O O B-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O O O O O O O B-URL O O O O O O O B-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 O O O O O O O O O B-Survey O O O O O O O O O O O O O B-CelestialRegion O B-CelestialRegion I-CelestialRegion 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O

review by Somerville Davé 2015 ). At z ∼ 5–7, the excess of bright sources compared to the semi-analytical predictions appears to be even more pronounced than at lower redshifts but we caution that the most constraining measurement is based on a small number of sources only, and thus needs to be put on a firmer statistical footing. Meanwhile, the observations at z ∼ 2–3 appear to be consistent with Vallini et al.’s ( 2016 ) empirical predictions, and thus with what is expected from estimates of dust-obscured star formation activity at high redshift based on infrared luminosity functions. 4.2.2. Cold Gas Density of the Universe The observational constraints on the evolution of the cold gas density with redshift remain in agreement with both semi-analytical (Obreschkow et al. 2009 ; Lagos et al. 2011 , 2012 ; Popping et al. 2014a , 2014b ) and empirical (Sargent et al. 2012 , 2014 ) model predictions at z ∼ 2–3. Since most of the semi-analytical models include a varying α CO between individual galaxies, a simple interpretation of the consistency—despite the disagreement in the luminosity function estimates—remains challenging. In addition, the predictions do not account for the sensitivity limits of the CO surveys, or uncertainties due to cosmic variance. Given the differences in the CO luminosity functions between models and observations at high z , this effect could in principle lead to up to a factor of a few difference in the corresponding gas densities at high redshift. However, as discussed in Section 3.4 , the impact of the sensitivity limits, which would bias the measurements toward lower values, appears to be relatively minor based on the preferred model Schechter function fits to the COLDz data. Meanwhile, cosmic variance due to large-scale structure in the distribution of gas-rich galaxies (which is assumed to be uniform in our analysis) could bias the measurements either low or high. To obtain an approximate estimate of systematic uncertainties introduced by cosmic variance, we follow the prescription by Driver Robotham ( 2010 ), based on the distribution of galaxies near the characteristic stellar mass at a given redshift. 40 40 This method is based on a generalized expression (their Equation (4)) calibrated through an examination of galaxies within ±1 mag of the characteristic optical magnitude out to z ∼ 0.1 in the Sloan Digital Sky Survey (SDSS), which represent the most common galaxies at a given redshift. See cosmocalc.icrar.org for additional details. The field sizes and CO( J = 1 → 0) redshift ranges in Table 1 are used for all calculations. Including both Poisson uncertainty and cosmic variance scaled to the volume of the COLDz survey, we find a sample variance uncertainty of ∼30%–40% and ∼25% for the COSMOS and GOODS-North fields, respectively. Alternatively, adapting results based on models of the evolution of the most massive galaxies (i.e., M ⋆ > 10 11 M ⊙ ) by Moster et al. ( 2011 ) 41 41 For our estimate, we have made


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We thank Don Melrose for introducing us to key references in the quantum plasma literature, notably including BM07 . We also thank Bryn Haskell, the first reviewer Taner Akgün, and the anonymous second reviewer for their insightful comments, which have significantly improved the quality and clarity of this paper. This work was supported by an Australian Research Council Discovery Project Grant (DP110103347) and an Australian Postgraduate Award.


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ACKNOWLEDGEMENTS The authors thank Lars Bildsten, Jared Brooks, Sterl Phinney, Evan Kirby, Selma de Mink, Thomas Tauris, and Onno Pols for useful discussion. IK is supported by the DOE NNSA Stockpile Stewardship Graduate Fellowship Program. This research is also funded in part by the Gordon and Betty Moore Foundation through Grant GBMF5076. DK is supported in part by a Department of Energy Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of theU.S. Department of Energy under Contract No. DE-AC02-05CH11231.


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

on the individual galaxies. We derived the source counts using a circular aperture with 13′′ radius, which, at a distance of 65 Mpc, corresponds to 4 kpc. To account for the background emission, we used annuli with 60′′–120′′ radii. We did not obtain statistically significant detections for any of the individual galaxies. To increase the signal-to-noise ratio, we co-added the X-ray emission associated with the individual galaxies. For the full sample of 51 LSBGs, this resulted in a total exposure time of 381.1 ks. We did not detect statistically significant emission from the stacked data, implying that the X-ray brightness of LSBGs remains below the detection threshold. We also stacked the subset of 17 UDG candidates and the 17 LSBGs as well as the subset of blue and red galaxies in our sample. We did not detect X-ray emission in any of the subsets. In the absence of detections, we set upper limits on the average luminosity of galaxies by calculating the confidence bounds of the stacked signal. We defined the 95% confidence region of the distribution, and used the upper confidence bound of the count rate as an upper limit. To convert the count rate to flux, we assumed that the emission from the hot gas can be described with an optically thin thermal plasma model. Specifically, we assumed a gas temperature of kT = 0.2 keV and a metallicity of 0.2 solar, which are typical in low-mass elliptical galaxies (e.g., Boroson et al. 2011 ; Goulding et al. 2016 ). Based on the resulting count rate upper limit of , we estimate the upper limit on the flux of for the full sample of 51 galaxies, which corresponds to a luminosity of , where d represents the average distance of the sample in Mpc. We obtained similar upper limits for the subset of UDG candidates and LSBGs and for the blue and red subsamples, which are listed in Table 1 . Table 1 X-Ray Upper Limits on the Stacked LSBGs 5. Discussion 5.1. Constraining the Halo Masses The prototypical UDG, Dragonfly 44, has a virial mass of (van Dokkum et al. 2016 , 2017 ). Using its effective radius of 4.6 kpc and assuming a Navarro–Frenk–White (NFW) dark-matter halo profile, we estimate that it has a total mass of . Based on the L X – M (5 r eff ) scaling relation, this total mass is linked with an X-ray luminosity of L 0.3–8 keV ≈ 2.4 × 10 39 erg s −1 in the 0.3–8 keV band. However, the luminosity upper limit measured for the sample of 51 field LSBGs, with an assumed distance of 65 Mpc, is in the 0.3–1.2 keV band. After converting the X-ray upper limit luminosity to the 0.3–8 keV band, we obtain . This value is ∼40 times lower than that expected for a galaxy with a massive dark-matter halo (see Figure 2 ). A similar conclusion is obtained for the subset of 17 UDG candidates and the subset of 17 LSBGs with 0.3–8 keV, as well as for the blue and red galaxy subsets. Figure 2. Empirical relation between the 0.3−8 keV band X-ray luminosity of hot diffuse gas and the total gravitating mass within 5 r eff (red


