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

40.7 Mpc with a standard deviation of 2.36 Mpc, corresponding to the measured distance and quadrature sum of statistical and systematic errors reported in Cantiello et al. ( 2018 ). Here we have assumed a Gaussian distribution on this distance measurement, which we deem valid for a measurement of this precision and for the purpose of exploring upper and lower bounds. Using the EM observations as the prior on the luminosity distance results in significantly narrower posteriors on inclination angle and source-frame chirp mass shown in Figure 2 . The improved chirp mass measurement is due to the reduced error on d L , as the d L posterior samples are used to convert from the measured detector-frame chirp mass to the source-frame chirp mass (Schutz 1986 ; Finn Chernoff 1993 ). However, the improved precision on distance has no effect on our measurements of the component masses or spins, because at leading order the mass ratio q = m 1 / m 2 and spin parameter χ eff (Cutler Flanagan 1994 ) are not correlated with distance. With the EM observations as the prior on d L and a prior on the inclination angle uniform in , we find that the viewing angle is degrees (90% confidence). Figure 2. Comparison of posterior probability distributions without and with combined EM information. The black contours show the results for using only the GW signal, the blue contours show the results for the fixed sky location of NGC 4993, and the red contours show the results for both the fixed sky location and a Gaussian prior on distance of 40.7 ± 2.36 Mpc from Cantiello et al. ( 2018 ). These analyses used a prior on inclination angle that is uniform in . For each parameter, we quote the median value and the 90% credible interval (shown with vertical solid and dashed lines, respectively, on the posterior plot of each parameter). The EM information on the distance measurement greatly improves the precision with which we measure the inclination angle (and significantly reduces the uncertainty on the source-frame chirp mass). Errors in the calibration of the GW detectors can cause errors in the measured amplitude of the GW signal and hence in the inclination angle of the binary. We treat this as a systematic error, which we measure by shifting the amplitude calibration of the LIGO and Virgo detectors by the 1 σ uncertainty bounds for LIGO/Virgo’s second observing run (Cahillane et al. 2017 ). We find that shifting the calibration to its most sensitive and least sensitive extremes results in a ±17 shift in the peak of the viewing angle when using a prior on inclination angle that is uniform in . We quote this shift as the systematic error on our measurement. Changing the phase error of the calibration within the bounds reported in Cahillane et al. ( 2017 ) produces a negligible effect on the inclination angle. A prior uniform in goes to zero as the viewing angle approaches face on (or face off), so we repeat our analysis using a prior uniform in ι . Figure 3 shows a


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ACKNOWLEDGEMENTS AH acknowledges support from the 2018 NRAO summer research program, where the majority of the analysis was done. KPM is a Jansky Fellow of the NRAO. Thanks to Nimisha Kantharia, Preshanth Jagannathan and Gregg Hallinan, who provided help with the GMRT proposal and observing. We thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. We thank the anonymous referee for helpful comments on the manuscript.


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We thank an anonymous referee whose comments have contributed to improving the presentation of this paper. P.R. acknowledges a grant from the Greek General Secretariat of Research and Technology in the framework of the programme Support of Postdoctoral Researchers. F.J.C. acknowledges support by the Spanish ministry of Economy and Competitiveness through the grant AYA2012-31447.


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

any fixed z , and , where . Note that f is zero at the boundaries of these intervals and similarly g is zero at r = 0 and r = R 0 , so the functions are continuous. We solved for V Z 2 in Equation ( 26 ), in order to study the nature of the vertical motion induced by the magnetic shear and potentially explore the relationship between this type of perturbation and the mass flux observed in the chromosphere in the form of jets. The solution for V Z 2 in the zero-beta case is simply proportional to the square of B θ 1 ,and zero otherwise—see Figures 2 and 3 . Hence V Z 2 will be of a similar form to B θ 1 , i.e., a pulse propagating in the z -direction. We suggest that a pulse in the form of this example could possibly influence plasma and contribute to the formation of a jet. Using our perturbation model we can approximate the vertical mass flux of the plasma within the locality of the pulse, φ z = ρ v z ≈ ε 2 ρ 0 V Z 2 . Figure 2. A 2.5D representation of the given example of a V Z 2 pulse from Section 3.5 , at particular times: t = 0.2 τ , t = 0.5 τ , and t = τ . The pulse appears as two peaks due to the axisymmetry around the z- axis of the tube, and has been rescaled so that the V Z 2 (vertical) axis is in units of , while the r- and z- axes are in units of R 0 and v A τ , respectively. An animated version of this figure, showing the evolution of the pulse from t = 0 to t = 2 τ , is available online. (An animation of this figure is available.) Figure 3. Rotated views of the 2.5D plot in Figure 2 at t = τ , showing the z dependence (left) and the r dependence (right). Interestingly, the nature of the perturbation also suggests that there could be plasma with lower velocity near the center of the flux tube, since we would have φ z = 0 at r = 0. Once the pulse is fully formed at t = τ , it will maintain its shape while it propagates in the positive z- direction. For t ≥ τ , φ z will be constant on concentric toroidal surfaces, which can be partially seen in Figure 4 . The toroids degenerate into a cylinder, bounded by the limits for V Z 2 stated in Equation ( 31 ), as the magnitude of φ z approaches zero; outside of this cylinder there is no perturbation. The maximum magnitude of φ z is reached where both f and g are maximized, on the circle with radius r = R 0 /(2 1/ λ ) at z = v A ( t − τ /2). Other forms of the B θ 1 pulse are of course possible as solutions to the first-order equations, but solutions that are suitable for the model are often similar to our example in form and behavior. Figure 4. Left: a 3D plot of the vertical mass flux φ z at time t = τ /2, for the example in Section 3.5 (with scaled Cartesian axes for simplicity). At this point the pulse is “half formed” and there is positive mass flux for 0 ≤ z ≤ v A τ /2 within the tube. The blue arrows at the lower boundary represent the driver for the torsional magnetic field perturbation. An animated version of this figure, showing the evolution of the pulse from t = 0 to t = τ /2,


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

The authors acknowledge support from NewCompstar, COST Action MP 1304, and HIC for FAIR. R.O. Gomes would like to thank V. Dexheimer and S. O. Kepler for fruitful discussions and suggestions. P. Char acknowledges support from the Navajbai Ratan Tata Trust.


