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We thank the referee for useful suggestions and comments that improved the quality of this manuscript. The NANOGrav project receives support from NSF Physics Frontier Center award number 1430284. NANOGrav research at UBC is supported by an NSERC Discovery Grant and Discovery Accelerator Supplement and by the Canadian Institute for Advanced Research. We thank our colleagues in the International Pulsar Timing Array for comments and useful discussions. We thank Alberto Sesana for commenting on our astrophysical modeling and interpretation. M.V. and J.S. acknowledge support from the JPL RTD program. Portions of this research were carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. S.R.T. was partially supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Oak Ridge Associated Universities through a contract with NASA. S.R.T. thanks E.R.S. for fruitful discussions. J.A.E. was partially supported by NASA through Einstein Fellowship grant PF4-150120. S.B.S. was supported by NSF award #1458952. P.T.B. acknowledges support from the West Virginia University Center for Gravitational Waves and Cosmology. M.A.M. was partially supported by NSF award OIA-1458952. W.W.Z. is supported by the CAS Pioneer Hundred Talents Program and the Strategic Priority Research Program of the Chinese Academy of Sciences grant No. XDB23000000. R.v.H. was supported by NASA Einstein Fellowship grant PF3-140116. This work was supported in part by National Science Foundation grant No. PHYS-1066293 and by the hospitality of the Aspen Center for Physics. Portions of this work performed at NRL are supported by the Chief of Naval Research. This research was performed in part using the Zwicky computer cluster at Caltech supported by NSF under MRI-R2 award No. PHY-0960291 and by the Sherman Fairchild Foundation. A majority of the computational work was performed on the Nemo cluster at UWM supported by NSF grant No. 0923409. Parts of the analysis in this work were carried out on the Nimrod cluster made available by S.M.R. Data for this project were collected using the facilities of the National Radio Astronomy Observatory and the Arecibo Observatory. The National Radio Astronomy Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the NSF (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana and the Universities Space Research Association. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. Some of the algorithms used in this article were optimized using the Blue Waters allocation “Accelerating the detection of gravitational waves with GPUs.” The Flatiron Institute is supported by the Simons Foundation.


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Acknowledgments DLK was supported by National Science Foundation grant AST-1412421. TM acknowledges the support of the Australian Research Council through grant FT150100099. This scientific work makes use of the Murchison Radio-astronomy Observatory, operated by CSIRO. We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. Support for the operation of the MWA is provided by the Australian Government (NCRIS), under a contract to Curtin University administered by Astronomy Australia Limited. We acknowledge the Pawsey Supercomputing Centre that is supported by the Western Australian and Australian Governments.This research was conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. Special thanks to the anonymous referee whose comments greatly improved this manuscript.


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I thank Alexei Butkevich for help in providing me with the relevant chapter in Eddington’s rare 1914 book and for discussions on different aspects of the Malmquist bias. Good remarks by the referee are also acknowledged.


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We thank the referee for his/her constructive comments. We thank Martha Boyer, Jason Kalirai, and Guillermo Torres for generously sharing their data with us and Francis Timmes for his assistance with nuclear reaction networks in MESA. We thank Leo Girardi and Dan Weisz for fruitful conversations and comments on the manuscript. We thank Conny Aerts, Lars Bildsten, Jonathan Bird, Phillip Cargile, Selma de Mink, Falk Herwig, Jessica Lu, Marc Pinsonneault, Philip Rosenfield, and Victor Silva-Aguirre for sharing their expertise. We also thank the entire MESA community for making this work possible, with special thanks to the MESA Council. Finally, we thank the participants of the KITP workshop “Galactic Archaeology and Precision Stellar Astrophysics” for stimulating discussions. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. J.C. acknowledges support from the National Science Foundation Graduate Research Fellowship Program. A.D. received support from the Australian Research Council under grant FL110100012. C.C. acknowledges support from NASA grant NNX13AI46G, NSF grant AST-1313280, and the Packard Foundation. This work was supported in part by NASA grant NNX15AK14G. The computations in this paper were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.


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Acknowledgments Generous allocations of time on the 1m McLennnan Telescope and HERCULES spectrograph at the Mt John University Observatory in support of the Southern Binaries Programme have been made available through its TAC and supported by its Director, Dr K. Pollard and previous Director, Prof. J.B. Hearnshaw. Useful help at the telescope were provided by the MJUO management (N. Frost and previously A. Gilmore and P. Kilmartin). Assistance with the use and development of the hrsp software has been given by its author Dr J. Skuljan. Encouragement and support for this programme has been shown by the School of Chemical and Physical Sciences of the Victoria University of Wellington, as well as the Royal Astronomical Society of New Zealand and its Variable Stars South section ( http://www.variablestarssouth.org ). We thank VSSs former-director Tom Richards for advocating DSLR photometry in support of the Southern Binaries Programme, also the AAVSOnet Telescope Allocation Committee for telescope time in 2014 and 2015. We appreciate the hard work and dedication of AAVSOnet site managers Peter Nelson (BSM South) and Greg Bolt (BSM Berry). Dr P. Mayer kindly sent additional photometric details on QZ Car that were used in the construction of the OC curve. As well, Dr H. Drechsel made very useful comments regarding the effects of radiation pressure on the surficial distortions of very hot close binaries. The astrophysics group at COMU have been supportive of this research.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 nonrotating case. Reconnection proceeds whenever the orientation of the BR is close to optimal and the continued disruption of the same section of overlying field eventually triggers a flare. The peak KE is higher for the corotating case because the flares are triggered at the same time unlike the counter-rotating case. The peak KE released for the simulations with two colliding rotating BRs is almost negligible. Looking at the simulation results more closely reveals that no flares are triggered in either simulation. This is likely because no section of the overlying field is disrupted for long enough to trigger a flare. Each rotating BR is in the optimal orientation only for a short time during rotation and never twice for the same section of overlying field. 4. Discussion The results from these simulations indicate that the motion of the emerging small-scale BRs that trigger flares can have a significant effect on the strength of those flares. In the most extreme cases the effect of motion alone caused over a threefold increase in the peak KE released by the flare. The proper motion of magnetic features such as these has been observed on the solar surface, for example, sunspots have been seen to drift at speeds of 0.14 km s −1 (Herdiwijaya et al. 1997 ) and moving magnetic features within sunspots move at ∼0.5 km s −1 (Zhang et al. 2007 ). Rotational motion of magnetic features has also been observed, the rotational velocity of sunspots has been measured at values of up to hr −1 during their emergence from the photosphere (Zhu et al. 2012 ). Photospheric motions are known to twist the coronal magnetic field into nonpotential configurations as discussed in Sundara Raman et al. ( 1998 ), Gerrard et al. ( 2002 ), Wang et al. ( 2018 ), and Yan Qu ( 2007 ). These magnetic fields can then be triggered resulting in a flare. In these simulations, however, which include a preexisting nonpotential field, we are only interested in how these motions effect the strength of the flare through the triggering process. In our first set of simulations we specifically considered linear oscillation of the emerging BR rather than simply drift; though, the results indicate that there may be little distinction. Interestingly the frequency at which the emerged BR oscillates does not seem to effect the strength of the flare. It is thought that this is because the frequency of the oscillation ultimately has no effect on how much of the overlying field is exposed to the disruptive trigger of the emerging small-scale BRs. The orientation of the oscillation on the other hand has been shown to be very important. Motion along the PIL generally increases the strength of the flare while motion across the PIL generally detracts from the strength of the flare. This is likely because the position of the emerging field on the PIL is the most disruptive to the overlying field and more of this field is disrupted if there is motion of the BR along the PIL. The most explosive


