug-cc-pVTZ. e CCSD(T)/cc-pCVTZ. Table A4. Adiabatic and vertical values of electron attachment (EA) and ionization (IP) energies computed for MgC 4 H linear chains at several levels of theory. Their most reliable estimates are depicted in italics and were used to deduce the chemical hardness η, chemical softness S , chemical potential μ, Mulliken electronegativity χ, and electrophilicity index ω. Energy unit is eV. a Δ-CCSD(T)/cc-pVTZ. b EOM-CCSD/cc-pVTZ. c Δ-CCSD(T)/cc-pCVTZ. d EOM-CCSD/cc-pCVTZ. e Δ-CCSD(T)/aug-cc-pVTZ. f .EOM-CCSD/aug-cc-pVTZ. g Δ-B3LYP/6-311++G(3DF, 3PD). h CBS-QB3. For sure, neither a DFT/B3LYP/aug-cc-pVTZ calculation like that found performing the best above nor whatever other much more sophisticated theoretical approach currently available is precise enough to enable detection in space. In view of this state-of-the-art of theory, aiming at guiding subsequent laboratory measurements and interpretation of not yet available rovibrational spectra (as the case of ), it is current practice in astrophysics (e.g. Pauzat et al. 1991 ) to estimate rotational


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This work was supported by NSF SHINE grant AGS1622413 to the University of New Hampshire (UNH). C.W.S. was also supported by Caltech subcontract 44A-1062037 to UNH in support of the ACE/MAG instrument. J.E.S. is supported by STFC(UK) grant ST/N000692/1.


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origin ( t = 61 minutes) up to its decay phase ( t = 70.7 minutes) in the vertical experiment for the three LOSs. (An animation of this figure is available.) To extend the analysis, it is also of interest to consider the total emitted intensity for each vertical column, i.e.,which, following Equation ( 1 ), is equal to the column density of the emitting species along the LOS (except for a constant factor). Equation ( 5 ) has been calculated separately for Si iv and O iv and with the emissivities obtained assuming either NEQ or SE ionization, to better gauge the importance of disregarding the NEQ effects. The results are shown in the middle and bottom panels of Figure 10 for Si iv and O iv , respectively. The top panel of the image contains the 2D map of the emissivity for Si iv for context identification. Combining Figures 9 and 10 , we are able to discern and describe characteristic features of the spectral profiles: 1. The most prominent feature in the synthetic profiles of Figure 9 is the brightening associated with the location of the internal footpoint of the surge. In the corresponding movie, we can see how that footpoint is formed at around t = 64 minutes, as the surge detaches from the emerged dome. During those instants, the associated synthetic profiles are characterized by large intermittent intensities and bidirectional behavior with velocities of tens of kilometers per second, as apparent, e.g., in the (b0) and (c0) panels at x ∈ [15, 16] Mm. In Si iv and O iv (panels (b) and (c)), we find that the internal footpoint is usually the brightest region, although there are some instants in which the brightest points can be located in the crests or the external footpoint. This is a potentially important result from the observational point of view because it can help us to unravel the spatial geometry of the surge in future observational studies: if strong brightenings are detected in Si iv and also in O iv within the surge, it would be reasonable to think that they correspond to the internal footpoint of the surge. In this region, the intensity ratio between Si iv and O iv ranges between 2 and 7, approximately. Note that, in general, the intensity ratio values vary depending on the observed region and features (Martínez-Sykora et al. 2016 ). In Section 5.2 we will see that LOS effects play a major role in causing the large brightness of the internal footpoint (and other bright features) compared to the rest of the surge. Here we consider the parallel question of the role of NEQ: what would be obtained for the intensity of the internal footpoint if SE were assumed? Comparing the values for Si iv in Figure 10 (middle panel, 13.8 ≤ x ≤ 16.1), there is roughly a factor of two, on average, between the NEQ and SE intensities; for O iv (bottom panel), there is no major difference in the intensity between both calculations. One could conclude that while NEQ is important for the Si iv diagnostics, SE could be applied for the O iv case;


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The Pan-STARRS1 Surveys (PS1) have been made possible through contributions of the Institute for Astronomy, the 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, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE). This publication makes use of data products from the 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. G.G. and D.F. are supported by NSF grant AST-1312891. E.S. acknowledges funding by Sonderforschungsbereich SFB 881 “The Milky Way System” (subproject A3) of the German Research Foundation (DFG). N.M. gratefully acknowledges the CNRS for support through PICS project PICS06183.


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ACKNOWLEDGEMENTS We thank the anonymous referee for helpful comments that improved this paper. We gratefully acknowledge support from the Science and Technology Facilities Council (HPE through grant ST/K501979/1, SR through ST/N50404X/1, TPR through ST/P000541/1). HPE acknowledges support under NASA contract NNG08FD60C. This research made use of data obtained from the 3XMM XMM–Newton Serendipitous Source Catalogue, based on archival observations with XMM–Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. We also acknowledge the use of public data obtained from the Chandra Data Archive and the Swift Data Archive.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Observatory B-Telescope 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 B-Model O O O O B-Observatory O O O O O O O O O O O O O O O B-Dataset B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O B-Model O B-Formula I-Formula I-Formula O O O O O O B-Dataset B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O B-Model O B-Formula I-Formula I-Formula O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O B-Model O B-Formula I-Formula I-Formula I-Formula I-Formula 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-Wavelength I-Wavelength O O O O O O B-CelestialObject I-CelestialObject O O O O B-Telescope O O O O O O O O O O O O O O O O O B-Observatory B-Telescope O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Dataset O B-Dataset 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 B-Citation I-Citation I-Citation I-Citation O O O O B-Software O O O B-Citation I-Citation O O O O O O O O B-Wavelength O O B-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O B-Wavelength I-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 B-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Telescope O