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

(UCD-C group; see Section 3.1.2 ) include two groups with v r > 400 km s −1 and v r 400 km s −1 . The mean radial velocity of the other UCDs with v r > 400 km s −1 ( = 977 km s −1 ) is lower than those of the dwarfs with v r > 400 km s −1 and the M87 UCDs. The mean radial velocity of the other UCDs with v r 400 km s −1 is −117 km s −1 . Figure 13. (a) Radial velocities of GCs and dwarfs as a function of galactocentric distance from M87. The filled circles, open circles, and crosses represent the IGCs, M87 GCs, and dwarfs in the survey region (Kim et al. 2014 ), respectively. The small and large open circles represent the M87 GCs in Strader et al. ( 2011 ) and in this study, respectively. The dashed horizontal line indicates v r = 400 km s −1 , where a dip in the radial velocity distribution can be seen (see Figure 12 ). (b) Mean radial velocity of GCs and dwarfs in each radial bin as a function of galactocentric distance from M87. The symbols are the same as in (a). We divided the IGCs and dwarfs into two groups according to their radial velocities: v r > 400 km s −1 and v r 400 km s −1 . The vertical error bars indicate the root mean square velocities of the objects in each bin. Figure 14. (a) Radial velocities of UCDs and dwarf galaxies as a function of galactocentric distance from M87. The open squares, filled squares, and crosses represent the UCDs in the M87 region, the UCDs not in the M87 region, and the dwarfs in the survey region, respectively. The small and large open squares represent the UCDs in Zhang et al. ( 2015 ) and in this study, respectively. (b) Mean radial velocity of UCDs and dwarfs in each radial bin as a function of galactocentric distance from M87. The symbols are the same as in (a). We divided the dwarfs into two groups according to their radial velocities: v r > 400 km s −1 and v r 400 km s −1 . The vertical error bars indicate the root mean square velocities of the objects in each bin. Figure 15 shows the radial velocity dispersion profiles of the GCs and UCDs. The radial velocity dispersion of the GCs, UCDs, and dwarfs in each radial bin as well as its error is calculated following the formula in Pryor Meylan ( 1993 ). We use the IGCs, UCDs, and dwarfs with v r > 400 km s −1 that are not probably affected by infalling populations to derive the velocity dispersion for each tracer. The radial velocity dispersion of the combined M87 GCs is almost constant at 333 km s −1 . The radial velocity dispersion of the IGCs is similar to that of the GCs in M87 ( σ = 314 km s −1 ). Both are much lower than the radial velocity dispersion of dwarfs in the same survey region ( σ = 608 km s −1 ) and that of ICPNe superposed on the M87 region ( σ = 881 km s −1 ; Longobardi et al. 2015 ). Strader et al. ( 2011 ) suggested that the stellar halo of M87 is not truncated at R GC ∼ 30′, which is different from the result from the planetary nebulae (PNe) of M87 (Doherty et al. 2009 ). Our results are consistent with Strader et al. ( 2011 );


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IRTF spectral library and the present spectrum of V1534 Sco, and to the Fitzpatrick ( 1999 ) reddening law. Figure 2. Upper panel: expanded view from Fig. 1 around the far-red Ca ii triplet and head of the Paschen series. Lower panel: a plot of the residuals after subtracting the M6III spectrum from that of V1534 Sco. The strongest emission lines are identified. 3.2 The emission-line spectrum There are several emission lines visible in the IRTF spectrum of V1534 Sco, as illustrated in the zoomed views of Figs 2 – 4 . Fig. 2 focuses on the 0.84−0.94 μm region. The O i 0.8446 μm emission line is already evident in the direct spectrum of V1534 Sco of the top panel. Other lines like the Ca ii triplet and hydrogen Paschen series become more clearly visible once the template M6III spectrum is subtracted from that of V1534 Sco, as illustrated in the bottom panel of Fig. 2 . We have explored the large number of ∼200 spectra of symbiotic stars surveyed in the spectral atlas of Munari and Zwitter ( 2002 ), and found that Hen 3-1410 provides the closest match with V1534 Sco. Their observed spectra are compared in Fig. 3 . The strength of O i 0.8446 μm and the simultaneous absence of O i 0.7772 μm are direct evidence that a strong Lyman-β fluorescence (Bowen 1947 ) is at work in Hen 3-1410. This could also be the case for V1534 Sco, but the low signal-to-noise ratio (S/N) at the blue end of its spectrum does not allow us to judge about the presence and intensity of O i 0.7772 μm. Figure 3. Comparing the blue end of the IRTF spectrum with that of the M6III symbiotic star Hen 3-1410 taken from the spectral atlas of symbiotic stars by Munari Zwitter ( 2002 ). The spectral region explored in more detail in Fig. 4 is that of He i 1.0830, Paschen-γ 1.0938, and O i 1.1287 μm which are clearly present in emission in the spectrum of V1534 Sco. They well match what is normally seen in symbiotic binaries, as proved by the comparison with T CrB in the bottom panel of Fig. 4 (this IRTF spectrum of T CrB – itself a NwSS – was taken on the same night and with the same instrumental set-up of V1534 Sco.). The only significant difference between T CrB and V1534 Sco is the deep P-Cyg absorption that the latter displays for He i 1.0830 μm. It is not an observational artefact and there is no photospheric line at this position that could mimic such a P-Cyg profile, as proved by the over-plotted spectrum for the M6III template. P-Cyg profiles are sometimes observed for He i lines in symbiotic stars (e.g. Smith 1981 ), their presence and intensity being usually a function of orbital phase (e.g. Munari 1993 ). Figure 4. Similar to Fig. 2 , the upper panel shows an expanded view from Fig. 1 , this time around the He i 1.0830 μm line, while the central panel presents the result of the subtraction of the M6III spectrum from that of V1534 Sco. Note the presence of a deep P-Cyg absorption component for the strong He i line. For comparison a spectrum of T CrB, an M3III symbiotic star


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We are grateful to the entire Gaia collaboration for providing data and assistance which made this project possible. We congratulate them on their tremendous achievement to date. Support for this work was provided by the National Aeronautics and Space Administration (NASA) through programs GO-12879, 13334, 13335, 13344, 13571, 13678, 13686, 13928, 13929, 14062, 14394, 14648, 14868 from the Space Telescope Science Institute (STScI), which is operated by AURA, Inc., under NASA contract NAS 5-26555. B.B. and M.G.L. are indebted to the Italian Space Agency (ASI) for their continuing support through contract 2014-025-R.1.2015 to INAF, and to R. Morbidelli (INAF) and R. Messineo (ALTEC S.p.A, Torino) of the Italian Data Processing Center (DPCT) for their help with the Gaia data. A.V.F.’s group at UC Berkeley is also grateful for financial assistance from the TABASGO Foundation, the Christopher R. Redlich Fund, and the Miller Institute for Basic Research in Science (UC Berkeley). S.C. and A.G.R. gratefully acknowledge support by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe.” This research is based primarily on observations with the NASA/ESA Hubble Space Telescope , obtained at STScI, which is operated by AURA, Inc., under NASA contract NAS 5-26555. This publication makes use of data products from the Wide-field Infrared Survey Explorer (WISE) , which is a joint project of the University of California (Los Angeles) and the Jet Propulsion Laboratory/California Institute of Technology, funded by NASA. It has also made use of the SIMBAD database, operated at CDS, Strasbourg, France. Research at Lick Observatory is partially supported by a generous gift from Google. The HST data used in this paper are available at the MAST archive doi: 10.17909/T9G40B .