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ACKNOWLEDGEMENTS The authors acknowledge the National Computational Infrastructure (NCI), which is supported by the Australian Government, for providing services and computational resources on the supercomputer Raijin that have contributed to the research results reported within this paper. This research made use of the Argus Virtual Research Desktop environment funded by the University of Sydney. FL is supported by the University of Sydney International Scholarship (USydIS).


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et al. 1988 ) applied to IST EoS of quantum gases (see Bugaev et al. 2017 for details). This allows us not only to reproduce the properties of the normal nuclear matter but also to significantly extend the range of IST EoS applicability. The goal of this work is to study the constraints that can possibly be imposed on the IST EoS from the astrophysical observational data of NSs. This is necessary to find which set of parameters of this EoS simultaneously fits the experimental data from the A+A collisions and the astrophysical observations on NSs. The paper is organized as follows. In Section 2 we briefly review the novel IST EoS and in Section 3 we present the mass–radius relation, including a discussion of constraints coming from nuclear and high-energy nuclear physics experiments. The paper ends with a summary in Section 4 . 2. Equation of State: Model Description The novel thermodynamically consistent EoS is based on the virial expansion applied for the multicomponent mixtures with hard core repulsion (Sagun et al. 2014 ). In particular, proper consideration of the volumes of particles enables us to explicitly account for the surface tension that is induced by the interaction between constituents. In this formalism the IST EoS has the form of a system with two coupled equations, one for pressure p and another for the IST coefficient σ defined as follows,andwhere T , m i , , and R i are temperature, mass, chemical potential, and the hard core radius of the i -sort of particles. The eigenvolumes and surfaces are equal to and . The summations in Equations ( 1 ) and ( 2 ) are made over all types of particles and their antiparticles, with a corresponding partial pressure of point-like particles of type i . Here, denotes the shifted chemical potential due to the presence of the hard core repulsion. The dimensionless parameter α in Equation ( 2 ) was introduced due to the freedom of the Van der Waals extrapolation to high densities (Sagun et al. 2014 ) and accounts for the higher-order virial coefficients. As was shown in Sagun et al. ( 2014 ) to reproduce the correct phase-diagram properties of nuclear matter, such a parameter should obey the inequality . According to the conditions of wide causality range and compressibility factor, the value of the parameter α in the Statistical Multifragmentation Model was found to be equal to 1.25 (Sagun et al. 2014 ) . Further studies revealed the value α = 1.245 (Sagun et al. 2017b ) is best for reproducing the fourth and third virial coefficients. Another physical meaning of α is as a switcher between the excluded volume and the proper volume regimes (for details, see Sagun et al. 2017a ). As the value α = 1.245 was obtained for the Boltzmann statistics (Sagun et al. 2017a ) and could be different at zero-temperature, when quantum effects are significant, the baryon radius and α parameter are chosen to be free parameters in the model. On the other hand, when fitting the mass–radius curve to existing


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. For the bifurcation point μ = 0, we derive from ( 6 ) the condition for the cycle-frequency ν to be given by equationThe solution with the lowest value, ν *, defines the critical dynamo number, at which the zero solution becomes unstable to be given byAt this point, Equation ( 4 ) has the harmonic solution B ( t ) = A sin ν * t . However, the amplitude A is unstable. It decays to zero, for dynamo numbers below , and would grow unbounded for higher values, if it were not for B max , which stabilizes the solution again. Simulations show that, at , the zero solution bifurcates to the harmonic solution B ( t ) ∝ sin ν * t , with amplitude close to B max . Further increasing leads to periodic and chaotic modulations of both the amplitude and the period. (Figure 3 ). This period-doubling route to chaos is a robust feature of BL-type dynamos, which has been observed also in simpler iterative map models as well as more complicated spatially resolved models (Charbonneau et al. 2005 ). The amplitude-modulations are superimposed to an increasing trend, starting at around B max . The period, on the other hand, is modulated around the linear solution ν *. For the sake of simplicity, we refer to this entire mode of oscillation as the weak mode. Figure 3. Field amplitudes B 2 as a function of the dynamo number , for q = 0.82, exhibiting the transition between the weak and the strong mode around . The inset shows the corresponding periods against (same units). Gray vertical lines indicate the dynamo number used for the realization in Figure 4 . If we introduce B min , this generic picture persists. However, the zero solution remains stable for dynamo numbers beyond . Hence, there is a range of dynamo numbers, roughly between and , for which the dynamo admits at least two stable modes (the weak mode and the zero mode). For even larger values of the dynamo number, a fundamentally different mode of oscillation emerges (the branch in Figure 3 above dynamo number ). This is a mode where B ( t ) is above B max most of the time and both the amplitude and the period are constant. We call it the strong mode. It is the stable limit cycle that appears when we approximate in Equation ( 4 ). This approximation is valid for large , where the cycle period is much larger than q . For smaller values of , the approximation fails and the system can no longer be approximated by a second-order ODE, hence the emergence of the chaotically modulated weak mode. The cycles of the strong mode have a characteristic shape, similar to the large solar cycles that were observed in the sunspot records (Figure 2 ): a steep rising limb, followed by a falling limb with a kink. This shape has been interpreted as an effect of the B -field exceeding B max before by Stix ( 1972 ), albeit with a non-BL-type dynamo model. The fit in Figure 2 has been achieved through optimizing parameters q and . Interestingly, the optimized value turned out to be quite close to the critical point where the strong


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This research is part of the project Cosmic-Lab ( http://www.cosmic-lab.eu ) funded by the European Research Council (under contract ERC-2010-AdG-267675). E.V. acknowledges ESO DGDF (SL) 14/51/E. NSO/Kitt Peak FTS data used here were produced by NSF/NOAO. We warmly thank the anonymous referee for suggestions that improved the paper.


