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

parameter c = r c / r t , given by the ratio between the core ( r c ) and tidal ( r t ) radius. On the other hand, the tidal radius depends on the cluster orbit through the relation where Ω is the GC angular velocity, and d 2 Φ/d r 2 the second order derivative of the background gravitational field. 1 In the simplest approximation that the BHB separation is much smaller than its distance from the GC and that it dominates the dynamics, the equation reduces to being r p the GC periastron. Although equation ( 2 ) was originally derived for point-like mass moving on circular orbits, it approximate reasonably well the tidal radius of an extended object moving on an eccentric orbit during the passage at periastron (King 1962 ; Arca-Sedda et al. 2016 ). Once the GC orbit is assigned, the tidal radius can be calculated and combined with the value of W 0 chosen in order to get r c . Another degree of freedom is represented by the GC pericentre ( r p ) and eccentricity ( e ), as well as the orbit inclination with respect to the BHB orbital plane, i , and the mutual orientation of the two orbital ascending nodes ω. Note that the definition of the inclination angle i is as the one between the BHB and the GC orbital angular momentum vectors, where i = 0 corresponds to prograde and i = π to retrograde configurations. Finally, the galaxy background can significantly alter the first part of the GC orbital evolution. According to the widely used Dehnen ( 1993 ) models, the galactic density profile can be described as where M g , r g represent the galaxy mass and length scale, respectively, whereas γ represents the inner slope of the density profile. Therefore, a lower limit to the total number of parameters needed to characterize such a system is given by the combination of the BHB parameters (4), the GC structural and orbital properties (6) and the galaxy parameters (3), namely: BHB parameters: semi-major axis a BHB , eccentricity e BHB , total mass M BHB and mass ratio q BHB ; GC structural parameters: Mass M , potential well W 0 , concentration c ; GC orbital parameters: semi-major axis a , eccentricity e and pericentre r p ; galaxy parameters: galaxy mass M g , typical radius r g and density profile slope γ. Assuming only 3 values for each parameter would imply then a total number of ∼1.6 × 10 6 different models. In order to keep the number of models reasonable in terms of computational request and human times, we limited the number of degrees of freedom in our problem as follows: we assumed an equal mass BHB and kept fixed its apocentre; we fixed the GC W 0 , M and r p ; we assumed the GC and BHB orbits in a coplanar, counter-rotating configuration; we fixed the galaxy background. This choices reduced our problem to only three parameters: the BHB mass M BHB and its eccentricity, e BHB , and the GC eccentricity e . We assumed two different values for M BHB = 10 7 − 10 8 M ⊙ , three values for e BHB = 0, 0.5, 0.9 and two for e = 0.5, 0.9, thus


O O O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O O O O O B-Dataset I-Dataset I-Dataset 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 O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O B-Survey O O O O O B-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Observatory O O O O B-Survey O O O O O O O B-Survey O B-Observatory O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Dataset 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model 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 B-Model I-Model O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset

data using the observations from its Solar Optical Observing Network (SOON). Although in the past, the (SOON) data set was often used as a continuation of the RGO data set of sunspot areas, it has a known deficiency in the measurements of smallest sunspots and pores (e.g., Muñoz-Jaramillo et al. 2015 ). On the other hand, the observations of sunspot areas from the KMAS, which start in 1954, are more uniform and include the smallest sunspots and pores comparable to the RGO sunspot size limit. By their cumulative distribution, KMAS group areas are similar to RGO data (Muñoz-Jaramillo et al. 2015 , who established a proportionality constant between RGO sunspot group areas and KMAS as 1.07 or 0.93 to convert from KMAS to RGO). Thus, for the period 1977–2014, we employ sunspot areas observed at KMAS (Tlatov et al. 2016 ). 3. TWO POPULATIONS OF SUNSPOT GROUPS 3.1. Group Areas Sunspot groups are not static objects: as an active region develops its area increases and reaches a maximum within 2–3 days after its emergence (e.g., Pevtsov et al. 2003 ). According to a review article by van Driel-Gesztelyi Green ( 2015 ), a lifetime of active regions with fully developed sunspots varies between weeks and months. The rise phase takes between 3% and 15% of a group’s lifetime, which also translates to a few days from the beginning of the emergence of a group to the maximum of its development (maximum area). To take into account these evolutionary changes in group areas, for each group in the RGO–KMAS data set, we selected the largest area of this group. Since some groups will reach their maximum area on the side of the Sun not visible from Earth, one could expect a slight enhancement in small group areas. However, with a rapid growth phase of only a few days, we do not expect that such enhancement will have a significant effect on our conclusions. Figure 1 (a) shows the distribution of (logarithm of group areas) for the combined RGO–KMAS data set. The distributions were constructed using an equal bin size of Δ = 0.25 in the logarithm of group areas. The distribution is clearly bimodal, with one component peaking at about 16 M.S.H. (millionth of solar hemisphere, ) and the other at about 316 M.S.H. (). The former corresponds to a round feature with 7.6 Mm in diameter (a pore or a rudimentary sunspot) and the latter is about 350 Mm in diameter, or about the size of a regular sunspot. To separate the two components, we fit the observed distributions by a combination of two Gaussian functions. The fitting was done with the help of the data analysis software package “ORIGIN,” which uses the Levenberg–Marquardt algorithm to iteratively adjust the amplitude, mean, and standard deviation of each fitted Gaussian, until the best-fitted solution is found (e.g., Press et al. 1992 ). The fitted Gaussians are shown in Figure 1 (a) as blue profiles, and their sum is shown as a red double-peaked profile. Figure 1. (a) Distribution of group areas (log S ) from RGO data.