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

of the new fitting functions are shown in the second and fourth columns of Fig. 4 . In this case, the measurements of P θ θ are reproduced with a maximum systematic error of 3% on all scales below k = 0.7 h Mpc −1 , and for all redshifts and neutrino masses considered. We therefore use a total of only five free parameters k δ , b , a 1 , a 2 and a 3 to mimic, with a 3% level accuracy at k 0.7 h Mpc −1 , the nonlinear effects on both the auto- and cross-spectra P θ θ and P δ θ . Let us now focus on the sensitivity of these parameters to cosmology and specifically to the overall amplitude of the matter power spectrum. From our set of four simulations at four different redshifts we are able to span a large range of possible values of σ 8 , which we use as a proxy for the amount of nonlinearities. Regarding neutrino cosmologies it is necessary to choose whether we use the σ 8 defined for cold dark matter only, σ 8, c , or the one defined for the total matter, σ 8, m . It has been shown ( Castorina et al. 2015 ) that regarding the bias or the nonlinear effects on the density power spectrum P δ δ , what matters is the amplitude of the cold dark matter clustering and not the total one. We have analyzed the dependency of the fitted parameters with respect to both amplitudes σ 8, c and σ 8, m and we found that one should use the total matter σ 8, m parameter in order to assess the correct values of k δ , b , a 1 , a 2 and a 3 ; at least, this choice is the one that lowers the residual dependency with respect to the neutrino mass. Figure 5 shows that the cosmological dependance of the fitting parameters can be mostly encapsulated into the σ 8, m parameter evaluated at the corresponding redshift. The most relevant example is the good match at redshift 1.5 of the ΛCDM simulation with the M ν = 0.53eV simulation at redshift 1; these simulations share almost the same value of the total matter σ 8, m , while differing significantly in the power spectrum shape. For the two cases, we obtain the same values for the fitted parameters k δ and k θ . Fig. 5. Top panel : dependence of the fitting parameters k δ , b , k θ , a 1 , a 2 and a 3 on the total matter clustering amplitude σ 8,m at each redshift, in the corresponding simulation (symbols). Lines are showing the fit of the dependance. Bottom panel : residual between the fitted σ 8,m dependance and the measured one. On the contrary, when using the cold dark matter σ 8,c parameter (see Table 1 ) the residuals are increasing because of spurious neutrino mass dependence when going from one cosmology to another. This effect can be explained by the fact that if massive neutrinos have a weak effect on the dark matter clustering in the nonlinear regime, they add, instead, a relevant contribution to the velocity field which is felt by dark matter particles. As a result, it seems that the preferred dependence on the total matter σ 8,m comes from the fact that nonlinearities in the velocity field are generated by the


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ACKNOWLEDGEMENTS NN and EJ acknowledge financial support from the International Science Program (ISP). BB thanks the European Research Council (ERC Starting Grant 757448-PAMDORA) for their financial support.


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(by ∼400 km s −1 ) than in Cano et al. ( 2018 ). Figure 9. Time evolution of the pEWs for features 1, 3, 4, 7, and 8 together with the Si ii expansion velocity evolution (bottom right panel). Black circles are the measured pEWs after lens- and host galaxy subtraction and de-reddening. Transparent points and shaded bands are individual measurements and the binned mean (±1σ) of low-redshift SNe from Folatelli et al. ( 2013 ), for all (red) and ‘Normal’ (blue) SNe Ia in their sample. The black and red dashed lines shows the pEW and velocity evolution of the Hsiao template and SN 2007le, respectively. Turning to the pEW measurements, we do not see any significant deviations from the time-evolution of SNe Ia in Folatelli et al. ( 2013 ). In Fig. 9 , the black points show the pEW measurements of iPTF16geu compared to all (red points) or ‘normal’ (blue points and blue shaded region) SNe Ia in Folatelli et al. ( 2013 ). However, we note that some measurements are outside the 1σ range, e.g. late-time pEW1 (likely due to improper lens and host galaxy removal), pEW3 and pEW7 (where the telluric corrections are imperfect). 5 TIME-DELAY MEASUREMENTS FROM SPECTRA OF SPATIALLY RESOLVED LENS IMAGES In our single epoch of HST spectroscopy, we can spatially resolve two spectra: one spectrum corresponding to Image 2 and one spectrum corresponding to Images 1, 3, and 4. However, Images 3 and 4 are subdominant, contributing with 7 per cent and 5 per cent to the total flux in F 814 W at this epoch, respectively. Hence, we will treat this spectrum as stemming from Image 1. By comparing the time evolution of spectral features between the spectra, we can in principle provide an independent measurement of the time delays between the SN images. However, in our case we are limited by the coarse ( R ∼ 210) spectral resolution. To complicate things further, at the epoch (+29 d) the Si ii absorption feature is no longer well-defined, displaying two or more local minima. Age dating of SN spectra is routinely done using cross-correlation techniques (e.g. snid ; Blondin Tonry 2007 ), and have been successful in measuring cosmic time-dilation (Blondin et al. 2008 ). We construct a simple χ 2 -statistic, fitting Hsiao template spectra (Hsiao et al. 2007 ) at different phases to the spectra of the spatially resolved SN images. This allows us to simultaneously fit for residual lens and host galaxy contamination using our template spectrum, and subtract a fraction of that flux (0.80 ± 0.03 and 0.19 ± 0.02 for Images 1 and 2, respectively) from the resolved SN spectra, so that the subtracted SN spectra and Hsiao templates at each phase match the host subtracted F 814 W photometry (see upper panel of Fig. 10 ). Figure 10. Top panel: HST spectra of the spatially resolved Images 1 + 3 + 4 (blue line) and Image 2 (green line). The summed spectra (red line) show very good agreement with the ground-based Keck spectrum (black line), observed at the same time. Bottom panel: χ 2 minima of