which may not be particularly informative, as Fig. 9 demonstrates. To this end, we do not interpret the total flux from the nebula in terms of any particular spectral model; rather, we present a total integrated flux of the nebula emission to interpret the overall source strength. The resulting spectral flux obtained for the nebula from the summation of the 38 independent 0.26°× 0.26° spectral boxes is shown in Fig. 10 . For illustration, the HESS J1825–137 spectrum obtained from Fermi -LAT ( Grondin et al. 2011 ) is also shown, although we recall that the region from which this spectrum is obtained, based on a morphological symmetric Gaussian fit template to the Fermi data, does not fully correspond to the same spatial region. The 2011 analysis and the 3FGL (the third LAT Catalogue, 20 MeV to 300 GeV, Acero et al. 2015 ) both use a Gaussian with σ = 0.56° as the spatial template, whereas the 3FHL (the third LAT High-Energy Catalogue, 10 GeV to 2 TeV, Ajello et al. 2017 ) uses a Gaussian with σ = 0.75°, which is consistent with the Fermi Galactic Extended Source catalogue best-fit Gaussian with σ = 0.79 ± 0.04 ( Ackermann et al. 2017 ). Whilst these templates are only approximations to the source morphology, in Fig. 10 the IC peak may be inferred to occur at around 200 GeV. Fig. 10 Spectral energy distribution of HESS J1825–137 showing the total combined H.E.S.S. energy flux with statistical error bars, as determined with the method outlined in Sect. A . The Fermi -LAT spectral fit from Grondin et al. (2011) is also shown, together with spectra from the 3FGL and 3FHL catalogues ( Acero et al. 2015 ; Ajello et al. 2017 ), both of which were best fit by a log-parabola spectral model. A plausible IC emission model with multiple contributing radiation fields is shown, using the parameterisation of the Popescu et al. (2017) radiation model and the Naima modelling package ( Zabalza 2015 ). The emission is mostly dominated by the FIR field; the CMB becomes dominant at a few tens of TeV and below ~ 10 GeV. The total flux above 300 GeV was found to be (6.07 ± 0.13 stat ± 0.07 sys ) × 10 −11 cm −2 s −1 , corresponding to ~54% of the flux of the Crab nebula. Above 1 TeV, a flux of (1.12 ± 0.03 stat ± 0.25 sys ) × 10 −11 cm −2 s −1 was obtained, such that the proportion relative to the Crab nebula increases slightly to ~ 64% of the Crab nebula flux. The source remains strong at ~61% of the Crab nebula flux above 10 TeV. It is impressive that the γ -ray flux is so strong given that the distance to HESS J1825–137 is approximately twice that of the Crab nebula (at 2 kpc), despite (or perhaps because of) the significantly older age of the system. Interestingly, as part of the second HAWC catalogue, it was found that the confused source associated with the combined emission from the region, 2HWC J1825–134, is brighter than the Crab nebula at 7 TeV ( Abeysekara et al. 2017 ). This point is included in Fig. 10 and is compatible within the HAWC systematic


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MJ-H is supported in this work by a Marsden Grant administered by the Royal Society of New Zealand. SS was supported by a Victoria Doctoral Scholarship. We would like to thank Dr Phil Edwards for allocating Director's time for the H214 ARDES observations. Additionally, SS deeply thanks Dr Robin Wark for her assistance with remote-observing, and Dr Jamie Stevens and Dr Mark Wieringa for their invaluable comments on CABB data reduction and imaging in MIRIAD . Finally, we thank Dr Siamak Dehghan for assistance with the generation of the multipanel figures. The ATCA is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by CSIRO. The Digitized Sky Surveys were produced at the Space Telescope Science Institute under US Government grant NAG W-2166.


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

are the amplitude index (Belokurov et al. 2017 ) and the Gaia DR2 variability classification (Mowlavi et al. 2018 ), in the left and right panels, respectively. The local sample (without YSOs and MS/RGB stars) is also shown for comparison as a black unfilled histograms. We found that the amplitude index method seems to find variability in objects that were not classified as variables in the Gaia DR2. 5.2. Absolute Magnitudes for the Foreground Mira Population Several studies have been carried out to estimate IR absolute magnitudes of the AGB populations in the LMC, where the distance to the stellar system is known, and therefore, the distance modulus (and presumably also the IR extinction) can be assumed to be the same for each object (see e.g., Whitelock et al. 2008 ). From Figure 6 , we can determine an average absolute K magnitude of mag for the local sample. Although the magnitude values found roughly correspond to those found in the LMC (i.e., between −8.0 and −6.0 mag; see, e.g., Whitelock et al. 2008 ), one should keep in mind that we established a fainter limit of . Nevertheless, with the aim of analyzing the absolute magnitude distribution using the variability classification defined by Gaia (Mowlavi et al. 2018 ) and the amplitude index (Belokurov et al. 2017 ), we made Figure 9 , where the distribution of absolute magnitude for the local sample without considering the filtering of YSOs and MS/RGB (made in Section 4.3 ) is shown. Figure 9 shows that by including these younger sources, the distributions are much broader in terms of absolute magnitude range. This can be partly explained by the current sample being mostly based on a single 2MASS observation and including the effects of large amplitude variability. However, when we filter the sample by a variability qualification (as shown in both panels of Figure 9 ), the low-luminosity tail (in ) is cut out. In this sense, the Gaia classification as Mira or SR variable seems to narrow the distribution more. Following a similar discussion in Mowlavi et al. ( 2018 ), we argue that the low-luminosity tail in Figure 9 and also Figure 7 is due to contamination with YSOs and MS/RGB stars that can also peak in the IR but do not show the same variability (Lewis et al. 2020b ; Y. M. Pihlström et al. 2020, in preparation). 5.3. Bolometric Magnitudes for the Foreground Mira Population The bolometric luminosity is a fundamental property useful for classifying stellar populations and evolutionary stages (Srinivasan et al. 2009 ), as it measures the intrinsic stellar power. Although its definition is straightforwardly formulated as the total integrated power over all frequencies, in practice, complete photometric measurements that allow a direct bolometric luminosity estimate are hardly ever available. Therefore, under various assumptions, a limited set of photometric measurements, preferably near the peak of the SED, can be used to apply a bolometric correction (BC) in order to determine the