O O O B-Archive I-Archive O O O 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 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 B-Instrument B-Wavelength I-Wavelength 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 B-Instrument 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 B-Wavelength I-Wavelength 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 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 B-Instrument 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 B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength

In addition, the HARPS archive contains plenty of observationsof solar-type stars, including a rich set of solar spectra taken by observing solar system bodies for many years. All these characteristics make HARPS the ideal instrument to investigate the precision of the normalization method that we have developed. The fact that the solar-sibling observations have been repeated for several years allows us to also investigate the stability of this instrument in time, and to determine to the extent to which the HARPS H α profile has remained constant in time. The test is performed with all solar spectra set out in Table 3 , for which ’s were derived. The plot in the top panel of Fig. 14 visually summarises the results displayed in the table. For each date, values are represented by plus symbols. Their weighted mean and corresponding spread values are drawn with bars. Next to them, the number of spectra used and their average S/N ratio are noted to show the precision reached when measurements from several spectra are combined. The weighted mean and spread of all measurements are represented by the horizontal line and the shade at 5744 ± 10 K. Evidently, there is no trend with time and the scatter is very low, which confirms the blaze stability of HARPS. This value is in perfect agreement with that of Coudé (see values in Table 2 ), which implies that not only is the blaze stable but it is also fully removed through the flat-field procedure. Table 3 Solar proxies. Notes. The list is ordered by date of observation along with the S/N of the spectra and the effective temperature derived from H α profiles. Fig. 14 Top panel : temperatures of the HARPS solar proxies in Table 3 vs. the date upon which spectra were acquired. Daily values are represented by plus symbols and weighted means and errors for each month are drawn in red. The weighted mean and error of all the measurements are represented by the continuous line and the shade on 5744 ± 10 K. Next to the bars, the number of spectra analysed and the mean S/N are noted. Bottom panel : errors of individual measurements in the top panel are plotted vs. S/N. The exponential curve given by the equation in the plot is the best fit to the points. In the bottom panel of Fig. 14 we plot the precision obtained from individual spectra as a function of S/N. It is observed that ~40 K can be obtained from spectra of S/N = 400–500. Finally, we compare the temperatures derived from HARPS with those derived from Coudé spectra for the other stars in common in our sample. The comparison is shown in Fig. 15 against the three main stellar parameters. It shows an excellent agreement with a negligible offset between the two samples of − 13 ± 34 K with no trends. The temperatures of all stars agree within 1 σ errors, with the exception of two ( δ Eri and HD 184985) that agree within 2 σ . 11 Summary and conclusions With the aim of better understanding and minimising the errors that affect T eff measurements from H α


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

between the individual patterns. The middle panel of Fig. 9 shows the δ T b map at redshift 16. The number of sources drops quite drastically in this frequency channel as we are probing the initial stages of the cosmic dawn. The overlap between the individual patterns too is not that substantial. The decrease in the number of sources towards the lower frequency channels can be seen from the right-hand panel of Fig. 9 , where we show the light cone from our simulation box. The signal at the higher frequency end of the box is essentially the strong absorption signal arising from the significant overlap between the Ly α photons from the sources. Note that we have subtracted the mean from each frequency channel while making the image and thus the signal is a combination of emission and absorption regions. As the signals from the channels corresponding to redshifts 15 and 16 are dominated by the absorption regions, the mean of the expected signal is negative. The regions with positive values of the signal in the left-hand and middle panels of Fig. 9 arise because of subtracting the mean signal from the maps. In reality, these are the Ly α-deficient regions with almost no 21 cm signal. Figure 9. Left-hand panel: 24 × 24 map of the 21 cm signal (without smoothing) at the frequency channel ν c = 89 MHz generated from the simulation using the N -body simulation and a one-dimensional radiative transfer code. The ‘×’ marks represent the angular positions of the sources between a band ν c − 0.1 to ν c + 0.1 MHz. Middle panel: same as the left-hand panel, but at the frequency channel corresponding to ν = 84 MHz. Right-hand panel: the light-cone map of δ T b distribution. The arrows in the top label of the panel show the frequency channels corresponding to the maps in the left-hand and middle panels. The maps include the effect of redshift-space distortion and the light-cone effect. The top-left panel of Fig. 10 shows the smoothed image of the residual signal and noise at the central frequency channel after subtracting the foregrounds using the polynomial method. The noise in the panel corresponds to 200 h of observation, and the smoothing is performed using the Gaussian filter of size 30 arcmin. One can easily identify that even in the smoothed map, the signal is localized around the sources. The top-right panel of Fig. 10 shows the same but for 2000 h of observation. The SNRs of these top-left and top-right panels are 4.8 and 14.2, respectively. The bottom-left and bottom-right panels are the same as the top panels but at a different frequency channel corresponding to ν = 84 MHz ( z = 16). The corresponding SNRs in the bottom panels are 3.3 and 10.1, respectively. The Pearson cross-correlation coefficients χ, in this case, are given in Table 3 . We find that the foreground subtraction method works effectively in this case as well leading to reasonably high values of χ. Figure 10. Top-left panel: map of the residual signal and noise after foreground


