very well separated components () and with marginal distributions and pairwise scatter plots as shown in the diagonal and lower triangle of the matrix of plots in Fig. 3(a) . The upper triangle of the matrix displays the correlation between each pair of variables. Thus, the first two of the three variables have a very high (almost linear) pairwise correlation of 0.98, while the other two pairs have little to modest correlations between them. It is tempting to surmise that one of the first two dimensions are nearly redundant and that dropping one of them would not have much effect on the quality of clustering. We test this assertion by performing GMMBC (with BIC used to determine the optimal number of groups) on the dataset using each of the three distinct pairs of variables. Figs 3(b) –(d) display the results of clustering each pair of coordinates, with colours representing the obtained clustering and character denoting the true grouping. Including either one of the two seemingly redundant variables with the third variable identifies only two groups and a partitioning (Figs 3b and c ) that hardly matches the true with an adjusted Rand index of 0.37. Interestingly, clustering the two seemingly redundant variables (and ignoring the third) does better, identifying four groups and with . However, this is still a far cry from the perfect partitioning that is obtained when all three coordinates are used in GMMBC with BIC to determine the optimal number of groups. Therefore, it is important to consider the relevant variables in clustering. This fact becomes more important in the light of attempts by many researchers to cluster GRBs using, for instance, only the duration variables. This example also demonstrates that two variables having correlations even as high as 0.98 are not necessarily redundant and should be carefully analysed before arriving at decisions on their inclusion or exclusion in analysis. Raftery Dean ( 2006 ) proposed a method for selecting variables containing the most relevant clustering information by recasting the variable selection problem in terms of model selection where comparison of the models is done via BIC (refer to Chattopadhyay Maitra 2017 for a thorough review on variable selection). Figure 3. Result of clustering (a) data simulated from a three-dimensional five-component GMM , using (b, c, d) two and (e) all three variables. 2.3 Measuring distinctiveness of partitioning through the overlap Chattopadhyay Maitra ( 2017 ) explain that an overlap measure can be used to indicate the extent to which clusters obtained through a method are distinct from one another. We refer to that paper for further details, but note that they adopt Maitra Melnykov ( 2010 )’s definition of the pairwise overlap between two groups as the sum of their misclassification probabilities. To provide a sense of these pairwise overlap measures, we illustrate three two-dimensional examples in Fig. 4 . (For ease of display and understanding, we use two


of the Ramaty ( 1969 ) model fit to the radio spectra. Both spectral indices are listed on Table 2 . As can be seen from these results, the spectral indices of the energy distribution of the radio emitting electrons agree reasonably well with that of the hard X-ray producing electrons, when considering photons with energies higher than 400–700 keV or, conversely, electrons with energies ≥1 MeV. The reconstructed energy spectra of the accelerated electrons can be represented by a broken power law with break energy around 500 keV, and spectral index δ = 4 below this energy and δ = 2 above (see Figure 6 ). The photons detected below energies of ∼500 keV (representing E 2 ) are produced by lower-energy electrons with an energy distribution index of δ ≈ 4, whereas the higher-energy hard X-rays and radio emission (microwaves and millimeter waves) are generated by electrons with energies ≥1 MeV and δ ≈ 2. Previous works, such as Silva et al. ( 2000 ), showed that the spectral indices for the population of accelerated electrons emitting the radio and the X-rays do not match, with the radio index being harder than that of the X-rays by approximately 2 units. The authors explained this discrepancy by the fact that the radio emission is produced by higher-energy electrons than the X-rays, and that the common accelerated electron population has a power-law energy distribution that breaks up above 300 KeV. Since the hard X-rays analyzed in Silva et al. ( 2000 ) had energies lower than ∼200 keV, the results are in agreement with those presented here for the SOL2013-05-13 flare, as well as the two discrepancies in the spectral indices of hard X-rays and radio. Moreover, Vestrand ( 1988 ) and Dennis ( 1988 ) report giant flares observed in hard X-rays with energies larger than 1 MeV that showed a breakup in their photon spectra at ∼300 keV. More recently, from the analysis of an X8.2 solar flare detected in hard X-rays by RHESSI, Ning et al. ( 2019 ) found a broken-up power-law spectra originating from a coronal source. However, the break energy was only about 50 keV and the harder spectral photon index was ∼3. There are basically three possible explanations for electrons to exhibit such a broken-up power-law energy distribution. The first is that there are two components, or sources, of energetic electrons that were produced by two different acceleration mechanisms (Silva et al. 2000 ; Krucker et al. 2008 ). However, to produce a similar temporal evolution in radio and hard X-ray emission, there must be a close link between these two acceleration mechanisms. Alternatively, the second possibility is that the difference in spectral indices is due to physical characteristics of a certain acceleration mechanism and/or a transport process of electrons such as diffusive shock acceleration (Li et al. 2013 ), where a hardening of the spectrum occurs around 500–600 keV, or stochastic acceleration due to wave–particle interactions in the presence of Coulomb collisions


