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

because of enhanced mass outflow from the circumbinary disc. In the first case, we note the apparent dimming of the ruff on days 23 and 26 is suggestive that the effect may be partly artefactual. We also note that the ruff's extent of ≳50 mas is at the upper limit of angular scales to which the VLBA is sensitive, because the shortest VLBA baselines give only sparse coverage of the centre of the uv -plane. The third case is intriguing given optical observations of Blundell et al. ( 2011 ) that provided evidence that the inner circumbinary disc structure was disrupted during a flare in 2004 October. In the 2003 July observations, there are hints of detachment between the core components and the radio ruff from day 31 onwards, raising the possibility that the enlarged ruff is a manifestation of an ejected circumbinary disc. However, this would require a very fast outflow speed – at 5.5 kpc, 50 mas corresponds to a physical size of 4 × 10 13 m. To cover this in ∼10 d would require an outflow speed exceeding 40 000 km s −1 , which seems improbably high (cf. Mioduszewski et al. 2004 ). 5.4 The unified picture Despite the lack of contemporaneous optical and radio monitoring data, there are enough similarities between what we see in these milliarcsecond-scale observations and what is seen at other scales and frequencies that we can draw out some general characteristics. In Fig. 4 , we see that jet launch speeds appear to fall over a period of about 30 d before the flare begins and jet speeds increase dramatically on or around day 15. A similar decline in speed is seen in the optical jet lines in fig. 6(e) of Blundell et al. ( 2011 ), where jet speeds decline from ∼0.27 c to ∼0.24 c over the 20 d prior to a flare. Both in the 2011–2012 observations, and during the latter half of the 2003 campaign, we see bright, fast ejections, punctuated by gaps of 5 to 10 d. Again, almost identical behaviour is seen by Blundell et al. ( 2011 ) in the optical jet lines, where the intensity of the optical jet lines is lowest in the days immediately preceding the start of the flare. This stands in contrast to the behaviour of the jet in the early days of the 2003 campaign, where the jet has a more steady character. The difference is most clearly seen by comparing the first and last frame of Fig. 3 (noting that the images of all epochs are contoured to the same minimum level): in the first frame we see faint bolides set against an apparently steady background flow, while in the last we see a succession of bright, compact bolides separated by gaps of low/no emission. Taken together, we note that the variations in both the speeds of the optical emission lines and the speeds determined by the milliarcsecond scale bolides possess remarkably similar characteristics. In the absence of simultaneous, time-resolved optical and radio observations, this coincidence is intriguing evidence that the ejecta revealed by optical emission are indeed directly related to the ejecta seen


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Acknowledgements We thank the anonymous referee for reviewing our work and for insightful and constructive comments which improved the manuscript. The project is supported by CNRS, by the Agence Nationale de la Recherche (ANR-14-CE33-0018, GIPSE), the OSUG@2020 labex and the Programme National de Planétologie (PNP, INSU) and Programme National de Physique Stellaire (PNPS, INSU). Most of the computations presented in this paper were performed using the Froggy platform of the CIMENT infrastructure ( https://ciment.ujf-grenoble.fr ), which is supported by the Rhône-Alpes region (GRANT CPER07_13 CIRA), the OSUG@2020 labex (reference ANR10 LABX56) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir, supervised by the Agence Nationale pour la Recherche. P.K. and R.J.D.R. thank support from NSF AST-1518332, NASA NNX15AC89G and NNX15AD95G/NEXSS. This work benefited from NASA’s Nexus for Exoplanet System Science (NExSS) research coordination network sponsored by NASA’s Science Mission Directorate.


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We would like to thank the anonymous referee for suggestions that helped improve this manuscript. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number G04-15088X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics and Space Administration under contract NAS8-03060. TJG and PPP acknowledge support under NASA contract NAS8-03060. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France.


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The research leading to these results received funding from NASA OSS grant NNX14AJ56G.


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

ratio of 200. Table 5 Spearman’s Rank Correlation Coefficient of the Logarithmic MLR with Stellar Luminosity, Infrared Magnitude, and Colors Figure 12. The relation between MLR and luminosity. Figure 13. Comparison of the relation between MLR and luminosity with the works of de Jager et al. ( 1988 ), van Loon et al. ( 2005 ), and Beasor Davies ( 2018 ). Unlike the common slope, the intercept, i.e., the coefficient of proportion in the relation, is not the same. As discussed in Section 3.1 , the amount of MLR depends on multiple factors, including the dust species, the dust size, the stellar expansion velocity, and luminosity. The effects of dust species and size are discussed in previous sections, and can be as large as one order of magnitude. The expansion velocity and luminosity should have less effect, probably changing the MLR by a factor of a few. Taking all the factors into account, the MLR may differ by two orders of magnitude for a given observational SED, therefore the comparison of the vertical shift is meaningful only under the same model conditions. Taking T eff into account, the relationships become The fitting results are displayed in Figure 14 together with the value of R 2 , which implies an improved relation in comparison with the luminosity alone. In general, the fitting is reasonably good with the residual , but it deviates somewhat from the measurements, particularly for the silicate dust. This may be understood because MLR depends on other parameters in addition to L and T eff , such as stellar mass, radius or surface gravity (Reimers 1975 ; Beasor et al. 2020 ), and pulsation period (Goldman et al. 2017 ). But these parameters are not conveniently available from observation. Figure 14. The relation between MLR and the luminosity and effective temperature. The red line marks Y = X . 4.4. Relation of MLR with Infrared Brightness After examining the infrared-band brightness, a very good relation is found with the mid-infrared flux in the Spitzer/IRAC4 band at 8 μ m and the MIPS24 band at 24 μ m. Linear fitting yields the following relations with the absolute magnitude, for which the distance modulus is 24.32 for M31 and 24.50 for M33 (Paper I ). The fitting lines are shown in Figures 15 and 16 . The correlation coefficients are all large (−0.7) as listed in Table 5 , which implies a tight relation of the mid-infrared flux with the MLR. This relation is expected from the warm temperature of the circumstellar dust, which emits mainly in the mid-infrared. On other hand, the relation with near-infrared flux is weak and not presented. Figure 15. The relation between MLR and the Spitzer/IRAC4 absolute magnitude. Figure 16. The relation between MLR and the Spitzer/MIPS24 absolute magnitude. 4.5. Relation of MLR with Infrared Color Indexes Examining the infrared colors, it is found that the MLR is sensitive to IRAC1 − IRAC4: As seen in Figure 17 , the scattering around the fitting line is significant, and the correlation of MLR


