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ACKNOWLEDGEMENTS We thank the referee, Prof. Harald Ebeling, for his insightful comments that allowed us to strengthen the results presented in this paper. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 196.B-0578. We acknowledge funding from the INAF PRIN-SKA 2017 program 1.05.01.88.04 (PI Hunt). YJ acknowledges support from CONICYT PAI (Concurso Nacional de Inserción en la Academia 2017) No. 79170132.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

due to the forces connected to the torsional Alfvén wave. Therefore, by having these expressions to hand, the efficiency of collimation due to the atmospheric and equilibrium conditions together with the nonlinear forces connected to the torsional Alfvén wave can be better understood. This provides a helpful tool and a robust standing point for observation purposes and coronal seismology. If one asks how, the answer lies in Figures 2 and 3 , where the interplay of the plasma- β and the shear flow on the density perturbations and jet cross section is highlighted. It can clearly be seen that the efficiency of the shear flow is highly elevated in higher plasma- β regions. This means that in the solar photosphere, where the plasma- β equals unity, the density perturbation amplitude due to the nonlinear forces and the external pressure force increases to over twice that of the solar corona. Note in the absence of the shear flow, the plasma- β acts mutually for the density perturbations due to the nonlinear effects connected to the torsional Alfvén wave. Figure 2. Interplay of the plasma- β and the shear flow ( u 0 ) effective on the density perturbations inside the jet due to the nonlinear forces (left panel) and the external pressure force (right panel). The surface plot is created from Equation ( 25 ), and the shear flow is normalized by the Alfvén speed. The interplay of the plasma- β and the shear flow on the perturbations of the jet cross section is pictured in the two panels of Figure 3 . By glancing over the surface plots of Figure 3 it can beseen that for coronal conditions (low plasma- β ) the perturbations of the jet cross section are anti-phase with those inside the jet. This means that for coronal conditions the forces effective on the jet collimation prove more efficient compared with the photospheric conditions. Figure 3. Interplay of the plasma- β and the shear flow ( u 0 ) effective on the jet cross section perturbation due to the nonlinear forces (left panel) and the external pressure force (right panel. The surface plot is created from Equation ( 33 ), and the shear flow is normalized by the Alfvén speed. The reason for this anti-phase behavior for coronal conditions can be better understood when the parallel speed perturbations surf against the shear flow and plasma- β . Figure 4 shows that the parallel speed perturbations due to the forces working on the jet collimation connected to the torsional wave are in phase with the density perturbations. In the low plasma- β regime, an increase in the perturbation amplitude of the density is accompanied by an increase in the parallel speed of the plasma. The decrease in the jet cross section is therefore due to the Bernoulli effect. However for photospheric conditions (finite plasma- β regime), the jet cross section is in phase with the density and parallel speed perturbations connected to the nonlinear torsional Alfvén wave. Figure 4. Interplay of the plasma- β and the shear flow (


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

of the most massive stars to the core results in a runaway stellar collision (Portegies Zwart et al. 2004 ; van der Marel 2004 , p. 37). This collision produces a seed BH of several hundred to several thousand solar masses (Katz et al. 2015 ). 3. Over the next several billion years the halo continues to accrete gas, feeding additional star formation and the central BH. During this era, feedback from bursty star formation precludes the formation of a significant bulge (Guedes et al. 2011 ; Governato et al. 2010 ). 4. Between 5 and 10 Gyr ago, the dwarf falls into Centaurus A. This allows enough time for its gas, dark matter, and outer stars to be completely stripped (Smith et al. 2013 , 2015 ), therefore the DSCs would not be hosted in the surviving subhalos at z = 0. At z = 0, the only remaining sign of the lost dwarf is the remnant cusp of stars surrounding its central SMBH. Excepting its dynamics and metallicity, the surviving stellar cusp resembles a GC. Since these systems resemble GCs photometrically and structurally, it is only possible to disentangle their origin as lost dwarf galaxies through the dynamic signatures of their central BHs and the following observational criteria. Chemical composition : if the DSCs formed as dwarf galaxies their residual stellar populations should accordingly have dwarf galaxy-like chemical abundances; namely, a significantly elevated metallicity dex, a measurable metallicity spread (), and a higher ratio than expected for their present stellar mass on the –luminosity relation of stellar systems (e.g., Thomas et al. 2005 ; Smith et al. 2009 ). In addition, they should be above expectations from the L –[Fe/H] relation for systems with . From the selective enrichment by core-collapse supernovae we would also expect enhanced ratios of light elements (CNO) to iron, as well as a significant variance in iron-peak elements. X-ray flux : while the central BH is likely now quiescent, low-level accretion (∼10 −8 Eddington) is possible via AGB (asymptotic giant branch) winds and planetary nebulae. At Centaurus A’s distance, even these low accretion rates would be detectable by Chandra or XMM for the expected central BH masses. 6. SUMMARY AND CONCLUSIONS We have used a new set of high-resolution simulations of an isolated Centaurus A analog to investigate possible formation models for the DSCs found in T15 . We assume that the DSCs formed within dark matter halos before determining which Centaurus A subhalos at z = 0 have the highest probability of being DSC progenitors. We find that DSCs likely formed in dark matter halos that virialized at high redshift with . Since dark matter halos grow in mass in isolation, we assume that any DSC progenitor had . However, no dark matter profile associated with the Centaurus A system, whether for the subhalos at z = 0, z peak , or high redshift (e.g., z = 9.3), has a high enough central density to account for the dynamical mass derived for the DSCs. Even the densest DM halos fall


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This work is supported by NSF CAREER grant EAR-60023026 to W.R.P.. Special thanks to Ian Rose for creating the initial mass–radius code for the CIDER 2014 Summer Institute. The Python scripts for Figure 1 are available in latest release of the BurnMan software as planet_builder.py with code for creating other figures available upon request.