cube is the removal of the continuum and determination of the stellar kinematics. Because both the MUSE and SINFONI spectral resolutions are only moderate, we only fit for the stellar velocity and velocity dispersion. We also included an additive fourth degree polynomial in the fit to model any emission from the central AGN. To create the continuum-subtracted MUSE cube, we renormalized the best-fitting binned spectra to the median continuum level of each individual spectrum before subtraction. Fig. 4 shows the results of our ppxf fits for the MUSE cube. Figure 4. Results from fitting the MUSE cube with ppxf . The top row plots the stellar velocity ( left ) and dispersion ( right ). The bottom row plots the mean light-weighted stellar population age ( left ) and mean light-weighted metallicity ( right ). In all frames, North is up and East is to the left. 2.6.2 Emission line fitting To measure the bulk distribution and kinematics of the molecular and ionized gas in NGC 5728, we fit single Gaussians to the relevant emission line tracers of the gas. In particular, we fit the CO (2–1) line (ν rest = 230.538 GHz) in the ALMA cube; the H β, [O iii ] doublet, [O i ], [N ii ] doublet, H α, and [S ii ] doublet lines in the MUSE cube; and the [Fe ii ]λ1.64 m, [Si vi ], H 2 (1–0) S(1), and Brγ lines in the SINFONI cube. This set of lines represent the strongest emission lines observed in nearby galaxies and AGNs and provide diagnostic power into the state of gas in a range of phases from cold molecular gas [CO (2–1)] to warm molecular gas [H 2 (1–0) S(1)] to hydrogen recombination lines (H β, H α, Br γ) and forbidden lines ([O iii ], [O i ], [N ii ], [S ii ], [Fe ii ], [Si vi ]) from ionized gas in a range of ionization levels. For each line, we cut out the relevant sections of the continuum-subtracted spectra that contain the single line or multiple lines in the case of the [O iii ] doublet, H α and [N ii ] blended region, and [S ii ] doublet. We fixed the velocity and velocity dispersion to be the same for all doublets and fixed the intensity ratio to the expected theoretical value of 3 for the [O iii ] and [N ii ] doublets. For the fit of the [Si vi ] line, we also included Gaussian components for the nearby H 2 (1–0) S(3) and Br δ lines. As an estimate of the local noise around each line, we measured the root mean square (RMS) of the line-free regions. Using the RMS, we produced 100 simulated spectra for every emission line by randomly perturbing the original spectra assuming a Gaussian distribution with a standard deviation equal to the RMS. Each of the simulated spectra were fit in the same way as the original spectra and uncertainties on the integrated flux, velocity, and velocity dispersion were calculated from the standard deviation of the best-fitting values from the simulated spectra. Finally, all velocity dispersions derived from MUSE and SINFONI data were corrected for instrumental broadening. For lines from MUSE, we assumed an


We would like to thank the anonymous referee for the useful comments and suggestions which helped improve this paper. NPM and FAG would like to thank Monica Valluri for the very interesting discussion and useful comments that help to improve this manuscript. NPM, FAG, PMC and CMG are grateful to Carles Simó for his illuminating discussions, comments and suggestions. We are also grateful to Volker Springel, Simon White and Carlos Frenk for generously allowing us to use the Aquarius simulations. Finally, NPM wants to thank D. D. Carpintero, F. Bareilles and E. Suárez for their assistance with the lp-vicode as well as with the pre-processing of the data. NPM, PMC and CMG were supported with grants from the Consejo Nacional de Investigaciones Científicas y Técnicas (IALP UNLP–CONICET) de la República Argentina (CCT-La Plata) and the Universidad Nacional de La Plata (FCAG UNLP). FAG and BWO acknowledge support from the US NSF Office of Cyberinfrastructure by grant PHY-0941373 and by the Michigan State University Institute for Cyber-Enabled Research (iCER). BWO was supported in part by NSF grants PHY-0822648 and 1430152: Physics Frontiers Center/Joint Institute for Nuclear Astrophysics (JINA). APC is supported by a COFUND/Durham Junior Research Fellowship under EU grant [267209].