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

paper, as explained below. 3.1 Peebles–Hauser The Peebles–Hauser (PH) estimator is based on the correlation function proposed by Peebles Hauser ( 1974 ) and can be expressed as where DD (ρ) is defined as the pair of observed quasars counts within a separation radius ρ normalized by the the total number of pairs, N obs ( N obs − 1)/2 and RR (ρ) follows the same definition for the random catalogues. 3.2 Landy–Szalay The Landy–Szalay (LS) estimator is based on the correlation function proposed by Landy Szalay ( 1993 ). In addition to the quantities DD (ρ) and RR (ρ) defined above, DR (ρ) denotes the pair of quasar-random counts normalised by the available number of pairs. Hence, the LS estimator is given by For the PH and LS estimators, the quantity D 2 ( r ) is calculated by replacing equations ( 4 ) and ( 5 ) into equation ( 3 ), respectively. 4 THE HOMOGENEITY SCALE In order to estimate the homogeneity scale from the SDSS-IV DR14 quasars (henceforth ), we first obtain the values of D 2 ( r ) for each redshift slice using both estimators above. Then, a polynomial fitting is used to obtain the corresponding scale where the transition to homogeneity is identified (we refer the reader to Gonçalves et al. 2018 for more details). Following previous analyses (Scrimgeour et al. 2012 ; Laurent et al. 2016 ; Ntelis 2017 ), we define the homogeneity scale as the characteristic scale where the Universe can be considered homogeneous within 1 per cent of the expected fractal dimension for a homogeneous distribution, D 2 = 3 – thus, the scale where the spatial distribution of QSOs reaches D 2 = 2.97. Although arbitrary, the 1 per cent criterion is widely used in the literature, and is justified given some observational issues, such as the survey geometry and incompleteness, as well as the sample noise. Since we use 20 random catalogues to obtain D 2 , we also perform a bootstrap analysis over the 20 values of , quoting its mean and standard deviation as our measurement of the homogeneity scale and its corresponding uncertainty, respectively. 1 Our first measurements of are presented in the second column of Tables 2 and 3 . For the sake of example, Fig. 1 shows the results for both and D 2 obtained at the redshift using the PH estimator (similar results are also obtained for the LS estimator). The red points stand for the observational data with the respective errors. In the right-hand panel of Fig. 1 , the horizontal lines correspond to the D 2 = 2.97 and D 2 = 3 thresholds. From our analysis, we find that the PH estimator provides smaller error bars than the LS estimator. A possible explanation may be attributed to the fact that our approach does not use mock catalogues. Instead, we relied on an accurate bootstrap analysis of the 20 random catalogues we have produced. A full assessment of the homogeneity scale using mock catalogues that reflects the matter power spectrum, redshift distribution, QSO clustering, and angular selection function of the


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We thank the referee for constructive and insightful comments. This paper makes use of ALMA data ADS/JAO.ALMA#2011.0.00294.S; #2012.0.00307.S; #2013.1.00118.S; #2012.1.00090.S; #2015.1.01528.S; #2016.1.00434.S; and #2017.1.01492.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This work is based on observations taken by the CANDELS Multi-Cycle Treasury Program with the NASA/ESA HST , which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. P.L., D.L., and E.S., acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694343). I.R.S. and A.M.S. acknowledge support from STFC (ST/P000541/1). F.B., B.M., E.V., K.H. and EFJA acknowledge support of the Collaborative Research Center 956, subproject A1, funded by the Deutsche Forschungsgemeinschaft (DFG). S.L. acknowledges funding from Deutsche Forschungsgemeinschaft (DFG) Grant BE 1837/13-1 r. E.A.C. acknowledges support from the ERC Advanced Investigator Grant DUSTYGAL (321334) and STFC (ST/P000541/1). M.J.M. acknowledges the support of the National Science Centre, Poland, through the POLONEZ grant 2015/19/P/ST9/04010; this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778. S.T. acknowledges support from the ERC Consolidator Grant funding scheme (project ConTExt, grant No. 648179). The Cosmic Dawn Center is funded by the Danish National Research Foundation. E.V. acknowledges funding from the DFG grant BE 1837/13-1. J.L.W. acknowledges support from an STFC Ernest Rutherford Fellowship (ST/P004784/2), and additional support from STFC (ST/P000541/1).