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The authors are grateful to the referee, whose detailed and constructive comments greatly improved the manuscript. We would also like to thank P. Bonfini and T. Bitsakis for many useful discussions and comments on this work. This research made use of MONTAGE . It is funded by the National Science Foundation under Grant Number ACI-1440620, and was previously funded by the National Aeronautics and Space Administration’s Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. M. V. was supported by an IKY postdoctoral Scholarship.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Observatory 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

flux were fit simultaneously by varying and the gas-to-dust ratio. The outer radius was set by fitting the CO spectrum (the maxima in the spectra or double peaks that arise from the Keplerian motion) and provides outer boundaries for computing the gas masses. Using this surface density profile, the emission inside the cavity is constrained by the parameters (Fig. 4 ). The near-infrared excess determines the dust density in the inner disk through . The gas cavity radius and drop were fit to the CO emission. In some cases, an additional drop in gas surface density is required between and the dust cavity radius . This drop is indicated by . The main parameters that are varied are the gas cavity radius and the drop in gas density between and . The CO isotopologs provide better constraints on the density than the CO because they are less optically thick (CO) or even optically thin (CO). The effects of isotope-selective photodissociation are properly considered in the modeling and are discussed in Sect. 4.3 . 4. Results Table 3 Results for the gas density profile of each transition disk. Notes. (a) HD13 = HD 135344B. (b) The masses are only constrained within for the detected surface brightness. (c) The drop inside 7 AU could not be constrained by the ALMA data; we adopt the value from CO rovibrational spectroastrometry by Pontoppidan et al. (2008) . (d) The uncertainties on the gas cavity size are typically 5 AU and lower than one order of magnitude on the depth of the drop. Fig. 5 Modeling results and observations of the CO and CO emission for the best-fitting models in derotated images and spectra. The left panels show the direct image comparison of the zero-moment map: derotated observations, model, convolved model, and residual. In the residual map the overlaid contours indicate the 3 levels, where dashed lines are negative. The central panels show the gas density profiles with different drops as solid lines and the dust density profile as dashed lines. The right panels show the resulting intensity cuts for the major and minor axis for both CO and CO. The best-fitting model is indicated in red, other values in blue. The drop in density can be constrained to within an order of magnitude. Data and models are compared through the spectra and the zero-moment maps (intensity maps) of both CO and CO. For each target we show the direct comparison of the images of the intensity map of the best-fit model and the constraint on both and through spectra and intensity cuts through the major and minor axis of the zero-moment map. In three of the four targets an inner gas cavity (smaller than the dust cavity) was required to fit the data. In SR21 the 7 AU cavity previously derived from rovibrational emission was adopted, but no gas cavity is resolved at the spatial resolution of (24 AU) in our observations. In all disks, the depth is constrained to within an order of magnitude and the cavity size to within 5 AU, mainly through the comparison of the spatially


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GZ thanks insightful discussions with Andrew Vanderburg and Bryce Croll. JPM is supported by a UNSW Vice-Chancellor's Postdoctoral Fellowship. We thank the support staff at the AAO , who made the continued IRIS2 observations possible. This work makes use of observations from the LCOGT network. DD acknowledges support provided by NASA through Hubble Fellowship grant HST-HF2-51372.001 -A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.


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

and Ultrascale The evaluation of the pathlength from the SDE steps in x and z directions, as given by Equation ( 7 ), proved unphysical. However, it does provide a possibility to solve the problem of determining the pathlength of a diffusing particle, given a suitable physical framework. Here, we employ field-line random walk as the framework for determining the pathlength of a diffusing particle. In the SDE method, the stepsize does not have a physical meaning, but in the physical world it does. Particle cross-field diffusion is believed to be dominated by their following the turbulent random-walk of the magnetic fieldlines (e.g., Fraschetti Jokipii 2011 ). The fieldlines do not, however, meander at infinitesimal scales, since physical processes damp small-scale fluctuations. Thus, a length scale that would describe the meandering of the fieldlines is a good candidate for evaluation of the pathlength of a particle in turbulent magnetic fields. Such a length scale can be derived from the definition of a fieldline diffusion coefficient and the concept of an ultrascale, . The fieldline diffusion coefficient for 2D-dominated turbulence is given bywhere B is the magnitude of the ambient background magnetic field, and is the turbulence variance (Matthaeus et al. 1995 ). For 2D turbulence spectrum S ( k ), the ultrascale is defined aswhere k is the wavenumber. Matthaeus et al. ( 1999 ) gives the ultrascale an interpretation as the representative scale size of turbulent closed magnetic 2D structures, “magnetic islands,” in the cross-field direction, x . The fieldlines in 2D-dominated turbulence can be thought to be either trapped in magnetic islands or meandering freely around these islands (Ruffolo et al. 2003 ; Chuychai et al. 2007 ). We can thus consider the ultrascale to be the relevant cross-field length scale for the meandering of the untrapped fieldlines around the islands that are of size . The distance Δ z FL along the mean field direction as the fieldline propagates a cross-field length can then be evaluated using the fieldline diffusion coefficient, Equation ( 13 ), using the general definition of a diffusion coefficient , where the distance along the z -axis takes the place of time in the denominator for fieldline diffusion. If we consider the mean square cross-field step given as the ultrascale, , we can writeEquation ( 15 ) gives a natural interpretation to the fieldline diffusion coefficient in Equation ( 13 ): the fieldline random walk across the mean field direction is described as random walk with stepsize , with the ratio between the steps along and across the field, , equal to B / δB ⊥ . Using the steplength as defined by the turbulent island size, given by Equation ( 15 ), we can solve the pathlength of the meandering fieldline as Gaussian random walk withThe pathlength of a particle following such a fieldline can then be estimated and integrated using equationwith the steps along and across the field given by Equations (


O O O O O O O O O O O O O O O O O B-Wavelength 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O B-Wavelength O B-CelestialObject O O O O O O B-Wavelength O B-Wavelength O O O O O O O O B-Mission O O B-CelestialObject O B-CelestialObject O B-Telescope O O B-CelestialObject O B-CelestialObject B-CelestialObject O B-CelestialObject B-Telescope B-Instrument O B-Wavelength I-Wavelength I-Wavelength O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O B-Grant I-Grant O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject O O O O O O O B-Telescope I-Telescope 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 B-Wavelength B-Wavelength B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength B-Wavelength B-Wavelength I-Wavelength I-Wavelength O O O B-Wavelength O B-Wavelength 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 B-CelestialObject O O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-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 B-Wavelength O B-Wavelength O B-Mission O O O O B-Mission O B-Telescope O O O O O O O O O O B-Instrument 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 B-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject O B-CelestialObject 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 B-Software O O O

