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proportional to the disk pebble surface density, but weakly dependent on time. In the default model we adopt a constant pebble flux of Ṁ peb = 100 M ⊕ Myr −1 (consistent with Eq. ( 14 ) of Lambrechts Johansen 2014 ) and neglect the time dependence for simplicity. A lower Ṁ peb means an intrinsic metal-deficient/less massive disk and the planetesimals and planets take longer to grow by pebble accretion. On the other hand, the pebble flux cannot be too high as the density ratio between pebbles and gas would otherwise exceed unity ( ρ peb ∕ ρ gas > 1) and the streaming instability will be triggered over the entire disk. The above inequality can be written as Σ peb ∕ H peb > Σ gas ∕ H gas where the scale height of the pebble is given by ( Youdin Lithwick 2007 ) The pebble flux therefore needs to be smaller than 2 πrv r Σ gas H peb ∕ H gas . Our default value is well below this limit. We also explore two additional pebble fluxes, Ṁ peb = 200 M ⊕ Myr −1 and 50 M ⊕ Myr −1 , in Sect. 4 . The pebble mass can be measured from (sub)millimeter dust continuum emission from the young protoplanetary disks. The inferred values are from a few Earth mass to a few hundreds of Earth mass ( Ricci et al. 2010 ; Andrews et al. 2013 ; Ansdell et al. 2017 ), which is correlated with the gas disk accretion rates ( Manara et al. 2016 ). For a typical T Tauri star with a disk accretion rate of 10 −8 M ⊙ yr −1 , the dust mass is ~ 100 M ⊕ (Fig 1 of Manara et al. 2016 ), consistent with our adopted fiducial value. In Eq. ( 8 ), α t is the coefficient of turbulent gas diffusivity, which is different from the concept of turbulent viscosity α ν . We nevertheless note that the above two quantities are approximated to be the same when the turbulence is driven by magnetorotational instability ( Johansen Klahr 2005 ; Zhu et al. 2015 ; Yang et al. 2018 ). The value of α t can be constrained from the moleculeline broadening measurements ( Flaherty et al. 2015 , 2017 ) and the level of dust settling ( Pinte et al. 2016 ). We adopt a fiducial value of α t = 10 −3 and test the influence of a lower turbulent disk ( α t = 10 −4 ) in Sect. 4 . For pebbles we adopt a fiducial aerodynamical size of τ s = 0.1. This chosen value is consistent with the sophisticated dust coagulation model ( Birnstiel et al. 2012 ) and disk observations ( Tazzari et al. 2016 ). A lower τ s = 0.03 is also explored in Sect. 4 . A fraction of pebbles will be accreted onto a planetesimal when pebbles drift through its orbit. The pebble accretion efficiency ( ε PA = Ṁ PA ∕ Ṁ peb ) is taken from Liu Ormel (2018) and Ormel Liu (2018) . This quantity depends on the disk properties ( τ s , η , α t ) and the planet properties ( m p , a , e , i ). In the limit of 2D and 3D pebble accretion these are given by and respectively, where Δ v is the relative velocity between the planet and the pebble, h peb = H peb ∕ r , is the aspect ratio of the pebble disk. In Eq. ( 10 ) we have already assume that i h peb . The above


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WDs should have lower Ṁ than novae with lighter WDs. The fact that heavier WD novae require a smaller total accreted mass to ignite the thermonuclear explosion ( Shara et al. 2010 ; Glasner Truran 2009 ; Yaron et al. 2005 ) does not seem to provide any insight into how this would control Ṁ between OBs. Furthermore, while binaries with massive WD and high Ṁ may “disappear” from the diagram because they become common envelope systems ( Nomoto 1982 ), there appears to be no obvious way to hide the other missing M WD − Ṁ combinations (unless they become other kinds of CVs?). A tempting speculation, if this distribution is confirmed, is that the strip populated by the old novae discussed here may define the range of Ṁ and t 3 values where novae can occur. Observational Ṁ determinations for more (old) novae are clearly needed before exploring this idea any further. 12.5. Correlation between <italic>Ṁ</italic> and OB amplitude An interesting correlation exists between the OB amplitude and Ṁ (see Fig. 6 ) that associates large amplitude to low Ṁ . In hindsight, this is not completely surprising given the correlation between and Ṁ reported in Sect. 12.1 . Unlike that correlation, which requires knowledge of several physical parameters (distance, inclination, etc.), this one has as independent variable: the observed OB amplitude (i.e., the difference between two apparent magnitudes). Fig. 6. Correlation between accretion rate and the OB amplitude. Top panel : Ṁ computed using individual WD masses. Bottom panel : Ṁ computed using M WD = 1 M ⊙ for each nova. That the correlation exists without the correction for inclination is somewhat surprising, and may be due to the fact that for most of our novae the correction is relatively small. This would also explain why DQ Her, the nova in the sample with the largest i correction, appears as an outlier in Fig. 6 . Nevertheless, this correlation provides a direct way to estimate Ṁ for any nova for which only the OB amplitude is known. Thus, the OB amplitude acts as a proxy for Ṁ , much in the way that t 3 does (see Sect. 12.4 ). It should be noted that Schmidtobreick Tappert (2015) suggested that novae with large OB amplitudes are candidates for low-mass-transfer-rate systems, but they assumed that the absolute magnitude of a nova explosion differs only slightly for different systems, unlike what is shown by the L / L Edd and the MMRD relations; see Figs. 1 and 2 . The fits in terms of the explicit observables, computed as described in Sect. 2.2 , are 13. Concluding summary The new and precise distances from Gaia , together with the data of Paper I and from the literature, allowed us do determine new system parameters for our sample of 18 old novae with UV data (e.g., M v max , , L OB / L Edd , , Ṁ ). The final values include a detailed treatment of the errors and their propagation and are summarized in Table 2 . Functional relations are provided in the text for all correlations (either revisited or new) presented


