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component to the width. Dynamical studies of galaxies typically use Newton’s gravity. However, it has been argued that once galactic masses are considered, relativistic effects arising from large masses (rather than large velocities) may become important (Deur 2009 , 2017 , 2019 ). Their physical origin is that in general relativity (GR), gravity fields self-interact. In this article, we explore whether these effects can explain the relation in MLS2016 without requiring dark matter or modifying gravitation as we currently know it. The article is organized as follows. We first outline the self-interaction effects in GR, then discuss in Section 3 the empirical tight dependence of observed acceleration on baryonic mass in disk (i.e., lenticular and spiral) galaxies. In Section 4 , we use GR’s equations to compute the correlation. These CPU-intensive calculations allow us to study only a few galaxies, modeled as bulgeless disks. To cover the full range of disk galaxy morphologies, including those with a significant bulge, in Section 5 we develop two dynamical models of disk galaxies in different but complementary ways: uniform sampling (Section 5.1 ) and random sampling (Section 5.2 ) of the galactic parameter space. In Section 6 we show the results from these models and compare them to observations. Finally, in Section 7 , we summarize our findings and their importance. 2. Self-interaction Effects in GR Field self-interaction makes GR nonlinear. The phenomenon is neglected when Newton’s law of gravity is used, as is typically done in dynamical studies of galaxies or galaxy clusters. However, such a phenomenon becomes significant once the masses involved are large enough. Furthermore, it is not suppressed by low velocity—unlike some of the more familiar relativistic effects—as revealed by, e.g., the inspection of the post-Newtonian equations (Einstein et al. 1938 ). In fact, the same phenomenon exists for the strong nuclear interaction and is especially prominent for slow-moving quark systems (heavy hadrons), in which case, it produces the well-known quark confining linear potential. The connection between self-interaction and nonlinearities is seen, e.g., by using the polynomial form of the Einstein–Hilbert Lagrangian (see, e.g., Salam 1974 ; Zee 2013 ),where g μν is the metric, R μν is the Ricci tensor, T μν is the energy-momentum tensor, M is the system mass, and G is the gravitational constant. In the natural units () used throughout this article, . The polynomial is obtained by expanding g μν around a constant metric η μν of choice, with the gravitational field. The brackets are shorthand for sums over Lorentz-invariant terms (Deur 2017 ). For example, the n = 0 term is explicitly given by the Fierz–Pauli Lagrangian (Fierz Pauli 1939 ):While Equation ( 1 ) is often used to study quantum gravity—with questions raised regarding its applicability in that context, see, e.g., Padmanabhan ( 2008 )—we stress that the calculations and results


O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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 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

t b to be 23.0. Figure 3. Multi-band light-curve fitting of SN 2013dy using Equation ( 1 ) for estimating t 0 . The value of is fixed to be 1.90 and t b is fixed to be 23.0 during the fitting procedure. Diamond-shaped data points are included in the fitting, while cross-shaped ones are excluded. After applying the t 0 fit to each SN for each band, and for each case with different ( X varies from 0 to −7), we compare the estimated t 0 with the “known t 0 .” The result is shown in Figure 4 , where the upper panel shows the cases for each SN and each filter with different . For a certain , if there is more than one filter observed for an SN (as shown in Table 1 , except for the three Kepler SNe that were only observed with one broadband filter), a mean value of t 0 from all filters is also calculated. The bottom panel shows the histogram of the t 0 offsets compared with the “known t 0 ”; each filter is color-coded. Figure 4. Difference of first-light time t 0 estimated from Equation ( 1 ) fitting with the real t 0 . The upper panel shows the cases for each SN and each filter with different , arbitrarily shifted along the ordinate for clarity. The bottom panel shows the histogram of t 0 offsets for each filter, also arbitrarily shifted along the abscissa for clarity. In general, the smaller the X in (with earlier data), the smaller the offset. The B (or g ) band has the smallest offset, and appears to not change with X , with a 1 σ systematic error of ±0.7 days. Three important and clear conclusions can be drawn from Figure 4 . First, the offset between the fitting t 0 and the “known t 0 ” becomes smaller when earlier data are included—namely, the smaller the X value in , the smaller the offset. But once X reaches −3, then even earlier data do not help much for t 0 estimation. Second, B interestingly has the smallest offset, and no matter when starting with , the offset is always within ±1.5 days; we estimate a 1 σ systematic error of ±0.7 days by adopting only the B -band estimate of the t 0 offset. Third, the mean offset with multiple filters is similar to that of the B band; thus, for t 0 estimation, one should use either the mean value or the value estimated from B alone. Technically, it is not surprising to see why the B band gives the best estimate of t 0 ; in other bands, the peak is usually broader than that of B , making B better for estimating t 0 . Because of this, in the following we only adopt the t 0 estimate from B , even if the SN was observed with multiple filters. We will also add a systematic error of ±0.7 days for the t 0 estimated from B -band fitting. In addition, Figure 4 shows that the fixed value of is appropriate, giving a mean t 0 offset of 0.1 ± 0.7 days for the B -band, very close to 0 as expected. Furthermore, we performed two other sets of fitting with the value fixed to be 1.50 and 2.30 (respectively), and found t 0 offset by 1.2 ± 0.8 and −0.8 ± 0.7 for B , confirming that the fixed value of is appropriate. 2.4. A


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The project was partially supported by National Science Centre, Poland, grant no. 2017/26/A/ST9/00756 (Maestro 9). V.K. acknowledges Czech Science Foundation no. 17-16287S.


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ACKNOWLEDGEMENTS This work is based upon observations obtained with the Georgia State University (GSU) Center for High Angular Resolution Astronomy (CHARA) Array at Mount Wilson Observatory, and the University of Hawai‘i 2.2-m telescope on Maunakea. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The CHARA Array is supported by the National Science Foundation under Grants Nos. AST-1211929 and AST-1411654. Institutional support has been provided from the GSU College of Arts and Sciences and the GSU Office of the Vice President for Research and Economic Development. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation. The research was supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (Grant agreement no.: 267864). TRW and VSA acknowledge the support of the Villum Foundation (research grant 10118). DH acknowledges support by the Australian Research Council’s Discovery Projects funding scheme (project number DE140101364) and support by the NASA Grant NNX14AB92G issued through the Kepler Participating Scientist Program. LC is supported by the Australian Research Council Future Fellowship FT160100402. MJI was supported by the Australian Research Council Future Fellowship FT130100235. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. This research made use of NASA's Astrophysics Data System Bibliographic Services; the SIMBAD data base (Wenger et al. 2000 ) and VizieR catalogue access tool (Ochsenbein, Bauer Marcout 2000 ), both operated at CDS, Strasbourg, France; and the Jean-Marie Mariotti Center Aspro2 service 1 .