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

star discovered by Caffau et al. (2011a ). The other symbols are literature data. The black and yellow dashed lines delimit the low-carbon band. Details can be found in Bonifacio et al. (2018) . 6.3 <italic>α</italic> and neutron-capture elements Figure 6 shows the abundance ratios of [Mg/Fe] and [Ca/Fe] as a function of [Fe/H] for our sample of stars using the solar abundances from Lodders et al. (2009) . Literature data from Roederer et al. (2014) are also shown, which contain results from a rather large sample of evolved and main sequence stars. We were able to measure magnesium in the five stars. Among them, SDSS J081554.26+472947.5 seems to have a rather low [Mg/Fe] abundance ratio and a subsolar [Ca/Fe] upper limit abundance. This is due to our high upper limit of [Fe/H]. In fact, by adopting the very low [Fe/H] determined by González Hernández et al. (2020) , we obtain [Mg/Fe] = 1.62 dex in excellent agreement with the [Mg/Fe] = 1.66 dex abundance that these latter authors obtained. The stellar parameters we adopted for SDSS J081554.26+472947.5 are close to those used by González Hernández et al. (2020) with a difference of 15 K on the temperature, a difference of 0.6 dex in log g that has no strong effect (typically 0.1 to 0.15 dex on the neutral Ca and Mg) on the determination of the abundance of neutral species, and the same micro-turbulent velocity. We found three stars with subsolar values for calcium, confirming the existence of stars with low [ α /Fe] ratios as already suggested by Bonifacio et al. (2018) . However, we reiterate the fact that in very metal-poor stars, under the LTE hypothesis, the resonance line that we used to determine the abundance of calcium leads to an underestimation of the calciumabundance ( Spite et al. 2012 , and references therein). For turnoff stars, the amplitude of the effect is rather small. Spite et al. (2012) computed a correction of the order of +0.1 dex in a turnoff star with [Fe/H] = −3.2 dex. Figure 7 shows the [Mg/Ca] ratio as a function [Fe/H] (upper panel) and as a function of [Mg/H] (lower panel). We have added the literature data from Roederer et al. (2014) for comparison. The [Mg/Ca] ratio found in our sample of stars ranges from +0.2 to +0.5 dex. This ratio is slightly higher than the abundance ratio found in the [Fe/H] range of –2 to –3 dex. At lower metallicities, the results from Roederer et al. (2014) show that the spread in the [Mg/Ca] ratio increases as [Fe/H] decreases with values ranging from negative abundance ratios to highly enhanced [Mg/Ca] ratios. From our measurements, the [Mg/Ca] ratio seems to increase as [Fe/H] decreases. The result for SDSS J081554.26+472947.5 found by González Hernández et al. (2020) seems to corroborate this point. The increase of the [Mg/Ca] ratio is also visible when the ratio is plotted as a function of [Mg/H]. However, a high value of [Mg/Ca] at very low [Mg/H] is not found in all the stars. In particular, SDSS J102915+17292, the normal


O O O B-Person I-Person B-Person I-Person O O O O B-Mission O O O O O O O O O O B-Person I-Person O B-Person I-Person 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 B-Person I-Person O O O O O O O O O O O B-Instrument O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O B-Organization O O B-Person I-Person O B-Event I-Event I-Event I-Event B-Person O O O O B-Fellowship I-Fellowship I-Fellowship B-Person O O O B-Fellowship I-Fellowship I-Fellowship B-Telescope O O B-Location O O O O O B-Organization O B-Observatory O O O O B-Organization O B-Organization B-Location O O O O O O O O O O O O B-Organization O B-Organization B-Location B-Mission O O B-Organization O O O O O O O B-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization B-Organization B-Location O O B-Grant I-Grant O O B-Telescope O O O O O B-Observatory I-Observatory O O B-Organization I-Organization I-Organization B-Person O O O O O B-Grant O O B-Organization I-Organization I-Organization I-Organization

The authors thank S. Gunar, B. Gelly, and the team of THEMIS for assisting with the observations. We would like to thank Jean-Marie Malherbe and Thierry Roudier whoco-aligned the SOT frames. They tested, up to now unsuccessfully, the CST and LCT methods to derive the flow pattern in the plane of the sky. We thank J. Dudik who provided the time-distance code to track the knots in the SOT cube of data, and G. Aulanier and P. Démoulin for fruitful discussions. This paper was discussed during the ISSI workshop (PI N. Labrosse) on “Solving the prominence paradox”. P.J.L. acknowledges support from an STFC Research Studentship. N.L. acknowledges support from STFC grant ST/I001808/1. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research Centre, and major contributions to downlink communications funded by the Norwegian Space Center (NSC, Norway) through an ESA PRODEX contract. The AIA data are provided courtesy of NASA/ SDO and the AIA science team. M.Z. acknowledges support from the project RVO:67985815 of the Czech Academy of Sciences.


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

of a disc and also contributed to the increase of the central BH mass. The analysis of the formation histories of eagle galaxies and its connection to the scatter of the MZR will be the subject of a forthcoming article (Zenocratti et al., in preparation). Sharma Theuns ( 2019 ) propose a model of self-regulated galaxy formation, in which the SFR, stellar mass, gas mass, and metallicity depend on halo mass, cosmological accretion rate, and redshift, but regulated by feedback. In their ‘Iκεα’ model, the main astrophysical parameter ε is a dimensionless measure of the efficiency of stellar feedback: a large value of ε implies efficient feedback and low SFR, while feedback is inefficient and the SFR is high for a small ε. This leads to the following scaling for Z and f g with M ⋆ and efficiency ε: where n ≈ 1.4 is the slope of the Kennicutt–Schmidt star formation law. These relations show that when feedback is efficient (meaning ε is large, ε ≈ 1), Z is low and f g is high, whereas, inefficient feedback (ε ≪ 1) implies Z is high and f g low. We can connect this to the morphology of the galaxy by speculating that feedback in a thin disc – corresponding to a galaxy with high κ co – is more efficient than when κ co is low (a more spheroidal gas distribution). High-resolution simulations that resolve individual supernova energy injections in gas columns suggest this type of relation between feedback efficiency and disc morphology. For example, the simulations by Creasey, Theuns Bower ( 2013 ) show that supernova explosions that occur above or below the disc are more efficient at driving winds, because cooling loses are suppressed when the explosion occurs at the lower densities that prevail there (see also Girichidis et al. 2016 ). Thus, in eagle , accretion of metal-poor gas seems to trigger the formation of a disc but, once the disc has already been formed, feedback effects would play a role in regulating the subsequent metallicity evolution. We leave the analysis of feedback effects on eagle disky galaxies for a future work. 5 CONCLUSIONS We analysed the MZR as a function of morpho-kinematical parameters in the eagle cosmological hydrodynamical simulations. At z = 0, we found new secondary dependences of metallicity on the internal kinematics and morphology of galaxies. At low masses (), higher metallicities are found for more spheroidal and lower rotation-supported galaxies. A preliminary analysis of the star formation histories of low-mass galaxies indicates that late accretion of metal-poor gas dilutes the metal content of galaxies, triggers their star formation activity, and contributes to the formation of the galaxy disc. When the gas is in a thin, rotationally supported disc, feedback may be more efficient, which results in lower O/H and a higher gas fraction (Sharma Theuns 2019 ). The trends in more massive galaxies are generally less strong, with lower metallicities found in more prolate galaxies with lower levels of rotational