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

distribution of these galaxies in -space and compare it with the cumulative probability distribution function for a uniform distribution (i.e. a straight line). The Kologorov–Smirnov (KS) statistic for these distributions is D = 0.128 indicating consistency. Figure 2. The cumulative fraction of where α is the pitch angle is shown, using the central 90 per cent range of pitch angles from Yu Ho ( 2018 ). The dashed line shows a uniform distribution which is what would be expected if the spiral structure winds up at a constant rate (equation 5 ). The KS statistic for the comparison between these two distributions is D = 0.128, confirms a lack of statistical disagreement. As a consistency check, we also show the normalized distribution of pitch angles for different wavebands in Fig. 3 , again using data from Yu Ho ( 2018 ). As would be expected, the distribution of pitch angles are similar for the different wavebands. Within error bars (which we do not show for clarity), the pitch angles again exhibit a uniform distribution in the range for the B, V, R , and 3.6 μm bands. We leave any further studies across different wavelengths or other parameters to future observational studies. Figure 3. The distribution of pitch angles is shown for different wavebands, using the data from Yu Ho ( 2018 ). 4 DISCUSSION Recent work has attempted to correlate measurements of pitch angles with other galaxy properties as a means to distinguish between mechanisms for spiral arm generation. In these observational studies, the pitch angle is usually assumed to have a fixed value independent of radius or time. In particular, Yu et al. ( 2018 ) and Yu Ho (2018 , 2019 ) argue that measurements of pitch angles, and the correlations between these and other galaxy properties, are broadly consistent with the expectations of Lin–Shu modal density wave theory (Section 2.1 ). 3 We find nothing that contradicts this possibility. However, their arguments and analysis are predicated on the basic assumption of Lin–Shu theory, which is that each galaxy contains a spiral pattern whose pattern speed, Ω p , and pitch angle, α, are fixed in time (and space), being just dependent on the various properties of the galaxy, for example on morphology of the galactic rotation curve (fig. 11 in Yu Ho 2019 ) or the galactic shear rate (fig. 12 in Yu Ho 2019 ). Here, we investigate whether an alternative premise, i.e. that the pitch angles of galaxies evolve with time, is consistent with the observed data. Our finding that the distribution of pitch angles () is more or less uniform among their observed galaxies, opens up the possibility that the pitch angles are actually evolving in time, as is found in the simulations (e.g. Grand et al. 2013 ; Pettitt Wadsley 2018 ; Mata-Chávez et al. 2019 ). We note that in the modal density wave picture, this finding would need some other explanation. We argue here that the possibility of evolving pitch angles merits further investigation. Our simple


O O O O B-Mission I-Mission O O O B-URL O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization O O O O O O O O O O O B-Person O O O B-Organization I-Organization B-Organization O B-Organization B-Location B-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Fellowship O O B-Fellowship O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O O B-Grant B-Person O O O O B-Organization B-Grant I-Grant I-Grant I-Grant B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant

We are thankful to WIND Spacecraft data providers ( wind.nasa.gov ) for making interplanetary data available. We are also thankful to the Department of Physics (Autonomous), University of Mumbai, for providing us with facilities for the fulfillment of this work. A.R. also thanks the Solar-TErrestrial Physics (STEP) group, USTC, China SCOSTEP visiting Scholar program. W.M. is supported by the Chinese Academy of Sciences (CAS) Presidents International Fellowship Initiative (PIFI) grant No. 2015PE015 and National Natural Science Foundation of China (NSFC) grant No. 41750110481. A.B. is supported by the NASA Living With a Star Jack Eddy Postdoctoral Fellowship Program, administered by UCARs Cooperative Programs for the Advancement of Earth System Science (CPAESS).”


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The authors wish to thank Bryce Croll and Saul Rappaport for their helpful suggested regarding observing, interpretation of the spectra, explanations of systematics, and a wider range of compositions to consider. Thanks to James P. Lloyd and Dong Lai for their advice on the interpretation of the transits. Based on observations made from the Infrared Telescope Facility, which is operated by the University of Hawaii under contract NNH14CK55B with the National Aeronautics and Space Administration. M.Z. acknowledges support from NASA OSS grant NNX14AD22G and the Center for Exoplanets and Habitable Worlds at the Pennsylvania State University. 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.


O O O O O O O B-Telescope O B-Telescope O B-Organization O O O O O B-Organization O O O O O O O O B-Database I-Database I-Database O B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization B-Telescope O O O O O O O B-Organization O B-Organization O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Organization

We thank all the members of the AKARI project. AKARI is JAXA project with the participation of ESA. The CME catalog is generated and maintained at CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. SOHO is a project of international cooperation between ESA and NASA. This research is financially supported by Grants-in-Aid for Young Scientists (A) No. 26707008, and Scientific Research (C) No. 25400220. T.K. is financially supported by Grant-in-Aid for JSPS Fellows No. 25002536, and the Nagoya University Program for Leading Graduate Schools, “Leadership Development Program for Space Exploration and Research,” from MEXT.


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Acknowledgements We thank the anonymous referee for their careful reading of and helpful suggestions on the manuscript, and Andreas Korn for providing the FOCES spectra used in this work. AMA and KL acknowledge funds from the Alexander von Humboldt Foundation in the framework of the Sofja Kovalevskaja Award endowed by the Federal Ministry of Education and Research, and KL also acknowledges funds from the Swedish Research Council (grant 2015-004153) and Marie Skłodowska Curie Actions (cofund project INCA 600398). TN and MA acknowledge funding from the Australian Research Council (grant DP150100250), and MA also acknowledges funding through ARC Laureate Fellowship (FL110100012). Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. PSB acknowledges financial support from the Swedish Research Council and the project grant “The New Milky Way” from the Knut and Alice Wallenberg Foundation. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (grant DNRF106). This work made use of data from the UVES Paranal Observatory Project (ESO DDT Program ID 266.D-5655). This work was supported by computational resources provided by the Australian Governmentthrough the National Computational Infrastructure (NCI) under the National Computational Merit Allocation Scheme.