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

values of FWHM, namely ∣〈FWHM〉 N − 〈FWHM〉 N−1 ∣. The results of this analysis, for N up to 100, are presented in the left panel of Figure 7 . As shown in the figure, the mean FWHM converges to ≃2.85 px after only about 20 iterations, N, at which point the standard error of the mean, which decreases as (as in fact expected for a normal distribution of FWHM values with a standard deviation of the population Σ) exceeds the differential error ∣〈FWHM〉 N − 〈FWHM〉 N−1 ∣. Figure 7. Left: the estimated mean FWHM of the PSF modeled with 2D Gaussian, 〈FWHM〉 N ± Σ N , as a function of the number N of PSF simulations performed (upper panel); the successive difference in the mean values ∣〈FWHM〉 N − 〈FWHM〉 N−1 ∣, along with the standard error of the mean Σ N (dashed curve), are shown on the lower panel. Right: histogram of the emerging FWHM values after 100 PSF simulations, along with the best-fit normal distribution returning 〈FWHM〉 100 ≃ 2.84 px and Σ ≃ 0.21 px. Right panel of Figure 7 presents the histogram of the emerging FWHM values after 100 PSF simulations along with the best-fit normal distribution returning, 〈FWHM〉 100 ≃ 2.84 px and Σ ≃ 0.21 px. Given this, the radius for the extraction region encompassing 3 σ of the photons from a point source formally reads as, px. However, the source PSF is not well represented by a 2D Gaussian and particularly with limited photon statistics, broad wings of the PSF do matter. To illustrate this, in Figure 8 we plot the enclosed photon count fraction for each simulated PSF. As shown, the real 2 σ radius ranges between 2.5 px and 5 px, depending on a particular PSF realization, and the 3 σ radius is, in all cases, at ∼10 px. Hence, in the analysis of the surface brightness presented in this paper, instead of a 2D Gaussian approximation, we build a table model for the core PSF as a result from the averaging of over 100 PSF simulations. Figure 8. Enclosed count fraction for 100 simulated PSF images; horizontal dotted lines from bottom to top correspond to 1 σ , 2 σ , and 3 σ count fractions, respectively. Appendix B Surface Brightness Profiles Along and Across the Jet Axis We have also extracted the radial profiles of the net counts separately for the four quadrants of the concentric annular regions centered on the CGCG 292−057 nucleus, oriented to the east, to the west, to the north, and to the south from the center. The east and west quadrants correspond therefore to the surface brightness profiles along the axis of the inner jets in the system, while the north and south quadrants to the surface brightness profiles across the jet axis. Due to the limited photon statistics in separate quadrants, we had to increase the size of the annuli from 2 px (as adopted in Figure 3 ) up to 7 px. The resulting profiles are presented in Figure 9 . Figure 9. X-ray surface brightness profiles resulting from extracting the net counts from four quadrants of a concentric stack of annular regions (each with the bin size of 7 px)


O O O O O O O B-Mission O B-Mission O 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 B-Person I-Person O O O B-Person O B-Person O B-Person I-Person O O O O O O B-Survey I-Survey I-Survey I-Survey B-Person O B-Person O O O O B-Organization I-Organization I-Organization B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant O O O B-Grant I-Grant I-Grant I-Grant O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Mission O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Software O O O B-Organization O O O O O O O O B-Archive I-Archive I-Archive O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O


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The authors are grateful to an anonymous referee for constructive comments that helped to substantially improve the paper. Computations are performed on a 20 node HYDRA cluster (dual Xeon X5675 with 6 cores per processor and 3.06 GHz clock speed), FORNAX (dual Opteron 6220 with 8 cores and 3.0 GHz clock speed), and KASPAR (dual Xeon X5675 with 6 cores per processor and 3.06 GHz clock speed) computing facilities at the Indian Institute of Astrophysics.


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We acknowledge the partial support of the following grants: NASA NNX14AC08G, NASA/SWRI Subcontract A991132BT, NASA Subaward 37102-2, NNX14AJ53J GCR, NNX15AI65G. This paper uses data from the Heliospheric Shock Database, generated and maintained at the University of Helsinki.


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outflow. Left: HST image of the young stellar jet HH 34 and its bow shock (from Hartigan et al. 2011 ). Right: expanded views of the bow shock and the putative Mach stem. The structured bow shock in HH 47 (Hartigan et al. 2011 ) is another potential example where transient Mach stems may occur. This object resolves into what appear to be dozens of small knots in high-resolution images. Surprisingly, these bright points form and dissipate on timescales of a decade, which is difficult to explain if they represent discrete knots of high density that plow through the working surface of the flow. In both HH 34 and HH 47, the shock velocity is ∼100 km s −1 and the knot size ∼7.5 × 10 14 cm, and so τ F ∼ 2.4 years. The numerical models imply that we should expect any transient Mach stems to evolve on a timescale of about a decade, in agreement with the observations. The postshock regions of cooling astrophysical shocks are complex and contain various zones of ionization for each element. Hence, these regions are not characterized by a single value of γ . However, the overall dynamical effects of cooling in bow shocks have been well-established for some time (e.g., Blondin et al. 1990 ). A critical parameter is the ratio of the cooling-zone distance d COOL to the obstacle size . When this ratio is ≳1, the gas acts like an adiabatic flow with γ = 5/3 where the maximum size of a Mach stem will be comparable to . In the opposite limit, when the obstacle is very large compared with the cooling length, the gas behaves dynamically as if it is isothermal. An isothermal shock has γ = 1 where no Mach stems are possible. In this case, Mach stems only exist on scale sizes ≲ d COOL . Hence, the maximum size of a Mach stem should be the smaller of d COOL or . The cooling distance scales inversely as the preshock density and directly as a power of the shock velocity (e.g., Hartigan et al. 1987 ), and also depends on the strength of the magnetic field (Hartigan Wright 2015 ). Hence, whether or not two intersecting bow shocks create a substantial Mach stem depends on the shock velocity, density, magnetic field strength, and the sizes of the bows. Overall, Mach stems should be most common when size scales are small enough to render cooling unimportant in the dynamics. The distribution of clumps in the flow and ambient medium ultimately determines whether or not Mach stems will form and grow in any situation, with the optimal separation for Mach stem growth being several times the diameter of the obstacles in a flow with moderate Mach number. The widest range of allowable obstacle separations occurs when cooling is least important (Section 4.1.2 ). Cooling distances in the HH 34 and HH 47 bow shocks are on the order of the size of the transient bright knots in these objects (Hartigan et al. 2011 ). Hence, the effective γ for these spatial scales is ∼5/3, which is favorable for Mach stem growth. In a future paper, we will present simulations of intersecting