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

( 1986 ) asand C H is the heat transfer function defined byIn these equations, γ is the specific heat ratio, k B is the Boltzmann constant, μ is the mean molecular weight of a gas particle, m H is the mass of a hydrogen atom, and s a is a ratio of the drift velocity and the thermal gas velocity defined byEquation ( 10 ) can be solved for the dust temperature at which the heating of the dust by the gas is in equilibrium with the radiative cooling,which can be further rewritten as where the C values are constants with respect to s a defined by and α values are functions of s a defined by With this reduction of the equation, Equation ( 18 ) is solved for T dust using the minpack 's hybrd and hybrj routines with the modified Powell method (Moré et al. 1980 ). For the purposes of guiding the algorithm, initial guesses were computed byApplying the temporal evolution of the gas temperature, density, and drift velocity determined in the previous section, we are able to compute the dust temperature across the evolution of the shock. In the pre-shock gas, the gas and dust are assumed to be in thermal equilibrium, or T dust = T gas . In addition, we deviate from the formalism used in Jiménez-Serra et al. ( 2008 ), by setting an additional constraint of the velocity when used to calculate the rate of dust heating. Specifically, we assume that as the gas and grains begin to recouple, the drift velocity will eventually fall below the random thermal velocities of the gas. In the hot gas regime, this thermal velocity may be nontrivial. As such, the velocity of collisions may be more accurately described for these purposes as As can be seen in Figure 2 , the grain temperature is found to initially track with the velocity structure within the shock, peaking at the same corresponding time as the peak velocity owing to adiabatic heating. However, as the gas continues to heat up, the grain temperature undergoes a secondary heating regime owing to the conductive heating from the hot gas. As such, while the sputtering rate (see Section 2.2.3 ) will fall off rather rapidly, the ability for species to redeposit onto the grains is delayed until the gas can cool sufficiently. 2.2.3. Sputtering One major physical process that is common in astrophysical shocks is the nonthermal desorption of molecules from the ice into the gas phase through the collision of moderately fast gas-phase particles with the dust grains (e.g., sputtering). This process is a key mechanism for lifting complex molecules into the gas phase nondestructively. For typical C-shock velocities (e.g., 10–40 km s −1 ), the sputtering is significant enough to desorb most species from the ice mantle without destroying them or having significant grain core erosion, both of which are common in high-velocity J-shocks (Requena-Torres et al. 2006 ). In order to include these processes, the sputtering yields must be computed for each species on the ice, which is dependent on the conditions of the shock, the nature


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

them from single stars. Triple and quadruple star disruptions naturally bring binaries in the vicinity of the MBH. Fig. 6 shows the cumulative distribution function of binary S-stars semimajor axis and eccentricity as a function of a in for Model 1, which shows a clear correlation between the final and initial binary semimajor axis. More than of binary S-stars have a b ≲ 0.5 au to avoid tidal disruption by the MBH and the eccentricity cumulative distribution is nearly independent of the initial a in and is ∝ e , i.e. the eccentricity distribution is constant. Future data, as those expected by the James Webb Space Telescope, may observe near-infrared sources with higher photometric precisions, hence helping in identifying binaries in the GC. Figure 6. Cumulative distribution function of binary S-stars semimajor axis (left) and eccentricity (right) as function of a in for Model 1. More than ≈90 per cent of binary S-stars have a b ≲ 0.5 au to avoid tidal disruption by the MBH. The cumulative distribution of eccentricities is nearly independent on the initial a in and is ∝ e , i.e. the eccentricity distribution is constant. 4 DISCUSSIONS AND CONCLUSIONS Most of the observed HVSs support the standard Hills scenario, but the main-sequence HVS HE0437-543 and the candidate HVB require different production mechanisms than the standard binary disruption. While HE0437-5439 is likely to come from the centre of the Large Magellanic Cloud (Erkal et al. 2018 ), the candidate HVB as well as the other HVSs whose traveltimes exceed their main-sequence lifetime would require disruption of triple starsby the MBH, which would produce a HVB that can later evolve into a blue straggler star as a consequence of binary evolution (Perets 2009 ). However, the recent detailed N -body simulations byFragione Gualandris ( 2018 ) have showed that the ejection rate is too low to explain these hypervelocity outliers. In this work, we discussed the 2+2 quadruple tidal disruption scenario by means of high-accuracy scattering experiments. While less abundant than triple stars, 2+2 quadruple stars constitute of the stars in the solar neighbourhood (Tokovinin 2014a , b ) and have been shown to have interesting dynamics dealing with white dwarf-white dwarf collisions (Fang et al. 2018 ) and gravitational wave emission (Seto 2018 ). We studied a wide range of parameters of the quadruple stars and performed simulations with both point masses and finite stellar radii. We found that only a very small fraction () of encounters results in the ejection of a HVB. Taking into account that the estimated ejection rate for the Hills mechanism is (Yu Tremaine 2003 ) and that 2+2 quadruple stars are roughly a third of triple stars, we conclude that also 2+2 quadruple disruption leads to a HVB production rate of , similarly to the triple disruption scenario. We conclude that quadruple disruption, as long as triple disruption, is an unlikely source of HVBs, which would require a non-GC


B-Person O O O B-Organization B-Organization I-Organization I-Organization I-Organization O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person I-Person I-Person O O O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Archive B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Software I-Software O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation O B-Model I-Model B-Citation I-Citation I-Citation O O O B-Software I-Software

ALS acknowledges support from NOVA (Nederlandse Onderzoekschool voor Astronomie). We thank Adam Ingram, Lucy Heil, Victoria Grinberg, Michiel van der Klis, and the participants of ‘The X-ray Spectral-Timing Revolution’ Lorentz Center workshop (2016 February) for useful discussions that contributed to the development of this paper. We also thank the anonymous referee for their helpful comments. This research has made use of data and software provided by the HEASARC; NASA's Astrophysics Data System Bibliographic Services; Numpy v1.9.3 and Scipy v0.16.0 (Jones et al. 2001 ); Astropy v1.0.4 (Astropy Collaboration et al. 2013 ); Matplotlib v1.4.3 (Hunter 2007 ); ipython v3.2.0 (Perez Granger 2007 ); and the AstroBetter wiki.


O O O O O O B-Grant I-Grant O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Survey O O O B-URL O O O O O O O O B-Telescope O O O O B-Organization I-Organization I-Organization O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization

Acknowledgments This work was supported by NSF-AST 1514835. We use data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the US Department of Energy Office of Science and the Participating Institutions. The SDSS web site is www.sdss.org . When the data reported here were acquired, UKIRT was operated by the Joint Astronomy Centre on behalf of the UK Science and Technology Facilities Council.


O B-Telescope I-Telescope I-Telescope I-Telescope O O O B-Observatory I-Observatory I-Observatory O O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O B-Observatory O O O O B-Organization O O O O B-Telescope O B-Telescope O O

The 45 m radio telescope is operated by Nobeyama Radio Observatory, a branch of the National Astronomical Observatory of Japan. We wish to thank the 45 m telescope team, including Hiroyuki Iwashita, Tetsuhiro Minamidani, Cheko Miyazawa, Yoshio Tatamitani, and Hiroyuki Nishitani for the support of our observation. SDO data are courtesy of NASA/SDO, as well as the AIA and HMI science teams.


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

This work has been supported by the National Natural Science Foundation of China (11403043, 11473034 and 11273029), and the Strategic Priority Research Programme ‘The Emergence of Cosmological Structures’ of the Chinese Academy of Sciences (grant no. XDB09010200).