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 B-Person I-Person O B-Person I-Person O O O O O O O O B-Software O O O O O B-Person O B-Person 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 B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant B-Grant B-Grant O O O O O O O O O O O O O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory 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 O O O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Person O O O O B-Organization I-Organization I-Organization O B-Grant O B-Grant B-Person O O O O B-Organization I-Organization I-Organization O B-Grant O B-Grant

We wish to thank Sourav Chatterjee for carefully reading the manuscript and providing useful comments that helped to improve this paper. We wish to thank Rainer Spurzem and Sverre Aarseth for their advice regarding the adjustment of the nbody6 software package for our study. LW and XCZ were supported by the Department of Astronomy at Peking University and the Kavli Institute for Astronomy and Astrophysics. MBNK was supported by the Peter and Patricia Gruber Foundation through the PPGF fellowship, by the Peking University One Hundred Talent Fund (985), and by the National Natural Science Foundation of China (grants 11010237, 11050110414, 11173004). This publication was made possible through the support of a grant from the John Templeton Foundation and National Astronomical Observatories of Chinese Academy of Sciences. The opinions expressed in this publication are those of the author(s) do not necessarily reflect the views of the John Templeton Foundation or National Astronomical Observatories of Chinese Academy of Sciences. The funds from John Templeton Foundation were awarded in a grant to The University of Chicago which also managed the programme in conjunction with National Astronomical Observatories, Chinese Academy of Sciences. RPC was supported by the Swedish Research Council (grants 2012-2254 and 2012-5807). MBD was supported by the Swedish Research Council (grants 2008-4089 and 2011-3991).


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

BH (), but in this case the BH shadow at millimeter wavelengths is also illuminated by the counter-jet, which is geometrically more extended compared to our GRMHD numerical models. Broderick Loeb (2009) did not restrict the orientation of appropriate baselines to E-W direction in their analysis because their counter-jet emission is more uniform and extended compared to ours. At 7 mm, the size of the jet emission in their model is sensitive to the jet collimation parameter, . It is quite possible that our model will also be sensitive to the exact value of the BH spin or the disk size that may control the jet collimation. We leave this issue for a future study. 4.6. Matter content of the jet funnel Unlike those by Broderick Loeb (2009) and Dexter et al. (2012) , our model does not make any assumption about the jet matter content. At the jet wall (sheath), the plasma is baryonic, and it is constantly supplied from the accretion disk. Inside of the jet funnel, electron-positron pairs are produced in collisions. We calculate the pair production rate directly from the RT model following Mościbrodzka et al. (2011) . In model RH100, the pair production rate near the SMBH horizon is (based on Eq. (26) in Mościbrodzka et al. 2011 , assuming that the luminosity of the source around the electron rest-mass energies is ). This gives an estimate for the pair plasma density near the event horizon . Using Eq. 45 in Mościbrodzka et al. (2011) , we can calculate the Goldreich–Julian density , i.e. the pair density required to enforce the ideal MHD condition () in the rest frame of the plasma ( Goldreich Julian 1969 ). We find that in model RH100; i.e., the pairs cannot be produced in cascades and multiply themselves. In summary, the pair density in the jet funnel (spine) remains low. 4.7. Emission from the jet sheath in radio Finally, we briefly discuss the effect of the jet vertical stratification (jet spine and sheath) on the observational properties of jets in general. A recent work by Boccardi et al. (2015) reports the detection of the edge-brightened jet in Cyg A. The jet in Cyg A jet is not resolved by radio observations as well as is the M 87 jet. Therefore we should keep in mind that their scales are different and their inclination angles are also probably different. The authors report that the counter-jet is narrower than the approaching jet. To clarify what our models predict we plot our 43 GHz images of the M 87 jet at various inclination angles in Fig. 11 . Here we do not notice any evident difference in the opening angle of the jet and counter-jet owing to the geometrical effects of light propagation. However, we find that the jet edge-brightening depends on inclination, and it becomes more notable for . In the images presented in Sect. 3 , the signal-to-noise ratio is greatly improved thanks to the time-averaging of many frames. However, we notice that single images of the jet at longer wavelengths exhibit some numerical artifacts. These are most


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

LMXBs. The disc temperature of GX 339–4 ranged from ∼0.6 to ∼0.9 keV (Plant et al. 2014 ) and the temperature of Cyg X–1 ranged between 0.5 and 0.6 keV (Shaposhnikov Titarchuk 2006 ). The temperature of 4U 1636–53 ranged from ∼0.3 to ∼0.8 keV in the best-fitting results (Zhang et al. 2017 ) and the disc temperature of MXB 1658–298 ranged from ∼0.6 to ∼0.9 keV (Sharma et al. 2018 ). The disc temperature of MAXI J1727–203 was lower than these four systems. A potential explanation for a lower temperature in MAXI J1727–203 than in other sources could be related to the mass of the compact object. Assuming that the accretion disc is at the innermost stable circular orbit (ISCO), the temperature at the inner disc radius is proportional to , where is the mass accretion rate and M is the mass of the compact object (Frank, King Raine 2002 ). According to Muñoz-Darias, Casares Martínez-Pais ( 2008 ), M 6 M ⊙ for GX 339–4. We take the temperature of GX 339–4 in the soft state (0.79 keV) from Plant et al. ( 2014 ) and we also take the disc temperature of the softest observation in the HID of MAXI J1727–203 (0.45 keV). From that, if we assume that is the same for two sources in the same spectral state, we estimate a lower limit for the mass of MAXI J1727–203 of ∼19 M ⊙ . Therefore, the high mass of the compact object can explain the low temperature of the inner disc. Alternatively, as suggested by Gou et al. ( 2011 ), the low temperature at the inner disc radius can be a consequence of a low inclination of the accretion disc with respect to the line of sight. We can repeat this analysis to estimate the mass of MAXI J1727–203 with the NS Aql X–1. For this, we took the temperature of Aql X–1 in the soft state of its 2007 outburst (∼0.66 keV, Raichur, Misra Dewangan 2011 ). Considering a mass of ∼1.4 M ⊙ for the NS in Aql X–1, we obtained a mass of ∼2 M ⊙ for the compact object in MAXI J1727–203. If we consider a higher mass for Aql X–1, the mass of MAXI J1727–203 also increases. Considering the latter, this mass estimates suggest that the compact object in MAXI J1727–203 is massive NS or a low-mass BH. Based on all the above comparisons, although we cannot unambiguously identify the nature of the compact object in MAXI J1727–203, the evolution in the HID, RID, and RHD, and the temperature at the inner radius of the accretion disc during the softest observations suggest that it is a BH. 4.2 Anticorrelation between the fractional rms amplitude and the flux of the disc component Fig. 9 shows that the relation between the fractional rms amplitude and the disc flux is continuous and that both quantities are anticorrelated during phases A and C (orange diamonds and black circles) of the outburst. While in phases B and D (blue triangles and red crosses), the rms amplitude is consistent with being independent of the disc flux, those measurements extend the relation seen in phases A and C to low (phase D) and high (phase B) values of the disc flux. The simplest


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ACKNOWLEDGEMENTS We thank A. Babul, S. Clesse, J. Garcia-Bellido, S. Khochfar, I. Musco, T. Nakama, and M. Volonteri for useful discussions. We are also grateful to Y. Sendouda for help in drawing one of the figures. BC thanks Institut d’Astrophysique in Paris for hospitality received during this work. JS acknowledges the support of the European Research Council via grant 267117.