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

a method to infer the slope of the underlying DM halo at the average half-light radius , finding that both the Fornax and the Sculptor dSph must be embedded in DM haloes with constant-density cores, in conflict with the centrally divergent density cusps of haloes in DM-only simulations (the cusp/core problem ). Laporte, Walker Peñarrubia ( 2013 ) subsequently showed that also for triaxial DM haloes, the Walker Peñarrubia ( 2011 ) method gives reliable lower limits on the slope Γ. Sawala et al. ( 2015 ) use halo masses derived by Peñarrubia et al. ( 2008a ) for Milky Way dSphs using the Walker et al. ( 2009c ) estimator to motivate their corrections to stellar mass–halo mass relations obtained from abundance matching based on DM-only simulations. More recently, Fattahi et al. ( 2018 ) make use of the Wolf et al. ( 2010 ) estimator to study the tidal evolution DM haloes of the apostle simulations compatible with the observed kinematics of Milky Way dSphs. In this contribution, we study a virial mass estimator which is minimally affected by our ignorance on two key parameters: (i) the shape of the inner DM halo profile, and (ii) the spatial segregation of the stellar tracers within the DM halo. The use of the projected spherical virial theorem has several advantages over Jeans analysis for the construction of mass estimators: The virial theorem does not contain any functional dependence on β( r ) and thereby avoids the mass–anisotropy degeneracy. Also systematic biases of inferred enclosed masses and slopes Γ follow directly from the assumptions made on the DM and stellar density profiles and are independent of sample size. Furthermore, the average squared dispersion is a sum over all stars and does not require any binning of data. This makes mass estimators based on the virial theorem applicable also to systems with only few stellar tracers – carefully factoring in the uncertainties due to sample size on the measured squared velocity dispersion as pointed out by Laporte, Agnello Navarro ( 2018 ). This paper is structured as follows: in Section 2 we introduce the spherical virial theorem and discuss the systematics of mass estimators for dwarf galaxies consisting of a stellar tracer population embedded inside a DM halo. In Section 3 , we construct a mass estimator which is tailored to minimize the uncertainty introduced by our ignorance on the central slope of the underlying DM profile as well as on how deeply embedded the stellar component is within the DM halo. We do test this mass estimator on a catalogue of N -body mocks. Section 4 discusses how to obtain the total halo masses of dwarf galaxies, breaking the degeneracy between structural parameters constrained by use of the virial theorem with the help of controlled cosmological simulations. In Section 5 , we estimate the masses of Milky Way dwarf galaxies using the methods introduced in the previous sections, and discuss implications of the derived stellar mass–halo mass relation for


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T.N.-C., M.G.L., and A.V. are supported by NASA through the LWS program. T.N.-C. is supported by MFI/ Wind and SECCHI/STEREO NASA missions. A.V. is supported by JHU/APL internal funds. C.F. and W.Y. are supported by MNX13AP39G.


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We analyzed the burst spectra of the RB with the same model, and yielded an acceptable reduced χ 2 . However, the disk kT is up to 3 keV, which is too high for an NS X-ray binary. 4. Discussion and Summary We have analyzed the decay phase of the outburst experienced by the RB during 2017 observed by Insight-HXMT in a broad energy band. By stacking the type-II bursts with recurrence time of 100–300 s, we find for the first time a time delay of about 3 s at hard X-rays. The energy spectrum of the burst can be denoted by a Comptonization model, for which the temperature of the seed photons, the optical depth, and the temperature of the hot plasma are derived with values of 0.2 keV, 9–10, and 2–3 keV, respectively. These findings put more constraints upon the models at work for the RB. The tight relation between the burst strength and the waiting time (Lewin et al. 1976 ) leads to a series of models in history proposed via focusing on the sudden release of the accretion power in the disk. Type-II bursts can be caused by the instability of the disk on viscous (Lightman Eardley 1974 ) or thermal timescales (Shakura Sunyaev 1976 ), the magnetic barrier (D’Angelo Spruit 2010 , 2012 ), or the magnetic reconnection on the disk (Jiang et al. 2014 ). However, all models have their own shortages in covering all the features observed in the RB (Lewin et al. 1993 ). The possible breakthrough to discriminate different models may come from the joint observations carried out in 2015 by XMM, Swift/XRT, and NuSTAR (van den Eijnden et al. 2017 ). With this campaign, both the continuous and the mode-0 burst spectra were well measured in a rather broad energy band of 1–30 keV. It turns out that the inner radius keeps staying at round 41 R g ( R g = 2 GM /c 2 ) for both burst and pre-burst emissions, and the corona temperature of the pre-burst is 7.19 keV, which is significantly larger than 2.42 keV measured for the nonthermal temperature of the burst. Comparison for the corona temperatures between burst and pre-burst are always challenged by the contamination source 4U 1728–34, which is located only 05 away from the RB. We note that less change of the burst temperature with respect to the pre-burst was reported in ACSA (Mahasena et al. 2003 ) and BeppoSAX (Masetti et al. 2000 ), which is probably due to limited bandwidth (i.e., below 10 keV) of the former and the relatively poorer statistics of the latter that does not allow us to well constrain the parameters in the comptt model. If the burst is caused by the temporary accretion on the disk, via either disk instability or the magnetic barrier, the inner disk radius should evolve to be smaller than that of the pre-burst. Regarding the temperature difference of the corona between burst and pre-burst, the hot corona wherever it is located, either in the boundary layer or around the disk, can in principle be cooled by the seed photons of the burst shower. However, in history there are no hints for detecting such a


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Acknowledgements Rosetta is a European Space Agency (ESA) mission with contributions from its member states and the National Aeronautics and Space Administration (NASA). This work has made use of the Automated Multi Dataset Analysis (AMDA) and Rosetta Plasma Consortium Quicklook database, provided by a collaboration between the Centre de Données de la Physique des Plasmas (supported by Centre National de la Recherche Scientifique (CNRS), Centre national d'études spatiales (CNES), Observatoire de Paris and Université Paul Sabatier, Toulouse), and Imperial College London (supported by the United Kingdom Science and Technology Facilities Council). Support by the Swedish National Space board is acknowledged, including contracts 109/12, 135/13, 166/14 and 168/15. The work at the University of Oslo is partly supported by the Norwegian Research Council, grant number 240000. The contribution from the Space Research Institute of the Austrian Academie of Sciences was made possible by the funding of the Austrian Science Funds FWF P 28100-N36.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O B-Instrument I-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O O B-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey B-Dataset I-Dataset O O O B-Survey 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 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 B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength B-Wavelength O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength 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