we averaged spectra from 2004 October to 2016 December with the same criteria, using 57,000 spectra for S(0) and 86,000 spectra for S(1). Although these large averages were necessary to improve the signal-to-noise, the resulting atmospheric profiles (temperature and para-H 2 ) are averaged over a broad region of the planet, and in the case of Saturn, over different seasons from southern summer to northern spring. As shown in Section 4 and Figure 4 , these spectra reveal dimeric structure around S(0) on both planets, and tentatively around S(1) on Saturn. Figure 4. Spectral fits to the S(0) and S(1) lines detected on all four giant planets, using Cassini data for Jupiter and Saturn and Spitzer data for Uranus and Neptune. Uranus and Neptune. Spitzer /IRS acquired 7–36 μ m disk-integrated spectra of Uranus during Directors Discretionary Time on 2007 December 16–17, shortly after Uranus’ equinox (program 467; full details of the data reduction process are provided by Orton et al. 2014a ). Disk-integrated spectra of Neptune were acquired on 2005 November 19–20 during Spitzer ’s Cycle 2 (program 20500), and reduced using the same process as Orton et al. ( 2014a ). For both planets, the observations were designed to sample multiple longitudes during a complete rotation, but we averaged all longitudes to form a single spectrum. Here, we focus on high-resolution ( R ∼ 600) observations in the “Short-High” (SH) 9.95–19.30 μ m and “Long High” (LH) 19.27–35.97 μ m ranges, revealing the S(0) and S(1) lines in Figure 4 , respectively. Note that Orton et al. ( 2014a ) identified offsets between low-resolution and high-resolution Uranus spectra related to flux losses from different slit sizes, and ultimately scaled the SH data to match the low-resolution modes, and abandoned the LH data from their analysis entirely. In the present work, where only narrow spectral ranges are considered to identify the dimer features, we do not find it necessary to perform such a scaling and present good fits to both SH and LH data. Voyager/IRIS: to supplement the high-resolution Cassini and Spitzer observations, we also reanalyze the low-resolution (4.3 cm −1 ) IRIS observations of all four giant planets. These 180–2500 cm −1 spectra were acquired by a Michelson interferometer in a series of north–south scans executed during the close flybys between 1979 and 1989. The selection criteria for the spectra and zonal averaging techniques have been previously described for Jupiter (Fletcher et al. 2017 ), Saturn (Fletcher et al. 2016 ), Uranus (Orton et al. 2015 ), and Neptune (Fletcher et al. 2014 ). Dimer features were previously identified only in the Jupiter and Saturn spectra (Frommhold et al. 1984 ), with the Uranus and Neptune data being too low in signal to reveal the dimer absorptions. The zonally averaged 300–550 cm −1 regions of these spectra are re-analyzed with the new opacity database in Section 4 . 3.2. Spectral Retrieval Model The NEMESIS spectral retrieval algorithm


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

X-ray emitting corona. The energetic contribution to the SED of the former is observed to increase over the latter with increasing ṁ ( Vasudevan Fabian 2009 ; Jin et al. 2012 ). This is explained with the increased inner radial extent of the UV disk, at the expenses of the X-ray corona, at larger ṁ compared with lower ṁ . Assuming a constant radiative efficiency above ṁ ∼ 0.01, the relative UV/X-ray flux ratio will thus increase with increasing ṁ , moving from low-luminosity Seyfert galaxies toward higher luminosity-Seyfert galaxies and QSOs. A consequence of our scenario is therefore that the X-ray coronae in Seyfert galaxies will be extended up to a few tens R g , different than in QSOs where they will be very compact, only a few R g in size. Recent observations of distant microlensed QSOs revealed very compact X-ray coronae only ≲10 R g in size ( Chartas et al. 2009c ; Dai et al. 2010 ; MacLeod et al. 2015 ). In comparison, deep and broadband X-ray spectroscopic observations of the local Seyfert Ark 120 suggest an extended corona (∼10 − 40 R g , Matt et al. 2014 ), and a decrease of the corona size with increasing flux of the continuum source ( Porquet et al. 2019 ). Studies of larger samples of sources are clearly needed in order to assess the presence of a statistical difference in X-ray coronal size between Seyfert galaxies and QSOs. Radiation-driven disk winds driven by pressure on spectral lines are a physical component that can explain many observational features of AGN, but not all of them: for example, the BALs observed in the FR I radio galaxies ( Fanaroff Riley 1974 ), which are accreting at low ṁ , must be driven by magnetic pressure. In our scenario, the low and very low ṁ AGN appear as radio loud because they lack strong optical and UV emission, and would correspond to the FR I, or LEG (low excitation galaxies, Laing et al. 1994 ). At higher ṁ , radio-loud AGN appear as FR II (or HEG, high excitation galaxies) and do have an accretion disk (e.g., Ghisellini Celotti 2001 ; Grandi Palumbo 2004 ). The radio loudness associated to their powerful radio jets is probably driven by the efficient extraction of rotational energy from both the disk ( Blandford Payne 1982 ) and the black hole ( Blandford Znajek 1977 ); however, the exact physical mechanism behind the launching and acceleration of the most powerful radio jets is still under investigation (see Czerny You 2016 , for a recent review). We note how there are no apparent differences in observed properties such as black hole mass, Eddington ratio, and BLR size between radio-loud and radio-quiet BAL QSOs ( Bruni et al. 2014 ), suggesting that the physical difference between them might reside in different black hole spin values. The scarcity of powerful radio-loud FR II BAL QSOs is probably due to the combination of a large black hole mass needed to have a RL AGN ( Laor 2000 ), which is possibly related to the merger history of the host galaxies, where coherent mergers can increase


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ACKNOWLEDGEMENTS We thank the organizers of SPHERIC2018 for a useful and stimulating conference in Galway, Ireland. DP acknowledges funding from the Australian Research Council via FT130100034 and DP180104235.