O O B-Person I-Person O O O O B-Grant I-Grant I-Grant I-Grant B-Grant O B-Organization I-Organization I-Organization O B-Location O B-Survey O O O O O O B-Organization I-Organization I-Organization B-Location O B-Grant I-Grant O B-Person O B-Survey O O B-Person I-Person I-Person O B-Person I-Person O O O O B-Survey O O O O O O O O O B-Survey O O O O O O O O B-Person O O O B-Organization O B-Grant O O B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization B-Organization O O B-Organization O O B-Fellowship I-Fellowship I-Fellowship O O O B-Organization I-Organization I-Organization I-Organization O O B-Person O B-Person O O O O O O O B-Fellowship I-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O B-Telescope O O B-Person I-Person I-Person O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O B-Telescope O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization

Work by C. Han was supported by the Creative Research Initiative Program (2009-0081561) of National Research Foundation of Korea. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to A.U. The OGLE Team thanks Profs. M. Kubiak and G. Pietrzyński, former members of the OGLE team, for their contribution to the collection of the OGLE photometric data over the past years. Work by A.G. was supported by JPL grant 1500811. Work by J.C.Y. was performed under contract with the California Institute of Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. Work by C.B.H. and Y.S. was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Universities Space Research Association through a contract with NASA. The Spitzer Team thanks Christopher S. Kochanek for graciously trading us his allocated observing time on the CTIO 1.3 m during the Spitzer campaign. We acknowledge the high-speed internet service (KREONET) provided by Korea Institute of Science and Technology Information (KISTI).


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

from the MIST isochrones, that is, only using the SED of the star, its parallax from Gaia DR2, and the light curves and radial velocities. The uncertainties from this analysis are 35% for the planetary mass, surface gravity, and density, and 3.3% for the radius. These are consistent with the uncertainties derived from the analysis using the MIST evolutionary tracks as constraints. The fractional uncertainties from the original paper and the analysis without constraints are shown in sky blue (with constraints) and green (without) in Figure 1 . We conclude that the inferred parameters of the system derived using purely empirical constraints are as precise (and likely more accurate) than those inferred using theoretical evolutionary tracks. Therefore, at least for systems similar to KELT-26, we see no need to invoke theoretical priors. 4.3. Kepler-93b Kepler-93b is a terrestrial exoplanet with a 4.7 day period discovered by Ballard et al. ( 2014 ). It has a mass of M p = 4.02 ± 0.68 M ⊕ and radius of R p = 1.483 ± 0.019 R ⊕ . With a radius uncertainty of only 1.2%, it is one of the most precisely characterized exoplanets to date. Ballard et al. ( 2014 ) used asteroseismology to precisely constrain the stellar density, and then used it as a prior in their MCMC analysis, leading to the remarkably precise planet radius. Their analysis did not use external constraints from stellar evolutionary models, however. Dressing et al. ( 2015 ) revisited Kepler-93 and collected HARPS-N (Mayor et al. 2003 ) spectra, which they combined with archival Keck/HIRES spectra to improve upon the planet’s mass estimate. They thus reduced the uncertainty in the mass of Kepler-93b from ∼40% (Ballard et al. 2014 ) to ∼17%. We used the photometric parameters ( T , τ , and δ ) from Ballard et al. ( 2014 ) and the semi-amplitude K ⋆ from Dressing et al. ( 2015 ) to test our analytic estimates. We compared our results to the reported uncertainties in M p , g p , and ρ p from Dressing et al. ( 2015 ), since they provide slightly more precise properties. The uncertainties in the properties of Kepler-93b are all ∼17%, and 1.2% for the radius, which are in excellent agreement with our analytic estimates, as shown in Figure 1 and Table 1 . Interestingly, this implies that the asteroseismological constraint on ρ ⋆ does not significantly improve the overall constraints on the system. 4.4. HD 21749b HD 21749b is a warm sub-Neptune on a 36 day orbit transiting a K4.5 dwarf discovered by Dragomir et al. ( 2019 ). The planet has a radius of determined from TESS data, and a mass of constrained from high-precision, RV data from the HARPS spectrograph at the La Silla Observatory in Chile. Dragomir et al. ( 2019 ) performed an SED fit combined with a parallax from Gaia DR2 to constrain the host star’s radius to R ⋆ = 0.695 ± 0.030 R ⊙ . They then used the relations of Torres et al. ( 2010 ) to derive a stellar mass of M ⋆ = 0.73 ± 0.07 M ⊙ , although they do not specify what values of T