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sample of SNe included in this data release, our adopted classifications and dates of peak brightness (if available), and the values we used to perform redshift and dust-reddening corrections. Table 3 provides a description of the spectra included in our sample. Our research group utilizes a database of observations and associated metadata (the SNDB; Silverman et al. 2012a ) to orchestrate our observational campaigns, to facilitate access to and analysis of our large repository of data, and to share those data publicly – all of the spectra described herein are publicly available through the SNDB web page (see footnote 1). Table 3. The spectra presented in this paper. Notes. (Truncated; full table available online) α Days relative to peak brightness, if date of peak is constrained. β Estimated average resolution across the spectrum. γ Original publications for already-published spectra. δ This historical spectrum was observed under unique conditions – we exclude from our analyses below but we include it here for completeness. The majority of SNe in this sample have only a few spectral observations each, though several well-observed examples of each subtype are also included – Fig. 3 shows the distribution of observation count across SNe in our sample. Our sample includes spectra taken within days of core collapse out to several years [for those SNe that show ongoing, luminous interaction with circumstellar material (CSM)]. Fig. 4 illustrates the phase coverage for spectra of those SNe having either a photometrically or SNID -measured peak-brightness date. Figure 3. The distribution of spectral observation counts for SNe in our sample. Totals are binned over five-spectra intervals, and we group spectra of peculiar subtypes and of stripped-envelope SNe without a clearcut subtype classification together into the ‘other’ category. Figure 4. The phase distribution of spectra having a measured date of peak brightness, grouped by spectral type and binned over 50-d intervals. Spectra having photometric peak dates are shown in solid, while the lighter shade also includes those with snid -determined peak dates. This plot is truncated at 450 days; a small number of observations exist at later phases. 4 RESULTS Below we examine the evolution, relative to date of peak brightness, of several different observational signatures in order to probe the kinematics and composition of the ejecta and to compare to previous results. In summary, we confirm that the O i λ7774 feature has both a higher pseudo-equivalent width (pEW) and a higher characteristic velocity in SNe Ic than in SNe Ib or IIb, supporting the interpretation that SNe Ic are stripped further down toward the C-O core than SNe Ib/IIb but they explode with similar energies. However, we do not find supporting evidence for that scenario from an analysis of the nebular spectra: one may expect that SNe Ic, having lost more of their envelope but exploding at similar energies, would exhibit wider full width at


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Acknowledgements The authors would like to thank the referee Francisco-Shu Kitaura and Stefan Gottlöber for providing comments that helped clarified the paper as well as Sergey Pilipenko for very useful discussions. JS acknowledges support from the Astronomy ESFRI and Research Infrastructure Cluster ASTERICS project, funded by the European Commission under the Horizon 2020 Programme (GA 653477) as well as from the ‘l’Oréal-UNESCO Pour les femmes et la Science’ and the ‘Centre National d’études spatiales (CNES)’ postdoctoral fellowship programmes. ET was supported by ETAg grants IUT40-2, IUT26-2 and by EU through the ERDF CoE grant TK133. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( http://www. gauss-centre.eu ) for providing computing time on the GCS Supercomputers SuperMUC at LRZ Munich and Jureca at JSC Juelich.


O O O O 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 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 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 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-Tag I-Tag B-Tag 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 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 B-Wavelength I-Wavelength I-Wavelength 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


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x -axis in all the panels are the observation wavelength. The horizontal dashed line in the lower right panel shows where τ obs = 0.6. On the other hand, we caution that the DSHARP opacity adopted here is for compact spheres without porosity, and that the mixture of different compositions are handled with the Bruggeman rule. Changing composition or porosity can change the opacity and albedo dramatically, as alluded to in Birnstiel et al. ( 2018 ). For example, the dust becomes more reflective with more water ice. Porosity reduces the resonant opacity features, making the opacity curve smoother. Carbonaceous materials have a substantial effect on the dust opacity. The maximum absorption feature can be shifted to much longer wavelengths than 2 πs max with some choices of carbonaceous materials. On the other hand, the peak of albedo is still at 2 πs max with different choices of carbonaceous materials (Birnstiel et al. 2018 ), making both χ and α measurements (Section 3.3 ) less sensitive to the choices of carbonaceous materials. More detailed calculations exploring different dust compositions, porosities, and size distributions are needed in future. 3.3. Dust Properties and the Spectral Index <italic>α</italic> Just based on the DSHARP opacity, we want to explore how we can constrain the dust size distributions using the measured χ and the spectral index α . The spectral index α iswhere the approximation on the right is with the Rayleigh–Jeans approximation. Clearly, the measured α depends on totally different quantities in the optically thick and thin regimes. In the more familiar optically thin regime, it depends on how the absorption coefficient changes with the frequency. With κ abs ∝ ν β , α is β + 2. In the optically thick regime, α depends on χ . Assuming that χ ∝ ν γ , α is γ + 2. As shown in Figure 1 , ω changes monotonically with 1/ χ that changes as λ γ . Thus, if the albedo ω increases with wavelength ( γ > 0), α = γ + 2 measured at this wavelength span will be larger than 2, and vice versa. To be more specific, if the disk is optically thick, we can use the measured α from observations to derive γ . Then we can constrain the relationship between ω ν 1 and usingwhich is based on Equation ( 13 ). Figure 9 shows how κ abs , χ and the spectral index α change with different dust populations for different ALMA and VLA bands, using the DSHARP opacity. The panels in the second row show χ in the optically thick limit. The third row shows α in the optically thin limit (thus denoted as α thin ), while the bottom row is α in the optically thick limit ( α thick ). Here, we simply use β + 2 or γ + 2 to calculate α , and thus do not consider the deviation of the blackbody radiation from the Rayleigh–Jeans limit (Huang et al. 2018a ). χ and both α s have sharp transitions around s max ∼ λ /2 π . When s ≪ λ /2 π , scattering is not important and χ = 1, α thick = 2, α thin ∼ 4. When s ≳ λ /2 π , χ becomes less than 1, α thick becomes larger than 2,