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

of hydrogen was switched on at s and for the first published snapshot, at s. The non-equilibrium hydrogen ionization leads to much higher electron density in the cool pockets at 0.5–2 Mm and also higher electron densities up to 3.5 Mm height. There is not much change with time of this probability density function after s. 3.6. Velocity field Spectral lines are normally observed to be broader than what the thermal broadening of the opacity profile would give. An extra free parameter, called microturbulence, is often introduced in 1D semi-empirical models to account for this broadening. The “micro” in the name comes from the fact that this parameter is introduced as an extra broadening of the opacity profile, acting in exactly the same way as thermal broadening. This would be a physically correct description in the limit of zero length-scale for the velocity field. It is also often necessary to introduce a second free parameter to account for the observed lineshape. This is called macroturbulence and is equivalent to a Gaussian convolution of the emergent intensity profile (rather than a convolution of the opacity profile as is the case for microturbulence). Realistic 3D radiation hydrodynamic simulations of the solar photosphere give line profiles that are close to the observed profiles without the addition of extra free parameters – the non-thermal broadening comes from Doppler shifts arising from the convective flows and oscillations (e.g., Asplund et al. 2000 ). Also spectral lines formed in the outer atmosphere are broader than what thermal broadening alone predicts. The nature of this non-thermal broadening in the outer atmosphere is still unclear, but the presence of strong shocks ( Carlsson Stein 1992 , 1997 ; De Pontieu et al. 2015 ), torsional motions ( De Pontieu et al. 2014a ), and Alfvén wave turbulence ( van Ballegooijen et al. 2011 ) are some of the candidates. Fig. 14 Average non-thermal velocity calculated over 1 dex in (column mass) (red, left scale) and average temperature (blue, right scale) as function of logarithmic column mass for the simulation snapshot at s. There is no simple way to characterize the macroscopic velocities in the simulation that give rise to non-thermal broadening. The effect of a given velocity field on the spectral line width depends on whether the spectral line is optically thick or optically thin, where in the atmosphere the line is formed and the width of the contribution function to intensity. One possible way of quantifying the velocity field is the standard deviation of the vertical velocity over a given height range as function of height and horizontal position. At each column of the simulation box at s we calculate the column mass scale (which is more closely related to line formation quantities like optical depth than a geometric height) and take the standard deviation of the vertical velocity over a range of 1 dex in (column mass). We multiply the standard deviation by the square root


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 I-Wavelength B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength I-Wavelength B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O B-CelestialObject I-CelestialObject O O O O B-Wavelength O O O O B-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Observatory B-Wavelength I-Wavelength O O B-Observatory O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope O O O O O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O B-Wavelength B-CelestialObject I-CelestialObject O O O O O O O B-Telescope O O B-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Observatory B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O B-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Telescope O O O O O O O O B-Telescope O O O O O 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 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 B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O

tend to have the steepest radio spectra (), pointing to another possible bias against finding fast-spinning MSPs in ongoing surveys, which focus on central observing frequencies around 350 MHz (Deneva et al. 2013 ; Stovall et al. 2014 ) and 1.4 GHz (Cordes et al. 2006 ; Keith et al. 2010 ; Barr et al. 2013 ). As a result, radio pulsation searches at frequencies below 300 MHz have the potential of opening up a so far largely unexplored parameter space, in the cases where IISM scattering is low and eclipsing does not hinder detection either. Here, we present the discovery of PSR J0952−0607, a very-steep-spectrum MSP, which is now the fastest-spinning neutron star known in the Galactic field (outside of a globular cluster). PSR J0952−0607 was found in a radio pulsation survey using the Low-Frequency Array (LOFAR; Stappers et al. 2011 ; van Haarlem et al. 2013 ) to target unassociated Fermi γ -ray sources. This Fermi -targeted approach has been successful in finding many new MSPs (Ray et al. 2012 ), but our survey is the first to use LOFAR to survey at observing frequencies of 135 MHz (see also Pleunis et al. 2017 ). To enable this survey, a combination of coherent and incoherent dedispersion has been employed to limit the effects of dispersive smearing (Bassa et al. 2017 ). In Section 2 , we will highlight the discovery and multi-wavelength follow-up, with the results being presented in Section 3 . We discuss the broader implications of PSR J0952−0607's discovery and conclude this manuscript in Section 4 . 2. Observations and Analysis 2.1. Radio PSR J0952−0607 was discovered as part of an ongoing LOFAR survey at 135 MHz, continuing on the pilot survey by Pleunis et al. ( 2017 ). Unassociated γ -ray sources were selected from an all-sky source list based on seven years of Fermi -Large Area Telescope (LAT; Atwood et al. 2009 ) Pass 8 data. That list resulted from a preliminary version of the procedure that will be used to produce the next public release LAT source catalog. Among these is a new γ -ray source that has a test statistic of and a relatively small error radius of . The source’s γ -ray spectrum is strongly curved, peaking at 1.4 GeV, and no significant γ -ray emission is detected above 10 GeV. As the source lies well out of the plane (), these characteristics made it a prime millisecond pulsar candidate. The γ -ray source was observed for 20 minutes on 2016 December 25 with LOFAR. The high-band antennas (HBAs) from the innermost 21 LOFAR core stations (longest baseline of 2.3 km) were used to form seven tied-array beams ( FWHM), each covering a 39 MHz wide band centered at 135 MHz. This setup is identical to that of Pleunis et al. ( 2017 ). The complex voltage output for each tied-array beam—in the form of 200 Nyquist-sampled, dual-polarization subbands of 195 kHz each—was processed using GPU-accelerated software to perform coherent dedispersion and channelization with cdmt (Bassa et al. 2017 ) at steps of 1 pc cm −3 between dispersion


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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula 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 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 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model 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 B-Model I-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 O O O O O O O O O O O B-Software O O O B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

imposed in each layer and the wide and position required for the transition region inside the domain. In this simulation we take a 0 = 4.9 × 10 5 K, a 1 = 2 × 10 8 cm, a 2 = 0.5 × 10 8 cm, and a 3 = 5. × 10 5 K. In Fig. 4 the temperature profile obtained for these values and the consequent hydrostatic pressure distribution are shown, for ρ 0 = 10 −11 g cm −3 at the base domain, constant gravity g = 2.74 × 10 4 cm s 2 , specific heat ratio γ = 5/3, and particular gas constant R = 16.6289196 × 10 7 erg (K mol) −1 (totally ionized hydrogen). The numerical results of the hydrostatic condition shown in Fig. 4 are presented in Fig. 5 , where the convergence curves for both the linear and the local hydrostatic reconstruction MUSCL-Hancock schemes are plotted. As expected, the results of the scheme with linear reconstruction exhibit the aforementioned third order superconvergence but they present strong errors in the hydrostatic equilibrium preservation when low resolution grids are used. On the other hand, the results corresponding to the local hydrostatic reconstruction technique show a similar convergence rate for large numbers of cells ( M ≳ 100), but with smaller errors than the standard scheme, which can be even several orders of magnitude smaller when coarse grids are used. This behavior shows the potential of the local hydrostatic reconstruction scheme, since it allows for improvement of the results for very stratified atmospheres with large temperature gradients, as found in many solar astrophysical applications. Fig. 4. Temperature distribution and hydrostatic pressure profile in the solar atmosphere model by Vernazza et al. (1981) given in Eq. ( 63 ). Fig. 5. Convergence curves for the numerical results of the hydrostatic equilibrium atmosphere shown in Fig. 4 . The blue line with circles shows the L 1 -norm of the pressure error for the standard second order MUSCL-Hancock scheme (linear reconstruction), and the red line with crosses corresponds to the MUSCL-Hancock scheme with local hydrostatic reconstruction. 6.2. Diffusion analysis In this analysis we simply study the ability of the local hydrostatic reconstruction scheme to capture a shock wave traveling in a gravitationally stratified medium. The aim of the analysis is to verify that this scheme does not introduce an excessive numerical diffusion compared to the scheme with linear reconstruction to model the shock wave. In addition, we check the behavior of the hydrostatic scheme in the default AMR module of FLASH, which uses the PARAMESH 2 package ( MacNeice et al. 2000 ). This toolkit builds a hierarchy of sub-grids blocks with identical logical structure that cover the physical domain with different resolution levels according to the gradient magnitude of the set refinement variables. Each block is treated as an independent uniform grid, so that the local hydrostatic reconstruction is directly applied on adaptive meshes without the need to modify any subroutine. For this simulation