to apply to large amounts of spectroscopic data even in the presence of large redshift errors in the standard pipeline. This algorithm selects a relatively small number of candidates from the large data set for visual inspection to confirm the correctness of the identification. While the false negative rate is very small based on a small test sample of known post-starburst galaxies, the false positive rate to be removed by visual inspection is between 100% and 300%. At this point, the amount of visual inspection required is still manageable, but a more optimized algorithm with a lower false positive rate will be critical when the next generation of surveys generate significantly larger samples. Examples of such surveys are the fourth phase of the SDSS-IV (Dawson et al. 2015 ), the Dark Energy Spectroscopic Instrument (Levi et al. 2013 ), and the Prime Focus Spectrograph (Takada et al. 2014 ). For SDSS and BOSS data in particular, it was found in retrospect that the redshift determination by the spectroscopic pipeline is very robust, with less than 5% incorrect redshifts even for this rare class of objects. Therefore, selecting the post-starburst galaxies from SDSS and BOSS assuming the pipeline redshifts to be reliable would have simplified the process and reduced the number of false positives significantly. In light of this, there are some improvements to incorporate the future work selecting post-starburst galaxies from large spectroscopic surveys. One such data set in the near future would be the entire BOSS (SDSS DR12). This phase of SDSS contains twice as many spectra than what we used in this paper, and it is now public (Alam et al. 2015 ). The first improvement might be to do the selection based on the stellar population properties, rather than empirical cuts on parameters such as A/Total or equivalent widths. Ideally, this approach is more preferable since it would lead to selection based on physically meaningful properties of the galaxy population such as stellar population age and metallicity. For example, one might define post-starburst galaxies to be populations that are older than 300 Myr but younger than 1 Gyr. Yesuf et al. ( 2014 ) fit stellar population models using multiwavelength data while taking AGNs and dust obscuration into account. Selection of these objects from the next generation of multiband photometric surveys is another possibility. Doing so requires distinguishing between the 3600 Å Balmer break and the 4000 Å break at slightly different redshifts. One can potentially resolve this ambiguity using multiwavelength information, for example, in near-UV (NUV) and near-IR (NIR), since the old population would have almost no flux in NUV but large flux in NIR, and conversely for the young population. Wild et al. ( 2014 ) studied galaxy SEDs in optical and NIR and found that post-starburst galaxies have unique, identifiable colors. However, the presence of dust and AGNs would make this task challenging. 7. CONCLUSION The


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

that the age and metallicity distributions are Gaussian, with , σ T = 2 Gyr (e.g., Kalirai 2012 ), , and σ Fe/H = 0.5 (e.g., Xue et al. 2008 ). We model the resulting weighted CMD with a kernel density estimate (KDE), using a kernel bandwidth of 0.025. The resulting pdf’s for M F814W , for six different colors, are shown in Figure 11 . Figure 11. Normalized pdf’s for absolute magnitude for six different choices of m F606W − m F814W color. These pdf’s are derived from the KDE constructed from the VandenBerg et al. ( 2006 ) isochrones, weighted by a Salpeter IMF and the approximate age and metallicity distributions of the halo. Using the pdf for absolute magnitude as a function of color in conjunction with the halo density profile (Deason et al. 2011 ), we derive the pdf for the log distance distribution to our sample:where is the probability of log D given the Deason et al. ( 2011 ) density profile, and is the probability of object n having absolute magnitude M F814W (log D ) given its color m F606W, n − m F814W, n . 6 6 In the COSMOS field, in the area where we used additional catalogs for selection, we used the Subaru B and V photometric measurements from Capak et al. ( 2007 ) and converted these to STMAG F606W as directed by Sirianni et al. ( 2005 ). We used the F814W magnitudes as published in the Leauthaud et al. ( 2007 ) catalog. We then estimate the mean distance to each field . Each of the four fields has an average distance . Figure 12 shows the cumulative logarithmic distance pdf’s of our samples across the four fields, and average distances to each field are listed in Table 5 . We note that no kinematic information is incorporated into our distance estimate and that information from 3D kinematics will improve our distance estimates in subsequent work. Figure 12. Cumulative distance distributions for the four HALO7D fields. Distance distributions are computed as given by Equation ( 13 ), using colors and assuming an MW stellar density profile (Deason et al. 2011 ). All fields have . Figure 13 shows the LOS dispersions of the four HALO7D fields plotted as a function of mean galactocentric radius (where we have converted heliocentric distance to galactocentric radius ). Points indicate the median of the σ LOS posterior samples, and error bars indicate the 16th and 84th posterior percentiles. We compare our results to the velocity dispersion profiles measured in other studies. The figure also shows measured velocity dispersion profiles from SDSS BHB stars (Xue et al. 2008 ; black dashed line), BHB and blue straggler (BS) stars from the Hypervelocity Star Survey (Brown et al. 2010 ; gray dot-dashed line), and the SEGUE K -giant survey (Xue et al. 2016 ; connected black circles). The measured LOS velocity dispersions in the HALO7D fields using MSTO stars are consistent with other studies that have measured the LOS velocity dispersion profile over our distance range. Figure 13. LOS velocity dispersions of the four HALO7D fields, plotted


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The authors want to thank the referee for useful and constructive comments. We acknowledge the crucial contribution of the ESO staff for the management of service observations. In particular, we are deeply grateful to M. Hilker for his constant help and support of this program. Italian participation in VIPERS has been funded by INAF through PRIN 2008, 2010, and 2014 programs. L.G. and B.R.G. acknowledge support of the European Research Council through the Darklight ERC Advanced Research Grant (# 291521). O.L.F. acknowledges support of the European Research Council through the EARLY ERC Advanced Research Grant (# 268107). A.P., K.M., and J.K. have been supported by the National Science Centre (grants UMO-2012/07/B/ST9/04425 and UMO-2013/09/D/ST9/04030). R.T. acknowledge financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n. 202686. E.B., F.M., and L.M. acknowledge the support from grants ASI-INAF I/023/12/0 and PRIN MIUR 2010-2011. L.M. also acknowledges financial support from PRIN INAF 2012. Research conducted within the scope of the HECOLS International Associated Laboratory, supported in part by the Polish NCN grant Dec-2013/08/M/ST9/00664.


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ACKNOWLEDGEMENTS CC’s work is based upon research supported by the South African Research Chairs Initiative (SARChI) of the Department of Science and Technology (DST), the SKA SA, and the National Research Foundation (NRF). ND’s work is supported by a SARChI’s South African SKA Fellowship. LMW is supported by the Natural Sciences and Engineering Research Council of Canada through Discovery Grants. The numerical simulations were performed at the Centre for High Performance Computing.


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The authors thank the anonymous referee for useful comments and suggestions, which have improved this manuscript. Z.C.M. gratefully acknowledges support from the John F. Burlingame and the Kathryn McCarthy Graduate Fellowships in Physics at Tufts University. D.M. and Z.C.M. acknowledge the support of the Research Corporation for Science Advancement’s Cottrell Scholarship, the support from Tufts University Mellon Research Fellowship in Arts and Sciences. We thank Gabriela Calistro Rivera for her support on the implementation of AGNfitter . This study is partially based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under program ID 087.A-0514. Some of the data presented in this study were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. Keck telescope time was granted by NOAO, through the Telescope System Instrumentation Program (TSIP). TSIP is funded by NSF. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. This study makes use of data from the NEWFIRM Medium-Band Survey, a multi-wavelength survey conducted with the NEWFIRM instrument at the KPNO, supported in part by the NSF and NASA. We thank the NMBS and COSMOS collaborations for making their catalogs publicly available. The combination of NEWFIRM Medium-Band Survey and Herschel data was supported by the National Aeronautics and Space Administration (NASA) under grant number NNX13AH38G issued through the NNH12ZDA001N Astrophysics Data Analysis Program (ADAP).