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

considering equation ( 4 ) and measured P values of ∼1–10 h for AMXPs (Salvo Sanna 2020 ). Figure 2. Numerically computed neutron star spin frequency ( ν ) evolution curves due to transient accretion (see Sections 3.1 and 3.2 ). The dotted grey horizontal line shows a constant long-term average accretion rate () of 5 × 10 15 g s −1 . The solid grey curve shows an evolving with a fast decay (see Section 3.1 ) in the RLDP on the right of the dotted vertical line. Various ν evolution curves are for g s −1 , and based on if EM spin-down and evolution are included not, as mentioned on the plot. This figure shows that ν can increase in the RLDP (see Section 3.2 ). 3.2 Spin evolution of transient sources First, we study how ν evolves if the neutron star accretes transiently throughout the LMXB phase (see Fig. 2 ). For an evolution duration of two billion years and for the examples given in this figure, ν remains much lower than ν eq,eff (not shown in the figure) for g s −1 . Note that an –10 16 g s −1 is common for many neutron star LMXBs (Lamb Yu 2005 ), although could be significantly higher in the initial stage of the LMXB phase (e.g. see Tauris 2018 ; Chen, Liu Wang 2020 ). The aim here is to find out how ν evolves in the RLDP. Fig. 2 shows that ν can increase in the RLDP, even if decreases drastically, and regardless of the inclusion of an additional spin-down (e.g. due to the EM torque (see Bhattacharyya Chakrabarty 2017 ) in the quiescent phase; see Section 1 ). This is not unexpected, as ν neither approaches nor tracks ν eq,per during a transient accretion (see Section 2 ). However, we note that ν either approaches or tracks ν eq,eff for such an accretion. Hence, ν either increases or decreases due to transient accretion, both in the RLDP and before the RLDP, depending on whether increases or decreases (see Section 2 and equation 5 ). Therefore, ν can decrease in the RLDP, if decreases. But, since is expected to depend on the binary orbital period P (with an estimated relation of , Lasota 2001 ), and the change of P is moderate (e.g. Bhattacharya van den Heuvel 1991 ), ν should not considerably decrease in the RLDP. 3.3 Spin evolution of persistent sources How does ν evolve for a persistent source? The neutron star first spins up relatively quickly towards the spin equilibrium frequency ( ν eq,per ), and then tracks it (see Introduction and Section 2 , Fig. 3 ). In the RLDP, if decreases rapidly, ν decreases for a persistent source, but cannot track ν eq,per anymore, which was shown by Tauris ( 2012 ), and is confirmed in Fig. 3 . But in reality, a persistent source becomes a transient for , and consequently, ν increases, as it does not track the lower spin equilibrium frequency ν eq,per anymore, and now approaches a higher effective spin equilibrium value ν eq,eff (see Fig. 3 , and also Section 2 ). Therefore, since even an initially persistent source should become a transient at least in the RLDP due to the decrease of , ν should increase in


O O O O O O O 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 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 B-Model I-Model 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 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 B-Model I-Model 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 O O O O O O O O O O O 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 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

directions, uncorrected for Faraday rotation. The FWHM dimensions and orientation of the elliptical Gaussian restoring beam are indicated by a cross in the lower left corner of the map. Figure 4.4421. Source 1954+513 at epoch 2011-Aug-26. Each panel contains two contour maps of the radio source, the first consisting of I contours in successive integer powers of two times the lowest contour level, with linear fractional polarization overlaid according to the color wedge. A single negative I contour equal to the base contour level is also plotted. The second map includes the lowest positive I contour from the first map, and linearly polarized intensity contours, also in increasing powers of two. The sticks indicate the electric polarization vector directions, uncorrected for Faraday rotation. The FWHM dimensions and orientation of the elliptical Gaussian restoring beam are indicated by a cross in the lower left corner of the map. Figure 4.4422. Source 1954+513 at epoch 2015-May-18. Each panel contains two contour maps of the radio source, the first consisting of I contours in successive integer powers of two times the lowest contour level, with linear fractional polarization overlaid according to the color wedge. A single negative I contour equal to the base contour level is also plotted. The second map includes the lowest positive I contour from the first map, and linearly polarized intensity contours, also in increasing powers of two. The sticks indicate the electric polarization vector directions, uncorrected for Faraday rotation. The FWHM dimensions and orientation of the elliptical Gaussian restoring beam are indicated by a cross in the lower left corner of the map. Figure 4.4423. Source 1954+513 at epoch 2015-Nov-25. Each panel contains two contour maps of the radio source, the first consisting of I contours in successive integer powers of two times the lowest contour level, with linear fractional polarization overlaid according to the color wedge. A single negative I contour equal to the base contour level is also plotted. The second map includes the lowest positive I contour from the first map, and linearly polarized intensity contours, also in increasing powers of two. The sticks indicate the electric polarization vector directions, uncorrected for Faraday rotation. The FWHM dimensions and orientation of the elliptical Gaussian restoring beam are indicated by a cross in the lower left corner of the map. Figure 4.4424. Source 1954+513 at epoch 2016-Mar-05. Each panel contains two contour maps of the radio source, the first consisting of I contours in successive integer powers of two times the lowest contour level, with linear fractional polarization overlaid according to the color wedge. A single negative I contour equal to the base contour level is also plotted. The second map includes the lowest positive I contour from the first map, and linearly polarized intensity contours, also in increasing powers of two. The sticks indicate the


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ACKNOWLEDGEMENTS This study has benefited greatly from discussions with K. Doi. We also thank the reviewer for many useful comments on this paper. The present research used the computational resources of the HPCI system provided by Cyber Sciencecenter, Tohoku University; Cybermedia Center, Osaka University, Earth Simulator, JAMSTEC through the HPCI System Research Project (Project ID:hp160079, hp170047, hp180001, hp190035). This study was supported by JSPS KAKENHI Grant Numbers JP17K05387, JP17H02869, JP17H01101, and JP17H06360. Simulations reported in this paper were also performed by 2017 Koubo Kadai on Earth Simulator (NEC SX-ACE) at JAMSTEC. This work was partly achieved through the use of supercomputer system SX-ACE at the Cybermedia Center, Osaka University. Simulations were also performed by 2018 Koubo Kadai on Earth Simulator (NEC SX-ACE) at JAMSTEC.