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TGS would like to acknowledge the Department of Science and Technology (DST), Government of India for providing financial support through the project SR/FTP/PS-172/2012.


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( 2013 , 2014 ), and further details on the strong lensing modeling of MACSJ1149.5+2223 are provided in a dedicated paper (Grillo et al. 2015a ). 4.2.1. Definition of the Mass Model Different mass models have been explored for this galaxy cluster, but only the best-fitting one is discussed here. The projected dimensionless total surface mass density of 300 cluster members within the WFC3 field of view of the CLASH observations is modeled as a dual pseudoisothermal elliptical mass distribution (dPIE; Elíasdóttir et al. 2007 ) with vanishing ellipticity and core radius. The zero-core dPIE profile corresponds to the three-dimensional mass density profile:The galaxy luminosity values in the F160W band are used to assign the relative weights to their total mass profile. The galaxy total M / L ratio is scaled with luminosity as , thus mimicking the so-called “tilt” of the Fundamental Plane. The values of axis ratio, PA, effective velocity dispersion, and truncation radius of the two cluster members closest in projection to the central and southern images of the SN Refsdal host are left free. To complete the total mass distribution of the galaxy cluster, three additional mass components are added to describe the cluster dark matter halo on physical scales larger than those typical of the individual cluster members. These cluster halo components are parametrized as two-dimensional pseudo-isothermal elliptical mass profiles (PIEMD as defined by Kassiola Kovner 1993 ; see also Grillo et al. 2015a ). No external shear or higher-order perturbations are included in the model. The number of free parameters associated with the model of the cluster total mass distribution is 28. 4.2.2. Definition of the Inputs The positions of the multiple images belonging to the 10 systems of the gold sample and to 18 knots of the SN Refsdal host are the observables over which the values of the model parameters are optimized. The adopted positional uncertainty of each image is 0065. The redshift values of the 7 spectroscopically confirmed gold systems are fixed, while the remaining 3 systems are included with a uniform prior on the value of , where D ds and D s are the deflector-source and observer-source angular diameter distances, respectively. In total, 88 observed image positions are used to reconstruct the cluster total mass distribution. 4.2.3. Description of the Inference Process and Error Estimation The best-fitting, minimum- model is obtained by minimizing the distance between the observed and model-predicted positions of the multiple images in the lens plane. A minimum value of 1441, corresponding to an rms offset between the image observed and reconstructed positions of 026, is found. To sample the posterior probability distribution function of the model parameters, the image positional uncertainty is increased until the value of the is comparable to the number of the degrees of freedom (89), and standard Markov chain Monte Carlo (MCMC) methods are used. The


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

). Thus, a subsurface strengthened layer has to be very large and thick to avoid lifting by gas released beneath it. If we consider a disc of strengthened material with a 50-m radius and a 10-m thickness, then for a density of 531 kg m −3 and g = 2 × 10 −4 m s −2 , the gravity force exerted on the material underneath (e.g. gas cavity, pristine material) is F grav ∼ 8340 N. If the pressure is enhanced under a small fraction of the disc (i.e. 1 per cent), then the condition F gas > F grav can be met when p ∼ 0.1 kPa. When the edges of the strengthened layer are under elevated surrounding terrain, then the critical gas pressure is higher. In any case, the tensile strength of the strengthened material is important. 3.2 Tensile strength Fig. 3 plots the profiles of σ T versus depth, calculated when the initial tensile strength σ T0 = 1 kPa. The curves are drawn for selected locations for the times when the gas pressure in given locations satisfies conditions: p 0.1 kPa (upper panel), p > p crit,1 = 1 kPa (middle panel) and p > p crit,2 = 10 kPa (lower panel). Profiles shown in the middle panel are taken 113 h (nine rotation periods) after the profiles presented in the upper panel. During this period, the thickness of the strengthened layer increased by at least 0.5 m. In one location, a secondary strengthened layer formed above the crystallization front of the amorphous water ice. The thickness of the main strengthened layer is ∼1 m when the gas pressure approaches 0.1 kPa, 0.8–1.8 m when p > p crit,1 and 0.8–3.3 m when p > p crit,2 . A strengthened layer about 1 m thick will probably be broken or lifted. Thus, in locations marked with white triangles, the presence of uncovered ice-rich material should be expected. Increased emission of more volatile components (such as carbon monoxide) is also likely. Figure 3. Tensile strength versus depth, when the CO pressure p beneath the strengthened layer is p 0.1 kPa (upper panel), p > p crit,1 = 1 kPa (middle panel) and p > p crit,2 = 10 kPa (lower panel). The initial tensile strength is 1 kPa. The remaining parameters of the model parameters are given in the legends. It is interesting that when σ T0 = 1 kPa the ejection of material is possible in all considered locations, while the uncovered ice was found only in the pit. This difference can be explained by the non-uniform concentration of highly volatile CO, but other options should also be considered, such as the non-uniform granulation or porosity of the material. Fig. 4 is similar to the upper and lower panels of Fig. 3 . The profiles shown in Fig. 4 are calculated for σ T0 = 0.1 kPa instead of σ T0 = 1 kPa. It can be seen that the strengthening of the loosely bonded mixture of grains is slower than with moderate initial strength. The thickness of the strengthened layer at the moment when the CO gas pressure reaches the threshold value p crit,1 is ∼1 m for σ T0 = 0.1 kPa and 1.1–1.9 m for σ T0 = 1 kPa. The next threshold p crit,2 is exceeded when the