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O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization O O B-Grant B-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal O B-Grant B-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal O O O O B-Location B-Telescope O O O O B-Organization I-Organization I-Organization O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-URL O B-Observatory B-Observatory B-Instrument O O O O O O B-Organization

Acknowledgements Financial support by the Spanish Ministry of Economy and Competitiveness and the European FEDER Fund through projects AYA2014-60476-P (Solar magnetometry in the era of large solar telescopes) and AYA2014-60833-P (Spectropolarimetry: a window to stellar magnetism) is gratefully acknowledged. The German VTT is operated by the Kiepenheuer-Institut für Sonnenphysik at the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias (IAC). This paper made use of the IAC Supercomputing facility HTCondor ( http://research.cs.wisc.edu/htcondor/ ). NSO/Kitt Peak FTS data used here were produced by NSF/NOAO.


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T.M.D. and G.S.C. were funded by STFC grant ST/J001260/1. P.A.B. acknowledges the support of the Australian Research Council via the Australian Laureate Fellowship scheme. We thank the developers of iSALE ( www.isale-code.de ) and are grateful to Fred Ciesla for discussions about the equilibration timescale calculations. We thank the anonymous reviewer for their valuable comments.


O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Telescope B-Instrument B-Wavelength I-Wavelength I-Wavelength B-Wavelength O O O B-Wavelength I-Wavelength O B-Wavelength O O O B-Wavelength I-Wavelength O B-Wavelength O B-Wavelength O O O B-Wavelength I-Wavelength O O O O B-Wavelength O O O O B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength 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 B-Wavelength 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 B-Telescope O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Software O O O B-Wavelength 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Software I-Software 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 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 B-Telescope B-Telescope B-Wavelength O O O B-Telescope B-Wavelength O O O O O O O O O O

bin with observed rest-frame wavelength. Here, we supplement the FUV and NUV results from this study with data used in our previous study (Taylor-Mager et al. 2007 ), which includes HST WFPC2 mid- to near-UV (F255W, λ c = 255 nm and F300W, λ c = 293 nm) and NIR data (F814W, λ c = 823 nm), as well as ground-based UBVR ( λ c = 360, 436, 540, and 634 nm, respectively) data from the VATT. Solid error bars indicate the error on the median, while dashed error bars give the 25%–75% quartile ranges, which indicate the spread of the data. The number statistics in the FUV and NUV are vastly improved in this study, which has resulted in much smaller error bars for each of the spiral, irregular, and peculiar galaxy type categories. Figure 5. Median CAS values in each type bin as a function of wavelength. Solid error bars indicate the error on the median, and dashed error bars indicate the 25%–75% quartile range of the data. The GALEX data (two left-most data points in each panel) are supplemented with HST and ground-based data. Circled data points: low GALEX S values are due to its poor (5 arcsec stellar FWHM) resolution. Disregarding this effect results in higher S values more in line with the trend displayed at longer wavelengths. In general, galaxies are more asymmetric and more clumpy at shorter rest-frame wavelengths, especially in the UV. This causes them to appear overall later type than they would at longer wavelengths. Sa-Sc galaxies appear less concentrated at shorter wavelengths, while Sd-Im and pec/mer galaxies do not exhibit a strong concentration versus wavelength relationship. The effect in the UV is particularly pronounced for elliptical/lenticular galaxies, which have little difference in their CAS parameters in the near-UV through the NIR, but appear significantly less concentrated, more asymmetric, and slightly more clumpy in the far-UV. For Figure 5 we reprocessed the Taylor-Mager et al. ( 2007 ) data through the newest version of the CAS code, as it treats background removal differently (utilizing the entire image with objects masked out via SExtractor catalogs versus a small user-defined box of empty sky). This had a minor impact on a small number of data points as compared to our 2007 results from the previous version of the code, but the overall trends with wavelength remain the same. This demonstrates that the difference in background subtraction methods does not have a significant impact on our conclusions. We rejected any median data points derived from fewer than five HST galaxies, as these low number statistics would produce unreliable results. Most panels in Figure 5 show a consistent general trend in CAS values as a function of rest-frame wavelength. A major exception is the clumpiness ( S ) parameter for all galaxy types except E/SO, where S increases significantly with decreasing wavelength, then drops dramatically between the HST /VATT UV and the shorter GALEX NUV wavelength (the second data point from the left in each


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

with indirect estimates of the helium spread, based on the morphology of the HB. For the clusters for which these estimates were available, it was possible to verify a satisfactory consistency. The APOGEE data used in this work are of paramount importance, because they confirm that the material from which SG stars formed was exposed to a very advanced nucleosynthesis, with the activation of Mg burning and, in the most metal-poor clusters, the synthesis of silicon. This is of great help in the way towards the understanding of the possible GC polluters, because the possibility that either fast-rotating massive stars (Krause et al. 2013 ) or massive binaries (De Mink et al. 2009 ) played a role in this context can be ruled out. Indeed in neither of the two cases the temperatures of the nuclear burning regions are sufficiently hot to allow such an advanced nucleosynthesis. The only possibility left besides the massive AGB scenario is super massive main sequence stars. As shown by Denissenkov Hartwick ( 2014 ), the core temperature during H-burning reach ∼70 MK, thus triggering the activation of Mg burning and the production of aluminium. A straight comparison between the predictions of the AGB hypothesis and the chemical patterns expected when pollution from super massive stars is considered is cumbersome, because while it was shown that in the interiors of this class of objects the ignition of Mg burning occurs, the trend with metallicity, if any, needs further investigation. While in the AGB case the sensitivity of the HBB nucleosynthesis to the metallicity is a direct result of stellar evolution modelling, it is not clear how the chemical composition would affect the core H-burning of super massive stars. At the moment, this problem is still open. 6 CONCLUSIONS We discuss the chemical composition of giant stars in nine Galactic GCs, for which the abundances of C, N, O, Mg, Al, and Si are available. The wide range of metallicities ( − 2.4 [Fe/H] -0.7) and the simultaneous knowledge of the elements mentioned above offer a valuable opportunity to test the origin of multiple populations in these complex stellar systems. We concentrate on the possibility that the polluters of the intra-cluster medium, providing the gas from which SG stars formed, were massive AGB stars (), which experienced HBB at the base of their external envelope. To this aim, we calculated ad hoc AGB models, with the same metallicity and the same mixture of the stars belonging to the FG of each cluster. In agreement with previous studies on GCs in the Milky Way, we find that all the clusters show the presence of SG stars, as deduced on the star-to-star chemical differences, which define abundance patterns in the different observational planes. We find that the chemical patterns observed (Mg, Al, Si, and O in particular) are in good agreement with the theoretical expectations: (a) on the qualitative side, the spread observed for the different species follows the results from AGB