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

of the mean pitch angle remains similar over the whole energy range . However, evolution timescales and peak amplitudes change as expected. Next, the influence of the amplitude of the magnetic field of the plasma wave has been studied (Section 5 ). Again, simulation results and analytic predictions have been compared. Since QLT works with the assumption that the wave’s amplitude is negligible compared to the background magnetic field B 0 , it could be expected that the analytic model fails to describe simulations with larger . We have shown that this is the case, although the model still yields a surprisingly good approximation. However, the magnetostatic QLT model fails to describe the interaction of particles and several waves correctly, as further simulations have shown. In a study of the trajectories of individual particles in a simulation with only one plasma wave we have found that particles follow closed trajectories in pitch angle space, i.e., that their motion is deterministic rather than diffusive (Section 6 ). This situation only changes if several plasma waves with different wave numbers or frequencies are included. 7.2. Conclusions In the fully kinetic PiC simulations the propagating waves lead to changes of the absolute momenta p of the individual particles in the plasma frame. This momentum diffusion is not included in the magnetostatic QLT model, where is assumed. However, a comparison of magnetostatic and full PiC simulations, as well as an analysis of the change of particle energy over time in a PiC simulation have shown that momentum diffusion plays only a minor role. The assumption of constant particle energy, which was a prerequisite for the analytic expressions developed by Lange et al. ( 2013 ), can still be applied in the electrodynamic model of PiC simulations. This explains why the electric fields can still be neglected and why the magnetostatic model describes PiC results reasonably well after the transformation of the model equations into the plasma frame has been performed. We found that the analytic model has difficulties in describing the effect of several waves on particle scattering. In Sections 5.2 and 5.3 we present data from simulations with two and four plasma waves. It can be seen that the predicted scattering amplitudes only match the simulation data if the resonances for the different waves are well-separated in pitch angle space. Looking at single particles in pitch angle space, as illustrated in Figure 11 in Section 6 , it can be seen that in the case of single waves (or sufficiently separated resonances) each particle travels along a closed, elliptical trajectory. In the case of single plasma waves we therefore conclude that a particle starting at some pitch angle will be scattered to different pitch angles, but will always come back to at some point in time. This is consistent with the idea of particle trapping developed by Sudan Ott ( 1971 ): the magnetic field of the wave leads to effective


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

The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This research has made use of data obtained from the high-energy Astrophysics Science Archive Research Center (HEASARC) provided by NASA’s Goddard Space Flight Center; the SIMBAD database operated at CDS, Strasbourg, France; and the NASA/IPAC Extragalactic Database (NED) 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 archives, catalogs, and software tools from the ASDC, a facility managed by the Italian Space Agency (ASI). Part of this work is based on the NVSS. The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under contract with the National Science Foundation. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. 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, funded by the National Aeronautics and Space Administration. 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 Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. Facilities: Fermi LAT .


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

outward flux is not conserved; its losses are a source for the photon angular momentum flux (Fig. 4 ). But in the model solution, the disc can only supply the flux from the relatively small amount of material within the ISCO, because just outside the ISCO the disc velocity is outward: it is not accreting! This cannot go in indefinitely – unless the outward flux is somehow being fed externally. The fact that the integrated total luminosity of our solutions formally diverges as t → ∞ is a clue: something must be feeding this. This could in principle be a magnetic couple to the black hole itself (or a vertical accretion process), but how would a turbulent/viscous model resolve this issue? Our solutions must not be the true t → ∞ disc solutions; they represent instead an extended phase of disc evolution in which the accretion is stalled. While this may be very useful for understanding observations, it raises an important point of physics: how does a real disc ‘unstall’ itself? Figure 4. The normalized angular momentum flux divergences, stemming from the three terms in equation ( 47 ), at a particular time (τ = 0.67) in the disc evolution. Throughout the bulk of the disc, the angular momentum loss balance is predominantly between the radial flow (the first term) and the turbulent stresses (second term). In the region r ≲ 8 r g , however, the photon losses (third term) dominate over the radial flow stress. This balance can be maintained as an extended phase, but not indefinitely. 4.3 Modelling the angular momentum gradient in the inner disc The presence of a non-zero radial velocity means that the azimuthal motion is only approximately Kerr metric circular. We have argued that the correction is second order in the fluctuation amplitude, but , the derivative of the angular momentum, appears as a singular denominator in the evolution equation. Since strict adherence to the idealized model leads to long-term unsustainable behaviour, it is of interest to consider a generic change to the angular momentum gradient of the form where now U φ indicates the mean fluid angular momentum of equation ( 10 ), and is the idealized angular momentum of a Kerr circular orbit. The function ε( r ) is left somewhat arbitrary, but it must satisfy two simple properties: (i) it reaches a maximum at the ISCO, and (ii) it vanishes sharply at large radius. The idea is that the assumption of purely circular orbits is a good approximation at large radii, but become progressively worse as the ISCO is approached. The development of this theory is the topic of the companion paper. We note here, however, that a modification of the angular momentum gradient in the inner disc regions would also affect the steady-state modelling of relativistic thin discs. The steady-state solution of equation ( 10 ) leads to a disc temperature profile where F 1 and F 2 are constants related to the mass and angular momentum flux throughout the disc, respectively. A substantial modification of in the