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

We thank the anonymous referee for comments that have greatly improved this manuscript. The simulations were performed at the National Energy Research Scientific Computing centre (NERSC), Lawrence Berkeley National Laboratory , and at NASA Advanced Supercomputing (NAS) at NASA Ames Research centre. The analysis was performed on the Astric cluster at HU. This work was supported by ISF grant 24/12 , by BSF grant 2014-273 , by GIF grant G-1052-104.7/2009 , by the I-CORE Program of the PBC , ISF grant 1829/12 , by CANDELS grant HST-GO-12060.12-A , and by NSF grants AST-1010033 and AST-1405962 . DC has been partly funded by the ERC Advanced Grant, STARLIGHT: Formation of the First Stars (project number 339177).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O 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 B-Model O O O O O O B-Model O B-Model O B-Citation I-Citation I-Citation I-Citation O B-Model O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O B-Event I-Event B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O B-Model 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

We then investigated the possibility that these objects could form a cluster in some bi-dimensional projections of the parameter space. We tried all the possible magnitudes, colours, and redshifts combinations without finding any obvious clustering (some of these combinations are shown in Appendix C ). We also checked whether the group could correlate with a specific (high) error measure associated with any of the used features, but no any evident correlations were found. The nature of the objects in the overdensity region is still under further investigation. Figure 6. The scatter plot in the top left corner (a) shows the distribution of outliers in the SFRs spectroscopic versus SFRs photometric space with a superimposed density map, while the diagrams int the top right (b) and bottom left (c) corners show highlighted in orange all the objects with a density, respectively, six and eight times higher than the average point density. The histogram in the bottom right corner (d) shows the outliers density distribution. 4.7 Comparison with a recent work In order to compare our regression models with the k-NN used by Stensbo-Smidt et al. ( 2017 ) and their feature selection, we performed an experiment using the full training set and the set of 8 features found by Stensbo-Smidt et al. ( 2017 ). In Table 12 , we present the statistical results, which show a comparable performance among the three methods, although with a lower RMSE obtained by RF and MLPQNA. Using the features found by ΦLAB, the RF and MLPQNA can achieve even better performance, as shown in Table 6 . This is not surprising as k-NN is much more sensitive to the dimensionality of the parameter space (the so-called curse of dimensionality) than other two models. These latter can, therefore, take advantage of the information carried by a larger number of features than a k-NN model. Table 12. Comparison between our RF and MLPQNA against (Stensbo-Smidt et al. 2017 ) k-NN using the full train set and the best eight features found by Stensbo–Smidt. 5 DISCUSSION AND CONCLUSIONS In this work, based on our preliminary analysis of the problem presented at the ESANN-2018 conference (Delli Veneri et al. 2018 ), we estimated star formation rates for a large subset of the SDSS-DR7 and produced a catalogue of SFRs derived using photometric features only (magnitudes and colours) and the MLPQNA ML model (see Appendix B ) trained on a knowledge base of spectroscopically determined SFRs. By looking at Fig. 3 and the statistics in Table 6 , the regression results appear very promising. This is particularly true, considering that the dynamical range of SFR is between −12 and −7, and also that we have ∼5000 outliers out of the objects of the blind test set and, finally, taking into account the low percentage of outliers (∼2 per cent). However, from the results obtained by varying the size of the model training set (Tables 7 and 8 ), we think that a larger knowledge base of SFRs would further improve the


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

perpendicular HTS and find that the PUIs and thermal gas are more heated and energized at the parallel than the perpendicular shock. We also model a quasi-parallel HTS and a quasi-perpendicular HTS to consider the case of an oblique HTS. In the last section, we summarize our results about the structure of collisionless oblique shock waves when mediated by energetic particles. 2. Model In this section, we present a brief review of the formulation of the PUI or SEP-mediated plasma model presented by Zank et al. ( 2014 , 2016 ), Zank ( 2016 ), and Mostafavi et al. ( 2017b ). The heliosphere comprises thermal solar wind, suprathermal energetic particles such as PUIs or SEPs, and neutral atoms (beyond an ionization cavity of about 6–10 au). The charge exchange mean free path in the IHS is approximately 2500 au and greater than 200 au in the supersonic solar wind beyond 10 au (Zank 2015 ). Thus, the charge exchange mean free paths are very large, and we can ignore the coupling between neutral atoms and solar wind protons when studying the structure of shocks. Using appropriate parameters for the supersonic solar wind beyond 10 au, the IHS, and the VLISM, Zank et al. ( 2014 ) estimated the equilibration timescales of PUIs and thermal plasma in these regions. They showed that the PUIs are not equilibrated with the background thermal plasma. Zank et al. ( 2016 ) showed that SEPs with energies greater than 5 keV cannot equilibrate in the inner heliosphere. Therefore, energetic particles such as PUIs, SEPs, and ACRs are a distinct component in the plasma system. The plasma flow is described by a multi-component model comprising thermal solar wind ions and electrons with Maxwellian distributions, and an energetic ion component (PUIs, SEPs, or ACRs). The multi-component model is too complicated for most problems, but it can be reduced to a single-fluid-like model by making some assumptions (see details in Zank et al. 2014 ). The collisionless diffusion or heat flux tensor and pressure tensor for the energetic particles may be expressed, respectively, as where η ≃ P p τ s is the viscosity coefficient and τ s is PUI-scattering timescale. P p is the PUI scalar pressure and Π p a stress tensor. The assumption is that the magnetic field is along the x -axis. K ∥ and K ⊥ are diffusion coefficients parallel and perpendicular to the magnetic field. The reduced single-fluid-like model equations, together with the Maxwell equations, are given by (Zank et al. 2014 , 2016 ) where μ 0 is the permeability of free space and J is the current density. B and E denote the magnetic and electric fields, P p the PUI pressure, P g the thermal gas (sum of electrons and protons) pressure, U the bulk flow velocity, and ρ the total density. We denote all quantities pertaining to PUIs and thermal gas with the subscripts p and g , respectively. γ p/g denotes the adiabatic index for PUIs/thermal gas. The viscosity and heat flux dissipation terms introduce distinct length scales into