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XMM-Newton spectra of HD 54879 (high-resolution RGS spectra have an insufficient signal and are not useful). The X-ray spectra of magnetic hot stars are usually well described by multi-temperature thermal plasma models (e.g., Oskinova et al. 2011 ; Nazé et al. 2014 ). This is also the case for HD 54879. As a first step, we fitted the observed spectra in the 0.2–10.0 keV band with a thermal two-temperature spectral model that assumes optically thin plasma in collisional equilibrium. At this step, the absorption was modeled as originating in the cold interstellar medium ( Wilms et al. 2000 ). The resulting spectral fit is statistically significant, with a reduced . The best fit parameters are shown in Table 3 . There is no physical motivation for restricting the plasma temperature distribution to two temperatures. In fact, spectroscopic analyses show a continuous temperature distribution in hot stars ( Wojdowski Schulz 2005 ). Therefore, as a next step, we fitted a three-temperature spectral model to the observed EPIC spectra of HD 54879. Also in this case, the fit is statistically significant, with . The three-temperature model fit is shown in Fig. 10 , and the associated parameters are shown in Table 3 . The three-temperature fit reveals the hottest plasma component with a temperature of about 2 keV (20 MK). Better S/N is required to confirm the presence of this high-temperature plasma. We also tried to fit a four-temperature plasma model. However, the quality of the data is not sufficient to further constrain the temperature distribution. Fig. 10 XMM-Newton PN, MOS1, and MOS2 spectra of HD 54879 (black, red, and green curves, respectively) with error bars corresponding to 3 with the best fit three-temperature thermal model (solid lines). The model parameters are shown in Table 1. Table 3 X-ray spectral parameters derived from the XMM-Newton observations of HD 54879 assuming a three-temperature plasma model. Notes. (a) Corrected for the interstellar absorption in the 0.2–12 keV band. In the framework of the magnetically confined wind shocks (MCWS) model ( Babel Montmerle 1997 ; ud-Doula Owocki 2002 ), the wind plasma streams collide at the magnetic equator and give rise to a shock that heats the plasma. Hence, the maximum temperature follows from a Rankine-Hugoniot condition and cannot exceed a value determined by the maximum streaming velocity. Motivated by the recent discovery of a non-thermal component in the X-ray emission of the magnetic star HR 7355 ( Leto et al. 2017 ), we also fitted the observed spectra with a composite two-temperature thermal plasma and a non-thermal, power law component. The model provides a fit of similar quality to the observed spectra ( for 138 degrees of freedom). The best fit thermal plasma temperatures are [keV], [keV], and the power-law exponent is . Thus, the quality of the data is not sufficient to discriminate between three-temperature thermal and two-temperature thermal plus non-thermal component models.


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X-COP data products are available for download at https://www.astro.unige.ch/xcop . We thank Ricardo Herbonnet and Henk Hoekstra for providing us with their weak-lensing results in advance of publication, and the anonymous referee for helpful comments. The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the AHEAD project (grant agreement no. 654215). Based on observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. S.E. acknowledges financial contribution from contracts NARO15 ASI-INAF I/037/12/0, ASI 2015-046-R.0 and ASI-INAF n.2017-14-H.0. F.V. acknowledges financial support from the ERC Starting Grant “MAGCOW”, no.714196. M.G. is supported by NASA through Einstein Postdoctoral Fellowship Award Number PF5-160137 issued by the Chandra X-ray Observatory Center, which is operated by the SAO for and on behalf of NASA under contract NAS8-03060. Support for this work was also provided by Chandra grant GO7-18121X. E.R acknowledges the ExaNeSt and Euro Exa projects, funded by the European Union’s Horizon 2020 research and innovation programme under grant agreements no. 671553 and no. 754337 and financial contribution from the agreement ASI-INAF n.2017-14-H.0. H.B. acknowledges financial support from ASI Grant 2016-24-H.0.


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

negligibly, which suggests that for those cases, the lengthening of the spiral arms resulting from stripping can also give an appearance of unwinding without actually affecting the pitch angles. Schulz Struck ( 2001 ) noted possible winding of the inner spiral arms due to compression and ‘annealing’ of the disc in addition to unwinding of the outer regions of their face-on stripped galaxies. With the given sample, we do not have sufficient evidence to investigate this; however, with a larger sample of galaxies the effect of RPS on the more central spiral arms could be tested. The unwinding tails were found to be comprised of only the youngest stellar populations, in many cases only stars 20 Myr, when analysed with the sinopsis spectrophotometric fitting code. These have likely formed in situ , confirming that the unwinding effect only occurs in the gas component of the galaxy. Moreover, the age gradients observed in some unwinding arms possible capture the process in action, revealing a trail of progressively younger stars left by the opening arms of stripped material. Simulations were carried out of RPS interactions in different inclinations with respect to the ICM wind to investigate how the unwinding effect can arise and to compare the resulting morphology with observed features in the MUSE sample. The resulting snapshots were analysed throughout the stripping process, and used to produce ‘observations’ from different viewing angles to compare with the observed sample of galaxies. The two main effects that can, individually and in combination, give rise to an unwinding pattern are as follows: In edge-on wind interaction cases, the differential ram pressure in the leading and trailing edges of the disc causes a build-up of material in the leading edge. The tail becomes asymmetric and the slowed rotation of the gas causes the pitch angle to increase. In face-on wind interactions, the gas from the outer spiral arms is stripped and withdrawn from the potential well of the galaxy disc, causing it to move to higher orbits and increase the pitch angle in all directions from the disc. In most cases, a combination of these two effects will occur as a galaxy is stripped at angles between face-on and edge-on with respect to the ICM wind. Cases in which the galaxy is moving mostly edge-on to the wind appear to be more asymmetric and have tails that are further collimated to one side of the disc, while cases closer to face-on such as JO201 and JO85 show gas extending in a much wider range of directions from the disc. Furthermore, the simulations, combined with the phase-space positions of our galaxies and the sinopsis stellar population analysis, as well as similar effects found in the literature (Steinhauser et al. 2016 ; Roediger et al. 2014 ), all point towards the idea that the unwinding effect occurs only for galaxies undergoing first infall on radial plunging orbits, and appears to be a short-lived phase during stripping, containing stars


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This work was supported by the Swedish Research Council. M.M. has received funding from the People Programme (Marie Curie Actions) of the EUs FP7 (FP7/20072013) under REA grant agreement No. 623898.11. W.V. acknowledges support from ERC consolidator grant 614264.


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ACKNOWLEDGEMENTS The Torino polarimeter was built at the INAF (Instituto Nazionale Di Astrofisica) – Torino Astrophysical Observatory using dedicated funds provided in the framework of the INAF PRIN 2009 program. This work is based on data obtained at the C2PU (Centre Pédagique Planète et Univers) facility (Calern observing station, Observatoire de la Côte d’Azur, Nice, France) and at the Rozhen National Astronomical Observatory (Bulgaria). GB, ZD, TB, IB, AC, SB, and YK gratefully acknowledge observing grant support from the Institute of Astronomy and Rozhen National Astronomical Observatory, Bulgarian Academy of Sciences.