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becomes more and more noisy toward higher frequencies and therefore the de-convolved power spectrum will be more and more uncertain toward higher and higher frequencies. Figure 15. (a) Simulated red-noise light curve ( a = 2), containing 1000 data points with a sampling interval of one day (blue open circles), along with 30% of the time series selected at random times to mimic an unevenly sampled data set (magenta stars). (b) The corresponding power spectra of the unevenly sampled light curve derived using the LSP method (resulting in a = 0.3; magenta dashed curve), and the FT of the ACF (returning a = −0.1; cyan dashed curve). (c) Spectral window of power spectrum estimated from FT of the ACF (see the text of Appendix A for details). Appendix B Selection of (<italic>p</italic>, <italic>q</italic>) Parameters for the CARMA Process The order of the CARMA( p , q ) process is chosen based on how close the model is to the data using the minimum AICc criterion adopted in the present study. It has been argued that the models for various pairs of ( p , q ) values for which the minimum AICc is within 10 are not statistically indistinguishable from each other. Figure 16 shows power spectra corresponding to a few sets of ( p , q ) parameters of the analyzed Fermi -LAT light curve. As these overlap substantially, we choose the lowest-order model—CARMA(1, 0)—as the best-fitting model to describe the high-energy γ –ray variability in OJ 287. Figure 16. Power spectra corresponding to a few sets of ( p , q ) parameters of the analyzed Fermi -LAT light curve of OJ 287. The corresponding 1 σ confidence intervals are denoted by shaded areas. See the text of Appendix B for details. Appendix C Lack of ∼12 Year QPO in the Optical Light Curve Here, we discuss in more detail the lack of the claimed ∼12 year quasi-periodicity in the analyzed optical light curve. To demonstrate the robustness of the CARMA modeling in detecting QPO features against the background of red noise in the power spectrum for a finite time series covering only a few periods, an artificial light curve is generated with three components: (1) a pure red-noise ( β = 2) power spectrum using the method of Emmanoulopoulos et al. ( 2013 ), (2) a sinusoidal component with a 12 year period, and (3) a Gaussian white noise with mean 0 and standard deviation 0.1 representing measurement uncertainty. The data points are evenly sampled with a sampling interval of 1 day, and the total duration of the simulated time series is 14,600 days (40 years, corresponding to our relatively better sampled optical light curve starting from 1970; see Table 2 ). Next, we kept 20% of the data selected at random times to mimic an unevenly sampled data set. Figures 17 (a)–(e) present the results of CARMA modeling on our simulated light curve, while Figure 17 (f) shows the computed power spectrum. Since the simulated light curve covers only ∼3 periods, we do not detect a clear peak on the ∼12 year timescale against the


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

are quite discrepant (0.2 dex and 0.8 dex in our two stars, respectively). The 4215.5 Å line of the star S11–97 is affected by the CN molecular band in this region. Spectral synthesis taking into account the carbon abundance derived in the CH band led to an abundance that agrees better with the 4077.7 Å line. Yttrium. Two very faint lines ( 15 mÅ) of yttrium were detected in our spectra, but we were only able to place upper limits on the Y abundance in our stars. Barium. Four lines of barium are present in our wavelength ranges. One is very faint ( λ 5853 Å) and detected for only one star, and the other three lines are strong. Two of them are blended with weak iron lines ( λ 4934 Å and λ 6141 Å). Therefore we proceeded by spectral synthesis, taking into account all blends and the Ba HFS components. Barium has five isotopes; different fractions of even-A and odd-A (A=atomic mass) nuclei ( 134 Ba + 136 Ba + 138 Ba) : ( 135 Ba + 137 Ba) were tested: the 82:18 solar fraction, and the r -process fractions of 54:46 and 28:72. The Ba λ 4934 Å resonance line is more sensitive than the three subordinate lines to the adopted fraction. The solar 82:18 fraction led to the best agreement between the resonance and the subordinates lines. We refer to Jablonka et al. (2015) , Mashonkina et al. (2017b) for a more detailed investigation of the possible cause. 5. Discussion 5.1. Carbon Figure 3 shows that none of our stars can be considered as carbon-enhanced based on the Aoki et al. (2007) criterion. Nonetheless, our stars are evolved enough to have converted C into N by the CNO cycle, as they are above log( L ⋆ / L ⊙ ) = 2.3, that is, the limit above which a metal-poor 0.8 M ⊙ star is thought to undergo additional mixing between the bottom of the stellar convective envelope and the outer layer of the advancing hydrogen shell (see Placco et al. 2014 , and references therein for a discussion). Fig. 3. [C/Fe] as a function of log( L / L ⊙ ) for Galactic dwarf satellite and halo red giants with metallicities [Fe/H] –2.5. The Sextans stars we analyzed are represented by large red circles. Red squares are Sextans stars from Tafelmeyer et al. (2010) , the red triangle is the Sextans carbon-rich star from Honda et al. (2011) . Gray dots denote the [C/Fe] abundances of MW halo stars from Yong et al. (2013) . RGB stars in Sculptor ( Jablonka et al. 2015 ; Simon et al. 2015 ; Tafelmeyer et al. 2010 ), Fornax ( Tafelmeyer et al. 2010 ), and Draco ( Shetrone et al. 2013 ; Cohen Huang 2009 ) are shown in orange, blue, and green; respectively. The dotted line is the Aoki et al. (2007) dividing line for carbon enhancement, which takes into account the depletion of carbon with evolution along the RGB. Placco et al. (2014) developed a procedure for correcting the measured carbon abundances based on stellar model evolution and depending on the log(g) of the stars. They showed that when these corrections were applied to their dataset, the fraction of carbon-rich stars [C/Fe] >


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

We are grateful to the referee, Brent Groves, for very constructive comments that helped to improve the manuscript. We thank Stefanie Komossa (MPIfR), Pavel Kroupa (University of Bonn), Thomas Krichbaum (MPIfR), Madeleine Yttergren (University of Cologne), Bozena Czerny (CFT PAN), Mary Loli Martinez-Aldama (CFT PAN), and Swayamtrupta Panda (CFT PAN) for very helpful discussions and input. This work was done with the financial support of SFB956 – “Conditions and Impact of Star Formation: Astrophysics, Instrumentation and Laboratory Research” at the Universities of Cologne and Bonn and MPIfR, in which M.Z., G.B., A.E., N.F., S.B., J.-A.Z., K.H. are members of sub-group A2 – “Conditions for Star Formation in Nearby AGN and QSO Hosts” and A1 – “Understanding Galaxy Assembly”, with M.V. and L.F. being its former members. Michal Zajaček acknowledges the financial support by National Science Centre, Poland, grant No. 2017/26/A/ST9/00756 (Maestro 9).