Zr The neutron-capture element Zr is predominately produced by AGB stars and is a first s -process peak element. The s -process contribution to Zr in the Solar system is 80percent (e.g. Simmerer etal. 2004 ; Sneden, Cowan Gallino 2008 ; Bisterzo etal. 2014 ). By determining the abundance of Zr, we expand on the measurements of Y, another first s-process peak element whose abundances were previously obtained by NS11 . Fig. 3 (a) shows [Zr/Fe] as a function of [Fe/H]. The dispersion in [Zr/Fe] is 0.12dex, which is larger than the error of 0.04dex. When considering the two populations, the scatter in [Zr/Fe] is smaller for the low- stars with a dispersion of 0.06dex compared to a dispersion of 0.13dex when combining the high- and TD stars. In addition to the difference in the dispersion of [Zr/Fe], the low- stars have a systematically lower [Zr/Fe] abundance compared to the high- and TD stars. Figure 3. Four s -process elements (Zr, La, Ce and Nd) versus [Fe/H]. The red circles indicate low- stars, the blue open circles indicate high- stars and the plus signs indicate TD stars. The 1 error is shown in the bottom left of each plot. This possible separation in the high- and low- populations is in agreement with the slight separation in abundance measurements of [Y/Fe] for the two populations seen in NS11 . As Zr and Y are both first-peak s -process elements, they are expected to follow the same trend. Fig. 4 demonstrates the difference in the Zr abundance for a low- star (HD 194598) and a high- star (HD 111980) at nearly the same metallicity (see Table 1 ). The low- star has a weaker Zr ii line than the high- star. While the effective temperature differs between these two stars by approximately 150K, all other lines in this region exhibit very similar strengths. Figure 4. MIKE spectra around the Zr line at 4208.98 for a low- star (HD 194598) and a high- star (HD 111980). A comparison between [Y/Fe] as measured by NS11 and [Zr/Fe] is presented in Fig. 5 . The abundance of Zr follows the abundance of Y, which is expected if Y and Zr have a common origin. While there is a systematic offset between [Y/Fe] and [Zr/Fe] that may be due to errors in the gf values of the lines, the important point is that the slope of the data is close to 1. The high- stars have a tighter correlation between [Y/Fe] and [Zr/Fe] compared to the low- stars. Figure 5. Comparison of [Y/Fe] (taken from NS11 ) and [Zr/Fe]. The red circles indicate low- stars, the blue open circles indicate high- stars and the plus signs indicate TD stars. The dashed line shows the one-to-one correspondence line. The 1 error is shown in the top left. 3.2 La, Ce and Nd We extend upon the Ba measurements of NS11 by determining abundances for other elements belonging to the second s -process peak, namely La, Ce and Nd. The s -process contribution to La in the Solar system is 75percent and there are a number of advantages with using La as an s -process indicator compared to Ba (e.g. Simmerer etal.


We thank the anonymous referee for a thorough report and many constructive comments, which helped us improve the presentation of this work. This work is supported by the 973 program (2015CB857005, 2012CB821804), the NSFC (11522324,11421303), the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences, grant No. XDB09010400 and the Fundamental Research Funds for the Central Universities. H.J.M. would like to acknowledge the support of NSF AST-1517528. The numerical calculations were done on the supercomputing system in the Supercomputing Center of the University of Science and Technology of China.