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

L183 (L134N), Taurus, and IC 5146). In the discussion that follows, we must recognize that the observed (i.e. line of sight) extinction to a source is not necessarily the same as the ‘local’ extinction, that is, to say the extinction of the source relative to the interstellar radiation field, so there will always be some uncertainty/natural scatter in the values of A th . However, the near-universality of these dependencies implies that the relevant processes must be largely independent of the dust properties; such as the size distribution and the dust grain morphology and porosity, etc. In the following section, we describe the nature of interstellar ices and the criterion for ice mantle growth. In Section 3 , we describe the various microscopic mechanisms that determine A th , and in Section 4 we compare the relative importances of these processes. Section 5 describes our chemical model, and the results are presented in Section 6 . Possible alternative causes of the A th phenomenon are discussed in Section 7 . Our conclusions and discussion are presented in Section 8 . 2 THE REQUIREMENT FOR ICE MANTLE GROWTH Interstellar ices are predominantly composed of H 2 O, CO, and CO 2 , with CO and CO 2 having abundances of ∼27–32 per cent and ∼19 per cent, respectively, relative to H 2 O in Taurus and low-mass young stellar objects (YSOs) (Chiar et al. 2011 , table 4). CO, being more volatile, is typically less abundant in high mass YSOs. Other species (such as CH 3 OH, NH 3 , OCN − , and other organics/COMs) typically account for ≲10 per cent of the ice. The relative abundances of the major ice components are fairly similar in different environments, although real differences exist and there are often significant variations in the abundances of the complex organics. Whilst there is evidence for significant source to source variations in the relative abundances of H 2 O, CO, and CO 2 , the total contribution of O-bearing ice molecules to the oxygen budget follows similar trends in different souces (e.g. Whittet et al. 2009 ). The chemistry of the main components is straightforward; CO ice is believed to be formed (primarily) due to the freeze-out of CO from the gas phase. By contrast, H 2 O and CO 2 are probably formed by surface reactions. At least four distinct H 2 O formation mechanisms are possible (van Dishoeck et al. 2013 ), but in the relatively low density/high hydrogen atom abundance environments that we are considering in this study, the main channel is simple hydrogenation: The latter reaction being in competition with As gas-phase chemistry is not believed to be important, this means that the formation rate of H 2 O ice is mainly determined by the rate at which oxygen atoms stick to grains and are subsequently hydrogenated to H 2 O molecules. If these are the only relevant reactions, then it also follows that the abundances of H 2 O and CO 2 ice should be approximately correlated, which is indeed seen to be the case (e.g. Noble et al.


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

region. Several studies ( Jacq et al. 1990 , 1999 ; Lubowich et al. 2000 ; Polehampton et al. 2002 ) suggested that deuterium may be up to 10 times less abundant in the Galactic center region than in the local interstellar medium owing to stellar processing. The levels of COM deuteration found in Sgr B2(N2) are indeed systematically lower (by a factor of a few up to a factor 10) than those reported in the Orion-KL Hot Core or Compact Ridge. While a chemical or evolutionary origin for this difference cannot be excluded without further modeling, the low deuteration level of complex organic molecules in Sgr B2(N2) may result from deuterium being less abundant in the Galactic center region by maybe up to a factor ten. 7. Conclusions We searched for deuterated complex organic molecules in a complete 3-mm interferometric line survey performed toward the hot core Sgr B2(N2) with ALMA. We report the secure detection of CHDCN and tentative detections of CHDOH, CHDCHCN in its out-of-plane conformation, the chiral molecule CHCHDCN, and DCN. We also derive column density upper limits for CHOD, CHDCHCN in its in-plane conformation, the three deuterated isotopologues of vinyl cyanide, the four deuterated species of ethanol, and CHDOCHO in its in-plane and out-of-plane conformations. The detections are characterized by compact emission consistent with a hot-core origin. We obtain a deuterium fractionation level of 0.4% for CHDCN and values between 0.05% and 0.12% for the other (tentatively detected) species. Stringent upper limits are derived for the in-plane conformer of CHDCHCN () and CHOD (). The deuteration upper limits for the other nondetected deuterated species lie in the range 0.5–1.8%. The following conclusions arise from this analysis: 1. Ethyl cyanide is less deuterated than methyl cyanide by at least a factor five. This may be due to their different formation pathways (grain surface versus gas phase). 2. The relative abundances of the three deuterated species of ethyl cyanide are most likely consistent with a statistical distribution. 3. The [CHDOH]/[CHOD] abundance ratio in Sgr B2(N2) is higher than 1.8. It may still be consistent with the value obtained in Orion KL but a value closer to (or, as in low-mass Class 0 protostars, even higher than) the statistical value cannot be excluded. 4. Except for methyl cyanide, the levels of deuterium fractionation measured toward the hot core Sgr B2(N2) lie at least a factor four below the predictions of current astrochemical models that were designed for lower mass objects (hot corinos in the Class 0 phase). 5. The levels of deuterium fractionation derived for complex organic molecules in Sgr B2(N2) are lower by a factor of a few up to a factor ten than in the Orion-KL Hot Core or Compact Ridge. The discrepancy between the deuteration levels measured in Sgr B2(N2) and the predictions of current chemical models for complex organic molecules, and the difference between Sgr B2(N2) and Orion KL may both be due


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ACKNOWLEDGEMENTS This research was supported by the Netherlands Organization for Scientific Research (AAM), RFBR grant 18-502-12025 (GVL), the Royal Society (AI), the Väisälä Foundation (SST) in a part of development of a theoretical model and by the grant 14.W03.31.0021 of the Minestry of Educartion and Sciense of the Russian Federation (AAM and SST) in a part of data analyses and data comparison with the theoretical results. The authors would like to acknowledge networking support by the COST Actions CA16214 and CA16104. We are also grateful to Victor Doroshenko and Nikolai Shakura for discussion and a number of useful comments.


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The authors cordially thank the referee for helpful comments on the manuscript. They furthermore thank Eiichiro Komatsu for helpful discussions about the definition of f NL with respect to the commonly used WMAP parametrization. JC is supported by the Royal Society as a Royal Society URF at the University of Manchester, UK. ED acknowledges support from the DOE under grant No. de-sc0008016. MK was supported by NSF Grant No. 0244990, NASA NNX15AB18G and the Simons 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 B-TextGarbage I-TextGarbage O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage 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 O O O O O O O O O B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O B-TextGarbage I-TextGarbage O O O O