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

to account for the radiative recombination continuum and lines, a cutoff power-law model to account for the off-nuclear X-ray sources, in addition to the AGN-related emission, which is parametrized by two different MYTorus scattered and line components, in addition to the transmitted one described by the zeroth-order component of that model. In our fitting, in addition to our baseline model, we added the Bremsstrahlung and cutoff power law with all parameters fixed at the values provided by Bauer et al. ( 2015 ), and a Gaussian line to roughly model the excess around 6.5 keV. To account for the multiple absorption components, we also added a second Borus model, whose best-fitting parameters are , CFtor = 83 per cent, and A Fe = 1. Our best-fitting parameters are broadly consistent with the results presented by Bauer et al. ( 2015 ). The observed flux in the 2–10 keV energy band is 5.4 × 10 −12 erg cm −2 s −1 , and the intrinsic one (i.e. corrected for absorption) 1.3 × 10 −10 erg cm −2 s −1 . A0.2 NGC 1194 The starting model for the spectral fit of this source is provided by the work of Masini et al. ( 2016 ), who fitted the NuSTAR spectrum with the MYTorus model in the decoupled mode, with the addition of a Gaussian line at 6.8 keV, and a scattering fraction of the primary continuum of . In our fitting, we used our baseline model and found the main parameters (Γ, N H , and f s ) to be fully consistent with their best-fit results. The 2–10 keV observed flux is 1.2 × 10 −12 erg cm −2 s −1 , and the intrinsic one 1.0 × 10 −11 erg cm −2 s −1 . A0.3 NGC 2273 The starting spectral model for this source is again provided by the work of Masini et al. ( 2016 ), who fitted the NuSTAR spectrum with the Torus model that favoured a heavily absorbed scenario with . In our fitting, we used our baseline model, which yielded a best fit broadly consistent with their results. The 2–10 keV observed flux is 9.2 × 10 −13 erg cm −2 s −1 , and the intrinsic one 3.6 × 10 −10 erg cm −2 s −1 . A0.4 NGC 3079 The starting spectral model for this source is again provided by the work of Masini et al. ( 2016 ), who fitted the NuSTAR spectrum with the MYTorus model in a coupled mode. The results obtained with our baseline model are consistent within the respective uncertainties with their results. The 2–10 keV observed flux is 6.4 × 10 −13 erg cm −2 s −1 , and the intrinsic one 1.2 × 10 −10 erg cm −2 s −1 . A0.5 NGC 3393 The starting spectral model for this source is provided by the work of Koss et al. ( 2015 ) and Masini et al. ( 2016 ), who fitted the NuSTAR spectrum with both MYTorus and Torus models. The results obtained with our baseline model are broadly consistent with the results presented by these authors with a slightly larger value of N H (10 25 versus ). The 2–10 keV observed flux is 4.4 × 10 −13 erg cm −2 s −1 , and the intrinsic one 8.3 × 10 −11 erg cm −2 s −1 . A0.6 NGC 4388 The starting spectral model for this source is once more provided by the work of


O O O O O B-Organization O O O O O O O O B-Instrument O O O O B-Observatory I-Observatory O O O B-Instrument O B-Organization I-Organization O O O O B-Collaboration I-Collaboration O O O O O O O O B-Person O B-Organization I-Organization I-Organization B-Person O O O O B-Grant I-Grant I-Grant O O B-Organization I-Organization B-Grant 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

We are grateful to the STScI staff members for help in scheduling the intricate STIS observations. We thank the Paranal Observatory for conducting the UVES observations. Stony Brook’s continuing involvement in the SMARTS Consortium is made possible by generous support from the Provost of Stony Brook University. A.M. was co-funded under the Marie Curie Actions of the European Commission (FP7-COFUND). We thank Jose Groh for valuable discussions and comments on the paper draft. We thank the anonymous referee for insisting that we distinguish the two lines of sights described in this paper more clearly.


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

component of Fe K α emission (log ξ = 0). A very similar result is reached by performing the same test on the 2014 mean EPIC-pn + NuSTAR spectrum (Δ χ 2 = 52), resulting in a modest reflection strength, R ∼ 0.6, while the photon index and Fe abundance remain unchanged: Γ ∼ 1.8; A Fe ∼ 3. The remaining key parameters in the relxill model are largely consistent with those reported in Table 2 ; i.e., log ξ ∼ 1.2, q ∼ 3, θ ∼ 40, r in 6. The black hole spin, a *, is unconstrained although we find a lower-limit on the high-energy cutoff of E cut > 130 keV. Finally, we return to check for the presence of highly-ionized absorption in the contemporaneous NuSTAR data. In terms of the EPIC-pn analysis, the two absorption grids modeling the highly-ionized two-velocity outflow are highly significant, with a combined contribution to the fit statistic of Δ χ 2 = 42 (for six additional parameters; meanwhile, the highly-ionized emission and soft-band absorption grids improve the fit by Δ χ 2 = 39 and Δ χ 2 = 44, respectively). Zoghbi et al. ( 2015 ) detected no significant discrete absorption features in the NuSTAR spectrum. We now find, in direct comparison with XMM-Newton , including the same two xstar absorption zones to the same baseline model fitted to just the contemporaneous NuSTAR observations offers a far less significant improvement to the fit statistic, with Δ χ 2 = 9. As such, even though the highly-ionized outflow is now well established thanks to XMM-Newton , we also confirm the main result from Zoghbi et al. ( 2015 ) that it was not detectable by NuSTAR alone. This demonstrates the importance of long-look observations with XMM-Newton in addition to the broad-band coverage of NuSTAR . 4. DISCUSSION AND CONCLUSIONS An extended XMM-Newton observation of PG 1211+143 has revealed spectral structure in the Fe K band, unseen in previous (shorter) observations. Utilizing the high throughput of the EPIC-pn, Pounds et al. ( 2016a ) showed that highly-ionized outflow resolved two velocity components ( and ), while an analysis of the high-resolution RGS data in Pounds et al. ( 2016b ) found lower-ionization co-moving counterparts of that dual-velocity flow. Here, we have extended our modeling over a wider energy range, incorporating contemporaneous NuSTAR data. The power of this approach—i.e., combining XMM-Newton and NuSTAR data—has previously been demonstrated in a precise measurement of the higher-energy continuum and thereby helping to disentangle absorption and reflection in a number of AGNs—e.g., NGC 1365 (Risaliti et al. 2013 ; Walton et al. 2014 ; Rivers et al. 2015 ), NGC 5548 (Kaastra et al. 2014 ; Ursini et al. 2015 ; Cappi et al. 2016 ) and PDS 456 (Nardini et al. 2015 ). In Section 3.1 , we fitted the hard X-ray spectrum with relativistic reflection, following the recent analysis of Zoghbi et al. ( 2015 ). Using the NuSTAR data alone, we confirm their solution, finding a steep photon index (Γ ∼ 2.4) and high reflection fraction ( R ∼