O O 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 B-URL O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-URL O O O O O O O O O O O O O B-Telescope O O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O B-URL 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 B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


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fixed tile must be smaller than the image separations, which are not known a priori. The sky area spanned by strongly lensed images, however, is ≲arcsec 2 ( Schneider et al. 2006 ; Collett 2015 ), and investigating it at such fine resolution is highly time-consuming. Nevertheless, when both galaxies or galaxy clusters and microlenses are involved, a complete solution of the system requires identification of strongly lensed and microlensed images. In addition, the overall potential may vary profoundly on short length scales. This is particularly true when many microlenses are involved: standard integrators may stall and oscillate between points corresponding to nearby solutions without converging. Finally, gravitational-wave analysis is performed using signal templates predicted by general relativity (GR). The inference of compact source parameters relies on matching gravitational-wave detector strains to a bank of known gravitational waveforms ( Allen et al. 2012 ). This method allowed LIGO and Virgo to unveil a stellar-mass population of binary black holes and produce a catalog of their properties ( Abbott et al. 2019a ), to perform tests of GR ( Abbott et al. 2016c , 2019b , c ), and to detect a binary neutron star coalescence ( Abbott et al. 2017 ). However, lensed signals resulting from the superposition of multiple images can differ significantly from unlensed GWs. As a consequence, matched filtering of lensed GWs with unlensed templates could result in missed detections or possibly biased measurements of the binary parameters. Lensed gravitational waves might also constitute a probe of microlensing. Even when microimages are as close as microarcseconds, observable beating patterns may originate in the GW signal if the time delays between the images are higher than the millisecond time resolution of the interferometers ( Lai et al. 2018 ; Abbott et al. 2019a ). Thus, lensed templates might unveil microlenses and dark matter substructures on the path traveled by the wave ( Liao et al. 2018 ). Therefore we must be able to predict GW signals from arbitrary lens configurations. LENSING GW has been designed to address these necessities: on the one hand, it implements a new solver tailored to handle very different scales in the lens potentials; on the other hand, it supplies unlensed and lensed GW signals from arbitrary lensed systems through dedicated modules. Such lensed waveforms can serve as injections in parameter estimation (PE) studies to demonstrate the inference of astrophysical parameters of lensed compact sources through Bayesian analysis. We will demonstrate Bayesian PE of lensed systems solved with LENSING GW in a follow-up study (Pagano et al., in prep.). The source code of LENSING GW and examples are hosted on GitLab 2 . 3.1. Lens equation solver The numerical solver implemented in LENSING GW introduces two novelties: a two-step procedure designed to simultaneously resolve strongly lensed images and microimages, and a dedicated


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Acknowledgements We thank the anonymous referee for valuable comments. GH would like to acknowledge CSIR, India for financial support. ARCs research is supported by J. C. Bose fellowship granted by DST, India.


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

agree well with Equation ( 19 ), though there are substantial differences at lower masses. Better agreement with our models is obtained if , and that is our suggested value. The breakdown below 12 is not particularly surprising. These low-mass SNe have low energy (10 50 erg), but also low 56 Ni mass (). The combination is still appreciable even though the mass of radioactivity itself is very small. If the mass fraction of 56 Ni in a given zone, after mixing, is less than about 0.001, the decay energy, erg g 1 , of 56 Cowill, after time , be only a small fraction of the internal energy at recombination, erg g 1 , and recombination will not be greatly affected. For the very low mass explosions and mixing prescription assumed, the cobalt abundance is below this limiting value in all zones except at the very base of the hydrogen envelope. In any case the correction factor is small, less than 10, in these low-energy explosions. Combining our best fit to the no-radioactivity models with this best-fit correction factor results in good agreement with the full set of models with radioactivity included (Figure 34 ). As expected, most of the large deviations are for the lightest and heaviest stars. For small stars, the scaling relation overestimates the plateau duration because the correction term, , is too big. At high mass, there are cases with a large amount of fallback (Figure 13 )and therefore no 56 Ni production. Indeed, such short plateaus in massive stars with normal luminosities (Figure 31 ) may be an observable signature of BH formation. Figure 34. The scaling laws that showed good agreement in Figure 32 are now compared against the standard explosion models with their 56 Ni included. The models used are from the Z9.6 and N20 series. A red vertical bar represents a range of possible plateau durations calculated from the models assuming that (1) the photospheric radius had receded to 50 of its maximum value (lower bound)or (2) the whole star had recombined (upper bound). Black points result from multiplying Equation ( 14 ) with C t = 88 by the correction term, Equation ( 19 ), with C f = 50. 7.1.3. Systematics Given the generally good agreement of our SN IIp model characteristics with analytic expressions, it is worth exploring whether these systematics can be exploited to obtain insights into the masses and energies of observed events. Another interesting question is whether SNe IIp, or some subset, can be used as standard candles. Neglecting the radioactive correction, Equation ( 19 ), the luminosity and plateau duration are proportional to powers of the explosion energy, pre-SN radius, and envelope mass. These are not independent variables. The radius of the pre-SN star increases monotonically with its main-sequence mass, ,andto good approximation in the mass range where most SNe IIp occur (920 ), (Figure 35 ). Above 20 , the hydrogen envelope mass of the pre-SN star declines with owingto mass loss, but below 20 , it too has a monotonic


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ACKNOWLEDGEMENTS We sincerely thank the referee for valuable suggestions on the paper. This research is in part based on the data obtained from the Chandra Data Archive, and has made use of software provided by the Chandra X-ray Center (CXC) in the application packages ciao, ChIPS , and Sherpa . This research has used observations obtained with XMM–Newton , and the ESA science mission, with instruments and contributions directly funded by ESA Member States and NASA. C-PH and C-YN are supported by a GRF grant from the Hong Kong Government under HKU 17300215P. WCGH acknowledges support from STFC in the UK through Grant No. ST/M000931/1.