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

The authors thank the staff at the Subaru Telescope for their excellent support in the observations. The authors thank Takaya Nozawa for his constructive comments on the manuscript. The work by K.M. is supported by the JSPS Grant-in-Aid for Scientific Research (No. 26800100) and by the WPI Initiative, MEXT, Japan. Support for H.K. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. H.K. acknowledges support by CONICYT through FONDECYT grant 3140563. The work by M.T. is supported by JSPS Grant-in-Aid for Scientific Research (15H02075, 15H00788). The work by K.N. is supported by the JSPS Grant-in-aid for Scientific Research (No. 23224004 and 26400222).


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

Hazra et al. 2014 ; Passos et al. 2014 ). Indeed, LC17 observed that when their model enters into an extended grand minimum of the weaker magnetic field, the generation of poloidal field stops due to a lack of BMRs, and the model never recovers from that quiescent phase. Their model recovers only when the magnetic field does not fall below a certain level. 2. Model In this Letter, we explore the Babcock–Leighton dynamo mechanism during grand minima, focusing in particular on how the dynamo might recover from such episodes through the Babcock–Leighton process alone. To do so, we first produce grand minima. In our study, we build on our recent work, KM17 , which is an updated version of the original model (Miesch Dikpati 2014 ; Miesch Teweldebirhan 2016 ). In this model, BMRs are produced near the surface based on the toroidal flux at the BCZ and most of the statistical properties of BMRs are based on solar observations. We refer readers to Section 2 of KM17 for the details of this model. From KM17 , we consider Runs B10–11, in which the diffusivity in the bulk of the CZ is in the order of 10 12 cm 2 s −1 . The BMR flux distribution is fixed at the observed value and the time delay between two successive BMR emergences is obtained from the observed log-normal distribution, which changes in response to the toroidal field at the base of the CZ to allow more frequent BMRs when the toroidal field is strong and vice versa. The BMR tilt has a Gaussian scatter around Joy’s law with standard deviation ( σ δ ) of 30° (15°) for Run B11 (B10). Another key ingredient of the model is the downward magnetic pumping which has the same form as in KM17 and it is given bywhere γ CZ = 2 m s −1 and γ S = 20 m s −1 . Thus, the pumping has a value of γ S only near the surface, while in the rest of the CZ it is γ CZ . Pumping is a process in which the magnetic flux can be transported in a stratified convective medium due to the topological asymmetry in the convective flow. A variety of theoretical and numerical models suggest that it is operating in the solar CZ, particularly near the surface where both the velocity amplitude and the density stratification are largest (e.g., Drobyshevski Yuferev 1974 ; Krause Rädler 1980 ; Petrovay Szakaly 1993 ; Tobias et al. 1998 ). Although at present, we do not have a stringent constraint on the strength of the pumping, previous studies (Käpylä et al. 2006 ; Karak et al. 2014b ) suggest its value to be at least a few tenths of the convective velocity. Keeping in mind that the upper layer of the Sun is highly convective with the observed surface convection speed of a few km s −1 , a value of 20 m s −1 pumping speed is realistic (Spruit 1997 ; Nordlund et al. 2009 ). This value is also large enough to make the magnetic field near the surface approximately vertical, which improves the agreement between Babcock–Leighton dynamo models and Surface Flux Transport (SFT) models. 4 4 Cameron et al. ( 2012 ) showed that the inclusion of


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

layer is still unknown. It may be either an ice-rock layer between a rocky core and a water-rich outer mantle, or an outer rocky core composed of hydrous silicates (Lunine et al. 2010 ; Fortes 2012 ). If a mixed ice-rock layer indeed exists in the interior of Titan, then a newly discovered high-pressure solid solution in the H 2 O–CH 4 binary system called MH-III (also CH 4 filled-ice Ih) may hinder the outer transport of internal CH 4 into the atmosphere. The formation of MH-III was first reported by Loveday et al. ( 2001a ). Contrary to what was previously assumed for the H 2 O–CH 4 system, upon increasing the pressure above about 2 GPa, at room temperature, the classical structure H cage clathrate transforms into MH-III, rather than experiencing phase separation into water ice VII and solid CH 4 . In this way the solubility of H 2 O and CH 4 is kept throughout the entire pressure range inside Titan. This is also likely true for the much higher pressures spanning water ice mantles of water-rich exoplanets, given that MH-III was found to be stable up to about 100 GPa (Hirai et al. 2006 ), and temperatures higher than 1000 K (ichi Machida et al. 2006 ). We refer the reader to Loveday et al. ( 2001b ) for a detailed description of the crystallographic nature of MH-III. If CH 4 is indeed locked in grains of MH-III, scattered within a deep ice-rock layer above the rocky core of Titan, then how much of it may be transported outward depends on the buoyancy of these grains with respect to melt pockets and the solubility of CH 4 under such conditions. Such an analysis requires thermophysical data for MH-III at the appropriate conditions. In the context of Titan-like exoplanets, previous work on the transport of CH 4 across the interior pinpointed the necessary thermophysical data and the lack thereof (Levi et al. 2013 , 2014 ). Quantifying the needed thermophysical data is the prime object of this work. In Section 2 we probe the pressure regime in a possible undifferentiated ice-rock layer inside Titan, to better pinpoint our molecular simulations and the possible role of MH-III. In Section 3 we explain our computational methods. In Section 4 we derive the thermal equation of state (EOS) and thermal expansivity. Section 5 is dedicated to the heat capacity. In Section 6 we estimate the thickness of an MH-III enriched layer in Titan’s interior, and its carbon content capacity. In Section 7 we use a 1D thermal evolution model to asses the stability of such a layer. Section 8 is a discussion, and Section 9 is a summary. 2. The Pressure Regime in the Undifferentiated Ice-rock Layer In this section we estimate the pressure at the boundary between a possible internal ice-rock layer and Titan’s inner rocky core. We consider three basic constraints for Titan, its radius, mass and normalized MOI. We adopt a layered model for the internal structure (see Figure 1 ). The outermost condensed layer is a shell composed of ice Ih with a mass density of