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

and C + 1, with If we assume m C ≪ m j , then the coagulation between any grain of bin j and a grain of bin i with a mass lower than m C , − − m j produces a grain in bin C . The fraction υ of grains transferred to bin C is therefore given by However, if m C , − − m j m i , − , then the product of coagulation is too massive for bin C and υ = 0. Conversely, if m C , − − m j > m i , + then υ = 1. The integrals of Eq. ( B.21 ) need to be calculated analytically due to the computational cost of performing a numerical integration for each pair of bins at each time step. In particular, if the distribution is steep, one end of the bin may not be captured accurately, yielding large errors. For coagulation kernels that are in the form , the analytical calculation is tedious but straightforward. Fortunately, this is the case for the kernel used in this paper (see Eqs. ( 9 ) and ( 14 )), The analytical expression of υ is a function of m β , which can lead to inaccuracies due to numerical truncation errors where the distribution is steep (| β | is large). Fortunately, for high values of | β |, some terms can be simplified. This is not the case for specific lower values (if we have to integrate m −1 into a log function instead of a power-law), however, so that the simplification cannot be generalized to all β . We also have to ensure that the simplification can be applied to both the top and bottom of the fraction. We detail here the procedure used in Ishinisan to minimize numerical inaccuracy. We define the following functions: and r ( m 1, − , m 1, + , m 2, − , m 2, + , β 1 , β 2 ), so that We therefore have for the turbulent kernel where κ k = m k , − if s k −5, and κ k = 1 else, for k = 1, 2, to match the criteria of function q ( B.23 ). When the value of υ is known, the variations rates of mass density in the four involved bins are After summing all the variation rates, we chose the time-step Δ t so that the relative variation of mass in each bin does not exceed a number ε prec , typically smaller than one, to ensure numerical accuracy, The densities are then updated and the new slopes, average size, and average mass of bins are calculated according to the calculations detailed in Appendix B.1 . B.3. Tests We tested the coagulation algorithm using two simple kernels, namely the constant and additive kernels, Menon Pego (2004) showed that these two kernels possess self-similar solutions, The mass density in each bin i is given by where erf and erfc are the error function and the complementary error function. In each case, the two formulae are mathematically equivalent but are written in this form to avoid numerical truncation errors. The fraction υ has a similar form as the turbulent kernel presented in the previous section (Eq. ( B.24 )). The function q is the same, and function r for the constant kernel reads and for the additive kernel We used Ishinisan to reproduce these self-similar solutions. We set up 30 bins between m min = 4 × 10 −6 and m max


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

These values are compatible with our results based on the cleaned open cluster sample, whereas the use of the complete data set always yield somewhat steeper slopes. However, the most apparent difference in the RMD of Cepheids and open clusters is that Cepheids show a continuous decline of metallicity out to 18 kpc. Fig. 8 RMD of the open clusters and Cepheids compared to Galactic chemical models. Upper panel : the running average and the spread in iron of the Cepheid sample is shown as a grey line and a light grey area. The red line is the chemical model for the gas by Minchev et al. (2013) , the black dashed line shows the gradient derived for the youngest cluster age group (Table 3 ). Lower panel : in grey we show the running average of intermediate-age clusters (0.53 Gyr), the red dashed line is the chemodynamical model by Minchev et al. (2013) for 2 Gyr, the black solid line is the mean value of outer disc clusters, and the black dashed line is the gradient that we derived for all clusters in the outer disc. We used the Cepheid data to derive a running average with the same criteria that we adopted for the open clusters in Sect. 4.1 . We did not detect any significant difference by using a better sampling. The upper panel of Fig. 8 compares the results for open clusters with the Cepheids. Obviously, the gradient of the youngest cluster group is somewhat steeper than the one based on Cepheids. The slope of the cluster groups does not show a clear dependence on age, thus the steeper gradient might be attributed to the smaller sample and the narrower distance range that is covered by the young clusters. The sample of the Cepheids represents a very young population with a mean age of about 60 Myr. Thus, they have not moved much from their birthplace, and a comparison with a Galactic chemical model for the gas is justified. Figure 8 shows that the model by Minchev et al. (2013) agrees very well with the observations. We shifted the model by about 0.05 dex towards lower metallicities to match the Cepheids and young open clusters at the solar position. Genovali et al. (2014) identified some candidate Cepheid groups that show an enhanced metallicity by about 0.05 dex (the groups VI to X in their paper) and are located close to the Perseus spiral arm. These can also be identified in Fig. 8 at 910 kpc. The Cepheids also show an enhancement of the metallicity in the innermost Galactic region with a much steeper gradient than the chemical model predicts. These objects could be related to the CarinaSagittarius arm. The spiral arms are the star-forming machines of the disc, thus the effect of the spiral arms cannot be ignored ( Lépine et al. 2011 ). However, a simple extrapolation of the metallicity towards the Galactic centre is not justified because inner disc and Galactic bulge and bar show different trends (see discussion by Genovali et al. 2013 , and references therein). Minchev et al. (2013) also presented a model that includes the dynamical


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 sight is chosen to be along the x- axis, it is useful to express the x positions of each surface with a specific r rc asDefining a new functionyields denotes the two line-of-sight ( x ) positions for a surface defined by a particular value of r rc at sky position ( y , z ). Functions a , b ( y , z ), and c ( y , z ) are defined by the geometry of the object in question. Equations ( 6 )–( 8 ) describe the appropriate functions representing a spheroid with axial ratio α and inclination i. E ( y , z ) is a function that is entirely dependent on the object's shape; the following section discusses its conceptual meaning further. 3.1. Discrete Derivation It is possible to define an object as a discrete series of shells, each of which is defined as the region between an inner () and an outer () surface with an average volume density () within the shell. The depth along the x- axis of each such shell at different ( y , z ) positions will vary according towhere is the total depth along the line of sight at position ( y , z ) for the shell made up of two surfaces defined by and . Substituting Equation ( 11 ) into Equation ( 12 ) yieldsEquation ( 13 ) describes the depth of each shell; however, this representation is of limited use since r rc is not an observable quantity. Similarly, E ( y , z ) is a function that is directly dependent on the object's unknown shape. Equation ( 13 ) must be put in terms of observable quantities: the observed column density, and the area within each column density contour. Each surface as described by Equation ( 11 ), when projected onto the line of sight, produces a closed boundary composed of those ( y , z ) positions where . In view of Equation ( 11 ) the projected boundaries of each shell are defined bySolving for E ( y , z ) using the spheroid model above yields a familiar relation,which is a simple ellipse that results from projecting a three-dimensional spheroid surface onto a two-dimensional plane. Equation ( 14 ) makes clear that each contour of equal E ( y , z ) corresponds to the boundary of a particular volume density surface, with a specific value of r rc , and possesses a unique projected area. In general, the projected area of a surface of a particular r rc can be expressed aswhere is a geometry-dependent unknown constant(). All positions with equal correspond to the projected boundary of a surface with with corresponding area A c . The additional subscript c denotes a specific contour. Therefore, Equation ( 13 ) can be reformed in terms of areas aswhere represents the depth along the line of sight of the shell between surfaces defined by and at all positions defined by the contour formed by the projected boundary of the surface defined by . The observed column density can then be defined as N c represents the column density at all positions ( y , z ) defined by the projected boundary of the surface. represents the mean volume density within the shell whose surfaces are defined by and . The column density