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

other words, the PDFs are equal, because the system self-adjusts, not because glitch sizes are correlated with forward waiting times, as in the α ≪ α c (β) regime in Section 4 . The explanation for the qualitative behaviour seen in Fig. 20 is the same as for Fig. 13 . Figure 20. Correlation between sizes and forward/backward waiting times: Pearson coefficient, r , as a function of the control parameter α, for separable η with φ( x ) = x δ . For each value of α, we sample Δ t and Δ X over the course of a single simulation of N = 10 6 glitches, after the system reaches stationarity. We then calculate the pairwise correlation between the two sets for each α. Parameter: δ = 7. 6.5 Lag-dependent spin-down For the sake of completeness, we extend the results of Section 6 to the case of a general lag-dependent spin-down torque in Appendix E . 7 SAMPLING SIZE BIAS We now consider more carefully how we sample the different random variables used throughout this paper: X , N , Δ t , ΔΩ c (∝Δ X ), X e , and X s . Both X and N differ fundamentally from the other variables, because they are defined continuously for all t . The other variables are defined at discrete instants, when N ( t ) jumps by one due to a glitch. We therefore sample X ( t ) and N ( t ) by running an ensemble of simulations and observe each simulation at some time t 0 . The other variables are sampled at every glitch in a single simulation once it reaches stationarity. As an example of the subtle consequences of sampling bias, consider the ordering of the first moments 〈 X 〉, 〈 X s 〉, and 〈 X e 〉. Fig. 21 shows p ( x ), p e ( x ), and p s ( x ) for the non-separable power-law η ( 18 ) and ( 19 ) from Section 4 . Note that p s ( x ) is skewed towards larger values than p ( x ). By integrating the curves, we find 〈 X s 〉 = 0.600, 〈 X 〉 = 0.579, 〈 X e 〉 = 0.667, and hence 〈 X 〉 〈 X s 〉 〈 X e 〉. This seems wrong: X s , the value of X immediately after a glitch, ought to be smaller, on average, than X measured at some arbitrary time t . However, X is sampled from an ensemble at fixed time t 0 , whereas X s and X e are drawn from a different ensemble (every glitch event in a single simulation). If we observe the system at time t , we are more likely to land in a longer inter-glitch time interval than a smaller one, in which the (biased) X s and X e are spaced farther apart. Figure 21. Stationary PDFs p s ( x ), p e ( x ), and p ( x ) for the λ and power-law η used throughout Section 4 . Both p e ( x ) and p s ( x ) are sampled from a single simulation of N = 10 8 glitches after stationarity. We obtain p ( x ) by sampling an ensemble of S = 10 6 simulations at t = 8. Parameters: β = 10 −2 and α = 5. Sampling bias has an important observable consequence, even though p s and p e cannot be observed. We can obtain an ensemble distribution of waiting times by choosing a time t 0 ≫ 1 and measuring the length of the interval T ( i + 1) − T ( i ) for every simulation in the ensemble, where T ( i ) is


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O O O O 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 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-Identifier 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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-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-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O B-Observatory 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 B-Citation I-Citation I-Citation I-Citation O O B-ObservationalTechniques I-ObservationalTechniques O O B-ObservationalTechniques I-ObservationalTechniques O O O B-Citation I-Citation I-Citation I-Citation O O

where the rise speed of the flux tube at a depth of 20 Mm is more than about 150 m s −1 produce preemergence diverging flows that are not consistent with the observations. Norton et al. (2017) found from HMI vector magnetograms that the surface magnetic flux increases during the emergence process more slowly than predicted by simulations of flux emergence with rise speeds of 500 m s −1 at 20 Mm. Norton et al. (2017) suggested that these observations imply that the rise speed is too high in the simulations. There are, however, case studies that suggest very high rise speeds for some individual active regions. As one example, Kosovichev et al. (2018) measured an upward pattern motion of the horizontal divergence (inferred from time-distance helioseismology) of about 1.3 km s −1 at 20 Mm for AR11726, which emerged in April 2013. This particular active region was not in the sample used by Schunker et al. (2016) , which covered the time period May 2010 to November 2012. Here we extend the work of Birch et al. (2016) and measure the spatial variations and temporal evolution of near-surface flows before and during the emergence of the active regions described by Schunker et al. (2016) . Our goal is to determine whether statistically significant flow patterns are associated with the emergence of active regions. We expect that these flows will be useful for constraining models for the origin and formation of active regions. 2. Data reduction The catalog of Schunker et al. (2016) describes 105 active regions that emerge on the visible disk. It also contains an associated set of quiet-Sun control regions that have the same latitude and distance from the central meridian. Schunker et al. (2016) assigned each active region a P -factor that describes the amount of preexisting flux near the emergence location. The P -factors are determined by examining line-of-sight magnetograms by eye. A P -factor larger than two indicates emergence into an area with preexisting magnetic field. Here we only consider emerging active regions with a P -factor of two or lower. These emerging active regions and their partner quiet-Sun control regions form the basis for the data analysis carried our here. We refer to the emerging active regions as “AR” and to the quiet-Sun control regions as “QS” regions. For each AR and associated QS region there is a set of SDO/HMI Dopplergrams, continuum intensity images, and line-of-sight magnetic field observations as described by Schunker et al. (2016) . The data cubes of Dopplergrams were used as input for the helioseismic holography (Sect. 2.1 ). The data cubes of continuum intensity images were used as input to a local correlation tracking algorithm (Appendix B ). The magnetograms were used to determine the emergence location and emergence time, and to classify the complexity of the emergence (as described in Schunker et al. 2016 ). 2.1. Helioseismic holography We used surface-focusing holography as described in Birch et al. (2016) . The