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ACKNOWLEDGEMENTS This work was supported by the UK Science and Technology Research Council (STFC) No. ST/M001334/1 and the COST action MOLIM No. CM1405. This work made extensive use of UCL’s Legion and DARWIN and COSMOS high performance computing facilities provided by DiRAC for particle physics, astrophysics and cosmology and was supported by STFC and BIS.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O 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 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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

data. Therefore, as a first step, we have computed the autocorrelation function (Equation ( 9 )) on timescales of up to 100 years for different directions on the celestial sphere. These autocorrelation functions can be formally approximated by a superposition of several components decreasing exponentially with different characteristic times T i . In contrast to the standard deviation, the characteristic decay time of exponents depends not only on the direction on the celestial sphere but also on the lower limit of integration over coordinates ( R min ), as can be seen from Figure 4 . Note, that the behavior of autocorrelation functions for both galactic models (DB and BS) is similar; therefore, in the following analysis, we are restricted only by the DB model. With increasing of R min , i.e., with increasing the minimal impact parameter, the characteristic decay time of exponents becomes larger, which seems quite natural. At the same time, varying the parameters of calculation does not affect an exponential form of the normalized autocorrelation function. Figure 4. Normalized autocorrelation functions calculated for the DB model for two directions in the sky at different minimal impact parameters. For the autocorrelation function in a form of a decaying exponent , the PSD is simplywhere T is characteristic time of the exponent, and . From this formula and Figure 5, it is clearly seen that on the reasonable observing timescales (up to one hundred years) the PSD index equals −2 for any direction on the celestial sphere and does not depend on the characteristic time. Thus, if an analysis of the apparent celestial positions of extragalactic sources, including the reference sources of the ICRF, reveals a component with a slope of −2 in their power spectra, this component can be explained by the collective influence of stars and compact objects in the Galaxy. Figure 5. Spectral index of PSD calculated for two exponents with the characteristic time of 100 and 1000 days. For the analysis of astrometric observations of staggering precision, it is important to know an expected value of the jitter of reference sources, arising due to the local non-stationarity of the Galactic gravitational field, for a specific time interval. Intuitively, the larger the time interval between observations, the greater the relative offset of sources can be. If we know the behavior of the autocorrelation function of the studied process in time, we can predict the expected value of the jitter (dispersion) for any time interval. For illustration purposes, the dependence of the coefficient (Equation ( 3 )) on time is shown in Figure 6 . This coefficient has been calculated for the DB model for different directions in the sky, and for . To obtain maps of the conditional standard deviation (see Equation ( 3 )), the corresponding coefficients were determined for all sky directions for three time intervals (three months, one year, and ten years) and convolved with the


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We thank the anonymous referee for their helpful comments which improved the clarity of the paper. This research was based on data taken with the Anglo-Australian Telescope. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO) through project number CE110001020. SMC acknowledges the support of an ARC future fellowship (FT100100457).


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

intrinsic to the sources, while intervening material introduces a small but pervasive broadening of the FD distribution. We explore further the implications of the latter effect in Section 6. Further exploration of the properties of the background sources from QU-fitting (O’Sullivan et al. 2012 ; Sun et al. 2015 ) and analysis of the shape of the plots is beyond the scope of the current work, but we plan to develop this further in the future. The results of the QU-fitting will also be very interesting to be compared with . 6. DISCUSSION In this section, we will try to be more quantitative about the size of the Faraday Effects that are associated with the presence of intervening material, as revealed by Mg ii absorption. This will enable us to better characterize the physical properties of this material. We estimate the dispersion of φ introduced by intervening systems. The largest separation in the empirical distribution functions for sources with and without interveners is observed at m −2 . As noted earlier, this value should be treated with caution because the φ resolution limit of our experiment is roughly m −2 for VLA and m −2 for ATCA. The difficulties of the RMSF can to a certain degree be circumvented by simply subtracting in quadrature the median of sources with and without absorbers (since the RMSF has been subtracted from both equally). This yields an estimate for the excess m −2 . The maximum separation seen in the distribution is at m −2 . However, here this value should also be treated with caution because of the non-monotonic structure in and the rather ad hoc approach to choosing the wavelength range for the fit (only longwards of the peak in polarization). Likewise, subtracting the median values of the distribution with and without absorbers in quadrature gives an estimate for the excess m −2 . and attempt to trace by different approaches. The fact that their values are similar gives some confidence that the proposed scenario is self-consistent. From the current work, we will use a value of order 10 rad m −2 as a crude order of magnitude estimate of the FD dispersion that is associated with intervening systems. This is an estimate of the range of the observed φ within (i.e., across the face of) a given intervening system. To convert to the rest-frame of the absorber, we must multiply by , i.e., by a factor of the order of two for our median absorber redshift of , yielding of the order of m −2 . This value is of the same order of magnitude as the spread in Galactic RMs m −2 as estimated by Schnitzeler ( 2010 ). Other works have claimed m −2 for the Large Magellanic Cloud (Gaensler et al. 2005 ) and m −2 for the Small Magellanic Cloud (Mao et al. 2008 ). As in Bernet et al. ( 2008 ), we can crudely associate a φ with an estimate of magnetic field strength using an estimate of the free electron column density in the interveners based on the known Mg ii column density. Assuming a compact absorber system at redshift z and the


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The authors thank the referee Ludovic Petitdemange for numerous useful comments and suggestions, which improved the paper. The simulations have been carried out on supercomputers at GWDG, on the Max Planck supercomputer at RZG in Garching, in the HLRS High Performance Computing Center Stuttgart, Germany through the PRACE allocation “SOLDYN” and in the facilities hosted by the CSC-IT Center for Science in Espoo, Finland, which are financed by the Finnish ministry of education. J.W. acknowledges funding by the Max-Planck/Princeton Center for Plasma Physics and from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 623609. This work was partially supported by the University of Colorado through its support of the George Ellery Hale Visiting faculty appointment, the Swedish Research Council grants Nos. 621-2011-5076 and 2012-5797 (A.B.), and the Academy of Finland Centre of Excellence ReSoLVE 272157 (J.W., M.R., S.T., P.J.K., M.J.K.) and grants 136189, 140970, 272786 (P.J.K).


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ACKNOWLEDGEMENTS We thank Dr. Eleanor Sansom for a helpful and detailed review of an earlier version of this manuscript. Also, we thank Dr. Auriane Egal for suggestions about the modelling of the Draconids. Funding for this work was provided by the NASA Meteoroid Environment Office under cooperative agreement 80NSSC18M0046. PGB acknowledges funding support from the Canada Research Chair program and the Natural Sciences and Engineering Research Council of Canada.