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

We would like to thank Jo Dunkley from Princeton University, Johannes Hubmayr from NIST, and Jeff McMahon from the University of Michigan for useful comments and discussions. David Alonso acknowledges support from the Science and Technology Facilities Council (STFC) and the Beecroft Trust and Jonathan Ward acknowledges support from the NASA Space Technology Research Fellowship Program.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O B-Software O O O O O O O O O O O O O O O O O O O B-Software O B-Software 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 B-Software O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

counting pairs of i and j objects with unitary weights; and the weighted case, accumulating the product of the weights w i * w j , selected randomly (in this case) from a Gaussian distribution with (σ, μ ) = (1.0,0.1). This is a mock-up of a common scenario for deriving 2PCFs from real surveys, where numerous bias and observational effects are accounted by means of properly chosen weights. From an implementation point of view, this means dealing with extra weight vectors and at least an extra floating-point multiplication deeply nested inside loops. For this reason, Gundam uses slightly different versions of the counting algorithm to accommodate these two cases. From the figure it can be seen that our code, which is based in a completely different algorithm, performs as well and even better than Corrfunc . In ( r p , π) space, it can be up to 1.4 × faster. In angular space Gundam can be slightly slower. However, if non-unitary weights are required, our code can run up to 30 per cent faster. The timings for very few particles, e.g. below few times 10 4 , should be ignored as the dominant component there is most likely the overhead of grid creation or array manipulation. Gundam , as well as Corrfunc , are intended primarily for processing much larger samples. Figure 5. Single-core run time to calculate DD pairs with Gundam and Corrfunc codes for samples up to 2 × 10 6 objects, using random Gaussian weights or a single constant weight equal to 1 (unweighted pair count case). Performance is evaluated in ( r p , π) space (left) and angular space (right). Bottom panels show the speed-up factor of Gundam respect to Corrfunc for the weighted and unweighted case. 3.2 Multithread We run a series of tests in the described set-up, running the same pair counts with 2, 3, and 4 threads that execute in each of the physical CPU cores. There is little benefit in using extra virtual threads (i.e. the Hyper-Threading technology of Intel CPUs) because the code is already computationally intensive, making extensive use of available CPU resources and floating-point pipelines. Also, since logical processors share the caches, they might actually compete for cache utilization, which can lead to a degradation of performance. Therefore, we only report up to four threads, noting that eight threads can potentially bump the performance by 25 per cent. In Fig. 6 , we can see that below 3–4 × 10 4 objects there is a bias towards slightly longer run times independent of the number of threads. As said before, this is due to the overhead of allocating memory and arranging data into convenient structures. In fact, a naive pair counting algorithm might probably run faster for very small samples. For larger samples, the overhead is less relevant and the advantage of using multiple threads in parallel starts to become significant. For around 10 6 particles in ( r p , π) space, we get a close to constant speed-up factor of 1.9, 2.8, and 3.6, when we duplicate, triplicate, or


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

13 C ratio is larger. Fig. 7 12 CN/ 13 CN ratio as a function of n H , for different temperatures, at t 1 ( top right panel ), t 2 ( bottom left panel ), and t 3 ( bottom right panel ). The large pink circles in the bottom panels represent the result of the model that simulates the physical conditions in the centre of the pre-stellar core B1b observed by Daniel et al. (2013) . The 12 CN/ 13 CN ratio observed by Daniel et al. (2013) is represented by the green star. We note that the error bar is within the symbol. In all panels, the black horizontal dashed line represents the initial 12 C/ 13 C ratio of 68. We also performed a parameter-space exploration for a fixed n H of 2 × 10 4 cm −3 , varying the temperatures from 10 up to 50 K and the cosmic-ray ionisation rate between ζ low and ζ high . In particular, as already done in Sect. 3.2 , we focused the analysis on HNC, HCN, and CN ( Figs. 11 – 13 ). The main trend is that the 12 C/ 13 C ratios are highest for ζ high . This is related to the fact that secondary photon reactions maintain a high efficiency of low-temperature isotopic exchange reactions that involve C 3 , and the atomic 12 C/ 13 C ratio (and that of related molecules) remains higher than 68 (see also Fig. C.2 , right panel). 4 Conclusions We developed a new chemical network to study, in detail, how important isotopic exchange reactions are to the chemistry of carbon-containing species in the low temperature (10–50 K) gas in star-forming regions with n H = 2 × 10 3 –2 × 10 7 cm −3 . In particular, we suggest the occurrence of 13 C exchange involving C 3 with atomic carbon and study the possible consequences of this reaction. The main results and conclusions of this work are summarised below: 1. We found that reaction ( 10 ) is mainly important for T gas 27 K (owing to its exothermicity), and leads to 12 C/ 13 C 68 for molecules that form from atomic carbon (e.g. C 2 , C 3 , and nitrile-bearing species). This behaviour occurs in the time period between the conversion of atomic carbon into CO, andthe time when CO is almost completely frozen out onto dust grains. 2. We performed a detailed study of the 12 C/ 13 C ratios for the nitrile-bearing species HCN, HNC, and CN, as a function of density and for different temperatures. Our model can partially reproduce the carbon isotopic ratios derived by Daniel et al. (2013) and Magalhães et al. (2018) from observations towards low-mass pre-stellar cores. 3. We also used our grid of models to evaluate how far we are from the correct 12 C/ 13 C ratio, assumed to be 68 in the local ISM, to derive the 14 N/ 15 N ratios in the sample of high-mass star-forming regions analysed by Colzi et al. (2018a ). Our chemical model predicts that we are overestimating or underestimating the assumed 12 C/ 13 C ratios by factors ~0.8–1.9, even up to ~3.5, depending on the evolutionary time that we choose for the analysis. Considering these factors, the average nitrogen fractionation value of ~330 derived by


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

this solution to be unrealistic. Figure 7. T eff –log( g ) diagram of the primary star in EVR-CB-004 (red star). The EHB/BHB evolutionary tracks for different stellar masses (bottom to top: 0.471, 0.473, 0.475, 0.480, 0.490, 0.500, and 0.510 M ⊙ ), that is, increasing hydrogen envelope mass (0.000, 0.002, 0.004, 0.009, 0.019, 0.029, and 0.039 M ⊙ , respectively), and solar metallicity according to Dorman et al. ( 1993 ) are shown with solid lines. In addition, the post-AGB tracks according to 0.524 M ⊙ are displayed with dotted lines (Bloecker 1995 ), and the pre-He WD track calculated with MESA (Paxton et al. 2011 , 2013 , 2015 , 2018 , 2019 ) is shown with dashed lines. The hot subdwarfs are confirmed binaries with WD companions taken from Kupfer et al. ( 2015 ). The BHB stars are taken from Saffer et al. ( 1997 ), Ramspeck et al. ( 2001 ), Vennes et al. ( 2007 ), Naslim et al. ( 2010 ), Copperwheat et al. ( 2011 ), Østensen et al. ( 2012 ), Geier et al. ( 2014 ), and Schneider et al. ( 2018 ). The plotted error bars include 1 σ statistical and systematic uncertainties as presented in the text (see Section 3 for details). If, instead, the progenitor filled its Roche lobe after He burning started, the envelope would get stripped and form a He core–burning hot subdwarf star that is expected to burn He for ≈100–150 Myr. Depending on its hydrogen envelope, it is considered to be an EHB star (for hydrogen envelopes ≲0.01 M ⊙ ) or a BHB star (for hydrogen envelopes of a few hundredths M ⊙ ). Once burning exhausts the He in the core, the star evolves toward hotter temperatures. As the core contracts, residual hydrogen is predicted to burn in a shell, pushing the surface to a larger radius (Østensen 2009 ) and hence lower surface gravities. This is seen in the solid tracks shown for different masses in Figure 7 . This stage of the evolution is expected to last for only ≈10–20 million yr and is commonly referred to as post-EHB or post-BHB evolution. A helpful discussion of EHB/BHB stars and their evolution can be found in Moehler ( 2001 ), Østensen ( 2009 ), and Heber ( 2016 ). Figure 7 shows the position of the primary of EVR-CB-004 in the T eff –log( g ) diagram, which is consistent with a post-BHB sequence with a mass of ≈0.5 M ⊙ . We note here the limitation of using the EHB/BHB evolutionary models in their current form to describe the primary of EVR-CB-004, since their radii exceed the Roche radius of EVR-CB-004 between leaving the BHB and the present. We suggest more involved modeling, beyond the scope of this work, to explore the post-BHB space specific to EVR-CB-004. If the post-BHB interpretation is correct, the primary of EVR-CB-004 is even rarer, as we would have to have caught the object during this transitioning state. The only other reasonably similar system (compact binary with a WD companion, ellipsoidal deformation, Doppler boosting, gravitational limb darkening, similar mass, and an old evolved primary) we found in the