it is challenging to reproduce this effect in our simulations without additional feedback. Stars from cold accretion mostly formed at high redshifts in small haloes that later assembled into the massive galaxies. The most efficient way to remove them from our simulations is to have stronger winds, i.e. stronger mass-loading factors in those haloes. However, having too much winds early will unavoidably fail to match observations at higher redshifts. The right-hand panels of Figs 10 and 11 show that cold accretion has nearly stopped after = 2 for these galaxies but hot accretion and wind recycling continue growing rapidly at low redshifts, and is responsible for most of the excess stars formed. After = 2, the stars in massive galaxies that must be prevented from forming come from almost equal parts: hot accretion, hot wind re-accretion, and cold wind re-accretion. Hence, preventing hot gas from cooling and forming stars at these times will eliminate both the hot mode accretion and hot wind re-accretion and will lessen the tension in massive haloes. There are several potential mechanisms, such as AGN and cosmic ray heating, that could reduce the amount of this cooling gas but they are not yet included in our simulations. The hot wind recycling would be harder to affect by extra heating, because the higher metallicity of this gas makes it cool faster. In hydrodynamic simulations, mixing between ejected wind elements and the surrounding gas may have a large impact on the amounts of hot and hot wind accretion. It is, however, unclear whether this type of feedback could prevent the ∼1/3 of stars formed through cold wind re-accretion after = 2 from forming, which is also necessary to match the observations. It is possible that a more accurate treatment of the cloud-CGM interaction would allow a larger fraction of these winds to become hot, alleviating this problem. 6 THE HIGH-RESOLUTION SIMULATION OF THE REFERENCE MODEL In this section, we present key results from the high-resolution RefHres simulation. It adopts the new wind launch algorithm as described in the previous sections using our fiducial set of wind parameters listed in Table 1 . It is also implemented with the numerical improvements to the SPH hydrodynamics introduced by Huang et al. ( 2019 ). We will focus on those predictions that have changed significantly from Huang et al. ( 2019 ) and from our previously published work with our new wind algorithm. 6.1 The stellar content Fig. 14 shows that the GSMFs from our fiducial simulation, shown as black lines in each panel, are mostly consistent with observations at all redshifts from = 0 to 4. The agreement is particularly good at the faint end except for = 0, where our simulation slightly underproduces the number of these low-mass galaxies. At the massive end, our GSMFs agree with observations at = 1 and 4. However, our fiducial simulation produces too many massive galaxies at = 0 and too few massive galaxies at = 2, even after taking account


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We are grateful to Jacek Niemiec, Martin Pohl, Oleh Kobzar, Arianna Ligorini, and Artem Bohdan for fruitful discussions. Numerical computations and analyses were carried out in part on Cray XC30 and computers at Center for Computational Astrophysics, National Astronomical Observatory of Japan. This work used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (Project ID: hp150263), and was supported in part by JSPS KAKENHI grant No. 17H02877. This work also used the computational resources of the HPCI system provided by Information Technology Center, Nagoya University through the HPCI System Research Project (Project ID: hp170158).


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ACKNOWLEDGEMENTS A.C., M.S. and E.Z. acknowledge support from CONICET, and E.Z. acknowledges support from SeCyT-UNC.


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

for VLM stars and BDs have high uncertainties at ages younger than 1 Myr ( Baraffe et al. 2002 ), we assumed an age of 1 Myr for [GKH94] 41. The temperature of 2795 K then corresponds to a mass of 41 . If the uncertainty of 1.5 subclasses in the spectral type is taken into account, a possible mass range for [GKH94] 41 is from 14 to 97 . We also calculated the luminosity of the source itself (without any contribution from its surrounding envelope) to constrain the mass range. We first dereddened the 2MASS -band magnitude () using the extinction law with ( Mathis 1990 ) and the visual extinction ( Bulger et al. 2014 ). The value was obtained from the best-fit atmospheric model (see Bulger et al. 2014 and references therein) over the 2MASS bands. Using the bolometric correction in -band versus spectral type relation as given in Filippazzo et al. (2015) , we derived a luminosity of 0.025 . Figure 3 shows the luminosity versus temperature diagram for [GKH94] 41 with the theoretical evolutionary models from Chabrier et al. (2000) and Baraffe et al. (1998) . The location of [GKH94] 41 in the diagram indicates that the upper limit (including the uncertainties) to its current mass is just above the substellar limit and below 0.09 , which is consistent with the upper limit value of 97 estimated above. We therefore conclude that the upper limit to the mass of [GKH94] 41 is in the range of 1497 . Second, we estimated the envelope mass of [GKH94] 41 based on the modeling of a modified blackbody with fluxes from 70 m to mm wavelengths (Table 2 ) as used to estimate the envelope mass of IC348-SMM2E (see Palau et al. 2014 ). We obtain the dust temperature , dust emissivity and envelope mass by searching these three parameters minimizing the in the following ranges: from 10 K to 40 K, from 0.1 to 1.8 and from 1 to 60 . We assumed a dust opacity coefficient dependence on wavelength with , cm g (see Palau et al. 2014 and references therein) and a gas-to-dust ratio of 100. The best fit (Fig. 4 ) then gives = 34 K, = 2 , and = 0.4. The obtained dust emissivity index value is significantly lower than the typical value of about 1.4 for class I objects in Taurus ( Chandler et al. 1998 ). This is probably because the best fit is obtained from only three available data points. If we take = 1.4 and = 34 K, we obtain an envelope mass of 8 , a factor of 4 higher than the value estimated from the fitting. We therefore take the final mass of [GKH94] 41 to be 49 , which the sum of the current mass (41 ) and the envelope mass (8 ). If the uncertainty in the spectral type is taken into account, this upper limit will be 49. As the outflow process also ejects accreting material and dissipates material in the envelope, the final mass of [GKH94] 41 thus will very likely be below the substellar limit. Fig. 3 H-R diagram for [GKH94] 41 and IRAS 04191+1523B. Isochrones and mass tracks from the theoretical evolutionary models of Chabrier et al. (2000) for and Baraffe et al.


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Acknowledgements ME and HH acknowledge support from the European Research Council under FP7 grant number 279396. The authors thank Jerome Amiaux, Mark Cropper, Jean-Charles Cuillandre, Thomas Kitching, Yannick Mellier, Jason Rhodes, and Gijs Verdoes Kleijn for discussions and comments. In this project we used the scikit-learn (Pedregosa et al. 2011 ), pandas (McKinney 2010 ), scipy (Jones et al. 2001 ), matplotlib (Hunter 2007 ), and ipython (Perez Granger 2007 ) software packages. This research has made use of NASA's Astrophysics Data System.


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I appreciate support of this publication by the Solar Physics Laboratory of Goddard Space Flight Center. I thank the referee for suggesting a better ordering of the manuscript. I am grateful to PMOD/WRC, Davos, Switzerland, for supplying their irradiance record (Frohlich 2006 ), composite_42_65_1709.dat, with new data from Virgo on the ESA/NASA Satellite Mission, SOHO .


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The authors would like to thank J. D. P. Kenney, E. J. Murphy, and Olaf Wucknitz for useful comments on the article.