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We thank the referee for a thorough, probing report that has improved the manuscript. We also thank Holly Capelo, Alan W. Harris, and Anders Johansen for useful discussions. BTG and DV benefited by support by the European Union through ERC grant number 320964. SE would like to acknowledge the support of the NEOShield project funded by the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement no. 282703 (NEOShield) as well as Paris Observatory's ESTERS (Environnement Spatial de la Terre : Recherche Surveillance) travel grants.


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

however, is insufficient for the pressure gradient to change sign. The top panel of Figure 6 shows the mdot1e-7 case with parameters as in Table 2 , but N 2 = 3 and N 3 = 170. It shows that the active zone inside the rounded-off rim is in its final size. After the active zone has reached a certain size small temperature deviations start to occur and travel through it. These small deviations manifest in the depiction as walls where the dust is present. Since the simulation does not include latent heat it is not possible to decide whether these small deviations have to occur or not, but they were consistently found for every parameter set that produced a dust-free zone. The surface density in Figure 7 mirrors the cavity that is also present in Figure 6 . The dust density falls to g cm −2 in the dust-free zone. To further analyze the equilibrium in the dust-free zone an alternative sublimation formula is in progress. Figure 7. Comparison of gas (solid line) and dust (dotted line) surface density for model mdot1e-7 . The optical depth at constant radiusfor near-infrared radiation in Figure 8 suggests that the dust-free zone forms after a large enough depth in the θ direction is reached because diffusion of radiation energy is no longer sufficient to cool the disk. Figure 8. Vertical optical depth in NIR for model mdot1e-7 . 5. Discussion This work represents an early stage in developing a self-consistent model of the inner rim of protoplanetary disks. In this section some important limitations of the model will be discussed. The simplifications introduced in Flock et al. ( 2016 ), such as a uniform dust-to-gas ratio in the shadowed region and a non-frequency-dependent gas opacity are also applied in this work. A more elaborate sublimation formula is needed in the future, especially with respect to the dust-free cavity inside the disk. A detailed implementation of gas line radiation transfer would go beyond the scope of this work. Further, the value of α was chosen to be constant throughout the box. However, the strength of the turbulence is expected to be influenced by the temperature and could be lower in MRI inactive regions (Lesur et al. 2014 ; Turner et al. 2014 ; Simon et al. 2015 ). A temperature-dependent α will be explored in further work. The temperature deviations and dust walls described at the end of Section 4.3 will have to be further scrutinized in combination with the modeling of the dust-to-gas ratio. Small differences in the temperature can lead to significant changes in the dust-to-gas ratio around the sublimation temperature. This is therefore a delicate problem that needs to be explored tentatively and might necessitate the inclusion of further effects like dust diffusion, latent heat, and temperature-dependent viscosity. 6. Conclusions and Outlook This paper presents a 2D model for protoplanetary disks that consistently includes viscous heating and thermal conduction. The model expands previous works (Flock et al. 2016 )


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compared to the unambiguously identified [Si ii ] 34.81 and [S iii ] 33.48 μ m makes the [O iv ] identification much more plausible. If [Fe II] 25.98 μ m is not detected, the putative identifications of the intrinsically weaker [Fe II] 35.35 and [Fe II] 17.94 μ m (Smith et al. 2009 ) in the PR equilibrium ejecta are also doubtful. Isensee et al. ( 2012 ) clearly saw the 17.94 μ m line, and we interpret this as coming from the reverse shock. Gerardy Fesen ( 2001 ) saw even higher excitation [Fe II] lines with wavelengths in the range ∼1–2 μ m that are clearly from fast-moving knots or quasi-stationary flocculi and therefore must result from a shock–clump interaction. Koo et al. ( 2016 ) and Lee et al. ( 2017 ) presented mid- and near-IR observations of [Fe II] from ejecta and CSM knots in Cas A. Koo et al. ( 2016 ) demonstrated that in radiative shock models of this emission, most of the [Fe II] radiation comes from the postshock cooling zone, similar to our Figure 5 . Lee et al. ( 2017 ) found ejecta knots with abundances commensurate with O burning, with elements like Si and S present, as well as a sample of ejecta knots showing strong [Fe II] lines but no Si or S. They interpreted these knots as products of complete Si burning leaving almost “pure” Fe, as found in X-rays by Hwang Laming ( 2009 , 2012 ), or in some cases the products of α -rich freeze-out. It is unclear why such ejecta should be in knots, as opposed to diffuse clouds inflated by radioactivity, but compared to SN 1987A, Cas A was a smaller progenitor at explosion, with a presumably faster expansion and lower opacities leading to a reduced effect of this sort. Koo et al. ( 2018 ) estimated a mass of [Fe II]-emitting shocked dense ejecta of ∼3 × 10 −5 M ⊙ . Extrapolating this clumping to the whole inner ejecta is difficult to do with any accuracy, but assuming that the Fe clump density is the same throughout the inner ejecta as it is at the reverse shock, the total Fe mass should be 3 × 10 −5 M ⊙ multiplied by the ratio of the volumes represented by the inner ejecta (6 × 10 56 cm 3 ) and the reverse shock emission. This last piece is ambiguous, but taking it to be cm 3 , where R r = 1.7 pc = 5 × 10 18 cm is the reverse shock radius and the knot diameter 2 r knot ∼ 2.5 × 10 17 cm gives a ratio of volumes of 7.5 and an implied Fe mass in knots of 2 × 10 −4 M ⊙ . This could be uncertain by at least an order of magnitude either way but is likely to be smaller than the Fe mass in the diffuse Fe–Co–Ni bubbles, estimated below. Features coinciding with [Fe V] 20.85 and 36.34 μ m, which would imply Fe masses of order ∼10 −3 M ⊙ , are also visible in the inner ejecta region. These only appear at marginal significance and must wait for better data for confirmation. The [O iv ] 25.89 and [Si ii ] 34.81 μ m morphologies (Smith et al. 2009 ) and the mass estimate of Arias et al. ( 2018 ) suggest that most of the inner ejecta mass expected by Hwang Laming ( 2012 ) are clumped into a volume