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

A.C.N.Q. and P.G. are grateful for support from the National Science Foundation grant AST1412648 and NASA/STScI grants GO12055, GO-14268, and GO-14769. The research of L.C. is supported by the Comité Mixto ESO-Chile and the DGI of Universidad de Antofagasta. We would also like to thank the anonymous referee for the helpful comments that added to the depth of this paper. We appreciate the significance of Maunakea to the indigenous Hawaiian community and acknowledge that we are fortunate to be able to use observations taken from its summit.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Model I-Model O B-Model I-Model O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O

fraction, χ i , of the gas that inflows from the i + 1th annular ring to the i th ring during the simulation time-step of 1 Myr. If we assume that the entire interstellar gas fraction within an annular ring participates in the radial inflow, the percentage area of the annular rings involved in the radial mass inflow across a ring during 1 Myr with the chosen radial inflow velocities of 0, 0, 0.5, 1, 2, 3, and 3.7 km s −1 would be 0, 0, 0.02, 0.05, 0.09, 0.14, and 0.17 per cent, respectively, from the first to the seventh ring. This corresponds to a substantial inflow of gas causing a strong depletion of gas as well as the total surface matter density in the outer annular rings at the cost of matter accumulation in the inner rings. In order to circumvent this excessive inflow of gas towards the centre, we assumed 0.1 mass fraction of the total available gas fraction to be actively involved in the inflow. Thus, we used the values of 0, 0, 0.002, 0.005, 0.009, 0.014, and 0.017 per cent for χ i , from the first to the seventh ring. The assumed radial profiles of the halo surface mass density in Models I and J are presented in Table 1 . The radial stellar formation efficiency parameter, , in these simulations is assumed to be unity over the entire Galaxy. As discussed later in Section 4 , the radial gas inflow provides a natural mechanism to obtain the observed elemental abundance gradients without adopting a preferred set of stellar efficiency parameters. Finally, the choice of the simulation parameters made in this work is certainly not restricted (Mott et al. 2013 ). We have also simulated a Model J in order to incorporate the radial gas inflow superimposed over the radial gas mixing. The mixing was performed in a manner identical to that of Model F with a mixing velocity of 1 km s −1 . We have not specifically performed the simulation with radial gas outflows that are mainly caused by the energetic winds from supernovae and other massive stars. The radial gas mixing models take care of this aspect to an extent. 3 RESULTS The major aim of this work was to develop a Monte Carlo based GCE model for the Milky Way Galaxy. We ran a large number of simulations to optimize the various simulation parameters based upon the observational constraints. A selective set of simulation results for our three best models A, H, and J are presented in Figs 1 – 10 and Table 1 . We have avoided a detailed discussion and presentation of the simulation results for Models B–G and I in the main text. The results of these models can be found in figs 11–31 in the supplementary data . However, we summarize the major findings of these models in the main text. We present a comprehensive account of the deduced evolution of the , the [Fe/H], the metallicity , and the stellar birth rate for the various annular rings of 2 kpc width each, starting from 2 to 18 kpc from the Galactic centre. The deduced temporal evolution of the total surface mass density (stars +


O O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O O O O O O B-Person I-Person I-Person O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O O O B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O B-Organization 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 I-Grant B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Person O O O O O B-Organization I-Organization I-Organization O O B-Grant O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-ComputingFacility I-ComputingFacility I-ComputingFacility

The authors would like to thank the anonymous referee for constructive criticism, as well as Shane P. O’Sullivan for providing his unpublished rotation measure synthesis data, and S. Ann Mao for providing her newest data set in digital form. The results in this publication have been derived using the NIFTy 4 package ( Selig et al. 2013 ), as well as the HEALPix 5 package ( Górski et al. 2005 ). This research has made use of NASA’s Astrophysics Data System. It was supported by the DFG Forschergruppe 1254 “Magnetisation of Interstellar and Intergalactic Media: The Prospects of Low-Frequency Radio Observations”. T.A. is supported by the Japan Society for the Promotion of Science (JSPS). B.M.G. acknowledges the support of the Australian Research Council through grant FL100100114. Some of the calculations were carried out on the Canada Foundation for Innovation funded CITA Sunnyvale cluster.


O O O O O O O O O O O O O O B-Database I-Database I-Database O O O O O O B-Organization O O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person 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 O O O O B-Person I-Person I-Person O O O O O O O O O O O O O

In this research, we have used and acknowledge with gratitude, the data from the AAVSO International Database, based on observations submitted to the AAVSO by variable star observers worldwide. A part of the data in this study was obtained from the NRO Data Archive System. The authors wish to express their gratitude to S. Oizumi, H. Yamamoto, S. Tanada, H. Toujima, T. Yasuda, Y. Arao, K. Ando, K. Ueda, D. Namikawa, N. Matsumoto, M. Kuroki, Y. Kodama, and M. Suzuki for their help with data analysis. We also acknowledge the contribution of Dr. S. Deguchi who provided us with scientific advice. Thanks to the referee for constructive comments.