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

fluencies (chemical equilibrium). The chemical equilibrium during ice processing by photons, electrons or ions occurs at large fluences when parent and daughter species reach abundances that keep each other's abundance constant during reciprocally production-destruction reactions in the presence of incoming energy. This steady state scenario explains the horizontal plateau in chemical abundances observed at fluences larger than ∼1.4 × 10 13 ion cm −2 (see for example Fig. 4 ). Additionally, in the case of ion bombardment, the sputtering may affect drastically the molecular abundances as function of time, mainly in the beginning when parent species are more affected by sputtering. At high fluences, the molecular abundance reaches the chemical equilibrium, the sputtering affects equally all the species and their column densities decrease (in a constant rate) as function of fluence. The chemical equilibrium is also affected by the sample temperature since volatile products tend to desorb from the ice. More details on chemical equilibrium induced by radiation in ices are given elsewhere (Vasconcelos et al. 2017 ). Studying the radiolysis of N 2 : CO (1:1) ice at 10 K by electron beam irradiation with final energy dose similar to the exposure of astrophysical ice to 5 × 10 6 year in the ISM, Jamieson et al. ( 2005 ) have found the result N 2 O/N 2 > 6.0 × 10 −4 . Bombarding N-rich ices by protons and considering the band strengths in the infrared for N 2 O and N 2 derived by Jamieson et al. ( 2005 ), Loeffler et al. ( 2010 ) have found N 2 O/N 2 ∼ 2.0 × 10 −3 for the equilibrium chemistry attainted at longer fluencies. This value is very similar to the one observed in the gas phase at Sgr B2, as shown above (Womack, Ziurys Wyckoff 1992 ). The current manuscript investigates the survival of solid N 2 O against ionizing field (1.5 MeV N + cosmic ray analogues). From the measured destruction cross-section (σ d ) and the ion flux (Φ) in the laboratory, the photodissociation rate at laboratory (k d = σ d × Φ), turns out to be about 7.0 × 10 −4 ions s −1 . Same equation can be employed to derive the photodissociation rate in space. Considering first order kinetics for the destruction of N 2 O by swift ions, the evolution of N 2 O abundance as a function of time is described by equation ( 25 ) where N(t) and N(t 0 ) represents the molecular abundance at a given time (t) and at the beginning of experiment. κ d is the dissociation rate in units of ions s −1 , σ d is the dissociation cross-section in units of cm 2 and Φ is the ion flux in units of ions cm −2 s −1 . To extrapolate the current laboratory results to astrophysical environments, the flux of medium-mass ions (3 Z 11) having energies between 0.1–10.0 MeV/u estimated by Pilling et al. ( 2013 ) is used. The values considered are 3.0 × 10 −1 and 1.0 × 10 −1 ion cm −2 s −1 , for the ISM and inside the Solar system at Pluto orbit, respectively. Fig. 5 presents the evolution of N 2 O abundance, for ices


O O O O O O O O O O O O B-Person I-Person B-Observatory O O O O O B-Organization B-Observatory O B-Telescope O B-Telescope O O B-Instrument O O O O O O B-Telescope B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O B-Instrument O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O B-Observatory I-Observatory I-Observatory B-Observatory O B-Instrument O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O O O B-Grant B-Person O O O O O B-Observatory I-Observatory I-Observatory O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event O B-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O O O O O O B-Telescope O B-Observatory B-Telescope O B-Observatory B-Telescope O B-Telescope B-Instrument O B-Software B-Software B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Software B-Citation I-Citation O

This work is dedicated to the memory of our friend and colleague, Mike Bradford. SDO data are provided courtesy of NASA/ SDO and AIA and HMI science teams. EUVI data are provided courtesy of the STEREO Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) team. FIRS has been developed by the Institute for Astronomy at the University of Hawai‘i, jointly with the National Solar Observatory (NSO). The FIRS project was funded by the National Science Foundation Major Research Instrument program, grant number ATM-0421582. T.A.S. gratefully acknowledges colleagues at the High Altitude Obseratory for interesting discussions regarding this work during a scientific visit. This work also benefited from discussions at the International Space Science Institute (ISSI) meetings on “Sub-arcsec Observations and Interpretation of the Chromosphere” and “Implications for Coronal Heating and Magnetic Fields from Coronal Rain Observations and Modelling.” This research has made use of NASA’s Astrophysics Data System. The authors thank the referee for a careful review and fruitful comments. Facilities: Dunn(FIRS) , SDO (AIA) , SDO (HMI) , STEREO (EUVI-A). Software: SSWIDL, SolarSoft, Crispex (Vissers Rouppe van der Voort 2012 ), HeLIx + (Lagg et al. 2004 ; Lagg 2007 ), PIKAIA (Charbonneau 1995 ).


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 O O O O O O O O O O O O O O O O O O O O O O O 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 I-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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Dataset I-Dataset O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O

between and M * in the top panel of Figure 1 for isolated galaxies with ALFALFA data and the residuals () between the observed and the predicted in the bottom panel. Equation ( 2 ) is plotted as the solid curve. The dashed lines in the bottom panel are ±1 dex from the relation, which roughly corresponds to the 3 σ scatter. We use the −1 dex residual as a reference point throughout the paper as an arbitrary line of demarcation. Figure 1. Top panel: the isolated to M * relation of gas-rich galaxies. Only isolated galaxies with detections from the 70% ALFALFA survey are plotted here as black contours and dots. The fit from Equation ( 2 ) is plotted as the solid curve and noted in the legend. Bottom panel: H i mass residual ( −1 dex) as a function of stellar mass with the same symbols at the top panel. The ±1 dex (3 σ ) residuals are shown as dashed lines. 2.4. Emission Line Measurements Optical emission line flux ratio diagnostics are often used to differentiate between various physical phenomena that ionize the ISM of galaxies Baldwin et al. ( 1981 ), Veilleux Osterbrock ( 1987 ). Differentiating between excitation sources (actively accreting black holes, star formation, shocks from AGB stars, etc.) depends on the ionization mechanism strength. Reines Volonteri ( 2015 ) measure emission line strengths of ∼67000 galaxies selected from the NSA catalog. The authors cull the spectral catalog with an S/N cutoff of three and an equivalent width cutoff of one for the H α , [N ii ], [O iii ] emission lines and an S/N cutoff of two for the H β line. They iteratively subtract continuum and absorption lines using the models of Tremonti et al. ( 2004 ) from the observed spectrum, carefully masking out the emission lines. Next, a one- or two-component Gaussian is fit to the [S ii ] doublet and used as a template for the remaining emission lines of interest, excluding [O iii ]. We use the data set from this study without any modifications. 2.5. BPT Emission Line Diagnostics We examine the emission line diagnostics of all galaxies from Reines Volonteri ( 2015 ), regardless of environment or H i data using the [O iii ]/H β and [N ii ]/H α narrow-line BPT diagram (Baldwin et al. 1981 ; Veilleux Osterbrock 1987 ; Kewley et al. 2006 ). We adopt the division into the star-forming, composite, and AGN categorization that has been performed by Reines Volonteri ( 2015 ) using the Kewley et al. ( 2001 ) and Kauffmann et al. ( 2003 ) categorization. The Kewley et al. ( 2001 ) demarcation line represents the division between a theoretical maximal starburst model and emission that can only be explained by AGN activity. The Kauffmann et al. ( 2003 ) demarcation line is an empirical separation between the star-forming sequence and the AGN sequence. Galaxies below the Kauffmann et al. ( 2003 ) line are considered to be purely star-forming and galaxies above the Kewley et al. ( 2001 ) line are considered Seyferts and LINERs. The region between these two demarcation lines


O O O B-Survey O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Survey O O B-URL O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Mission O O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Telescope O B-Mission O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS website is http://www.sdss.org/. This publication makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, and NEOWISE , which is a project of the Jet Propulsion Laboratory/California Institute of Technology. WISE and NEOWISE are funded by the National Aeronautics and Space Administration.