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

along an almost perfect line in the northwest–southeast direction. The centroids, however, depart from this line at high velocities, especially for the blueshifted gas (≤−8 km s −1 ), although some of the associated positional errors are large. This suggests the presence of a second kinematic component. As shown in Section 4 , this configuration is consistent with the presence of an almost edge-on ionized disk, and a disk wind. 4. Modeling of the H21<italic>α</italic> RRL Similar configurations to the RRL centroid map obtained for MonR2-IRS2 have been observed for MWC349A (Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ; Zhang et al. 2017 ) and MWC922 (Sánchez Contreras et al. 2019 ). This configuration has been modeled assuming that the massive star is surrounded by a (partly) ionized Keplerian disk and an ionized wind. We have thus adopted a similar physical structure to model the H21 α centroid map derived for MonR2-IRS2. The set of input parameters that best fit our ALMA observations is described below (see also Table 1 ). Table 1 Input Parameters of the Best Fit of the MonR2-IRS2 H21 α Data Note. a r is in units of au and angles are measured relative to the polar axis; θ and θ a , are in degrees. In our model, the ionized wind lies inside a double cone with a semi-opening angle of 57° (the neutral disk), while the ionized disk layer is contained within an opening angle of 65 on the surface of the double cone (Figure 4 ). The ionized wind expands radially at a constant velocity, v 0 , while the circumstellar disk rotates following a Keplerian law with the velocity rotation component being added to the expansion velocity of the wind (Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ). The inclination angle is measured from the direction perpendicular to the disk and is −25°. Figure 4. Sketch of the double-cone geometry used for the modeling of MonR2-IRS2 (see also Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ). We have used the non-LTE 3D radiative transfer code MORELI (MOdel for REcombination LInes; Báez-Rubio et al. 2013 ) and the departure coefficients of hydrogen, b n and β n , calculated by Walmsley ( 1990 ). The velocity separation between the H21 α emission peaks (blueshifted and redshifted; Figure 2 ) constrains the central mass of the MonR2-IRS2 source to 15 M ⊙ . This mass corresponds to a B0-type star on the zero-age main sequence, which is consistent with the luminosity of MonR2-IRS2 (∼0.5–1 × 10 4 L ⊙ ; Howard et al. 1994 ). The radial density distribution of electrons within the ionized double cone, N e , follows a r −2 law with an inner radius of 13 au (Table 1 ). We choose a r −2 law because it fits nicely the 1.3, 0.85 and 0.4 mm free–free continuum fluxes of MonR2-IRS2, and it allows us to simultaneously model the disk and the expanding wind in a simple way. The predicted mass-loss rate for MonR2-IRS2 is 2.8 × 10 −7 M ⊙ yr −1 , and the mass of the ionized disk is 2.4 × 10 −5 M ⊙ , a factor ≥10 lower


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The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We acknowledge the exellent commentary by two referees and the ApJ statistician on the paper’s manuscripts. This work was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. C.M.T. is supported by an Australian Research Council DECRA Fellowship through project number DE140100316.


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Y.I.I. and N.G.G. thank the hospitality of the Max-Planck Institute for Radioastronomy, Bonn, Germany. They acknowledge support from the Program of Fundamental Research of the Department of Physics and Astronomy (Project No. 0117U000240) of the National Academy of Sciences of Ukraine. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.


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We thank Prateek Agrawal, Imre Bartos, Luke Kelley, Frans Pretorius, Jakub Scholtz, and Kip Thorne for extremely useful conversations on several aspects of our paper. L.R. is supported by NSF grants PHY-0855591 and PHY-1216270. Z.-Z.X. is supported in part by the Center of Mathematical Sciences and Applications, Harvard University.


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Acknowledgments SJP is supported by a Royal Society University Research Fellowship.


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More specifically, we can summarize our findings as follows: 1. Because the drag force experienced by small dust grains is very strong, a specific implicit numerical scheme was implemented in the code RoSSBi to accurately follow the dynamics of the disk. This method is very accurate for any value of the Stokes number of the pressureless dust fluid, and we use it to study the evolution a vortex model with dust characterized by Stokes numbers in the range . 2. Dust is systematically accumulated inside the vortex for every value of the Stokes number. The exponential growth rate of the dust density at the vortex center follows the analytical model we developed in our previous study. The timescale depends on the grain size, but the density enhancement reached at the end, when the gas is perturbed by the drag force, is similar regardless of the Stokes number, and produces dust-to-gas ratios of order unity. We highlight the existence of a generic capture process, characterized by a timescale that scales with the Stokes number, which allows us to compare disks with different dust sizes at an equivalent state of evolution, but corresponding to intrinsically different physical timescales. 3. The vortex instability is triggered at the end of the capture, regardless of the grain size. The growth rates of the excited modes also depend weakly on the Stokes number. This effect is highly correlated with the similarity of the dust capture, and the concept of equivalent states of evolution, producing almost the same perturbation of the gas vorticity profile. 4. A new phase of dusty vortex evolution is discovered for Stokes numbers on the order of 10 −3 and below, where a succession of vortex instabilities followed by dust capture events occurs. This period lasts several hundred of disk orbits and produces strong mixing and a fast reorganization of the dust during the relaxation of the vortex. The dust-to-gas ratio increases progressively to high values, up to 8 at the vortex center. The very dense core that forms and survives even after eventual vortex dissipation could be a preferential place for planetesimal formation. 5. When the timescale of the drag effect is too long compared to the resistance and relaxation of the vortex, the formation of a dust ring becomes unlikely. In our case, the runs with St = 10 −3 were still in the unstable phase by the end of the simulations. Even when it forms, for St 10 −2 , the dust ring produced by well-coupled grains has fewer eddies than with larger Stokes numbers. Even if the dust-to-gas ratios are comparable, they suffer diffusion, and their role in planetesimal formation is less promising than the unstable phase. There are a number of caveats to our model that need to be pointed out. First, the fact that the simulations are still only two-dimensional, which could have a relevance both for the development of two-fluid turbulence during and after the vortex instability phase (see the discussion in Surville et al. 2016