O O O O O O O O B-Tag 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 B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O B-Observatory B-Telescope O O O O O O O B-Formula I-Formula I-Formula O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Telescope O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Telescope B-Instrument O O O B-CelestialObject I-CelestialObject O O O O O O B-Telescope 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 B-Telescope 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 B-Observatory B-Telescope O O O O O O O O B-Telescope 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-Telescope O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O

115 ks with 25 ks on-source exposure. 4.1 <italic>INTEGRAL</italic> context Previous studies of this source with INTEGRAL have revealed a long (30 d), eccentric (e ∼ 0.3–0.4) orbit and shown detections in more than 60 per cent of neutron star periastron passages. SAX J1818.6−1703 was not detected by INTEGRAL in an observation carried out between 2013 March 12 and 2013 March 13 during Revolution 1271, at a time that corresponds to an orbital phase of 0.804–0.862. During this region of a long eccentric orbit, the stellar wind, through which the neutron star passes, is not expected to be sufficiently dense or structured so as to produce detectable emission from accretion. A bright flare from SAX J1818.6−1703 detected by Swift /BAT on 2013 March 17 (corresponding to phase, φ = 0.970) was reported by Romano et al. ( 2014 ). During this flare the source reached a peak flux of 146 mCrab (15–50 keV), clearly showing that the source exhibited enhanced X-ray emission a few days prior to the XMM observation reported here. The source was also detected by INTEGRAL during Revolution 1274 at a significance of ∼13σ. A more detailed analysis of this revolution shows that the source was first observed between UTC 11:10:03 and UTC 20:44:48 on 2013 March 20, corresponding to orbital phases φ = 0.086–0.099, with a total source exposure of 7.5 ks. During this observation, the source was detected with an average count rate of 2.17 ± 0.22 counts s −1 (18–60 keV) or ∼10 mCrab. The source was subsequently observed between UTC 09:00:11 and UTC 20:13:27 on 2013 March 22, corresponding to orbital phases φ = 0.150 – 0.165, again with a total source exposure of 7.5 ks. The average count rate in this observation was 1.27 ± 0.22 counts s −1 (18–60 keV). In order to compare these fluxes to previous periastron passages, we performed the recurrence analysis of Bird et al. ( 2008 ) using an INTEGRAL /IBIS light curve of SAX J1818.6−1703 from the first 1000 revolutions of INTEGRAL . We calculated the mean flux detected by INTEGRAL during a 4-day period centred on periastron and from this, we find that during the first observation of Revolution 1274, the source is brighter than 80 per cent of periastron passages observed by INTEGRAL . The flux detected between UTC 09:00:11 and UTC 20:13:27 on 2013 March 22 is consistent with fluxes observed by INTEGRAL during the majority of periastron passages. However, it is different from the distribution of apastron flux measurements and still represents a significant detection of the source. When considering both the Swift /BAT bright flare on 2013 March 17 and the INTEGRAL observations during Revolution 1274, it is clear that SAX J1818.6−1703 was in an atypically active state during the periastron passage covered by the INTEGRAl and XMM observations presented in this work. 4.2 Source distance Knowledge of the source distance is critical in order to calculate associated luminosities and hence disentangle the accretion processes


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This work has been supported by the Israeli-French ASTROPHYSICS program and by the French GdR PCHE/PNHE. Ehud Behar received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 655324, and from the I-CORE program of the Planning and Budgeting Committee (grant number 1937/12). The authors are gratetful to Suzy Collin, Jonathan Stern and Agata Różanská for their helpful comments on this paper. Finally, we thank the anonymous referee for constructive remarks.


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

to orbital phase 0.9364, close to the primary eclipse, for which the contribution of the secondary is minimum. Figure 5. Same as Fig. 4 , but for one of the MagE spectra corresponding to orbital phase 0.9352. The results of the quantitative spectral analysis of all ALFOSC and MagE spectra are summarized in Fig. 6 . In the left-hand panels (ALFOSC), the apparent variations of the effective temperature with phase and an amplitude of ∼2500 K are obvious. The lowest temperatures (∼40 kK) occur near primary eclipse and in the secondary eclipse, where the contribution by extra light should be minimal. Hence, the increase during other orbital phases is caused by reflected light and, therefore, not real. Similarly, variations of the helium abundance are observed. The apparent variations of the surface gravity, however, are small. The mean values adopted for T eff , log g , and log y , summarized in Table 2 , are obtained by selecting six spectra close to the primary eclipse with phase between −0.1 and +0.1 and adding one spectrum at phase 0.52. The analysis of the MagE spectra also results in effective temperatures and helium abundances that seem to vary with orbital phase (cf. Fig. 6 , right-hand panels), but with amplitudes less pronounced than those from the ALFOSC spectra. For this reason, we use all the MagE spectra to compute mean values and standard deviations of T eff and log y (cf. Table 2 ). Figure 6. T eff , log g , log y , and v rot sin i variations as a function of the orbital phase. Left-hand panels: ALFOSC. The green dotted–dashed horizontal lines mark the adopted T eff , log g , and log y and the associated errors (cf. Table 2 and text). Note the two points with low T eff near phase 0.5 (secondary eclipse), when the contribution of the secondary is strongly reduced. Right-hand panels: MagE. The orange dotted–dashed horizontal lines mark the average values and associated errors of T eff , v rot sin i , and He abundance. In the central panel, note the outlier near phase zero (primary eclipse). Table 2. SdOB atmospheric parameters and rotational velocity. The effective temperature and surface gravity of EPIC 216747137 ( T eff = 40400 K and log g = 5.56) are very similar to the hot HW Vir systems AA Dor (Klepp Rauch 2011 ) and V1828 Aql (= NSVS 14256825, Almeida et al. 2012 ). EPIC 216747137 also shares an underabundance of helium (log y = −2.59) with the two others. The projected rotational velocity, as derived from the individual MagE spectra (central right panel of Fig. 6 ), results in a mean v sin i = 51 ± 10 km s −1 , significantly less than ∼70 km s −1 expected for tidally locked rotation. Mean rotational velocity of 51 km s −1 and standard deviation of 10 km s −1 are obtained excluding only a single outlier close to phase 0 (see central right panel of Fig. 6 ). 5 STELLAR PARAMETERS: RADIUS, MASS, AND LUMINOSITY The second data release of Gaia provided a precise (5 per cent) parallax measurement which allows the stellar