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field, and the interaction between them in a conservative way using Godunov, finite-difference methods (Rezzolla Zanotti 2013 ). The radiation is evolved adopting the M1 closure scheme (Levermore 1984 ). The simulations assume axisymmetry and run in 2.5 dimensions, that is, allowing for non-zero azimuthal vector components. We assume a black hole mass of 10 M ⊙ and evolve the models for roughly 1.2 s, corresponding to ∼165 orbital periods at the pressure maximum of the initial model. The numerical domain extends from r min = 5 to r max = 14 along the radial direction, and from θ = π/2 − 0.3 to θ = π/2 + 0.3 along the θ direction, and it is covered by a uniform (in radius and polar angle) grid composed of 448 × 448 grid-points. We note that the radial resolution is therefore Δ r = 0.02. Standard outflow/no-inflow boundary conditions are adopted at all the boundaries. 2 For simplicity, in this work we adopt only the scattering opacity κ s = 0.34 cm 2 g −1 , and we account for the Comptonization using the ‘blackbody’ method (see Sadowski Narayan 2015 ). Since we do not assume any external heating source, the tori are expected to cool down by emitting the radiation that supports them. 3 RESULTS 3.1 Torus dynamics All the models have been evolved up to t = 25 000, corresponding to ∼165 orbital periods computed at the maximum density radius r c = 8.35. Two purely hydrodynamic models, namely Hydro43 and Hydro53, have been also studied, in order to provide a comparison with respect to the radiative models, which is especially useful in the spectral analysis of Section 3.2 . Because of the radial perturbation introduced, the tori start oscillating in the potential well. However, since the initial models are significantly below the marginally stable configuration, no appreciable mass accretion is induced by the oscillations and the periodic behaviour can last for a long time. In Fig. 1 , a full oscillation sequence at t ∼ 0.1 s is monitored through six snapshots for the model Rad30. The left- and the right-hand panels report the distribution of the rest-mass density and of the radiation energy density, respectively. The arrows in the radiative panels reflect the free-streaming radiation leaving the torus surface. As expected, during the evolution the energy density of the radiation remains concentrated towards the centre of the torus, where the optical depth is the largest. Radiation diffuses out following the gradient of radiative energy density and ultimately leaves the surface of the torus. The distribution of the out coming radiation is determined by the shape of the photosphere. In the case of the tori studied here, most of the radiation is emitted roughly in the direction perpendicular to the equatorial plane. Figure 1. Illustration of a typical oscillation sequence for the model Rad30 through six snapshots (from top to bottom). Left-hand panels: distribution of the rest-mass density with the velocity represented by orange arrows. Right-hand


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ACKNOWLEDGEMENTS The cosmological simulations described in this work were performed using the enzo code ( http://enzo-project.org ) that is the product of a collaborative effort of scientists at many universities and national laboratories. We gratefully acknowledge the ENZO development group for providing extremely helpful and well-maintained on-line documentation and tutorials. Most of the analysis done in this work was performed with the julia code ( https://julialang.org ). F.V. and D.W. acknowledge financial support from the ERC Starting Grant ‘MAGCOW’, no.714196. We acknowledge the usage of computational resources on the Piz-Daint supercluster at CSCS-ETHZ (Lugano, Switzerland) under project s701 and s805. We thank F. Zandanel, J. L. Han, and T. Akahori for useful scientific feedback, and our anonymous referee for valuable suggestions.


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

and reported that the amplitude of cycle 25 will be weaker than that of the current cycle 24. Macario-Rojas, Smith E ( 2018 ) also applied a similar model-based method and predicted the cycle 25 will be 14.4 per cent ( per cent) weaker than the cycle 24. Kakad, Kakad Ramesh ( 2017 ) used the estimation of Shannon entropy to predict a very weak solar cycle (ISSN peaks at 63), similar to th Dalton minimum. Predictions of a very weak solar cycle were also reported by Kirov et al. ( 2017 ), who used a precursor method and the original version of the ISSN. They found that the smoothed monthly mean sunspot number at the maximum of cycle 25 will be within 50–55 range. It should also be noted that the original version of the ISSN is statistically 45 per cent lower than the new version 2. Hathaway Upton ( 2016 ) and Gopalswamy et al. ( 2018 ) used a precursor method and predicted moderate amplitudes of cycle 25, similar to the current cycle 24, while Cameron, Jiang Schüssler ( 2016 ) reported that cycle 25 may slightly stronger than the current one. Pesnell Schatten ( 2018 ) also applied a precursor method by using SODA Index, which is determined by polar magnetic fields and the spectral index. They estimated the next cycle’s smoothed peak activity will be with a possibility of exceeding this early estimation due to the increasing trend of the SODA Index. Jiang Cao ( 2017 ) used a surface flux transport model-based method and concluded that cycle 25 might be stronger than cycle 24. Predictions of similar or stronger cycle 25 as compared to the current cycle 24 are in agreement with our predictions presented in this study. Precursor methods use some measure of geomagnetic activity or polar magnetic fields at a particular time to predict amplitude of the next cycle. In general, this particular time is chosen at the minimum phase of a cycle it may produce misleading results if the selection is made before the ISSN reached the minimum. To the contrary, the approach presented here can be applied at any time during the descending phase, but the starting point should be chosen carefully. There is additional advantage that this method allows us to also predict fluctuations of sunspot numbers during a solar cycle such as double or multiple maxima as can be seen in Figs 2 and 3 . These plots clearly show the accurate predictions of maximum times and amplitudes as well as main fluctuations occurred during solar cycles. Further analysis showed that apart from the embedding dimension and delay-times, performance of this non-linear method is highly dependent on the starting point of the prediction. This is mostly because the algorithm searches for nearest neighbours to the prediction vector, which is formed from the last (( m *τ))) +1 points before the starting point. In this case, the consecutive starting points may yield different prediction vectors and eventually different outcomes. Another explanation for the starting point dependence can be made by analysing