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ACKNOWLEDGEMENTS We thank the anonymous referee for the detailed comments that helped to improve this manuscript. We thank Patrick Diamond, Ellen Zweibel, Michael Norman, and Todd Thompson for insightful suggestions and advice, Eve Ostriker for pointing out a typo, and Bili Dong for his help with yt . We would like to thank the Simons Foundation and the participants of the Galactic Superwinds symposia for stimulating discussions. TKC and DK were supported by NSF grant AST-1715101 and the Cottrell Scholar Award from the Research Corporation for Science Advancement. Support for PFH was provided by an Alfred P. Sloan Research Fellowship, NSF Collaborative Research Grant #1715847, and CAREER grant #1455342, and NASA grants NNX15AT06G, JPL 1589742, 17-ATP17-0214. EQ was supported in part by a Simons Investigator Award from the Simons Foundation and by NSF grant AST-1715070. The Flatiron Institute is supported by the Simons Foundation. CAFG was supported by NSF through grants AST-1517491, AST-1715216, and CAREER award AST-1652522, by NASA through grants NNX15AB22G and 17-ATP17-0067, and by a Cottrell Scholar Award from the Research Corporation for Science Advancement. The simulation presented here used computational resources granted by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant no. OCI-1053575, specifically allocation TG-AST120025. Numerical calculations were also run on the Caltech compute cluster ‘Wheeler’, allocations from XSEDE TG-AST130039 and PRAC NSF.1713353 supported by the NSF, and NASA HEC SMD-16-7592. This work uses data hosted by the Flatiron Institute’s FIRE data hub. This work also made use of yt (Turk et al. 2011 ), matplotlib (Hunter 2007 ), numpy (van der Walt, Colbert Varoquaux 2011 ), scipy (Jones et al. 2001 ), and NASA’s Astrophysics Data System.


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

aberrations and we anticipate good astrometry results with the mean PSFs of each cluster. However, PSFs from stars with a magnitude of 11 have small and almost randomly distributed clusters. Although the mean PSFs of two different clusters are almost the same in Fig. 12(f) , this might be induced by the average of many different PSFs. To fully reflect the classification performance, we perform PSF-fitting astrometry in these data, using the Fourier-based registration method (Stone et al. 2001 ) with the mean PSFs obtained from our method. This method assumes that the PSFs in the same cluster are morphologically similar and only have a different subpixel shift. We can obtain this subpixel shift by maximizing the correlation coefficients between the stamp images of stars and the mean PSFs in an oversampled Fourier domain. The subpixel shift and the position of the brightest pixels in the images of the celestial objects can then be used to calculate the star's position in the image. For comparison, we also use the Gaussian function as a PSF template and we calculate the positions of stars with the least-squares fitting method (Stone 1989 ). The Gaussian function has a FWHM of 2 pixels. The positions we calculated with the above two methods are compared with the Tycho-2 catalogue (Høg et al. 2000 ) as follows. We obtain the star positions (α i , ξ i ) from the Tycho-2 catalogue as the theoretical positions of these stars and we construct the association between that position and the position of these stars in the image using as proposed in Sun, Zhao Zhang ( 2013 ). Here, (α 0 , δ 0 ) is the corresponding equatorial position of the frame centre. With this association, the observed position (α c , ξ c ) of these stars can be obtained from the pixel position ( x c , y c ), and the residual position errors of each star (α c − α i , δ c − δ i ) are obtained. The astrometry error of these two methods from the Tycho-2 catalogue is shown in Fig. 13 . The systematic errors of Tycho-2 are nearly 0.01 arcsec so this does not have an effect on the calculation. Compared with the Gaussian fitting method, we can see that stars with a magnitude of 10 have better astrometric accuracy with the mean PSF and stars with a magnitude of 11 have almost the same astrometric accuracy. Figure 13. Astrometric residuals of stars with magnitudes of 10 and 11 of telescope B. The number of stars with the magnitude of 10 is 517 and the number with the magnitude of 11 is 737. Top: the residuals of right ascension. Bottom: the residuals of declination. Crosses indicate Gaussian PSF-fitting centroid and circles indicate mean PSF fitting. It is worth noting that PSF classification is a clustering problem and for stars with the magnitude of 11, we do not know why the PSFs are not clustered distinctly. There are two possibilities: (i) these PSFs are nearly the same essentially, so applying the average of these PSFs for subsequent processing is a sound method (Sun Jia 2017 ); (ii) the


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ACKNOWLEDGEMENTS VW’s research is funded by an ERC Starting Grant (3DICE, grant agreement 336474). The authors acknowledge the CNRS program ’Physique et Chimie du Milieu Interstellaire’ (PCMI) co-funded by the Centre National d’Etudes Spatiales (CNES). LM also acknowledges the support from the NASA postdoctoral program. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.


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 B-Instrument 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 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 B-Instrument O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument B-Wavelength I-Wavelength O O B-Instrument O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument 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 O O B-Telescope O O O O B-Telescope O O B-Identifier I-Identifier O O O O O O B-Telescope O O O O B-Telescope O O B-Instrument O B-Instrument O O O B-Telescope 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 B-Identifier O B-Identifier O O B-Model I-Model O O

the EUVI-A stack plot does not show any clear upward-propagating structure. The result that it was unable to be picked up in the field of view captured by EUVI-A, combined with the observation of the slow-rise phase in the COR1 field of view, suggests that the eruption was initiated from higher altitudes. The EUVI stack plot does, however, show a large brightening around the time of the rapid acceleration phase beginning, likely to be post-eruption loops associated with the stealth CME. We then fitted exponential and quadratic curves to the CME position in the COR1 field of view. The curves can give indications of what mechanisms are driving the eruption (Schrijver et al. 2008 ; D’Huys et al. 2014 ). Numerical simulations matched with observations have demonstrated that an exponential rise profile occurs when an instability is dominating the eruption, such as the torus or kink instability, while a quadratic rise profile occurs during a breakout model scenario. For this event the exponential curve produced the best fit, suggesting an instability dominating the eruption. Both the torus and kink instability require a flux rope prior to eruption, and given that the concave-up structure could be tracked for a period of hours during the slow-rise phase, it is likely that in addition to the structure being initiated at a high altitude, the flux rope was also formed at a high altitude in the corona. Figure 2. Left: EUVI/COR1 image indicating the slice used to create the stack plot (solid line). Right: EUVI-B 195 Å (lower) and COR1-B (upper) stack plots. The height–time profile of the stealth CME observed on 2009 October 27 can be determined from the COR1-B data, which show the underside (concave-up structure) of the stealth CME. Exponential (red line) and quadratic (blue line) fits have been applied to the COR1-B data. The stealth CME is not observed in the COR1-A images until ∼15:30 UT on 2009 October 27, several hours after the eruption onset time as determined by Kilpua et al. ( 2014 ). The CME is also very faint and barely visible in the images, making it difficult to pinpoint the exact time that it enters the field of view. It also emerges from a bright streamer that acts to mask the CME structure. However, the stealth CME is seen more clearly, and earlier, in COR1-B, which could suggest that the eruption is closer to the limb of STEREO-B than STEREO-A . The estimated source region from triangulation techniques is of similar distance to the nearest limbs in both spacecraft, while the decayed AR is directly on the limb in STEREO-A and on disk in STEREO-B , and AR 11029 is directly on the limb of STEREO-B and on disk in STEREO-A . Using COR1 and COR2 from the twin STEREO spacecraft, the wire frame of the GCS model (representing the flux rope) was fitted to the concave-up cavity structure in the coronagraph observations (Figure 3 ). The footpoints of the erupting structure were found to be N03E05 and N03W18 from the GCS model, illustrated by