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

the particle sampling noise introduced by the LPT. Since most of the particles cluster in high-density regions, voids are impacted by higher uncertainty in the LPT. The field-level approach of the PPT overcomes this problem, showing a lower standard deviation in the void profile. Fig. 9. Comparison of density profiles obtained with PPT and LPT. Upper panel : cluster density profile obtained by evolving the same initial conditions with PPT and LPT. Lower panel : test for a void profile. This demonstrates that PPT and LPT provide equivalent cosmic structures. The shaded regions indicate the uncertainty region of the profiles, corresponding to the standard deviation of 50 realisations. While the PPT and LPT show similar uncertainty regions for the cluster profile, the LPT has a larger standard deviation than the PPT in the void profile. This larger uncertainty is due to the poor sampling of the voids in the LPT model since most of the particles cluster in high-density regions. 6. Inference results In this section, we present the results of applying our algorithm to Ly- α forest data in redshift space. We show that our method infers unbiased density fields and corresponding power-spectra at all scales considered in this work. We also perform a posterior predictive test for quasar spectra, showing that the inferred quantities can explain the data within the noise uncertainty. 6.1. Inferred density fields As discussed above, our method uses a forward modelling approach, fitting a physical dynamical model to Ly- α forest data. This provides the full posterior distribution, from which we draw samples of the initial matter fluctuations and the non-linear spatial matter distribution at z = 2.5. In this section, the dynamical model is the PPT in redshift space, described in Sect. 2.4 . Since the optical depth is conserved under the mapping between physical and redshift space, our inference in redshift space focuses on the optical depth field, while the density field is obtained in real space. Figure 10 shows slices through the true fields, and the ensemble mean and variances of inferred three-dimensional fields, computed from 600 samples. A first visual comparison between ground truth and the inferred ensemble mean final density and optical depth fields shows that the algorithm correctly recovered the large-scale structure from Ly- α forest data. We note that the optical depth field is in redshift space while the final density field is in physical space. The lower right panel of Fig. 10 shows the corresponding standard deviations of the amplitudes, which is estimated from the samples in the Markov chain. The estimated density standard deviation correlates with the inferred density field. The same is true for the optical depth field. This is expected for a non-linear data model, which couples signal and noise. Higher uncertainty regions correspond to over-densities since the absorption saturates at high density, making the signal weaker. Once the light


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

= PBH+CDM). We define the PBH+CDM mass fraction as where M PBH and M CDM are the total masses of PBHs and CDM particles. For our halo, we assume the Navarro–Frenk–White (NFW) form (Navarro et al. 1996 ) with scale density ρ 0 and scale length r s . The relaxation time is proportional to N /ln ( N ), where N is the number of particles. Assuming 100 M ⊙ PBHs and 10 7 M ⊙ halo, the particle relaxation will take between 1 and 12 Gyr depending on f m considered between 1 and 0.01. In comparison, the relaxation time for 10 8 (10 9 M ⊙ ) haloes are 10 (100) times longer than for 10 7 M ⊙ and longer than the age of the Universe, which is why we focus here on a 10 7 M ⊙ dwarf galaxy, starting at redshift z = 2 in the simulations. Given the halo mass and redshift, the halo concentration c 200 can be estimated from cosmological N -body simulations (Prada et al. 2012 ). Our halo is composed of DM and PBH particles with a total mass of 10 7 M ⊙ . To generate our NFW haloes, we use the initial-condition generator, magi . Adoption of a distribution-function-based method ensures that the final realization of the halo is in dynamical equilibrium (Miki Umemura 2018 ). We perform our simulations with the high performance collisionless N -body code, gothic (Miki Umemura 2017 ; Miki 2019 ). This gravitational octree code runs entirely on GPU and is accelerated by the use of hierarchical time steps in which a group of particles has the same time step. We have performed the simulations using NVIDIA GeForce GTX 1080 Ti (CUDA 9.0) on Intel Xeon Silver 4114 (GCC 4.8). We evolve different PBH+CDM haloes composed of 25, 50, 75, and 100 M ⊙ PBHs over 11 Gyr by adopting the softening length of ε 0 =1.331 pc and the accuracy control parameter of 2 −7 . All runs were made with CDM particles of 1 M ⊙ . We explored also PBH+CDM haloes with different mass fractions f m = [0.01, 0.1, 0.5]. In our simulations, we assume that the CDM and PBH components of PBH+CDM haloes initially follow NFW profiles with the same concentration. We tested two different scale lengths for the profile of the PBH component: and . The second corresponds to a scenario where the density of PBHs is enhanced in the central region. Indeed, we suppose that mass segregation of PBHs would occur, and this increases the density of PBHs at the centre. This scenario should also enhance the formation of cores due to dynamical heating of the CDM by PBHs. It will also accelerate the two-body relaxation. 3 RESULTS 3.1 Evidences for core formation from gravitational heating by PBHs First, we assess the impact on the PBH+CDM halo density profiles in our simulations of the two numerical parameters, which are the accuracy control parameter and the softening length ε. We tested 2 −6 , 2 −7 , 2 −8 , and 2 −9 for the accuracy control parameter in a PBH+CDM halo with f m = 0.1 and m PBH = 100 M ⊙ . The left-hand panel of the Fig. 1 shows that PBH+CDM density profiles hold the initial distribution for all the different values


O O O B-Person I-Person O B-Observatory I-Observatory O B-Person I-Person O B-Person I-Person O B-Observatory I-Observatory O O O O O O O O B-Telescope O B-Instrument O B-Person O O B-Observatory I-Observatory I-Observatory O O O O O O B-Person O B-Observatory I-Observatory O O O O O O O O O O O O O O O B-Person O O O O B-Organization B-Organization B-Organization I-Organization I-Organization O O B-Location I-Location I-Location O O B-Grant I-Grant I-Grant I-Grant O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization B-Mission O O B-Instrument O B-Instrument O O O B-Telescope O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O O O B-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O O B-Organization I-Organization I-Organization O O O O O O O B-Database O O O B-Database O O O O O O O O O O O O O O O B-Person I-Person O B-Observatory I-Observatory B-Database O B-Database O O O B-Organization B-Location I-Location 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

The authors thank Lou Boyd of Fairborn Observatory and Brian Skiff and Len Bright of Lowell Observatory for their years of crucial support to the APT and SSS programs. R.R.R. thanks the National Solar Observatory for support as an Emeritus Astronomer. G.W.L. thanks Lowell Observatory for informal emeritus status, access to facilities, and travel support in continuing post-retirement stellar research. G.W.H. acknowledges long-term support from NASA, NSF, Tennessee State University, and the State of Tennessee through its Centers of Excellence program. The referee’s careful reading and knowledgeable comments enabled us to improve the overall scholarship of our paper and expand our discussion of the results, and we appreciate that anonymous contribution. This research utilized data courtesy of NASA/ SORCE and the SIM and TIM science teams, and SOLIS data obtained by the NSO Integrated Synoptic Program (NISP), managed by the National Solar Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation. This research has made use of the SIMBAD database and its VizieR catalog access tool, especially the catalog of MK spectral types (B/mk/mktypes) created and maintained by Brian Skiff of Lowell Observatory. SIMBAD and VizierR are operated at CDS, Strasbourg, France (Wenger et al. 2000 ). For the two lead authors, this paper will likely be our final word on this subject.