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The authors thank the anonymous referee for constructive comments. This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG) via SFB 956. G. Busch is member of the Bonn-Cologne Graduate School of Physics and Astronomy (BCGS). L. Moser and S. Smajić are members of the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics Bonn/Cologne. J. Scharwächter acknowledges the European Research Council for the Advanced Grant Program Number 267399-Momentum. M. Valencia-S. received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 312789. 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. 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 is also based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.


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KL and IGH are funded via a University of Glasgow Lord Kelvin-Adam Smith Fellowship. IGH is supported by a Royal Society University Research Fellowship. The authors thank the International Space Science Institute (ISSI) for support for the team “Improving the Reliability of Solar Eruption Predictions to Facilitate the Determination of Targets-of-Opportunity for Instruments With a Limited Field-of-View”, where this work benefited from productive discussions. The authors would like to thank N. Gyenge for very helpful discussions about active longitudes and providing the data from Gyenge et al. (2016) .


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Support was provided by the National Aeronautics and Space Administration (NASA) through HST grant GO-13787 from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. Support was also provided by the National Science Foundation (NSF) through grants AST-1210599 and AST-1312221 to the University of Arizona. This study used data products from the Southern H-Alpha Sky Survey Atlas (SHASSA), which is supported by the National Science Foundation.


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shown separately (solid lines) as well as the dark matter at z = 8, 9, and10. The bottom panels show the associated scale-dependent bias, b g (defined as the square root of the ratio of the galaxy over dark matter correlation). The errors bars are delete-1 jack-knife errors with each jack-knife subsample corresponding to a subvolume obtained by removing one of the octants from the full volume of BLUETIDES . The one-halo term dominates at scales r 0.12 Mpc h −1 above which the two-halo term takes over. As expected, the brighter SAMPLE-H16 galaxies are more strongly clustered; furthermore, also note that clustering is steeper for the more luminous SAMPLE-H16 galaxies; therefore, as we go to smaller scales the clustering becomes more and more sensitive to the flux limit, with the one-halo clustering showing a significantly steeper dependence on the limiting magnitude as compared to two-halo clustering. These features have been found in observational studies of clustering dependence on luminosity (Kashikawa et al. 2006 ; Savoy et al. 2011 ; Harikane et al. 2016 ). Figure 5. Spatial clustering of galaxies predicted by BLUETIDES at redshifts 8, 9, and 10 from left to right for galaxy samples of different limiting magnitudes m UV corresponding to Bouwens et al. ( 2015 ) B15 and Harikane et al. ( 2016 ) H16 in red and blue lines, respectively. Top panels: Solid lines represent the one-halo and two-halo contributions of the two-point galaxy correlation function. The coloured dashed lines are the total correlation functions. Thin black dashed lines are the dark matter correlation functions. Bottom panels: Scale-dependent bias at redshifts 8, 9, and 10. The dashed lines are the large-scale linear biases. A significant scale dependence in the galaxy bias is seen at scales 0.5 Mpc h −1 ≲ r ≲ 10 Mpc h −1 (well within the two-halo regime) indicating the presence of non-linear effects at scales larger than the length scales associated with individual host haloes. Evidence of scale dependence in the halo bias has been previously reported using N -body simulations (Reed et al. 2009 ; Jose et al. 2016 ). Jose et al. ( 2016 ) (hereafter J16 ) uses simulations with volumes comparable or larger than BLUETIDES to study non-linear bias at redshifts z ∼ 2–5. J16 reports some universal properties of (redshift independent) in the scale-dependent bias and provides a fitting function. In our upcoming paper (Bhowmick et. al. in preparation), we investigate whether their results agree with the predictions of BLUETIDES by making a precise comparison for a wide range of halo mass bins. We find that our predictions are in fairly good agreement (only slightly lower by an amount ≲ 0.3 dex in general) with J16 , extending the validity of J16 results to regimes well beyond z ∼ 2–5; we have discussed this in more detail in Bhowmick et. al. (in preparation). The foregoing emphasize the importance of measuring clustering directly with simulations as (we shall see next) the