O O O O O O O O O O O O O O O O O B-Person O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O O B-Organization O B-Grant O B-Telescope B-Instrument B-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O B-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Person O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Instrument O O O O O O O O O O B-Organization B-Location O O B-Organization B-Location B-Organization I-Organization B-Organization B-Organization B-Location B-Organization B-Organization B-Location B-Organization B-Location B-Organization B-Organization B-Organization B-Location B-Organization B-Location O O O O O O O O O B-Organization B-Location B-Organization B-Location B-Organization B-Location B-Organization B-Location B-Organization B-Location O B-Organization B-Location B-Instrument O O O O O O O O O O B-Organization I-Organization B-Location O O B-Organization I-Organization B-Location B-Observatory B-Location B-Organization B-Organization B-Location B-Organization B-Organization I-Organization B-Location B-Organization B-Location B-Observatory I-Observatory B-Location B-Organization I-Organization I-Organization B-Organization B-Organization B-Organization B-Organization I-Organization B-Location O B-Organization B-Organization B-Organization B-Organization I-Organization B-Location O O O O O O O O O B-Organization B-Location B-Observatory B-Location B-Organization B-Organization B-Organization B-Location B-Organization B-Location B-Organization B-Location B-Organization B-Location B-Organization B-Organization B-Location O B-Organization B-Location O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization B-Location O O O O O B-Software O O O O O B-Software O O B-URL O O B-Software O O O O O B-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Grant O B-Organization O B-Organization O O O O B-Archive I-Archive I-Archive I-Archive

We thank the referee for useful comments and suggestions which significantly improved the quality of this paper. T.M.H. gratefully acknowledges the financial support from the Belgian Science Policy Office (BELSPO) in the frame of the PRODEX project C90370 ( Herschel PACS guaranteed time and open time programs: science exploitation). I.D.L. is a postdoctoral fellow of the Flemish Fund for Scientific Research (FWO-Vlaanderen). M.B. also acknowledges the financial support of the same Flemish Fund for Scientific Research. PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAF-IFSI/OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). SPIRE has been developed by a consortium of institutes led by Cardiff University (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the NASA (USA). This research made use of APLpy, an open-source plotting package for Python hosted at http://aplpy.github.com , and Montage, which is funded by the NASA (USA) Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and Caltech, and maintained by the NASA/IPAC Infrared Science 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 O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag I-Tag B-Tag I-Tag I-Tag I-Tag I-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 solar system icy satellites, it could still possess enough water to be an aquaplanet , the term aquaplanet refering here to a planet where water is abundant enough to flow efficiently on a planetary scale. In practice, in our simulations, this means that the surface acts as an infinite source of water. In this section, we thus make an attempt at quantifying how much is enough. Then, we discuss the various climate regimes available to an aquaplanet and point out the main differences with the dry case. 5.1. Transition from small to large water inventory The exact water inventory for which Proxima b would transition from a land planet (previous section) to an aquaplanet (this section) is difficult to define. In particular, the nature of the transition depends of the amount of greenhouse gas in the atmosphere. For a low atmospheric greenhouse effect (meaning that ice is stable somewhere on the planet), there is a bistability between two possible climate regimes around the transition. To understand this bistability, we introduce a thought experiment in which we consider a planet with two very different initial conditions: Case 1: warm- and/or water-rich-start. We assume that theplanet starts with a global ocean, possibly covered by sea icewherever cold enough. This experiment has been carried outby Yang et al. (2014) with a325 m deep ocean. They showed that in sucha configuration, winds carry sea ice toward hot regions and theocean carries heat toward cold regions, so that an equilibriumcan be found with less than 10 m of sea ice inthe coldest regions. They however acknowledge that the pres-ence of continents could significantly alter this value. Yanget al. (2014) only looked at a syn-chronous planet, but the argument remains qualitatively valid fora non-synchronous planet, even though numerical values willsurely change significantly. Therefore, water content as small as 10 m GEL (and maybe even lower) is sufficient to maintain aquaplanet conditions. If water were to be removed or the temperature decreased, at some point, the oceanic transport would shut down and the planet would transition to a dry, cold regime with glaciers. Case 2: cold- and/or water-poor-start. As discussed in the previous section, if the planet started cold or dry enough, all the water would be trapped in ice caps and glaciers. Now, we demonstrated earlier that in this state, more than m GEL of ice could be stored this way. If the water inventory and/or the temperature were to be increased, glaciers would progressively spill toward hotter regions. This state could resist until the oceanic transport becomes more efficient than the atmospheric transport. After that, an ocean would accumulate and, in turn, warm the cold regions, speeding up the transition to the aquaplanet regime. Therefore, between roughly and m GEL, two distinct climate regimes coexist, depending on the history of the planet. As both the water inventory and the amount of greenhouse gases play a role, it