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

independently confirms that the H 2 -bearing cloud is likely pressure confined. We note that while a high dust content reduces the H 2 formation time-scale, the number density can have major importance since t ∝ n −2 . It has two direct consequences: first, in low-metallicity environments, H 2 may trace only the densest regions in the patchy medium of DLAs. High number densities will obviously severely reduce the covering fraction of the H 2 -bearing gas. Secondly, the formation time-scale of H 2 can be shortened by supersonic turbulences that can create pockets of compressed gas, where H 2 is quickly formed, and consequently redistributed to the adjacent medium. In Section 4.2 , we showed that the H 2 -bearing gas in the DLA at z = 2.7865 has a kinetic temperature T ∼ 122 K, which is significantly higher than what is expected at such H 2 column density. We supposed that such high temperature was likely attributed to the low metallicity in the medium. The cooling time can be easily estimated from the cooling rate, l c , derived from C ii* , as ∼2 k B T / l c , where k B is the Boltzmann constant (the factor of 2 was chosen since the molecular fraction is not well constrained and the correct coefficients are 3/2 and 5/2 for monatomic and diatomic gas, respectively). This indicates a cooling time of about 0.1 Myr, which is at least an order shorter than the time-scales mentioned above. Hence, the cloud is likely in thermal equilibrium and the high kinetic temperature is indeed due to the low metallicity and not to the formation of H 2 in a shock-compressed medium. 5.3 CO content, <italic>X</italic>CO and CO-dark gas In spite of extremely high H 2 column density, we did not detect CO. This is not surprising given the facts that we measured a low associated extinction and possibly an enhanced UV flux: CO is easily photodestructed by UV photons in the diffuse medium and therefore at least moderate level of extinction A V ≳ 1 is required for this molecule to survive. Models indicate that the abundance of CO scales with the metallicity, but there are only scarce measurements at low metallicities (e.g. Shi et al. 2015 ). Our upper limit on N (CO) is therefore very valuable since it provides a stringent limit on X CO at Z ∼ 0.03 Z ⊙ for the first time. Fig. 17 shows the dependence of the CO column density on that of H 2 measured in both the MW and high-redshift ISM. Values for high- z DLAs are from Srianand et al. ( 2008a ) and Noterdaeme et al. ( 2010 , 2017 ) for quasar absorption systems and Prochaska et al. ( 2009 ) for the GRB-DLA. 6 We also derived upper limits on the total CO column density in known strong H 2 absorption systems, using the covered A-X bands in the archival spectra and assuming that the population of CO rotational levels is dominated by the CMB excitation. We found N (CO) 12.55 in the DLA towards Q 1232 + 082 with log N (H 2 ) = 19.57 ± 0.10 and N (CO) 12.81 in the DLA towards Q 0812 + 3208 with log N (H 2 ) = 19.93


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ACKNOWLEDGEMENTS This work was supported by United Kingdom’s Science and Technology Facilities Council. The authors would like to sincerely thank the anonymous reviewer for their careful and detailed review, and very helpful suggestions on how to improve the presentation of this paper.


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

the 615460 Å doublet and the set of stellar parameters derived according to Carretta et al. (2006) prescriptions with those derived by Carretta et al. (2006) . The right panel shows the good agreement between the spectrum-synthesis-based abundances and the (615460 Å doublet) EW-based values, based on our own set of stellar parameters. Here only LTE abundances are considered. Overall, we can then conclude that the different methods explored so far for the derivation of stellar parameters and/or abundances lead to small systematic differences (within the associated errors in our case), while the errors associated with the EWs/line-fitting measurements are mostly responsible for the dispersions around these values. To complete our diagnostic tests, we have also evaluated the effects of deriving the stellar parameters spectroscopically on our final Na. The results of this test are summarised in the Appendix. 4. Observed Na distribution along the RGB and AGB in NGC 2808 4.1. [Na/H] versus [Na/Fe] Fig. 7 Abundance distributions of our complete (AGB RGB) sample. Left : [Na/H]; middle : [Na/Fe i ]; right : [Na/Fe ii ]. Symbols are the same as in Fig. 2 . The horizontal dash-dotted lines mark the critical values distinguishing the 1P and 2P stars following Carretta et al. (2009b) criteria (see the text). The typical error bars are shown at the right-bottom corner of each panel (considering the similarity of the errors of the GIRAFFE and UVES samples and the clarity of the figure, we only show the error bars for the GIRAFFE sample which is the largest sample here). By comparing the errors in our derived metallicities () and the star-to-star dispersions (), we find the intrinsic spread in [Fe/H] of NGC 2808 to be within , when considering only the GIRAFFE sample (representing the large majority of our dataset). The stellar population in NGC 2808 can thus be considered homogeneous in its Fe content within a few hundredths of , as also pointed out by Carretta et al. (2006) . Figure 7 shows these effects on the observed abundance patterns, where we present our final Na abundance distributions for AGB and RGB stars in NGC 2808 as [Na/H], [Na/Fe i ], and [Na/Fe ii ] versus . Overall, the differences among the three panels are minimal. However, because of the extra uncertainties associated with Fe i (due to the NLTE corrections) and Fe ii (due to the paucity of lines), we chose to use the [Na/H] ratio to discuss our derived Na abundance distributions along the RGB and AGB. 4.2. [Na/H] distribution A quick inspection of Fig. 7 (left panel) shows that the AGB and RGB samples in NGC 2808 have similar Na abundance ranges. A two-sided Kolmogorov-Smirnov (K-S) test confirms this: the K-S statistic D (0.268) and the -value (0.137) derived for the [Na/H] distribution both indicate that there is only weak evidence to reject the null hypothesis, i.e. the two samples have the same distribution. Examining in more detail the dispersions () and the interquartile range (IQR)


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We thank Diego Muñoz and Smadar Naoz for useful discussions, and especially Cristobal Petrovich for useful discussion and comments on the manuscript. This work has been supported in part by NSF grant AST-1211061, and NASA grants NNX14AG94G and NNX14AP31G. KRA is supported by the NSF Graduate Research Fellowship Program under Grant No. DGE-1144153.