λλ1907, 1909, C iv 1548, 1551, and He ii λ1640. They find seven objects with [C iii ], C iii ] λλ1907, 1909 emission, some of them reaching extremely high equivalent width values (). Finally, they find that C iv 1548, 1551 and He ii λ1640 have equivalent widths below 2 Å and conclude that the detection of C iv 1548, 1551 atÅ may require extremely metal poor stars and gas. In SBS 0335−052E, which is more metal-poor that the previous sample, C iv 1548, 1551 shows a weak P-Cygni profile and nebular components. The EWs of the nebular [C iii ], C iii ] λλ1907, 1909 and C iv doublet emissions are 5 and 1.7 Å, respectively. The largest C iv 1548, 1551 EW which has been reported for a nearby starburst galaxy is Å. This is for galaxy J104457, which has 12+log(O/H) = 7.45 (Berg et al. 2019b ) and is at a very similar redshift (0.013) compared to SBS 0335−052E. Senchyna Stark ( 2019 ) present HST COS UV observations of six star-forming XMPs with 12+log(O/H) between 7.4 and 7.7, i.e. lower than in the work of Senchyna et al. ( 2017 ). They find stellar C iv 1548, 1551 in five of the galaxies and high [C iii ]+C iii ] equivalent widths (Å) in two objects. The highest EWs of C iv 1548, 1551 and He ii which they find are 4.4 and 1.7 Å, respectively. For SBS 0335−052E we find EWs of 1.7 Å for C iv 1548, 1551 and He ii λ1640. Although nebular C iv 1548, 1551 emission is present in some very high sSFR nearby systems, nearby systems do not reach the equivalent widths of C iv which are observed in individual lensed systems at z >6. Undisputed detections of nebular emission in He ii in predominantly star-forming systems at z >6 remain elusive (Senchyna Stark 2019 ). Objects located at z = 2-4 with high values of EWs(C iii ]), i.e. ≥10 Å, are analysed in Nakajima et al. ( 2018 ), who find that EWs(C iii ])>20 Å can only be modelled with a combination of photoionization by stars and an AGN. 6.2 C/O Berg et al. ( 2016 ) and Berg et al. ( 2019a ) studied the C/O ratio derived via UV collisionally excited emission lines of a sample of 12 low metallicity galaxies with significant detections of carbon and oxygen lines. At low metallicity, (12+log(O/H)8.0), they find that no clear trend is evident in C/O versus O/H. We find log(C/O) ∼ −0.45 via tests 2 and 3, and 12+log(O/H) = 7.48 / 7.42 via tests 4/5, respectively. This is very similar to what Berg et al. ( 2016 ) report for galaxy J120122, which is log(C/O) ∼ −0.45 and 12+log(O/H) = 7.45. 6.3 JWST observation As a simple exercise, we placed SBS 0335−052E at redshift z = 10, and used the COS G130M + G160M + G185M spectrum to simulate an observation of this galaxy with the near-infrared spectrograph (NIRSpec) onboard JWST . For this purpose, the spectrum’s flux was diluted using the luminosity distance for cosmological parameters H 0 = 69.6, Ω M = 0.286, and Ω vac = 0.714. In addition, we accounted for IGM absorption of UV photons using Madau ( 1995 ) attenuation. We degraded the spectrum to match NIRSpec’s prism


DKG acknowledges the support of an Australian Research Council Future Fellowship (project FT0991598 ). This paper utilizes preliminary analysis results from the Multi-INstrument Burst ARchive (MINBAR), which is supported under the Australian Academy of Science's Scientific Visits to Europe program, and the Australian Research Council's Discovery Projects funding scheme. This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.