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

results in Tables 3 , A.1 , A.2 ). The addition of this component also significantly improves all the fits. We consider “rdb-rfxconv-pl”, which includes the hard power-law component, rfxconv, as a reflection component smeared by the rbdblur component, to be our best fit model (see Table 3 ). The fit of the XMM-Newton spectra with the same model gave values of the parameters that agree overall with those obtained fitting the NuSTAR spectra. In this case, we found values of the ionization parameter log() ranging between 2.58 and 2.71 (slightly higher, i.e., approx. 3, for the XMM-Newton spectra) and reflection amplitudes between 0.2 and 0.3, indicating a relatively low superposition between the source of the primary Comptonization continuum and the disk (a value of 0.3 would be compatible with a spherical geometry of a compact corona inside an outer accretion disk). For the smearing parameters of the reflection component, we find values of the emissivity index of the disk ranging from 2.8 to 2.48, an inner radius of the disk from 10.6 to , and an inclination angle of the system with respect to the line of sight of . In our results, the inclination angle is higher than that found by ( Miller et al. 2013 ; who report an inclination angle less than ), but is very similar to that estimated from Chandra spectra (, see Chiang et al. 2016a ). Moreover, the inner disk radius we find is not compatible with the ISCO. Assuming a for the neutron star, the inner radius of the disk is located at km from the neutron star center. Note that this value is compatible to the estimated radius of the emission region of the soft blackbody component, which is in the range km. We interpret this component as the intrinsic emission from the inner disk since this is the coldest part of the system and because the temperature of the blackbody component appears to be too low to represent a boundary layer. 5. Conclusions The main aim of this paper is to test the robustness of disk parameters inferred from the reflection component in the case of neutron star LMXBs. To this aim, we used broad-band, moderately-high-resolution spectra of Serpens X-1, a neutron star LMXB of the atoll type with a very clear reflection spectrum that has been studied with several instruments. In particular, we carried out a broad-band spectral analysis of this source using data collected by NuSTAR and XMM-Newton satellites, which have the best sensitivity at the iron-line energy. These data have already been analyzed in literature. In particular, Miller et al. (2013) have analyzed the NuSTAR spectra and obtained a low inclination angle of approximately 8, an inner disk radius compatible with the ISCO, an ionization parameter between 2.3 and 2.6, along with an iron abundance of approximately 3. We performed the fitting using slightly different continuum and reflection models with respect to those used by other authors to fit the X-ray spectrum of this source. Our best fit of the NuSTAR spectrum of Ser


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Eoin Carley is supported by ELEVATE: Irish Research Council International Career Development Fellowship—co-funded by Marie Curie Actions. We would like to thank Sophie Masson and Etienne Pariat for some very useful discussions of this event. We would also like to thank the referee for very useful and constructive comments. We are grateful to the SDO, SOHO , SWAP, RHESSI , FERMI, and GOES teams for open access to their data. The NRH is funded by the French Ministry of Education and the Région Center. Orfées is part of the FEDOME project, partly funded by the French Ministry of Defense. The authors acknowledge the Nançay Radio Observatory / Unité Scientifique de Nançay of the Observatoire de Paris (USR 704-CNRS, supported by Université d'Orléans, OSUC, and RÃ©gion Centre in France) for providing access to NDA observations accessible online at http://www.obs-nancay.fr .


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higher rotational velocities than expected for single stars, we conclude that stellar multiplicity is an important enhancer of rotation in Sun-like stars. Blue stragglers are expected to have a strong enhancement on rotation owing to injection of angular momentum from the donor companion. 5. The rotational braking law We removed from this analysis all the spectroscopic binaries in order to correctly constrain the rotational braking. The non-SB HIP 29525 displays a that is much higher than expected ( km s), but it is likely that this is the result of an overestimated isochronal age ( Gyr). We decided to not include HIP 29525 in the rotational braking determination because it is a clear outlier in our results. Maldonado et al. (2010) found X-ray and chromospheric ages of 0.55 and 0.17 Gyr, respectively, for HIP 29525. We then divided the remaining 65 stars and the Sun in bins of 2 Gyr, and removed all the stars that were below the 70th percentile of in each bin from this sample. Such a procedure can be justified because we verified that 30% of the stars should have above 0.9 by doing a simple simulation with angles drawn from a flat distribution between 0 and . This allowed us to select the stars that had the highest chance of having above . In total, 21 solar twins and the Sun compose what we hereafter reference as the selected sample . Albeit this subsample is smaller, it has the advantage of mostly removing uncertainties on the inclination angle of the stellar rotation axes 7 . We stress that the only reason we can select the most probable edge-on rotating stars () is because we have a large sample of solar twins in the first place. We then proceeded to fit a general curve to the selected sample (see Fig. 5 ) using the method of orthogonal distance regression (ODR, Boggs Rogers 1990 ), which takes the uncertainties on both and ages into account. This curve is a power law plus constant of the form (the same chromospheric activity and vs. age relation used by Pace Pasquini 2004 ; Guinan Engle 2009 ), with (rotational velocity) and (asymptotic velocity) in km s and (age) in Gyr. We find that the best-fit parameters are , , and (see right panel of Fig. 5 ). These large uncertainties are likely due to i) the strong correlation between and ; and ii) the relatively limited number of data points between 1 and 4 Gyr, where the parameters are most effective in changing the values of . This limitation is also present in past studies (e.g., van Saders et al. 2016 ; Barnes 2003 ; Pace Pasquini 2004 ; Mamajek Hillenbrand 2008 ; García et al. 2014 ; Amard et al. 2016 ). On the other hand, our sample is the largest comprising solar twins and, therefore, should produce more reliable results. With more data points, we could be able to use 1 Gyr bins instead of 2 Gyr in order to select the fastest rotating stars, which would result in a better subsample for constraining the rotational evolution for young stars. The relation we obtain is in contrast with some


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Acknowledgements Financial support was provided by the German Federal Ministry of Education and Research (BMBF in the framework of the Verbundforschung, D-LOFAR 05A11BAA). The authors would like to thank Mark DeRosa’s help for extending the magnetic field calculations beyond the default distance, NASA’s SDO and ESA’s PROBA2 teams as well as the DAM and ARTEMIS observatories for providing open access to their data, and J. Anderson, A. Warmuth, J. Hessel, and G. Heald for their careful reading of the manuscript. LOFAR, designed and constructed by ASTRON, has facilities in several countries that are owned by various parties (each with their own funding sources) and are collectively operated by the International LOFAR Telescope (ILT) foundation under a joint scientific policy. C. F. acknowledges financial support from the “Agence Nationale de la Recherche” through grant ANR-09-JCJC-0001-01.


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We thank the SOFIA ground crew, flight crew, and Mission Operations for their successful execution of the SOFIA observations. We also thank an anonymous referee for making suggestions that led to the improvement of this paper. This work is based on observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA science mission operations are conducted jointly by the Universities Space Research Association, Inc. (USRA), under NASA contract NAS2-97001, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901. Financial support for FORCAST was provided to Cornell by NASA through award 8500-98-014 issued by USRA. This work is based on observations made with the Spitzer Space Telescope , which is operated by JPL/Caltech under NASA contract 1407. This work is based in part on observations made with Herschel , a European Space Agency Cornerstone Mission with significant participation by NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. R.D.G. acknowledges support from NASA and the United States Air Force. Facilities : Spitzer , SOFIA , Herschel .