O 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 O O B-Person O O O B-Organization O O B-Grant I-Grant I-Grant B-Grant B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Person I-Person I-Person O B-Person I-Person O O B-Grant I-Grant I-Grant O O B-Telescope B-Person O O O O O B-Organization O B-Grant O B-Organization O O O O O O B-Organization O B-Grant B-Organization O B-Grant O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Person B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O B-Organization O O B-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Fellowship I-Fellowship O O 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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 B-Grant O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Software O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O B-Organization O B-Survey I-Survey B-Survey O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O 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B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O O B-Observatory I-Observatory I-Observatory B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization O B-Organization O B-Telescope O O O B-Software I-Software I-Software B-Software O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O B-Telescope O O O B-Software O O O O O O B-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant B-Grant O B-Grant I-Grant I-Grant 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O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person O O O O O O O O O B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization B-Person O O O O B-Organization O O B-Grant O B-Grant B-Person O B-Organization O O B-Grant O O O O B-Organization B-Person O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization O O B-Grant O O B-Organization I-Organization O O O O B-ComputingFacility O B-URL O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization B-Organization I-Organization O O B-Grant B-Organization O O B-Grant O B-Grant O B-Organization B-ComputingFacility B-Grant I-Grant I-Grant B-ComputingFacility O O O O B-Organization I-Organization

ACKNOWLEDGEMENTS We would like to thank Federico Lelli, Harley Katz, Cameron Lemon, and the anonymous reviewer for helpful comments and discussions. APN thanks the Science and Technology Facilities Council (STFC) for their PhD studentship. EP acknowledges support by the Kavli foundation. ACD acknowledges partial support from STFC under grants ST/L000385 and ST/L000636. DS acknowledges ERC starting grant 638707 and support from the STFC. HD is supported by St John’s College, Oxford and acknowledges financial support from ERC grant no. 693024 and the Beecroft Trust. This work used the DiRAC ( www.dirac.ac.uk ) system: Data Analytic at the University of Cambridge [funded by 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]. DiRAC is part of the National E-Infrastructure.


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

that the 3:2 MMR of the orbital periods affect periodic variations of the Keplerian orbital parameters. She has obtained the expansion of disturbing function and identified only two first-order 3:2 resonance term. But we identify ( r + 1): r MMR terms in the expression of disturbing function and obtained the perturbations from the truncated disturbing function. In this manuscript, we have taken three exoplanetary systems namely Kepler-62, HD 200964 and Kepler-11 and as per our knowledge they contain planets in 2:1, 4:3 and 5:4 near MMRs, respectively. We apply theory discussed in Sections 3 and 4 individually in our three exoplanetary systems that we have chosen. This paper is organized as follows. In Section 2, we introduce the general three-body problem and the stability of exoplanetary system. The expansions of the disturbing function and perturbation equations of orbital elements are introduced in Section 3 . In Section 4, we present our secular resonance dynamics of exoplanetary system. Applications of the model for the case of 2:1 resonance are shown in Section 5 for Kepler-62 system. The case of the 4:3 resonance is discussed in Section 6 for HD 200964 system. In Section 7 , the case of 5:4 is discussed for Kepler-11 system. Finally, Section 8 is devoted to conclusions. 2 GENERAL THREE-BODY PROBLEM AND DYNAMICAL STABILITY Suppose the barycentric position vectors of star and two planets be , and , respectively. Let two planets of masses M 1 and M 2 orbiting a star of mass M ⋆ . Let the Jacobi coordinates and be the position of M 1 relative to M ⋆ and position of M 2 relative to the centre of mass M ⋆ and M 1 . We notice that this system is different from the restricted problems in which one of the bodies must have negligible mass. Also we ignore the effects of oblateness of star and the planets. We assume that the planets in all system are coplanar. This approximation of coplanarity makes sense because for exoplanets, their mutual inclination is not known with any precision, and is taken equal to zero (Beaugé, Ferraz-Mello Michtchenko 2003 ). Let a i , e i , λ i and ω i be the semimajor axis, eccentricity, mean longitude and the longitude of the pericentre of the i th planet for i = 1, 2. In the three-body problem, one of the interesting topic is the stability of the Solar system or exoplanetary system. Although, in celestial mechanics it is the unsolved problem till now, many scientist studied this because of its importance in many areas like space science, astronomy and astrophysics. In the context of planets and exoplanets formulation, Graziani Black ( 1981 ) studied conditions under which model planetary systems which consisting of a star and two planets with coplanar and initially circular orbits. Based on their results, they obtained a necessary condition for orbital stability where M 1 and M 2 are masses of planetary companions and M ⋆ is the mass of the star. The parameter Δ is the ratio of the separation distance between the


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

We are grateful to Desika Narayanan, Mark Sargent, and Anita Zanella for stimulating discussions, to Damien Chapon for help with the implementation of some post-processing modules, and to the anonymous referee for a very careful reading and useful comments. The simulations presented in this work were performed at the Très Grand Centre de Calcul of CEA under GENCI allocations 2013-GEN 2192 and 2014-GEN2192 and on SuperMuc at the LRZ under a PRACE allocation. We acknowledge financial support from the EC through an ERC grant StG-257720 (F.B., F.R.).