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 B-Instrument 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 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

mostly the and lines, and Mg for XMM2235. We note that the S/N significantly decreases in the blue part of the spectrum because of the lower throughput of KMOS in the bluer part of the YJ band, which affects the uncertainties of our measurements. Moreover, the blue part of the spectrum we fit covers a shorter wavelength range than the red part. This could potentially affect the set of templates applied by the fitting procedure. To circumvent this issue, we adopt the same combination of templates derived in the fit of the full spectrum in both the fit of the blue and red part. As discussed in Section 3.3 , before performing the kinematic fit, we smooth the KMOS spectrum with a variable kernel to a common FWHM to match the maximum FWHM. This should prevent us from adding systematics related to the KMOS resolution in the blue and red part of the spectrum. Figure 9 shows a comparison of the results obtained by fitting the full spectrum and the blue part (left panels), the full spectrum and the red part (central panels), and red and blue part (right panels). The actual value is determined as the mode of the distribution over the 100 bootstrap realizations and the error as the standard deviation. The actual value of the stellar velocity dispersion from our spectra is consistent within the errors with the mode of the distribution of derived from the bootstrap realizations. Figure 9. Comparison between the stellar velocity dispersion measurements in the blue and red part of the spectrum for XMM2235 (upper panel) and XMM2215 (lower panel). From left to right, the panels show the comparison between the fit in the full spectrum and the blue part, the full spectrum and the red part, and between blue and red part, respectively. For XMM2235, we find that the kinematics derived from the blue part and from the full spectrum have a median difference () and a scatter of 70.11 , while by fitting the red region of the spectrum, we find an offset () and a scatter of 56.20 from the fit of the full spectrum. The median difference between the fit of the blue and red part of the spectrum is () with a scatter of 72.54 . In XMM2235 the quality of some data in the “blue” part is particularly poor, resulting in a few objects with systematically higher than in the full sample. For XMM2215, we find that the kinematics derived from the blue part and from the full spectrum have a median difference () and a scatter of 60.80 , while by fitting the red region of the spectrum, we find an offset of () and a scatter of 60.00 from the fit of the full spectrum. The median difference between the fit of the blue and red part of the spectrum is () with a scatter of 121.41 . This test aims at assessing the systematic effect we can have from deriving stellar velocity dispersions from different absorption lines at different redshift. It did not result in a rejection of galaxies, which were mostly discarded at the stage of fitting the full spectrum through all the bootstrap


O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula 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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation 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-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 O O O O O O O O O O O O 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 B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O 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 scales of r > 1600 au ( j app ∝ r 1.6 on average, see Table F.2 ), consistent with the prestellar stage ( j ∝ r 1.6 ). We discuss the properties and physical origin of these two regimes in more details in the next sections. 5.3 Conservation of angular momentum in Class 0 inner envelopes In this section, we focus on the relatively constant values of specific angular momentum observed in the inner envelopes at scales of r ≤ 1600 au in the j ( r ) profiles due to rotation motions (see Fig. 17 ). From these flat profiles, we find that the matter directly involved in the formation of the stellar embryo has a specific angular momentum ~3 orders of magnitude higher than the onein T-Tauri stars ( j ~ 2 × 10 −7 km s −1 pc, Bouvier et al. 1993 ). We discuss constant values of specific angular momentum as conservation of angular momentum to test disk formation as a possible solution to the angular momentum problem. It is difficult to constrain the time evolution of specific angular momentum for a given particle from angular momentum distributions which are snapshots of the angular momentum distribution of all particles at a given time during the collapse phase. During the collapse of a core initially in either solid-body rotation or differential rotation, particles conserve their specific angular momentum during the accretion on the stellar embryo ( Cassen Moosman 1981 ; Terebey et al. 1984 ; Goodwin et al. 2004 ). In the case of a protostellar envelope with a density profile ρ ∝ r −2 , an observed flat profile j ( r ) = constant requires, since each particle at different radii has the same specific angular momentum, an initially uniform distribution of angular momentum. This does not agree with the steep increase in specific angular momentum we observe at scales of r > 1600 au in the j ( r ) profiles. The break in the specific angular momentum profile could be due either to a faster collapse of the inner envelope caused by an initial inner density plateau ( Takahashi et al. 2016 ) or to a change of dominant mechanisms responsible for the observed velocity gradients from inner to outer scales of the envelope. In our sample, we distinguish eight sources with a relatively flat j ( r ) profile in the inner envelope ( β 0.5, see Table F.1 ): L1448-2A, L1448-NB, L1448-C, IRAS2A, SVS13-B, IRAS4B, L1527, and GF9-2. We estimate a centrifugal radius that would be obtained when the mass currently observed at ~100 au collapses and based on the mean value of specific angular momentum observed today ⟨ j 100 au ⟩ as follows: Table 4 Centrifugal radius R cent assuming angular momentum conservation. Notes. ( a ) Weighted mean of specific angular momentum in the inner envelopes (50 au r ≤ 1600 au). ( b ) Range of the object mass at 100 au, the minimum and maximum values are defined in Sect. 5.3 . ( c ) Centrifugal radii estimated from ⟨ j 100 au ⟩ and M 100 au using Eq. ( 2 ), assuming conservation of angular momentum. ( d ) Candidate disk radius determined from the


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

peak value and rms noise. Both weighting methods provide comparable (12 per cent difference) integrated flux densities. We followed the same strategy to obtain the image of the line emission, by cleaning with different velocity resolutions up to 6.3 km s −1 . The H30 α recombination line was not detected in the data cube, using either Briggs or natural weighting. We were able to clean each velocity channel to 0.1 mJy beam −1 (rms), which may be taken as an upper limit to the line flux density. The recombination line flux estimated in local thermodynamic equilibrium using the emission measure from Section 3 falls below our detection limit. 3 RESULTS The continuum emission of the shell at 230 GHz is shown in Fig. 1a . This is the best resolution image calculated from our data. Fig. 1b displays the best resolution image contours superposed to the natural weighting, lower resolution map, which confirms the structures seen in the best resolution image. An even lower resolution image, aimed to match the Hubble Space Telescope ( HST ) point spread function at H α, simulates the expected emission of an optically thin recombination line ( Fig. 1c ). This image, derived directly from the high resolution image ( Fig. 1a ) using a Gaussian kernel convolution, is remarkably similar to the ring/bipolar shell morphology proposed by Harvey et al. ( 2018 ) for this nova. Most, if not all the large-scale structures seen in Fig. 1c is due to the blending of a distribution of smaller unresolved sources. Large contiguous emission regions that could be identified as ring or bipolar caps, are absent above the 2.5σ level in ALMA high resolution image, although they may be present at fainter flux densities. The total measured shell flux density is 9.4 ± 1.5 mJy. Figure 1. ALMA image of the V5668 Sgr shell at 230 GHz. The top panel (a) shows the full resolution continuum image above 3.0σ. Major tick marks are spaced by 100 mas. The middle panel (b) shows the natural weighted image with five superposed contour levels from the image in panel (a), starting at 2.5σ. The bottom panel (c) displays the image given in panel (a) after a Gaussian convolution to match the HST spatial resolution at H α. The flux unit is Jy beam −1 for panels (a) and (b), and arbitrary units for panel (c). North is at the top and east to the left. The power spectrum of the continuum image ( Fig. 2 ) shows that a significant fraction of the emission is formed in spatially resolved structures. It also indicates that features above the noise level are present at scales as small as 55 mas or 1 × 10 15 cm, i.e. near the resolution limit of the observations. A distance of 1540 pc is assumed in this work (Banerjee et al. 2016 ), a value that is in agreement with both the observed shell expansion parallax for V exp = 650 km s −1 and maximum magnitude and rate of decay relations. No parallax to this object could be found in Gaia DR2. Measurement of individual clump sizes in the image are consistent with