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

This work is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under the grant 113F354. MAA is a member of the Science Academy (Bilim Akademisi), Turkey. We thank Patrick Weltevrede for kindly providing us with unpublished post-glitch timing data, and Danai Antonopoulou, Anna Watts, Cristobal Espinoza and Patrick Weltevrede for useful discussions and for sharing with us their preprint with an alternative approach to the post-glitch behaviour of PSR J1119−6127. We thank the referee for useful comments.


O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization O O O O B-Organization I-Organization I-Organization O B-Organization O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization B-Telescope O O O O O O O B-Organization O B-Organization O B-Telescope O B-Software B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation O B-URL O

This work was supported by a grant from the US Air Force Office of Scientific Research in the Basic Research Initiative “Understanding the Interaction of CMEs with the Solar–Terrestrial Environment,” and by an STFC consortium grant to the universities of Dundee and Durham. The authors thank C. Prior, M. Weinzierl, P. Wyper, and T. Whitbread for useful discussions concerning the development of this work, which made use of the Hamilton HPC Service of Durham University. SOLIS data used here are produced cooperatively by NSF/NOAO and NASA/LWS. Facility: SOLIS. Software: Python, SunPy (SunPy Community et al. 2015 ), SciPy (Jones et al. 2001 ), NumPy (van der Walt et al. 2011 ), Mayavi (Varoquaux Ramachandran 2011 ), Matplotlib (Hunter 2007 ), FRoDO (Lowder 2017 , https://github.com/lowderchris/FRoDO ).


O O O O O O O B-Grant I-Grant I-Grant B-Grant O O O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization O O O O O O O O O O B-Telescope I-Telescope O O O O O B-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant B-Grant B-Grant O B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Grant B-Person O O O O B-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant O B-Telescope O B-Software B-Citation I-Citation I-Citation O B-Software B-Software B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O

This work uses data obtained through the Telescope Access Program (TAP), which is funded by the National Astronomical Observatories of China, the Chinese Academy of Sciences (the Strategic Priority Research Program, “The Emergence of Cosmological Structures” Grant No. XDB09000000), and the Special Fund for Astronomy from the Ministry of Finance. The observations reported in this study were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona. 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 work is supported by the National Basic Research Program of China (973 Program)(2015CB857004), and the National Natural Science Foundation of China (NSFC, Nos. 1320101002, 11433005, 11421303, and 11673004), and the Yunnan Applied Basic Research Projects (2014FB155). E.W. was supported by the Youth Innovation Fund by the University of Science and Technology of China (No. WK2030220019). Facility: MMT. Software: SExtractor (Bertin Arnouts 1996 ), xfitfibs, HSRED, STARLIGHT (Cid Fernandes et al. 2005 ), MPFIT (Markwardt 2009 ), PyNeb (Luridiana et al. 2015 ).


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We thank Lydia Heck and James Willis for their assistance with computational challenges. We thank the anonymous referee for their helpful comments. This work was supported by the Science and Technology Facilities Council (STFC) grants ST/P000541/1 and ST/L00075X/1, and used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grants ST/H008519/1 and ST/K00087X/1, STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. J.A.K. is funded by STFC grant ST/N50404X/1. V.R.E. acknowledges support from STFC grant ST/P000541/1. R.J.M. acknowledges the support of a Royal Society University Research Fellowship. L.F.A.T. and D.G.K. acknowledge support from NASA Outer Planets Research program award NNX13AK99G. L.F.A.T., D.C.C., D.G.K., and K.J.Z. acknowledge support from NASA Planetary Atmospheres grant NNX14AJ45G. C.L.F. was funded in part under the auspices of the U.S. Dept. of Energy, and supported by its contract W-7405-ENG-36 to Los Alamos National Laboratory.


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

This work is partly supported by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 247060-PEPS and grant No. 320478-TOFU). B.D. thanks the University of Exeter for support through a Ph.D. studentship. D.S.A. acknowledges support from the NASA Astrobiology Program through the Nexus for Exoplanet System Science. N.J.M. and J.G.’s contributions were in part funded by a Leverhulme Trust Research Project Grant, and in part by a University of Exeter College of Engineering, Mathematics and Physical Sciences studentship. This work used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. This work also used the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter.


An anonymous referee’s comments and suggestions are gratefully acknowledged.


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

frequency of the observed maser transition. We use A = 5.570 × 10 −8 s −1 , the highest Einstein coefficient in Lankhaar et al. ( 2018 ) for the ν = 24959.079 × 10 6 Hz CH 3 OH maser transition, and T b = 10 6 –10 7 K, ΔΩ ≃ 0.03–0.003 for the 25 GHz maser line (Leurini et al. 2016 ). Using these values in Equation ( 2 ), we obtain R ≤ 3 ×10 −3 s −1 . Meanwhile, g Ω ≈ 170 s −1 in our observations of OMC-1. This means that R ≪ g Ω, and thus it is unlikely that a rotation of the axis of symmetry for the molecular quantum states is responsible for the shape of the Stokes V profile. Finally, Houde ( 2014 ) found that maser radiation scattering off foreground molecules can increase the antisymmetry in the Stokes V spectral profile of SiO masers. Consequently, if the Stokes V profile were ascribed to the Zeeman effect, one would obtain a much larger value for the magnetic field traced by these SiO masers. While we cannot rule out this effect in our 25 GHz CH 3 OH maser observations, our values are not orders of magnitude higher than the fields expected in such regions, unlike in SiO masers. We will discuss this in more detail in the next subsection. 4.3. Magnetic Fields and Densities If the observed Stokes V profile is caused by a magnetic field in the source, and is not due to any instrumental effects or other non-Zeeman causes discussed in Section 4.2 , then we have a magnetic field from our 25 GHz Class I CH 3 OH maser observation of OMC-1 that is three to four times larger (depending on which hyperfine is responsible for the maser) than the highest magnetic field we have detected to date in Class I CH 3 OH masers at 44 GHz (Momjian Sarma 2017 ). Such a value is not implausible, however; if we assume that the fields are amplified in proportion to the density in the shocked regions where these masers occur, thenwhere B pre and B post are the magnetic fields in the pre- and post-shock regions respectively, and n pre and n post are the densities in these regions. We can use Equation ( 3 ) to calculate B pre and compare it to magnetic fields calculated from other observations. Since our measured fields are in the range 171–214 mG depending on which hyperfine is responsible for the maser transition (Table 3 ), we will use = 171 mG in our calculations; this is convenient because values corresponding to = 214 mG can then be found by multiplying our results by a factor of 1.25. Leurini et al. ( 2016 ) have found that bright Class I methanol masers likely occur in regions with densities in the range 10 7–8 cm −3 , so we will calculate corresponding to both n post = 10 7 and 10 8 cm −3 . For densities in the pre-shocked gas we draw upon the work of Kwan et al. ( 1977 ), who found that a minimum pre-shock density of 10 5 cm −3 is required to produce the observed intensities in the H 2 ν = 1−0 emission lines in OMC-1. Thus, densities in the pre-shocked material of interest are likely of the order of 10 5 cm −3 or higher, but unlikely to be as high as, or