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

This is well in the range of those measured for UCXBs. 4.2. The nature of the accretor Determining the nature of the compact object in an unclassified LMXB is often challenging. It can be assessed based either on a dynamical measurement of the mass of the compact object (via optical and near infrared spectroscopy during quiescence; see e.g. Casares et al. 1992 ), or on the detection of X-ray coherent pulsations and/or thermonuclear X-ray bursts, which would provide a straightforward observational evidence for a NS accretor. To-date, all confirmed UCXBs are known to contain a NS accretor, although there are a number of BH candidates (see e.g. Bahramian et al. 2017 ). Assuming that our identification of J0840 as a UCXB is correct, it is then tempting to conclude that this system hosts a NS as well. However, our non-detection of coherent pulsations or thermonuclear X-ray bursts leaves this as an open question. 4.2.1. On the lack of coherent X-ray pulsations Coherent pulsations are thought to be formed in NS systems where the magnetic field is large enough to truncate the accretion disk and channel part of the disk material onto a small region on the NS surface, close to the magnetic poles. The radiation emitted from the heated impact region (hot spot) or from a slab of shocked plasma that forms above it (accretion columns) appears modulated at the NS spin period, producing a pulsed emission component. About 30 accreting millisecond X-ray pulsars have been detected to date (for reviews, see Di Salvo Sanna 2020 ; Patruno et al. 2021 ) and some of them were seen to exhibit pulsed fractions as small as a few percent in outburst (e.g. Strohmayer et al. 2018 ), that is, below the upper limits estimated for J0840 (Sect. 3.2 ). Besides, three accreting NS–LMXBs have shown coherent X-ray pulsations only sporadically during their outbursts, with the most extreme case being represented by Aql X-1, which showed pulsations over a ∼150 s interval out of a total observing time of ∼1.5 Ms ( Casella et al. 2008 ). However, most NS–LMXBs are non-pulsating systems, and a systematic analysis by Patruno et al. (2018) suggested that weak pulsations might not form at all in (most) non-pulsating LMXBs. Our non-detection of pulsations from J0840 is thus not sufficient to conclusively rule out a NS accretor and might still point either to an accreting millisecond pulsar characterised by a very small X-ray pulsed fraction and/or intermittent pulsations, or a non-pulsating NS–LMXB. 4.2.2. On the lack of thermonuclear X-ray bursts Many NS–LMXBs exhibit thermonuclear (type-I) X-ray bursts due to unstable ignition of hydrogen and/or helium freshly accreted onto the NS surface (for a review, see Degenaar et al. 2018 ). Bursts triggering all-sky monitors (including Swift /BAT) have been detected from several NS–LMXBs and in some cases they even led to the discovery of new transient systems (e.g. Wijnands et al. 2009 ; Degenaar et al. 2012 ). These episodes typically last a few


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Acknowledgements I would like to thank the anonymous referee for valuable comments that improved this work. The author is supported by the Grants-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (16H07413, 17H02864).


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velocity distribution of the gas within the velocity range from 495 to 495kms 1 (1kms 1 steps). The emission for one square degree centred on the SMCNOD exhibits two main peaks: 94 and 186kms 1 (which are shown in Figs 8 and 9 , respectively). These velocities agree with the velocity field related to the MS at the SMCNOD position, at an MS longitude L MS 25. See for example fig. 8 in Nidever etal. ( 2010 ). We discuss details about H i gas distribution in Section 4 . Figure 7. H i gas column density map from Kalberla Haud ( 2015 ), in zenith equal area projection, close to the south celestial pole. A grid of equatorial coordinates ( and ) is indicated. The SMC is close to the centre of the figure and the LMC is located near the bright spot in the lower-left corner. No significant excess of H i gas is observed at the position of the SMCNOD (dotted ellipse). Figure 8. H i gas emission map from Kalberla Haud ( 2015 ), in equatorial coordinates for the velocity channel 94kms 1 v LSR 95kms 1 . The SMCNOD position is highlighted by an empty ellipse and the SMC centre by a plus symbol. Figure 9. Same as Fig. 8 but for velocity channel equal to 186kms 1 (186kms 1 v LSR 187kms 1 ). 4 DISCUSSION In this section, we discuss the characteristics of the SMCNOD: we compare its stellar populations to those of the SMC (Section 4.1 ), its gas content (Section 4.2 ), possible scenarios for its origin (Section 4.3 ) and in the last subsection we provide a brief summary of the discovery, discussing the SMCNOD fate and some prospects for future analyses (Section 4.4 ). 4.1 The SMCNOD and SMC stellar populations The ( g r ) colour distributions of SMCNOD and SMC stars for 3 mag ranges in the Hess diagram from Fig. 2 are shown in the left-hand panel of Fig. 10 , whereas their number counts in bins of g magnitude filtered by the CMD mask and normalized (to the areas) are presented in the right-hand panel of the same figure. The colour distributions look very similar. For RC stars (solid lines), there may be a slight preference for the SMCNOD being a little bluer than the SMC. However, a KolmogorovSmirnov (KS) test indicates that the two RC populations come from the same parent distribution ( p 0.42). As for the LF comparison, the two distributions look similar as well. Figure 10. Histograms in bins of colour (left) and in bins of g magnitude (right) filtered by the CMD mask for the SMCNOD (third panel in Fig. 2 ) and the SMC (fifth panel in Fig. 2 ). In the right-hand panel, the Poissonian uncertainties are shown as shaded areas. The stellar colour distribution is very similar between the SMC and SMCNOD in the left-hand panel (comparing dotted red and blue lines and dashed red and blue lines), as well as the histogram in bins of magnitude for the stars filtered with the CMD mask in the last two panels in Fig. 2 (right-hand panel). 4.2 The SMCNOD and H<sc>i</sc> gas The results of considering the H i gas velocity channels are inconclusive. The v LSR =186kms 1 channel


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ACKNOWLEDGEMENTS We are very grateful to the constructive and detailed review carried out by our anonymous referee. His/her numerous and wise comments have helped to significantly improve this paper. We thank Manuel Peimbert, Jairo Méndez-Abreu, Leticia Carigi, and Rolf Kudritzki for their useful comments. This paper is based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, in the island of La Palma, Spain. This research has made use of Aladin Sky Atlas developed at CDS, Strasbourg, France. This work has been funded by the Spanish Ministerio de Economía y Competividad (MINECO) under project AYA2015-65205-P. JGR acknowledges support from an Advanced Fellowship from the Severo Ochoa excellence program (SEV-2015-0548).