B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O O B-Location B-Organization I-Organization I-Organization O O O B-Grant O O B-Person I-Person O B-Person I-Person O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O B-Grant I-Grant I-Grant O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization I-Organization I-Organization O O B-Person I-Person B-Person I-Person O O O B-Collaboration I-Collaboration O O O O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O O B-Model O B-Model O O B-Model O O O O O O B-Collaboration I-Collaboration O O O O O O O O O O B-Organization O O B-ComputingFacility O O O B-Organization O O O O O O

B.V.L. was supported by a Stanford University undergraduate research grant. Y.Y.M. was supported by the Weiland Family Stanford Graduate Fellowship. This work received partial support from the U.S. Department of Energy under contract number DE-AC02-76SF00515. We thank Harry Desmond and Andrew Hearin for useful discussions. We thank Rachel Reddick for providing the measurement of observed galaxy statistics used in this work. This research made use of the Dark Sky Simulations, which were produced using an INCITE 2014 allocation on the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory. We thank Mike Warren, Matt Turk, and our other Dark Sky collaborators for their efforts in creating these simulations and for providing access to them. We thank Peter Behroozi for providing the halo catalogs and merger trees for the Bolshoi , BolshoiP , and MDPL simulations, which were run by the MultiDark Collaboration. Additional simulations and computations were performed using computational resources at SLAC and at NERSC. We thank the SLAC computational team for their consistent support.


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ACKNOWLEDGEMENTS The authors acknowledge the support from the program of development of M.V. Lomonosov Moscow State University (Leading Scientific School ‘Physics of stars, relativistic objects and galaxies’). We also would like to thank the Professor Maurizio Paolillo (Department of Physics, University of Naples Federico II) and Arina Morgunova (Sternberg Astronomical Institute, M.V. Lomonosov Moscow State University) for the useful discussion.


O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O O O O O O O O O O O O

ACKNOWLEDGEMENTS This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center. This work is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). We thank the referee for the constructive feedback and suggestions that improved the quality of the paper.


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The financial support by the Swiss National Science Foundation (SNSF) through grant ID 200021_159206/1 is gratefully acknowledged. The work of Alberto Paganini was partly supported by the EPSRC Grant EP/M011151/1. Special thanks are extended to L. Belluzzi and O. Steiner for reading and commenting on the paper. The authors also are grateful to the anonymous referee for providing valuable comments that helped to improve the article.


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

T 0 versus X-ray luminosity from equation ( 21 ) compared to data (Johnstone et al. 2015 ). The solid and dashed curves, respectively, correspond to the equilibrium temperatures for solar minimum and maximum, T x, ⊙1 = 0.97 × 10 6 K and T x, ⊙2 = 2.57 × 10 6 K (Johnstone et al. 2015 ). The plot shows that equation ( 21 ) is consistent with the data. Although the total wind power escaping from the scale height of the corona is given by , the total wind power escaping from the star is at least . Assuming constant , mean molecular mass m p /2, and thus c s = 2 k b T / m p and c V = 3 k b / m p (Hearn 1975 ), the relation between the total wind power and the coronal wind flux is where . Fig. 1(b) shows this total integrated wind power (blue) along with (green), and (orange) with all three quantities normalized to the same constant . We see that in regime II. Note also that when the equilibrium p 0 is plugged back into the expressions for F x and F W , the ratio of scales with . Therefore, although we focus on m * = r * = 1, for the temperature range of interest we would predict for a range of late-type stars, largely independent of mass since for the relevant stellar models (Kippenhahn, Weigert Weiss 2012 ). Figs 1(c) and (d) are similar to Figs 1(a) and (b) but apply when the last exponent in equation ( 16 ) is reduced by a factor of 2, highlighting the sensitivity of the temperature dependence. Here the power-law fit more accurately matches regime II than the exponential of equation ( 22 ). With the physics included in our present model, we do not identify a huge drop in mass-loss rate at high as suggested by two data points in Wood et al. ( 2014 ). More data are needed to confirm this is a statistically significant effect. There does not seem to be evidence of a corresponding change of magnetic configuration (Vidotto et al. 2016 ), so that would not provide an explanation if the effect were real. Suzuki et al. ( 2013 ) suggested that a decrease in mass loss for young active stars might arise because the increase in coronal density could lead to runaway cooling that drains the thermal energy that would otherwise accelerate the wind. This model does not employ coronal equilibrium arguments that we have used herein to determine our coronal properties. We leave further consideration of this for future work. 4.2 X-ray luminosity as function of magnetic field strength Having established that in regime II, we now connect both of these quantities to the source of magnetic energy. Blackman Thomas ( 2015 ) estimated from the dynamo-produced magnetic energy rising up through the convection zone. To accommodate our present result that 1/2 of source magnetic energy goes into , the relevant expression becomes where B ∼ B φ and Θ/4π is the solid angle fraction through which the field rises (proportional to, if not equal to of the previous section), and we have used the expression for u b below equation ( 12 ). Using equation ( 13 ) in equation ( 24 )