O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula B-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula B-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O

the analytical solution and the real solution that increases with time. This effect was observed for all the solutions studied for this work. Figure 3. Long-term error evolution in the radial distance, the latitude, and the longitude for a frozen sun-synchronous orbit. 6.3.2 Example: Molniya orbit As an example of this formulation to eccentric orbits, we select a typical Molniya orbit with initial elements: a = 26 600.0 km, e = 0.74, , , , and . Figs 4 and 5 present the results of applying this formulation to this particular initial conditions. From these figures, it can be seen that, even for very eccentric orbits, the formulation along with the perturbation theory used provides a very good approximation to the problem even for a first-order solution. In particular, the order of magnitude of the error in latitude and longitude remains the same as in the near-circular case, while the radial distance experiences an increase in its error due to the larger variation of this variable during the dynamic. Therefore, this example shows that this formulation can be applied without any problem even to high eccentric orbits. Figure 4. Evolution of radial distance, latitude, and longitude for a Molniya orbit. Figure 5. Evolution of error in radial distance, latitude, and longitude for a Molniya orbit. Moreover, and as done in the previous example, we can study the performance of a long-term propagation of this orbit. Fig. 6 shows the evolution of the error in radial distance, latitude, and longitude of the orbit as a function of the number of orbital periods that the orbit is propagated. In this figure, it can be observed the increase in error as the propagation time increases due to the approximation performed in the frequencies of the motion using this first-order solution. Nevertheless, even with this increase in error, there is an angular error smaller than , and a radial error of 0.5 km after 100 orbital revolutions. These results represent a relative error of 10 −5 after this long propagation when compared to absolute value of their variables, which shows the good performance of the methodology even for high eccentric orbits. Additionally, and if we compare this result with the long-term errors obtained from the sun-synchronous orbit (Fig. 3 ), we observe a decrease in the absolute accuracy due to the higher variation of the variables. Nevertheless, the relative error is still in the same order of magnitude. Figure 6. Long-term error evolution in the radial distance, the latitude, and the longitude for a Molniya orbit. 6.3.3 Example: hyperbolic orbit For the final example, we select an hyperbolic orbit to show that this formulation can also be successfully applied to this kind of trajectories. To this end, an orbit with the following initial orbital elements is used: a = −35 000.0 km, e = 1.2, , , , and . Figs 7 and 8 show the solution for these initial conditions. Note that, since the orbit is hyperbolic, only a section of the orbit was


O O O O O O O O O O O O O O O O O O O O O B-Person O B-Person I-Person O O O O O O B-Person I-Person O O O O O O O O O O B-Organization I-Organization O O O O O O O O O O O B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O O O B-Organization O B-Grant B-Person O O O O O B-Organization O B-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization O O B-Organization O O O O B-Organization B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-URL O O O O O O B-Organization B-ComputingFacility I-ComputingFacility B-Grant I-Grant I-Grant B-Organization B-Grant I-Grant I-Grant B-Organization B-Grant I-Grant I-Grant I-Grant O B-Organization I-Organization B-ComputingFacility O O O O B-ComputingFacility I-ComputingFacility B-Person O O O 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 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 B-Model 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 B-Telescope O O B-ObservationalTechniques O O B-ObservationalTechniques 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 B-Dataset I-Dataset O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Dataset I-Dataset I-Dataset 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 B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope 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 B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-ObservationalTechniques O O O O O O B-Telescope B-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope O O B-Instrument I-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope 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 O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O

the surface brightness of the SZE signature is independent of the cluster redshift, which together with the expected temperature and density evolution of the cluster ICM at fixed virial mass and the changing solid angle of clusters with redshift lead an SZE signal-to noise-selected sample to be approximately mass-limited (Haiman, Mohr Holder 2001 ; Holder, Haiman Mohr 2001 ). Because we plan to carry out a dynamical analysis, the cluster sample we analyse includes only those SPT systems with spectroscopic follow-up. This spectroscopic subsample is not a signal-to-noise-selected sample, but rather is the largest sample of SPT-selected clusters we could assemble for the analysis. We plot the sample of 110 clusters in the space of redshift versus mass in Fig. 1 , together with the full distribution of the SPT–SZ sample with the latest available redshifts (Bayliss et al. 2016 ; Khullar et al. 2018 ; Strazzullo et al. 2018 , Bocquet et al., in preparation) . Note that in comparison to the SPT–SZ cosmology sample (de Haan et al. 2016 ), the median redshift and mass for our sample is 0.56 and 7.26 × 10 14 M ⊙ as compared to 0.55 and 6.08 × 10 14 M ⊙ . Approximately 6 per cent of the sample lies at > 1 as compared to ∼9 per cent of the full SPT–SZ ξ > 5 sample (with updated redshifts from Bocquet et al., in preparation). Thus, in comparison to the complete SPT–SZ sample, the subset of those clusters we study here have somewhat higher masses and are somewhat under-represented at high redshift. Full information on the cluster sample is provided in Table 1 . From left to right, the columns correspond to the SPT cluster designation, the total number of passive galaxy redshifts available, the number of passive galaxy member redshifts, the cluster redshift, the SZE-based mass , and the corresponding virial radius (described in Section 3.3.1 ). Figure 1. Masses versus redshifts of the cluster sample. The coloured dots are coded according to the number of member galaxies in each cluster (see colour bar on right). Overplotted in grey is the full distribution of the SPT–SZ sample. Table 1. Cluster spectroscopic sample: we present the cluster name, total number of passive galaxies in the spectroscopic sample N tot , members used in our analysis after interloper rejection N mem , cluster redshift clus , and cluster mass and corresponding virial radius from Bocquet et al. ( 2015 ). 3.2 Spectroscopic sample We use spectroscopic follow-up including data taken using the Gemini Multi Object Spectrograph (Hook et al. 2004 ) on Gemini South, the Focal Reducer and low dispersion Spectrograph (Appenzeller et al. 1998 ) on VLT Antu, the Inamori Magellan Areal Camera and Spectrograph (Dressler et al. 2006 ) on Magellan Baade, and the Low Dispersion Survey Spectrograph (Allington-Smith et al. 1994 ) on Magellan Clay. We combine the data sets presented in Ruel et al. ( 2014 ) and Bayliss et al. ( 2016 ) with the one described in Sifón et al. ( 2013 ), obtaining a sample of


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We thank the referee for his/her helpful comments. This work is supported by the Natural Science Foundation of China (grants 11078014, 11233006 and 11220101002).