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FS, EV, and MR acknowledge the support from the DFG Cluster of Excellence “Origin and Structure of the Universe.” The simulations have been carried out on the computing facilities of the Computational Center for Particle and Astrophysics (C2PAP). SC acknowledges support from Premiale INAF “MITIC” and has been supported by INFN (Iniziativa specifica TAsP). The authors thank Francesco R. Ferraro for the very useful discussion on BSS and for providing advanced information of the color and magnitude distribution in the bulge cluster. Support for MZ and DM is provided by the BASAL CATA Center for Astrophysics and Associated Technologies through grant PFB-06, and the Ministry for the Economy, Development, and Tourism’s Programa Iniciativa Científica Milenio through grant IC120009, awarded to the Millenium Institute of Astrophysics (MAS). EV and MZ acknowledge support from FONDECYT Regular 1150345. DM acknowledges support from FONDECYT Regular 117012. SH, SC, and ES acknowledge grant 309290 form IAC and grant AYA2013-42781P from the Ministry of Economy and Competitiveness of Spain.


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dwarf—M dwarf eclipsing binaries. We drew sample 1 from Henry McCarthy ( 1993 ), Delfosse et al. ( 2000 ), and Benedict et al. ( 2016 ), excluding those in our calibration sample (Section 2 ). We added one target, GJ 2005A, for which the BC pair was analyzed in this paper, but Seifahrt et al. ( 2008 ) provide a mass determination for the A component. For sample 2, we drew eclipsing binaries from the compilations of Hartman et al. ( 2011 ) and Parsons et al. ( 2018 ), restricting the sample to double-lined eclipsing binaries, those with individual mass estimates better than 5%, and systems with a parallax from the second Gaia data release passing the Gaia quality cuts given in Appendix C of Lindegren et al. ( 2018 ). We removed 19e-3-08413AB because the distance is too large (≫500 pc) to assume zero reddening and excluded systems from Kraus et al. ( 2011 ) because they have no reported flux or luminosity ratios, which are needed to estimate Δ K S (detailed below). Lastly, we removed PTFEB132+19AB (Kraus et al. 2017 ) because it is young (≃650 Myr). In total this gives us individual masses for 29 stars with which to test our – M * relation. A significant advantage of eclipsing binaries is that we could adopt the much more precise parallaxes from Gaia , as they all have orbits that are too tight to show detectable centroid motion. For the astrometric binaries/triples, we drew parallaxes either from Gaia DR2 parallaxes of nearby companions (e.g., for Gl 644ABC we used the Gaia parallax from the wider companion Gl 643) or from sources that accounted for the high-order nature of the system. As with binaries analyzed in this paper, unresolved K S values were taken from 2MASS. We used AO data from VLT/NaCo to derive Δ K for Gl 866AC-B and our own Keck/NIRC2 measurements for Gl 644A-BC and GJ 2005A-B-C (all three are resolved), just as was done for binaries analyzed in this paper. For other systems, including unresolved components of the triples (Gl 866A-C and Gl 644B-C), the literature only provided contrast ratios in optical bands. We converted these to Δ K S using the synthetic and observed magnitudes given in Mann et al. ( 2015 ), following a procedure analogous to that outlined in Kraus et al. ( 2017 ). To briefly summarize, we found the combination of two single-star spectral templates that reproduced both the unresolved spectral energy distribution ( Gaia and 2MASS photometry) and the measured contrast(s) from the literature reference (usually V , R , or Kepler ) and then computed a Δ K S value for the best-fit template combination. This is similar to our conversion of Δ K X to Δ K S detailed in Appendix A . Correction from optical to NIR contrasts depends on metallicity (e.g., Schlaufman Laughlin 2010 ), and precise metallicities of these systems were not known. Instead, we assumed that all systems were −0.6 [Fe/H] +0.4, and we adopted uncertainties that encompass the range of values due to unknown metallicity. Errors introduced from these


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We thank the anonymous referee for useful discussions and comments which considerably helped us to improve the manuscript. DK was supported by RFBR grant 13-02-92119 and by the French national research agency ANR (COSMIS project). She thanks the Max-Planck-Institut für Astrophysik for the warm hospitality. SB was supported by RFBR grant 13-02-92119 and SAI MSU. This work was supported by the Deutsche Forschungsgemeinschaft via the Transregional Collaborative Research Center TRR 33 ‘The Dark Universe’ and the Excellence Cluster EXC153 ‘Origin and Structure of the Universe’.


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ACKNOWLEDGEMENTS We thank the referee for the constructive comments. Numerical computations were carried out on the Cray XC30 and XC50 at the Center for Computational Astrophysics, National Astronomical Observatory of Japan, and the octopus at the Cybermedia Center, Osaka University. This work is supported in part by the MEXT/JSPS KAKENHI Grant Number JP17H04827 (HY), 18H04570 (HY), and JP17H01111 (KN). YL acknowledges support from National Science Foundation through grants AST-1412719 and MRI-1626251. We are grateful to Dr. Ouchi for helpful comments on the dust temperature. KN thanks to Dr. Kawamata for useful discussions on galaxy size evolution. KN acknowledges the travel support from the Kavli IPMU, World Premier Research Center Initiative (WPI), where part of this work was conducted.


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Acknowledgements This paper is based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which 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 (CNRS) of France, and the University of Hawaii. It is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovacão (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). Observations were also obtained with FORS1 and FORS2 at the Very Large Telescope on Cerro Paranal, operated by the European Southern Observatory, Chile (ESO Large Programs 171.A-0486 and 176.A-0589). This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. We thank Mickaël Rigault, Adam Riess, Dan Scolnic, and David Jones for useful discussions.