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Dedicated to the memory of Janet C. Bradford . We thank the anonymous referee and Stacy McGaugh for helpful comments that have improved the quality of this manuscript. We would like to thank Stephane Courteau, Susan Kassin, Allison Merritt, and Erik Tollerud for helpful feedback on this manuscript, as well as Michael Blanton and the BS group for helpful discussions. J.D.B. acknowledges support from the Gruber Foundation and the National Science Foundation Graduate Research Fellowship Program. M.G. acknowledges a fellowship from the John S. Guggenheim Memorial Foundation. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1122492. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


O O O O O O O B-Model I-Model O O O O O O O O O O O O O B-Model 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 B-Model O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 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 B-Model 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 B-CelestialRegion I-CelestialRegion O O O O O B-CelestialRegion I-CelestialRegion 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 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 B-Model I-Model 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 B-Formula I-Formula I-Formula I-Formula I-Formula 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

(2009) applied an early version of the IGIMF theory where the IMF variation of individual star clusters was not applied. The modern IGIMF prescription used here with a possible top-heavy gwIMF further increases the resulting [Mg/Fe] value. 7. Conclusions This contribution publishes an open source galaxy evolution code that is able to vary the gwIMF according to the IGIMF theory (or any other variable IMF theory) at each time step, yielding the mass composition, supernova rate, and chemical composition evolution of the galaxy. Following Yan et al. (2017) and Jeřábková et al. (2018) , where the gwIMF for a single star formation epoch is derived according to the IGIMF theory, the newly developed code published here enables us, for the first time, to perform a comprehensive and detailed examination of the effect of applying a different IMF theory in the context of galaxy chemical evolution assuming an identical SFH. Our preliminary result of a high-mass starburst galaxy assuming different IMFs and the same SFH is shown in Sect. 6 ; the result assuming the same gwIMF (the IGIMF theory) but different SFHs is shown in Appendix A . A systematically varying gwIMF leads to a strong modification of the element composition of a galaxy (naturally reproducing the observed higher metallicity and α -enhancement of the massive elliptical galaxies), while the difference in SFH and recent star formation activity influences the interpreted property of a galaxy due to a difference in the luminosity-weighted observation. The star formation environment of massive ellipticals in the early Universe is very different from the local Universe where we calibrate the IGIMF theory. There is no guarantee that such an extrapolation of the theory would work, but it is certainly an inspiring step. We will use this open source code for more comprehensive and detailed studies for galaxies with different masses and SFHs and also develop a spatially resolved IGIMF formulation. Appendix A: Results for a log-normal SFH Fig. A.1. Same as Fig. 5 , but for the log-normal SFH shown in Fig. 2 that extends for 13 Gyr. Fig. A.2. Same as Fig. 6 , but comparing different SFHs instead of different IMF assumptions. The orange lines apply the boxy SFH and the red lines apply the log-normal SFH, both shown in Fig. 2 . The same colour-coding is applied from Figs. A.2 – A.7 . The serrated shape is caused by the dying stars with a lifetime shorter than 10 Myr (see Sect. 6.2 ). We note that the orange lines are the same as the orange lines in Fig. 6 . This section compares the simulation results applying the IGIMF theory, but with the two different SFHs shown in Fig. 2 . The log-normal SFH forms the same stellar mass, but on a more extended timescale. The tail of the SFH with a low SFR leads to a stellar population that receives a contribution every δ t = 10 Myr from a top-light gwIMF, which does not exist in the box-shaped SFH model described in the main text. Thus, a more realistic and extended


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

Acknowledgements This work has benefited greatly from discussions with the following individuals: Andy Burkert, Benedikt Diemer, Oliver Hahn, Andrew Hearin, Fangzhou Jiang, Johannes Lange, and Fred Rasio. We also acknowledge the referee, Chris Power, for an insightful, constructive referee report. FvdB is grateful to the Munich Excellence Cluster for its hospitality, and is supported by the Klaus Tschira Foundation and by the US National Science Foundation through grant AST 1516962. Part of this work was performed at the Aspen Center for Physics, which is supported by the National Science Foundation under grant PHY-1066293, and at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under grant PHY-1125915. GO is supported by funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 679145, project ‘COSMO-SIMS’). Some of the numerical computations were carried out on HA-PACS at the Center for Computational Sciences at University of Tsukuba.


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

is not taken into account. The observed seismic diagnostics are indicated in Fig. 1 . I also show the best model for each case in Tables 3 and 4 (red thin lines). These optimal theoretical values are barely distinguishable from one model to the other. This indicates that they may be equally valid in order to reproduce the data, and that statistical model comparison methods (see e.g. Robert 2007 , Chap. 7) alone will not suffice to distinguish them. Further discussions on model comparison are given in Sects. 3.2 and 3.1 . Visual inspection of Fig. 1 also indicates that the accuracy of the present results is similar to what was obtained by Metcalfe et al. (2015) . Figure 2 shows the MAP estimates of all non-seismic observations. They are all reproduced with good accuracy, within 1 σ of the observed values. Fig. 1. Seismic diagnostic for 16 Cyg A ( left panel ) and B ( right panel ). The squares, triangles, and circles denote the observed r 13 , r 02 , and r 01 observed ratios, respectively. The red lines show the best models for all runs in Tables 3 and 4 . Fig. 2. Non-seismic observations for 16 Cyg A ( left panel ) and B ( right panel ). The horizontal lines represent the observed values (full lines) and the corresponding uncertainties (dashed lines). The dots denote the estimated values (MAPs of the marginal densities) for the corresponding observation, for each run. The runs are labelled on the abscissa according to the numbering given in Tables 3 and 4 . The two-dimensional joint PDFs for this set-up are shown in Fig. 3 alongside the corresponding correlation coefficients. The mass correlates most significantly with X 0 . The age correlates extremely well with the mixing-length parameter and slightly less with X 0 . It may be counter-intuitive that the mass does not correlate strongly with the age. A likely explanation is that, due to the level of constraint imposed by the seismic data, these two parameters cannot vary enough to allow such a correlation to be observed. Interpreting these correlations is not straightforward because there is in general no one-to-one correspondence between a parameter and an observation. Thus elements of interpretation can be gathered by looking at the correlation between the stellar parameters and other quantities. The mass and X 0 (Pearson correlation coefficients ≳0.8) both correlate strongly with the luminosity and the radius on the zero-age main sequence (ZAMS). This is related to the mass-luminosity relation on the ZAMS, in which the mean-molecular weight enters (see e.g. Clayton 1968 ). To maintain a roughly constant luminosity, an increase in mass must be compensated by a decrease in the mean-molecular weight. This latter corresponds to an increase in the initial hydrogen-mass fraction and a decrease of the initial helium-mass fraction because the two quantities are perfectly anti-correlated. The interaction between the mass and the hydrogen-mass fraction thus sets the initial conditions of the


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

We thank Vasileios Paschalidis for useful discussions and comments on this work. C.R. is supported by the NSF Graduate Research Fellowship Program Grant DGE-1143953. F.O. and D.P. acknowledge support from NASA grant NNX16AC56G.