O B-Survey I-Survey O O O O O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant O O O 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The Pan-STARRS1 Surveys have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg, the Max Planck Institute for Extraterrestrial Physics, Garching, Johns Hopkins University, Durham University, the University of Edinburgh, Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under grant no. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE). Some observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. Based on observations obtained with the Apache Point Observatory 3.5 m telescope, which is owned and operated by the Astrophysical Research Consortium. C.W.S. and G.N. thank the DOE Office of Science for their support under grant ER41843. Partial support for this work was provided by National Science Foundation grant AST-1009749. The ESSENCE/SuperMACHO data reduction pipeline photpipe was developed with support from National Science Foundation grant AST-0507574 and HST programs GO-10583 and GO-10903. R.P.K.’s supernova research is supported in part by NSF grant AST-1211196 and HST program GO-13046. Some of the computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. Much of the analysis was done using the Midway-RCC computing cluster at University of Chicago. This research has made use of the CfA Supernova Archive, which is funded in part by the National Science Foundation through grant AST 0907903. This research has made use of NASA’s Astrophysics Data System. This work was generated as part of NASA WFIRST Preparatory Science program 14-WPS14-0048 and is supported in part by the U.S. Department of Energy under contract DE-AC02-76CH03000. This work was supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder Fred Kavli. We gratefully acknowledge support from NASA grant 14-WPS14-0048. D.S. is supported by NASA through Hubble Fellowship grant HST -HF2-51383.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. D.O.J. is supported by the Gordon and Betty Moore Foundation postdoctoral fellowship at the University of California, Santa Cruz. R.C. thanks the Kavli Institute for Theoretical Physics for its hospitality while this work was in the final stages of preparation. This research was supported in part by the National Science Foundation under grant no. NSF PHY11-25915. R.K. is supported by DOE grant DEAC02-76CH03000. The computations in this paper used a combination of three computing clusters. The bulk of the final analysis was performed using the University of Chicago Research Computing Center, and the earlier analysis was done at the Odyssey cluster at Harvard University. The Odyssey cluster is supported by the FAS Division of Science, Research Computing Group at Harvard University. Supernova light-curve reprocessing would not have been possible without the Data-Scope project at the Institute for Data Intensive Engineering and Science at Johns Hopkins University. Facilities: PS1 (GPC1) , Gemini:South (GMOS) , Gemini:North (GMOS) , MMT (Blue Channel spectrograph) , MMT (Hectospec) , Magellan:Baade (IMACS) , Magellan:Clay (LDSS3) , APO (DIS) .


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

( Schneider et al. 2017 ; Mapelli et al. 2017 ). Interestingly, Mapelli et al. (2017) predict that the distribution of metallicity of BH–BH merger progenitors peaks at around ∼ 0.1 Z ⊙ and declines towards lower Z , which conflicts with our Fig. 8 . The most likely explanation of this discrepancy is that we are overestimating the contribution from very low metallicities at close redshifts of star formation. The majority of the low-metallicity content of the recent Universe is locked in dwarf galaxies with little star formation, for which our simplification that the mean metallicity of the Universe ≈ mean metallicity of star formation is likely less accurate. This interpretation also agrees with the fact that Mapelli et al. (2017) did not find the clearly bimodal distribution of massive BH–BH merger birth redshifts as shown in the case of our simulations in Fig. 2 of B16, but rather only the single maximum around the peak of cosmic star formation at z ≈ 2. However, even if we were overpredicting the star formation in low metallicities Z 0.1 Z ⊙ at redshifts z 2 to the point at which we would have to discard all our mergers formed in these conditions, this would still not affect our predictions for the merger rates by more than a factor of 2. Although making predictions for CBM based on cosmological simulations as carried out by Schneider et al. (2017) or Mapelli et al. (2017 ; or, in a simplified way, also by Belczynski et al. 2018) may be burdened with additional biases, this ultimately seems to be the superior approach that hopefully will allow us to confront models with various galactic properties in the case of mergers with identified hosts (such as GW170817, Abbott et al. 2017d ). Finally, we wish to highlight that the small impact of IMF variations on merger rates (Sect. 6.2 ) is a general result that should also appear in the predictions based on cosmological simulations. Even though such simulations often provide SFR values as their output, changing the assumptions on the massive-star IMF without renormalizing the SFR make their results inconsistent with star formation tracers such as UV observations. 6.4. Comparison with LIGO/Virgo detection rates and other studies We show the merger (Gpc −3 yr −1 ) and detection rates (yr −1 ) from our simulations in Table A.1 . While our models perform relatively well in retrieving the BH–BH merger rate as constrained by the LIGO/Virgo observations R BHBH = 12–213 Gpc −3 yr −1 ( Abbott et al. 2017a ), they underpredict the rate of NS–NS mergers that was inferred after the recent detection of GW170817: ( Abbott et al. 2017d ) 6 . Recently, Chruslinska et al. (2018) analysed NS–NS merger rates within a large suite of S TAR T RACK models, varying multiple binary evolution assumptions, and found that it is, in fact, very difficult to obtain R NSNS consistent with the LIGO/Virgo constraints. The only three models marginally consistent with the reported NS–NS merger rates, which have R NSNS values of


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the photometry in all bands has been convolved to match the WFC3/ F 160 W resolution (Guo et al. 2013 ), any influence caused by different PSF sizes of HST filters has been eliminated. All galaxies receive the same statistical weight in a stack. The maximum radial extent to measure colour gradients is set to two times the SMA, where reliable photometry is still available. 4.2 Colour gradients uncorrected for beam smearing and stacked by radius scaled to SMA This subsection shows raw stacked colour gradients without any beam-smearing correction. First, we scale the radial colour profiles of each individual galaxy by its SMA (effective radius along the galaxy major axis), by interpolating between the apertures as described in Section 2 . Then these scaled colour profiles are stacked together to produce the average profiles as shown in Fig. 3 . Figure 3. UVI colour gradients for star-forming galaxies in mass–redshift bins, as indicated at the top and right margins. The radial colour profiles are scaled by effective radius before stacking, without correction for PSF smearing. For each panel, the stacked radial trajectories in U − V and V − I are plotted as the black curves. Dashed lines denote the Calzetti reddening vector. Mean integrated A V and the number of sample galaxies are indicated at upper left in each panel, and the typical standard deviation of the mean of stacked gradients is shown at lower right. The gradient trajectories follow the reddening vector, which indicates that most of the gradients are caused by dust variations and that sSFR is nearly constant with radius. The grid of panels in Fig. 3 shows the shapes of the stacked colour trajectories in UVI space as a function of mass and redshift. Each panel is a UVI diagram, and the black lines are the paths taken by the colours in going from the innermost radius (upper right) to the outermost radius (lower left). The three symbols indicate local colours at 0.2 SMA (star), 1 SMA (open circle) and 2 SMA (dot). The direction of dust reddening by the Calzetti law is shown as the dashed lines. The main feature of this figure is that gradient trajectories approximately follow the reddening vector, which indicates that most of the gradients are caused by dust variations and that sSFR is nearly constant with radius. This conclusion is unchanged under beam-smearing correction and stacking by radius rather than scaled radius, as shown in the next section. 4.3 Colour gradients stacked based on angular distance and beam-smearing correction Next, we turn to another stacking method of colour profiles and then evaluate and correct the beam-smearing effects caused by the PSF. To start with, galaxy colour profiles are stacked together based on the angular distance in arcsec to their centres, instead of the normalization used in Section 4.2 . The resultant colour gradients are shown as red curves in Fig. 4 . This stacking method ensures that the stacked profiles have a well-defined angular


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We thank the anonymous referee for a critical reading of the paper and valuable suggestions that helped improve the quality and clarity of this work. We also thank to Dany Page, John Beacom and W. H. Lee for useful discussions. CB acknowledges to CAPES–Brazil by the postdoctoral fellowship received through the Science Without Borders programme. This work was supported by the projects IG100414 and Conacyt 101958. The software used in this work was in part developed by the DOE NNSA-ASC OASCR FLASH Center at the University of Chicago.