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

data set in the context of ΛCDM is less than . This is an effect approximately at 2σ level. In fact, this probability is even smaller if we consider the exact σ differences that are shown in Table 1 and find the fraction of simulated data sets with simultaneous σ differences larger that the exact corresponding σ differences of the real data. In particular we find that the probability to have simultaneously 1.14σ difference (or larger) in the first bin, 1.48σ difference (or larger) in the second bin, and 0.99σ difference (or larger) in the third bin for , is . Similarly, for we find the same probability to be . Even though this decrease of probability is interesting to note, it is not generic as it is based on the fine tuned σ deviations of the real data bins from the full data best fits (1.14σ, 1.48σ, and 0.99σ). Thus, this is an aposteriori statistic constructed after looking at the data. Therefore, we adopt the more generic and conservative statistical level of significance of corresponding to the simultaneous deviation of at least 1σ for all three lowest z bins. Note that a similar oscillating effect was also observed in Refs. Kazantzidis Perivolaropoulos ( 2020 ), Sapone et al. ( 2020 ) even though its statistical significance was not quantified using simulated data as in the present analysis. Moreover, it is interesting to check if this behaviour is also evident for any three out of four bins. In 1000 Monte Carlo realizations we find that the number of simulated data sets where the derived in any 3 bins is more than 1σ away from the best fit to the whole (random) data sample is while the corresponding number of cases for is as it is demonstrated in Fig. 3 . The probability is smaller if we consider the exact σ difference of Table 1 . In particular, we derive the number of cases where the derived in any 3 bins is more than away from the best fit to the whole (random) data sample is , while the corresponding number of cases for is . A summary of the results can be seen in Table 2 . These results indicate that the aforementioned oscillating effect is much more prominent at low z ≲ 0.5 where the dark energy density is more prominent than in the fourth bin, which involves higher z . This fact favours the possibility that the effect has a physical origin since a systematic effect would probably affect equally all four redshift bins. Figure 3. Left-hand panel: Percent of simulated Pantheon dataset (including systematics) where any three out of four bins all differ simultaneously more than from the best fit of the full data set. Right-hand panel: Same as the left-hand panel for the parameter instead of . Table 2. Summary of the Monte Carlo deviations from the simulated and real data. The obtained results considering the exact σ real differences should be treated with care, since this decrease of the probabilities is not generic and it is based on a fine tuned σ value. 3 CONCLUSION – OUTLOOK We performed a redshift tomography of the Pantheon


O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O B-Telescope O O O O B-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Observatory I-Observatory I-Observatory O O O O B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization B-Telescope O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Location I-Location O O O O O O O O O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant O O O O O B-Software O O O O O B-Organization I-Organization I-Organization O O O B-Grant O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Grant O B-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization B-Archive I-Archive I-Archive O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person

We thank the anonymous referee and the MNRAS editorial staff for their comments on this paper. The Australian SKA Pathfinder is part of the Australia Telescope National Facility which is managed by CSIRO. Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. Establishment of the Murchison Radio-astronomy Observatory was funded by the Australian Government and the Government of Western Australia. ASKAP uses advanced supercomputing resources at the Pawsey Supercomputing Centre. We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. This research made use of Montage. It is funded by the National Science Foundation under Grant Number ACI-1440620, and was previously funded by the National Aeronautics and Space Administration's Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. This research has made use of NASA's Astrophysics Data System. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. IH acknowledges many useful discussions with Jan Noordam, Rick Perley and Oleg Smirnov.


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This work was supported by the Planetary Sciences and Exploration Programme, Indian Space Research Organization (ISRO), PRL, Ahmedabad under the sanctioned project scheme. Calculations reported in the present work were carried out at the Computer Centre, Banaras Hindu University.


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 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O B-Citation O O O B-Citation 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 B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject 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 O O 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 B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O B-CelestialObject I-CelestialObject 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-CelestialObject I-CelestialObject O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula 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 B-CelestialObject I-CelestialObject O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O

of these values, with discrepancies too large to be explained by instrumental errors (e.g. NGC 2509, Fig. 6 ). We also remark that on average, our distances estimated from parallaxes tend to agree more often with the more distant literature value. We suggest that the isochrone fitting procedure from which most photometric distances are estimated might be biased in many of those instances, as they might be affected by field contamination, as well as the degeneracies between distance, reddening, and metallicity. The strength of the Gaia data does not only reside in parallaxes from which distances can be inferred, and in precise and deep photometry, but also in our ability to obtain clean colour-magnitude diagrams from which astrophysical parameters can be infered. Fig. 6. Sky distribution ( top left panel ), colour-magnitude diagram ( top right panel ), and parallax as a function of magnitude ( bottom panel ) for the members of NGC 2509. The median parallax is 0.36 mas. Available literature distances for this cluster are 912 pc (DAML, blue), 1700 pc (MWSC, green) and 2900 pc ( Carraro Costa 2007 , red), which correspond to parallaxes of 1.09 mas, 0.59 mas, and 0.35 mas (respectively). 5. Specific remarks on some clusters It would be lengthy and impractical to devote a Section to every object under analysis in this study, but we provide additional comments on the specific cases of two clusters classified as OCs that are likely globular clusters, and on the previously unreported OCs discovered in this study. 5.1. BH 140 and FSR 1758 are globular clusters The colour-magnitude diagrams of BH 140 and FSR 1758 (shown in Fig. 7 ) present the typical aspect of globular clusters, with a prominent giant branch and an interrupted horizontal branch displaying a gap in the locus occupied by RR Lyrae. They are also clearly seen as rich and regular distributions on the sky. These two objects, located near the Galactic plane ( b = −4.3° and −3.3° for BH 140 and FSR 1758, respectively) also exhibit small parallaxes ( π = 0.16 mas and 0.09 mas), so their distances cannot be estimated accurately from parallaxes alone. FSR 1758, with a Galactic longitude l = 349.2°, seems to be located deep in the inner disk, as the distance estimated from its parallax yields a Galactocentric radius R GC = 1560 pc, and altitude Z = −470 pc. Fig. 7. Top left panel : colour-magnitude diagram for BH 140. Middle left panel : distribution on the sky for the same stars. Bottom left panel : proper motion diagram showing the field in light grey, and the cluster stars as black dots. Right column panel : same for FSR 1758. The broad appearance of the CMD of BH 140 can be explained by blended photometry in the inner regions. As discussed in Evans et al. (2018) and illustrated in Arenou et al. (2018) , the G BP and G RP fluxes of Gaia DR2 sources might be overestimated as a result of background contamination, and the effect is especially relevant in crowded fields such as the core of globular


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

We thank Andrew Hearin for help in using his mock catalogue, Yu Lu for using his semi-analytical data, and Zhankui Lu for helpful discussion and the anonymous referee for helpful comments that greatly improved the presentation of this paper. HJM acknowledges the support from NSF AST-1109354. This work is also supported by the 973 Programme (nos 2015CB857002, 2015CB857005).