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

CO core mass M CO , and the surface mass fractions of He ( X S (He)), C ( X S (C)), and O ( X S (O)) of the stellar models. We calculate the evolution during PPI stage using the stellar evolution code and a ppm hydrodynamic code (e.g. Colella Woodward 1984 ; Umeda Nomoto 2005 ) as follows. This is because it is difficult to solve unbound surface structure during the PPI mass ejection using the stellar evolution code. We describe the calculation method using the second pulsation of the 140 M ⊙ star model as an example. Fig. 1 shows the evolutionary track of the 140 M ⊙ star model on the plane of log ρ C (the central density) and log T C (the central temperature). Two points (A) and (B) in the second pulsation are assigned. First, we calculate the stellar evolution passing through points (A) and (B) without mass-loss by the PPI using the stellar evolution code. Figure 1. The evolution of the 140 M ⊙ model on the plane of log ρ C − log T C after He core burning. The shaded region shows unstable region against electron–positron pair instability. Details for points (A) and (B) are explained in text. Next, using the ppm code, we calculate the mass ejection of the star for about 10 4 s, corresponding to the period until the mass ejection is almost completed. The initial structure is set to be the structure at the time when the star has the maximum total energy during the pulsation (point (A) in the second pulsation). During the expansion, outermost region of the star accelerates and exceeds escape velocity. Thus, the mass exceeding the escape velocity is considered as the ejected mass. Then, we restart the stellar evolution calculation from the time when the central temperature is almost minimal (point (B) in the second pulsation). We artificially reduce stellar mass with a constant mass-loss rate evaluated in the previous hydrodynamic calculation. The mass-loss continues until the lost mass is equal to the ejected mass obtained from the hydrodynamic calculation. After several pulsations, the star forms an Fe core and collapses. We stop the calculation of the stellar evolution when the central temperature reaches 10 10 K. 2.2 Stellar evolution during PPI stage First, we show the evolution of the 140 M ⊙ model after the C-burning. Fig. 2 shows the mass fraction distribution after the C-burning. The central temperature is log T C = 9.14. The main component at the centre is O, Ne, and Mg. The mass fraction of Si also increases. The central C-burning occurs radiatively. The O/C/Ne layer is in the range of ∼6–48 M ⊙ in the mass coordinate. The surface component is mainly O and C, and 19 per cent 4 He by mass fraction remains as shown in Table 1 . Figure 2. Mass fraction distribution of the 140 M ⊙ model after the C-burning at log T C = 9.14. Black, sky-blue, blue, purple, dark-green, green, and orange lines indicate the mass fractions of 4 He, 12 C, 16 O, 20 Ne, 24 Mg, intermediate-mass elements (Si-Sc), and Fe-peak elements (Ti-), respectively. The time


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We thank Arecibo for the generous amount of observing time for the completion of this project and the observatory staff for the successful completion of our observations. We also thank Richard Crutcher for his help in the analysis of our data. This work took part under the program ISM3D of the PSI2 project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02. This work was supported in part by the National Science Foundation under NSF grant AST 0908841. 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. Facility: Arecibo.


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Acknowledgments We thank the referee for their comments that helped us to clarify and improve this paper. We have used DSS scans in this paper. Based on photographic data of the National Geographic Society–Palomar Observatory Sky Survey (NGS-POSS) obtained using the Oschin Telescope on Palomar Mountain. The NGS-POSS was funded by a grant from the National Geographic Society to the California Institute of Technology. The plates were processed into the present compressed digital form with their permission. The Digitized Sky Survey was produced at the Space Telescope Science Institute under US Government grant NAG W-2166. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France.


O O O O O B-TextGarbage O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O 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 the A-AB distributions, a -value of for the A-B distributions, and a -value of for the AB-B distributions (from the AD-tests we obtain -values of , and for each bin, respectively). Finally, to analyse the distribution of slopes depending on the luminosity of the galaxies, we divided the sample again into three groups: luminous (L, mag), intermediate (I, mag), and faint (F, mag) galaxies. We obtained these results: The statistical tests yield a -value of % for the KS-test in the case with the largest differences, that is, when comparing luminous and intermediate galaxies. The remaining KS-tests return a -value of for the comparison between luminous and faint galaxies and a -value of when analysing the intermediate and faint distributions (a -value of , and respectively, for the AD-tests). Similar results for all these separations are found when using any scale-length normalisation for the radial distance instead of the disc effective radius, either the radius or the physical scale of the galaxy (i.e. the radial distance in kpc). 4.3. Common abundance gradient The fact that the distribution of the oxygen abundance gradients for all the galaxies in the sample is well fitted by a Gaussian function suggests the existence of a characteristic value for the slope, independent of other properties of the galaxies, as the morphological type or the luminosity. This is true when normalising the radial galactocentric distances to the disc effective radius and limiting the fitted interval between 0.5 and 2.0 . Below this range (), a nearly flat distribution or even a drop towards the centre is found for some galaxies of the sample. At larger galactocentric distances (), a flattening can be observed in the abundance gradient of most of the galaxies. It is easier to illustrate this result if we represent the radial distribution of the oxygen abundance for all the galaxies in the same figure. This is shown in the left panel of Fig. 8 . The black contours represent the density distribution of the star-forming spaxels. Although the radial gradient can be discerned through the contour plot, the wide range of abundances blurs the result. To clarify the origin of this widening, we colour-code each represented abundance according to the integrated stellar mass of the host galaxy in log scale. For clarity, only the oxygen abundance values with a contribution of at least 1% of the total number of spaxels are plotted. Adopting this scheme, it is evident that the abundances present a common radial gradient, but with an offset depending on the mass, as expected from the relation (and as discussed in Sect. 4.1 ). To remove this dependence on the mass from the map, we rescaled the oxygen abundances of each galaxy following the analytical form of the relation ( Tremonti et al. 2004 ) derived by Sánchez et al. (2013) , applying an offset according to the integrated stellar mass of the galaxy and normalising to the average value for the whole sample of 8.5. The