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Y , X – Z , and Y – Z planes. The inner Sagittarius, the closest Local (Orion), and the outer Perseus spiral arm segments can be recognized in the X – Y projection (a top-down view of the Galactic disc) (cf. Hou Han 2014 , figs 5–7 therein; Nakanishi Sofue 2016 , fig. 7 therein; Xu et al. 2018 , fig. 1 therein; Reid et al. 2019 , fig. 1 therein; Cantat-Gaudin et al. 2020 , fig. 8 therein; Xu et al. 2021 , fig. 1 therein). Stars are indeed located within the extremely thin disc. The Sun is situated within the Orion segment, at the inner edge of this arm (cf. Simonson van Someren Greve 1976 ; Basharina, Pavlovskaya Filippova 1980 ; Cohen et al. 1980 ). Figure 2. Space locations of all 1972 (top panels) and selected 964 (bottom panels) OB stars. The Cartesian ( X , Y , Z ) coordinates are shown, and a dashed line indicates the solar circle and the Galactic mid-plane. The Sun is at (0, 8.2, 0.02) kpc. Fig. 3 gives a plot of los for all and selected stars as a function of the longitude l. A well-defined effect of the Galactic differential rotation is clearly seen. For these two samples of stars – all 1972 and selected 964 ones – the space and velocity distributions have approximately the same properties, as is apparent from Figs 2 and 3 . Figure 3. The heliocentric line-of-sight velocities of OB stars as a function of the Galactic longitude l. Top panel: the velocities of all 1972 stars. Bottom panel: the velocities of selected 964 stars. 3 RESULTS OF CALCULATION To compute the 11 mutually independent unknowns , , , , u 0 , 0 , 0 , , , φ 0 , and λ rad for a given m , we define the weighted sum, S , of squared residuals of measured and modeled (equation 3 ) velocities: where N is the total number of objects, q is the number of parameters to be derived, and is the uncertainty of . The best-fitting values of unknowns are found by fitting that minimizes S . The model depends linearly on the set of nine parameters , , , , u 0 , 0 , 0 , , and and non-linearly on two parameters φ 0 and λ rad . For each model m was fixed and minimization of S by the least-squares fitting was performed in φ 0 and λ rad (that is to say, in the phase of the wave φ 0 and in the pitch angle p at the solar position r 0 for a given number of spiral arms m ). The quantities and are periodic with respect to φ 0 with period 2, while the quantity S is periodic with respect to φ 0 with period . As usual, for a trailing pattern, we chose for the phase φ 0 the values that satisfy the condition (Mishurov et al. 1997 ; Griv Wang 2014 ; Griv et al. 2017 , 2020 ). The surface of S ( φ 0 , λ rad ) and cuts through the S space versus φ 0 and λ rad constructed over selected OB stars for the most interesting m = 1, 2, 3, 4 models are shown in Fig. 4 . A global and several local minima of S with respect to φ 0 and λ rad are seen from our simulation for all models as λ rad increases from 0 to 3 kpc (as | p | increases from 0° to 15°, respectively). Mishurov et al. ( 1979 ) and Pavlovskaya Suchkov


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We thank the organizers of and all participants in the MIAPP 2015 workshop on “The Many Faces of Neutron Stars” for many stimulating discussions. T.M.T. and M.U.K. acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) Grant No. TA 964/1-1. At Garching, the work was supported by the DFG through the Excellence Cluster “Universe” EXC 153 and by the European Research Council through grant ERC-AdG No. 341157-COCO2CASA.


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

of the material. At the surface of silicates, either hydrophilic silanol groups (Si–OH) or hydrophobic Si–O–Si groups are present. The ratio of these groups depends on the production process, the thermal treatment of the silicates, and on a possible processing of silicate surfaces. In silicates produced by laser ablation, the amount of Si–OH groups is small. However, reactions between water molecules and grains have probably increased the number of silanol groups on the surface of the grains. Consequently, the number of hydrophilic surface sites was increased. Thus, with our results, we demonstrate a principal difference between the surface properties of two classes of interstellar grains, namely, the finding of differently bound water ice molecules to silicate grains in contrast to fullerene-like carbon grains. However, this is not a general statement for carbon because carbon surfaces can be very different. For example, oxygenation of C-atoms can produce hydrophilic surface sites. 4.3. Astrophysical Implication The knowledge of the desorption properties of water ice mixed with dust is very important for the understanding of astronomical observations of water vapor in planet-forming regions and for the revealing of the architecture and evolution of planet-forming disks. The desorption of water ice triggering the release of other volatiles trapped in the ice influences the chemistry of the gas phase of disks by feeding it with molecules. In addition, the formation efficiency of larger bodies depends on the ice coverage of dust grains. Knowing the amount of ice relative to dust in a planet-forming disk and the kinetics of desorption of the ice, the structure and morphology of grains and larger bodies can be modeled. It will help to trace back the thermal history of the disk. Conversely, knowing the thermal history of a cosmic body seeded with molecular ice and the kinetics of desorption of ice, the abundance of molecules stayed in the ice and released into the gas phase can be estimated. It will improve our understanding of astrochemical processes in the gas phase and on surfaces. However, more systematic studies on the thermal desorption of molecular ices mixed with different dust analogs are needed. This work represents the first small step in this challenging direction. 5. Summary We measured the TPD of water ice, which had been premixed with amorphous carbon or silicate dust grains, and demonstrate the dependence of the kinetics of desorption of water ice on the dust/ice ratio. The desorption order increases with an increase of the dust/ice mass ratio and reaches 1, indicating the desorption of ice molecules from the large surface of dust grains. This result shows an important link between the structure and morphology of icy dust grains in planet-forming disks and the amount and the desorption properties of seeded ice. If more information on the thermal history of dust grains was known, more information about the structure and