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Batalha et al. 2013 ; Petigura et al. 2013 ). Radial velocity measurements (Weiss Marcy 2014 ) and transit timing variations (Wu Lithwick 2013 ) manifest that the masses of these super-Earths are in the range of 2–20 M ⊕ . The abundance of super-Earths presents a puzzle for the core instability theory. This theory indicates that when a protoplanet reaches super-Earth size, two physical processes make the survival of super-Earths difficult, leading to a planetary “desert” in this size range (Ida Lin 2004 ). Super-Earths excite density waves in protoplanetary disks (PPDs) and give rise to rapid type I migration. This type of migration causes the planet to be engulfed by its host star if the disk inner edge touches the stellar surface. Recent studies have sought various remedies for type I migration (Yu et al. 2011 ; Fung Chiang 2017 ). PPDs are expected to have an inner edge at the stellar magnetosphere (e.g., Long et al. 2005 ). For planets undergoing disk-driven migration, they are expected to pile up near this edge. They stay either at the edge because the gas runs out, inside the edge down to 2:1 resonance because that is where the tidal torque tapers off, or outside the edge because the standing waves generated by wave reflection off the inner edge stall planet migration (Tsang 2011 ). In this paper, we focus on another threat for super-Earths. Super-Earths have low mean density, which suggests that they must be surrounded by gas envelopes (Rogers Seager 2010 ). Since these observed super-Earths are in the range of critical mass, they trigger efficient gas runaway and accumulate massive gas envelopes. They become gas giants. As a result, super-Earths are supposed to be rare. However, Kepler ’s discovery wrecks these predictions. Lee et al. ( 2014 ) proposed a metallicity gradient inside the PPDs or the late assembly of cores to resolve the puzzle of super-Earth formation. Lee Chiang ( 2016 ) stressed that the late core assembly in transitional PPDs is more consistent with observations. In gas-poor environments, gas dynamical friction has weakened to allow proto-cores to stir one another and merge. In addition, this formation scenario ensures that super-Earth cores accrete mass with a few percent envelope mass fraction (EMF). Guillot Showman ( 2002 ) argued that the dissipation of the kinetic energy of the atmospheric wind, driven by intense irradiation, could bury heat inside the planet. Many studies extend this idea to explain the radius anomaly of hot Jupiters (Youdin Mitchell 2010 ; Ginzburg Sari 2015 ; Komacek Youdin 2017 ). These investigations focus on the late evolution after the disk dispersal. Unfortunately, this is invalid for the early evolution of super-Earths because they are still embedded within disks. The irradiation may not penetrate the disk and is not able to bury heat in the exoplanets. However, we note that tidal interactions between the host star and planet can periodically perturb the planet and generate mechanical


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TIM is supported by an appointment to the NASA Postdoctoral Programme at the Goddard Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA.


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A.-M.M. is supported by the National Aeronautics and Space Administration through Einstein Postdoctoral Fellowship Award Number PF2–130095 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8–03060.


O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-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

the deeper optical potential of antikaons , the earlier onset of K − and condensations in NS matter. Moreover, condensation in comparison with K − condensation always occurs at a higher density. It can be seen from equation ( 10 ) that the threshold condition for condensations is more difficult to fulfill compared with the threshold condition for K − condensation in NSs. In our model, condensations only appear in stable NSs when the optical potential of antikaons = −100, −110, −120 and −130 MeV, and the presence of them suppresses the increase of the fraction of K − mesons as indicated in Fig. 2 (a) and Table 1 . Besides, it can be also seen from Figs 2(b) and (c) that the increase of K − mesons makes the dramatical decrease of e and μ fractions in NSs. It is because that K − meson is boson in the lowest energy state, replacing negatively charged particles, makes the system energy lower. In order to keep the conditions of the electrical neutrality, the proton fraction grows faster and then the growth is suppressed when mesons appears in NSs. Eventually, the proton fraction turns out to be almost identical neutron fraction in NS matter. Therefore, according to equation ( 15 ), the Fermi momenta of neutrons decrease and the corresponding values of protons increase including K − and condensations in NS matter, which are displayed in Fig. 3 (a). Figure 1. EOSs and NSs masses as a function of nucleon density n N . In the paper, the black, red, blue, dark cyan, magenta, dark yellow and green lines represent the seven cases of = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. The dots stand for the maximum masses of NSs for the seven cases. Figure 2. Composition of NSs as a function of nucleon density n N with and without antikaon condensations. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Figure 3. The nucleon Fermi momentum, the effective mass and the single particle energy E N ( p F ) at the Fermi surface versus nucleon density n N in npeμ and npe matter. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Table 1. Maximum masses m max = M max /M ⊙ , and the corresponding radii R and the centre densities n C as well as the threshold densities and of K − and condensations for the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. Fig. 3 gives the nucleon Fermi momentum p FN , the effective mass and the single particle energy E N ( p F ) at the Fermi surface as a function of nucleon density n N including and not including K − and condensations in npeμ matter. We could see that the nucleon effective mass with K − and condensations is smaller than the corresponding values without K − and condensations, and it gradually declines along with the optical potential of antikaons growth in npe matter in Fig. 3 (b). The individual single particle energies of neutrons and protons in npe matter are all much less than their values in


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Acknowledgments This work was partially supported by the Consejo Nacional de Investigaciones Cientficas y Tcnicas (CONICET), and the Secretara de Ciencia y Tecnologa, Universidad Nacional de Crdoba, Argentina. Plots were made using r software and post-processed with inkscape . This research has made use of NASAs Astrophysics Data System. The authors would like to thank the anonymous reviewer for their valuable suggestions. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS web site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, the Ohio State University, the University of Pittsburgh, the University of Portsmouth, Princeton University, the United States Naval Observatory and the University of Washington.


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The authors appreciate the enlightening suggestions from the anonymous referee, which helped to improve the quality of this paper. This work is supported by National Basic Research Program of China (973 Program, grant No. 2015CB857005, grant No. 2013CB834905), the NSFC grant (grant No. 11233002, 11203022, 11421303, 11473025, 11033007), and the SOC program (CHINARE2015-02-03). 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/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


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ACKNOWLEDGEMENTS Parts of this research are supported by the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav) (project number CE170100004).