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We thank E. Zirnstein and P. Mostafavi for helpful discussions about PUI pressures and densities, shocks, and wave speeds in the heliosheath. We are grateful to both the Voyager and IBEX teams. This work was supported by NASA Grant 80NSSC18K0237 and by the IBEX mission, which is part of NASA’s Explorer Program. J.D.R. was supported under NASA contract 959203 from the Jet Propulsion Laboratory to the Massachusetts Institute of Technology.


B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O B-Model O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O B-Formula I-Formula I-Formula 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 B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Model 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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O B-Model O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula 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 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-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 B-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 O B-Model O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O

g ′) and Δμ( r ′ − i ′), with the maximum at only ρ = 0.30 and p = 0.08. The only exception is for the PAS profiles from the r ′ − i ′ breaks sub-sample, where there is a correlation of ρ = 0.49 and p = 0.02. This correlation is due to the same points as the correlation of h 0 with Δ h 0 ( r ′ − i ′0) in the PAS. 4.4.4 Correlations with absolute magnitude, maximum rotation and specific angular momentum Martín-Navarro et al. ( 2012 ) found that the truncation radius of a galaxy is strongly correlated with the maximum rotational velocity v rot of a galaxy, having a correlation of ρ truncation = 0.81. The breaks in their sample were correlated at only ρ break = 0.50. In contrast, Pohlen Trujillo ( 2006 ) report no correlation with rotation. They do report a weak correlation of the brightness at the feature with the absolute magnitude M B,abs . We explore possible correlations of the feature radii R f , surface brightness at the feature μ and differences in brightness between bands at the feature μΔ with absolute magnitude M abs and maximum rotation v rot in Table 7 . We find only one weak correlation in the difference between the g ′ and r ′ surface brightness at the feature radius, as measured with the EP method, with the rotation velocity v rot . The correlation strength is ρ = 0.36 and p = 0.03. Martín-Navarro et al. ( 2012 ) also perform a correlation test of the break and truncation radii with the specific angular momentum j , calculated using the empirical expression by Navarro Steinmetz ( 2000 ), 4 As this is a rescaling of v rot , the correlation remains the same. They find that the feature radius only correlates well beyond r b = 8 kpc. For a smaller disc with v rot 100 kms −1 , r break and v rot are essentially unlinked. When examining the full radii range, we also do not find a statistically significant correlation. The same holds when limiting ourselves to all features beyond r > 8. 4.4.5 Effect of inclination In Section 4.4.2 , we found that the PAS profiles typically tend to have sharper breaks than the ellipse-fit profiles and EP. As the PAS projects data as if it was edge-on, it is also interesting to compare the effect of inclinations in this. To this end, we have tested the correlation of a / b (major axis over minor axis) with scalelengths h 0 and h f , h 0 / h f and R f / h f , in Table 7 . The results are also visualized in Fig. 12 . Figure 12. Correlation of various parameters with inclination (expressed as a / b ). Top row shows with scalelength h 0 (left) and h f (right). Bottom row has the h 0 / h f (right) and R f / h f (left) correlations. The statistical correlation tests are plotted in each panel. Boxes represent the PAS points, while circles represent the EP points. Open markers represent truncations, while filled markers represent boxes. We find no significant correlation between a / b and inner scalelength h 0 . There may be a negative trend visible in the truncation-only sample, as both the EP and PAS profiles


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Acknowledgements A. P. acknowledges support from CONACyT 238631. G. B. acknowledges financial support under the INTEGRAL ASI-INAF agreement 2013-025.R01. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team ( Lister et al. 2009 ). This work was supported by UNAM-PAPIIT IA101214 and IA102816. We thank Prof. Robert Antonucci for his careful revision of the paper and useful comments.


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ACKNOWLEDGEMENTS This work was supported by the ERC Consolidator Grant CMBSPEC (No. 725456) as part of the European Union’s Horizon 2020 research and innovation programme. JC was supported by the Royal Society as a Royal Society URF at the University of Manchester, UK.


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ACKNOWLEDGEMENTS We thank Nir Shaviv and Reetanjali Moharana for helpful discussions. The research was supported by an ERC advanced grant TReX and by the CHE-ISF I-CORE center for excellence.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

transform Fig. A.4 Illustration of the backward interpolation. Interpolation is performed for inertial knots (bottom line) on intervals between comoving knots (top line). Interpolation weights are indicated on sloped lines connecting corresponding knots between the frames. Linear interpolation is used for internal inertial knots that lie on the internal comoving intervals with l.h.s. (solid) and r.h.s. (dotted) weights. Weights are named with respect to the comoving frame so that the line slopes are opposite to those in the forward interpolation. Constant extrapolation with unity weights is used for inertial knots exactly matching comoving knots , or for inertial knots that lie on the or intervals. Both end cases are given in gray color. Once has been fully accumulated, we compute the comoving profile ratio and keep it in memory for all frequency knots simultaneously. This makes the backward transform much easier than the forward one, because we can employ a standard interpolation. The backward transform can be directly evaluated because it is just an interpolation from the comoving frame to the inertial frame (see green notations in Fig. A.2 ): As follows from Fig. A.4 , each depends on either one or two comoving knots . It depends on two knots if the inertial knot lies on the comoving interval , where both and are internal knots (), that is, . In this case we do linear interpolation: For the backward transform, knots and weights are always denoted by and with no superscript to tell them from knots and weights for the forward transform. It depends on one knot if the inertial knot matches the comoving knot , that is, . It also depends on one knot if the inertial knot lies on intervals before or after , which means or , because we use constant extrapolation. Therefore, in those three cases: Appendix A.2: General interpolation One can perform the searches and interpolations described in Sects. A.1.4 – A.1.5 on the fly. This does not require any additional storage, and can be used for a frequency grid of arbitrary spacing, but the algorithm is slow. We call this algorithm general interpolation. Appendix A.2.1: General forward transform We search for all comoving knots that lie on the intervals and , that is, whose comoving frequencies are either between and , or between and . We take the current inertial knot and its left neighbor and right neighbor . We use and to keep the neighbors within the frequency grid range . For these knots we compute their frequencies in the comoving frame, which we denote by Therefore, the comoving knots related to the inertial knot are those whose frequencies belong to the or intervals. The knots lie either on the left or on the right side of , and they might fall outside the frequency coverage of the line. We thus have four different cases to test for and apply Eqs. ( A.15 )–(A.16). Algorithm 1 shows the forward transform in detail. Appendix A.2.2: General backward transform Algorithm 2 gives the backward transform,