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the stepwise trajectories of incident CH ions within Titan’s upper atmosphere, all starting at an energy of 50 keV under normal incidence. Three different cases are indicated in the upper panel. For each incident ion, the portion of its trajectory between two consecutive collisions is displayed as the projection to the local plane formed by the vertical direction and the direction of ion velocity, with the x -axis aligned with the projected ion trajectory on the horizontal plane. Our model calculations indicate that some of the incident ions are backscattered and escape at the top of the atmosphere. For the condition of incidence shown in Fig. 2 , the backscattered CH ions typically undergo 20 collisions before they leave the top of the simulation box. Throughout our calculations, the effect of the background magnetic field, typically at the level of several nT (e.g., Backes et al. 2005 ; Bertucci et al. 2008 , 2009 ), is ignored for simplicity since the gyroradii of the incident ions could be estimated to exceed substantially their mean free paths due to elastic scattering by ambient neutrals. Taking incident CH as an example, the mean free path ranges from 110 to 6500 km over the full incidence energy range of 10 to 100 keV, where we use for illustrative purposes a background N 2 density of 1.7 × 10 7 cm −3 at 1500 km ( Strobel 2012 ). For comparison, the CH gyroradius is typically a factor of 5 larger, suggesting that the effect of ion gyromotion is of minor importance here. In addition, we note that the effect of the background magnetic field has not been included in previous modelings of Titan’s atmospheric sputtering (e.g., Shematovich et al. 2001 , 2003 ; Michael et al. 2005 ), and a similar approximation adopted here facilitates a comparison of the derived sputtering yields between different studies in terms of the differentchoices of collision parameterization and of background atmosphere (see Sect. 5 for details). 3 Sputtering yields We show in Fig. 3 the N 2 and CH 4 sputtering yields as a function of the incidence energy of the three categories of incident ions, all assuming normal incidence. The two different collision models, ZBL and ZBL+Firsov, are compared. Several interesting features are immediately seen in the figure. First, both the N 2 and CH 4 sputtering yields increase steadily with the increasing energy of incident ions, which is a natural result of the fact that more energetic ions tend to produce more atmospheric recoils along their energy degradation processes. Second, the sputtering yields increase with the ion mass, maximized for N and minimized for H + , and this is explained by more efficient momentum transfer to atmospheric recoils for heavier incident ions. Third, the sputtering yields for ZBL are enhanced over ZBL+Firsov due to the extra energy spent in electronic excitation, but such an enhancement is suppressed for low energy incident ions because they are not able to excite atmospheric neutrals


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The authors thank the referee for useful feedback which helped improve the final manuscript. This research has made use of data obtained with the NuSTAR mission, a project led by the California Institute of Technology (Caltech), managed by the Jet Propulsion Laboratory (JPL) and funded by NASA, and with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. We thank the NuSTAR Operations, Software, and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software ( NUSTARDAS), jointly developed by the ASI Science Data Center (ASDC, Italy) and Caltech (USA).


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The present work was funded by STFC (UK) through the University of Cambridge DAMTP astrophysics grant and the University of Strathclyde UK APAP network grant ST/J000892/1.


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This work was supported by the Basic Science Research (2013R1A1A2061842) program through the National Research Foundation of Korea (NRF).


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to a redshift. The statistical uncertainty associated with estimation of the source-frame masses is increased relative to that of the detector-frame masses owing to these dependencies. From the inferred posterior distribution of D L we compute redshift assuming a Planck 2015 ΛCDM cosmology with Hubble parameter H 0 = 67.9 km s −1 Mpc −1 (Ade et al. 2016 ) (and we address the effect of taking a larger value of the Hubble parameter in Section 2.2 ). Unless stated otherwise, mass measurements are quoted in the source frame of the binary. 2.1. Method and Signal Models To infer the source properties of GW190521, we analyzed 8 s of data in the LIGO and Virgo detectors around the time of the detection. The data are downsampled from 16,384 to 1024 Hz, as we expect no signal power above several hundred Hz owing to the total mass of GW190521. The parameter estimation analysis is done with two independently developed coherent Bayesian inference pipelines, LALInference (Veitch et al. 2015 ) and RIFT (Lange et al. 2018 ; Wysocki et al. 2019 ), which produce consistent results for the inferred source parameters. Both parameter estimation algorithms assume stationary Gaussian noise characterized by the power spectral density (PSD), which is inferred from the data by the BayesLine algorithm (Littenberg Cornish 2015 ). We compute the event likelihood in the frequency domain, integrating over the frequency band 11–512 Hz. We used three distinct GW signal models of BBH coalescence in our analysis: NRSur7dq4 (NRSur PHM), a surrogate waveform model built by directly interpolating NR solutions (Varma et al. 2019 ); IMRPhenomPv3HM (Phenom PHM), an inspiral-merger-ringdown waveform model that uses phenomenological frequency domain fits combining post-Newtonian calculations of the GW phase and amplitude (Blanchet et al. 1995 , 2005 ; Damour et al. 2001 ; Arun et al. 2009 ; Blanchet 2014 ) with tuning to NR solutions (Khan et al. 2020 ); and SEOBNRv4PHM (SEOBNR PHM), an inspiral-merger-ringdown waveform model that is based on the effective-one-body formalism (Buonanno Damour 1999 , 2000 ) and calibrated to NR (Ossokine et al. 2020 ). These three waveform models employ different approaches to reproduce the predictions from analytical relativity and numerical relativity; we expect to see differences in the parameter estimation from these three models as a result of those different approaches, and we can interpret those differences as a form of systematic error associated with the modeling. Note that the effects of the astrophysical environment, such as the presence of gas, on the GW waveform are expected to be negligible (Fedrow et al. 2017 ) in the late stages of inspiral, merger, and ringdown that we observe. NRSur PHM is constructed based on NR simulations with component spins that are not constrained to be aligned with the orbital axis, thus including the effects of spin–orbit precession. The model covers dimensionless spin magnitudes χ i ≤ 0.8 and mass