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

the same plots as Fig. 5(a) but for the cases with more massive clouds with M cl = 10 6 M ⊙ , where the FUV feedback effects are more remarkable than other cases. In this case, T out is much higher than the threshold temperature 100 K for any range of Σ cl . This is due to the dependence of G out ∝ S FUV Σ cl / M cl again. With a fixed value of Σ cl , G out is larger with higher M cl because G out ∝ ε S FUV / M * = εΞ FUV and ε is enhanced following equation ( 22 ). The SFE required to disrupt the natal cloud is much smaller than the case only with EUV feedback. Fig. 5(b) also suggests that even with a large threshold temperature ≲700 K, the FUV feedback should still reduce the minimum SFE ε min . 3.3 Chemical compositions of molecular cloud remnants Our calculations suggest that the EUV and FUV radiative feedback from forming clusters jointly contribute to reduce the SFE of molecular clouds. In this section, we cast light on the gas that has not been used for star formation (i.e. the ‘remnants’ of the clouds). The cloud remnants still retain a large part of the cloud materials because the obtained SFEs are much smaller than unity for many cases. We focus on the chemical compositions of the cloud remnants, which are also followed in our calculations. We calculate the masses of H i , CO-dark and CO-bright H 2 gases as follows: First, we consider the cases with the fixed cloud mass M cl = 10 5 M ⊙ . Fig. 6(a) presents the mass fraction of the gas with the different chemical properties as functions of Σ cl . The neutral and molecular hydrogen are the dominant components of the cloud remnants, and they occupy 70 and 30 per cent of the total mass, respectively. In particular, we distinguish H 2 molecules associated with CO molecules and those without CO. The H 2 gas without CO molecules is the so-called ‘CO-dark’ molecular gas. Let us look at the cases where the minimum SFE is limited by the EUV and FUV feedback (Criterion 2, solid lines). Fig. 6(a) shows that most of the H 2 molecules contained in the remnants are actually CO-dark. Such a trend only has a weak dependence on Σ cl ; the mass of the CO-dark H 2 gas is generally much less than 10 per cent of that of the H 2 gas associated with CO molecules. This is caused by the different shielding processes of H 2 and CO molecules. As shown in Fig. 6(c) , the column density of the shell is roughly , corresponding to A V ≃ 1–3.5. The dust attenuation of the FUV radiation is not very efficient for such cases. In fact, Fig. 6(b) shows that the FUV flux at the shock front non-dimensional quantity ( G out ) is several to several tens, which is high enough to photodissociate CO molecules. However, H 2 molecules are protected against the FUV radiation by the self-shielding effect even with the small column densities. As self-shielding is not available for CO molecules, which only have small abundance, CO molecules are selectively destroyed. Figure 6. Chemical compositions of the gas that has not been


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We thank the referee for critical comments which helped to improve the paper. This research has made use of the MAXI data provided by RIKEN, JAXA and the MAXI team. We acknowledge financial support by the Polish NCN grant DEC-2012/07/N/ST9/04242.


O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O B-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-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O B-Survey O B-Telescope 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O 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 B-Person I-Person O O O B-Person I-Person B-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObject O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion 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

of Galactic anticenter, the kinematic method tends to gain larger distances, which may be caused by the deviation due to noncircular motion (Tian Leahy 2012 ) or the larger uncertainty of the rotation curve in the outer disk in comparison with inner disk due to invalidity of the tangent velocity method. The kinematic method suffers the well-known ambiguity problem as well. Ten estimates derived from the associated objects show the difference with our results on a similar level to the kinematic method. Distance measurements based on RC stars are mainly applicable to the SNRs in the first and fourth quadrants of the Milky Way because RC stars are much less abundant toward Galactic anticenter. So only 3 of 22 SNRs are studied with the RC stars. Two of them (G82.2+5.3 and G109.1–1.0) yielded much larger distances than ours as well as other results, and the estimate to G89.0+4.7 is comparable to ours. Distances derived from the Σ − D relation (seven cases) are much closer to our estimates compared to the results with methods of kinematics and associated objects. The five Sedov estimates all yield distances larger than ours. The three studies based on proper motion or shock velocity provide some informative restrictions on the SNRs in Level B whose distances are not well determined in this study. The detailed analysis of the differences can be found in the Appendix . 4.1.3. Distribution in the Galactic Plane With the measured distances, Figure 9 shows the spatial distribution of 22 SNRs in Level A and B projected on the Galactic plane. Due to the limits of the APOGEE and LAMOST spectroscopic surveys, most of the SNRs under investigation are in the second and third quadrants of the Milky Way. It can be seen that the SNRs are mainly located in the Local arm. Six SNRs are suggested to reside in the Perseus arm. Three cases, i.e., G89.0+4.7, G93.7−0.2, and G94.0+1.0, are found between the two arms. Figure 9. A face-on view of the distribution of the SNRs in Level A (15) and B (7). The red dots and squares with error bars show the measured distances and uncertainties. The black squares are the cases with distance upper limits. The sizes are proportional to their diameters. The background image, created by Robert Hurt in consultation with Robert Benjamin (Churchwell et al. 2009 ), is centered at the Sun, with the Galactic Center in the upward direction. 4.2. The Extinction Curve The extinction curves vary from one sightline to another, revealing the wavelength-dependent extinction law in different environments. As the absolute extinction is usually difficult to measure and uncertain, we use the color excess ratios (CERs), i.e., , to represent the extinction curves for the sightlines to the 32 SNRs, as well as the “ l 165” and the Rosette Nebula. For SNRs whose reddening profiles were well model-fitted, the color excess is then δA in Equation ( 3 )—the amplitude of the extinction jump at a given color. For the other SNRs, we first calculate the color