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

to be robust as they are obtained without any assumptions. Table 3. Ro-vibrational partition function values computed at different temperatures. Notes. (a) Includes all states up to 400 cm −1 : the ground, v 11 = 1, v 18 = 1, and v 17 = 1 states. (b) Includes all states up to 1600 cm −1 . To compute the ro-vibrational partition function of the manifold containing all states up to 1600 cm −1 (referred to as “Manifold 2” in Table 3 ), we have applied a vibrational correction to our new ground state partition function values. The correction factor was calculated at each temperature summing up the contribution of all the vibrational states below 1600 cm −1 . Since we have no direct information about the vibrational energies of the states between 400 and 1600 cm −1 , they were either estimated under the harmonic approximation or taken from low-resolution measurements ( Bak et al. 1975 ). Higher energy levels were not considered in the calculation because they do not contribute significantly to Q even at 300 K. The vibration-rotation partition functions of the three manifolds of aminoacetonitrile, computed at temperatures between 2.725 and 300 K, are listed in Table 3 . Based on our results, we prepared new catalog entries for aminoacetonitrile in the ground and excited states. The line intensity of each transition was calculated using the partition function values from Col. 4 of Table 3 (“Manifold 2”), while the permanent dipole moment values μ a = 2.577(7) D and μ b = 0.575(1) D were taken from Pickett (1973) and assumed not to change upon the vibrational states. 4. Astronomical observations 4.1. Observations We used the ReMoCA imaging spectral line survey carried out toward the protostellar cluster Sgr B2(N) with ALMA. Details about the observational setup and data reduction of this survey were reported in Belloche et al. (2019) . In short, the observations covered the frequency range from 84.1 GHz to 114.4 GHz with five tunings, with a spectral resolution of 488 kHz (1.7–1.3 km s −1 ). The angular resolution (HPBW) varied between ∼0.3′′ and ∼0.8′′, with a median value of 0.6′′, which corresponds to ∼4900 au at the distance of Sgr B2. The rms sensitivity ranged from 0.35 mJy beam −1 to 1.1 mJy beam −1 , with a median value of 0.8 mJy beam −1 . The field was centered at ( α , δ ) J2000 = (), a position that is halfway between the two main hot molecular cores, Sgr B2(N1) and Sgr B2(N2), which are separated by 4.9′′ or ∼0.2 pc. Here we analyze the spectrum at the offset position Sgr B2(N1S) defined by Belloche et al. (2019) to reduce the optical depth of the continuum emission, which is partially optically thick toward the peak position of the main hot core Sgr B2(N1). Sgr B2(N1S) is located at ( α , δ ) J2000 = (, ), about 1′′ to the south of Sgr B2(N1). In Belloche et al. (2019) , the continuum and line emission of the ReMoCA survey was separated in the image plane because the hot cores detected in the field of view have different systemic


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ACKNOWLEDGEMENTS We would like to thank Ming Sun for providing us with their data. We also thank Helen Russell, Stephen Walker and Elena Rasia for helpful discussions about X-ray data analysis. We are grateful to Volker Springel for making the arepo moving-mesh code available to us and to the Illustris collaboration for their development of the Illustris galaxy formation model on which this work is based. NAH is supported by the Science and Technology Facilities Council (STFC). EP acknowledges support by the Kavli Foundation. DS and SS acknowledge support by the STFC and the European Research Council Starting Grant 638707 ‘Black holes and their host galaxies: co-evolution across cosmic time’. This work made use of the following DiRAC facilities ( www.dirac.ac.uk ): the Data Analytic system at the University of Cambridge [ funded by a BIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations grant ST/K00333X/1] and the COSMA Data Centric system at Durham University (funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University). DiRAC is part of the National E-Infrastructure.


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gas is released in the inner region of the disk, a global transonic structure of such a slim disk surrounding a BH is crucial in modeling the observations. In this work, we derive a global solution to a slim accretion disk with outflows accelerated by radiation force of the disk. The calculations can be applied to model the accretion disks surrounding either massive BHs or stellar mass BHs. We describe our model calculations and results in Sections 2 and 3 . The last section contains the discussion of the results. 2. Model A set of equations describing a slim disk with outflows in cylindrical coordinates are summarized in the previous works (see Gu Lu 2007 ; Kato et al. 2008 ). We consider a steady axisymmetric accretion disk in this work, which is described by the momentum equations, energy equation, continuity equation, and the equation of state. The r -component of the momentum equation isAs was done in many previous works, we adopt the pseudo–Newtonian potential,to simulate the gravity of the BH, where M is the BH mass, and is the Schwarzschild radius (Paczyńsky Wiita 1980 ). The continuity equation is We integrate Equation ( 1 ) over z and obtainwhere Equation ( 3 ) is used, Σ is the surface density, Π is the vertically integrated pressure, Ω is the angular velocity of the gas in the disk, and Ω K is the Keplerian angular velocity. The φ -component of the momentum equation iswhere the α -viscosity of t rφ = − αp is adopted. Integrating Equation ( 5 ) over z -direction, we havewhere the velocity of outflow at the disk surface is v H = v z ( H ), as the outflows driven by the radiation force are considered in our model. By integrating Equation ( 3 ) vertically, it becomesThe term 2 ρv H in this equation represents the mass loss rate in outflows from the unit area of the disk surface. If we further integrate Equation ( 7 ) over r -direction, it becomeswhere the integral constant C can be determined with suitable boundary conditions. As the mass loss rate in the outflows from the unit area of the disk surface are , we haveso the mass accretion rate in the disk at radius r isand the total mass loss rate in the outflows driven from the disk region between r and r out is Substituting Equation ( 7 ) into Equation ( 6 ), we haveWe integrate the angular Equation ( 12 ) over r , which leads torespectively, where Equation ( 9 ) is used, is the angular momentum removed by the outflows from the corresponding disk region, is the mass accretion rate swallowed by the BH, and is rate of angular momentum of the accretion gas flowing into the BH ( j in is the specific angular momentum of the accreting gas swallowed by the BH). The vertical integrated equation of state iswhere μ is the mean molecular weight ( μ = 0.62 is used in this work), and T 0 is the temperature at the mid-plane of the disk (see Equations (7.43)–(7.45) in Kato et al. 2008 ). The isothermal sound speed is . The energy equation of the disk iswhere is the gravitational power released