rates and substellar velocities. Figure 13. Mid-tropospheric atmospheric temperature ( p = 658 hPa). The temperature reference in the lower right corner of each pane indicates the value of the highest temperature contour, with successive cooler contours at 2 K intervals. The central column (tidally locked) phase-curve examples are shown in Figure 12 . At this height in the atmosphere, , there is no frictional damping. In the stratified model, we find a more complicated relationship than in the shallow-water study. At the surface, the thermal response is tightly coupled to the forcing, and at all rotation rates, the peak integrated temperature is lagging the motion of the substellar point. However, at altitude, from where observed infrared emission will originate, the temperature distribution is sensitive to the speed of the diurnal cycle. Above the boundary layer, momentum and temperature are less strongly damped, thermal advection is efficient compared to friction, and the hot spot is advected by the wind field. Figure 13 shows the horizontal temperature structure in the mid-troposphere; for both eastward- and westward-propagating substellar points, eastward and westward hot spots are observed, depending on the rotation rate of the planet. As previously demonstrated in the hot Jupiter studies of Showman et al. ( 2015 ), a quickly moving substellar point, or rapidly rotating system results in a reduction in zonal variability. At the mid-troposphere example plots shown in Figure 13, there is an ∼65 K gradient between substellar and antistellar points in the equilibrium temperature T eq ; in contrast, the atmospheric temperature varies little, with an efficient thermal transport from dayside to nightside. The efficient heat transport and zonal redistribution with a rapidly moving substellar velocity predicts relatively warm nightside temperatures and a largely isothermal distribution of temperature in the upper atmosphere; this is perhaps expected from our intuition of Earth, which has a very rapid diurnal cycle relative to atmospheric radiative timescales, . The reduction in the meridional temperature gradient is also a result of the short diurnal timescale, providing an effective relaxation profile, as shown in Figure 7 and discussed above. The phase-curve offset is found by calculating the normalized phase curve relative to the substellar point using Equation ( 22 ) and then solving for the longitude of maximum integrated thermal emission. The panels of Figure 14 show the phase-curve offset as a function of substellar velocity near the surface and at several levels in the troposphere. Phase curves near the surface are a strong function of substellar velocity, with little influence from rotation rate; in general, the faster the substellar point moves, the further the thermal hot spot has lagged behind the point of maximal heating. This is due to the short timescales of both radiative and frictional damping in the bottom boundary of the


the sources H ii 1, 2 and 6 are the extrapolated thermal flux density estimated using H emission. For the sources H ii 2 and 6, comparing the best-fitting parameter m to equations ( 1 ) and ( 2 ), we estimate the thermal freefree emission to be optically thick ( ff 1) below 0.220.03 and 0.410.05GHz, respectively. Recently, Hindson etal. ( 2016 ) in a study of Galactic H ii regions, found evidence of a turnover in the freefree spectrum typically with turnover frequencies in the range 0.31.2GHz. We estimated 8 the EM to be (1.20.3)10 5 and (4.6 1.2) 10 5 pccm 6 for H ii 2 and 6, respectively which in turn is related to the average thermal electron density n e as (Berkhuijsen, Mitra Mller 2006 ): where, f is the filling factor and h HII is the size of the H ii region along the line of sight. Assuming a typical f 5percent for the clumpy star-forming disc (Ehle Beck 1993 ) and h HII 50pc, i.e. the spatial resolution of our observations, we estimate n e to be 11 and 22cm 3 for H ii 2 and 6, respectively, which are typical values for H ii regions (Hunt Hirashita 2009 ). Deeg etal. ( 1993 ) pointed out that such values of EM and n e are necessary to explain the radio continuum spectra of star-forming blue compact dwarf galaxies. To better constrain n e and the sizes of the H ii regions, high-resolution radio continuum observations at even lower frequencies with LOFAR will be necessary. The thermal emission independently estimated using extinction-corrected H emission well represents the emission in the three H ii regions (shown as black dotted lines in Fig. 6 ). This suggests that the extinction-corrected H emission is a good tracer of the thermal freefree emission on scales below 100pc. Since, the total radio continuum emission in these regions are already consistent with 100percent thermal emission, it is difficult to estimate the contribution of the non-thermal component. We have therefore blanked these pixels in our future calculations. 4.2.2 Non-thermal bubble An interesting feature observed in the maps of and nt lies towards the south-eastern edge of IC10 marked as the non-thermal bubble in Fig. 3 . The bubble was first identified in the radio continuum observations of Yang Skillman ( 1993 ). The sharp boundary of this region is distinctly visible only in the spectral index maps (see Fig. 4 ). The total intensity emission is merged with the bright H ii region H ii 1 and does not show the bubble distinctly. In Fig. 7 , we show a zoomed-in view of the spectral index map. We mark the sharp boundary of the bubble and determine its centre to be at RA = 00 h 20 m 29 s and Dec. = 591639.5. The non-thermal bubble extends 300pc in the north-east to south-west direction and 100pc in the north-west to south-east direction. Its north-western edge, where the spectrum flattens from being non-thermal with 0.6 to thermal 0.1, is bound by GMCs as observed by Leroy etal. ( 2006 ), shown as the black circles in Fig. 7 . This suggests that the GMCs likely confine


2019 ). Here, the uncertainty in the wavelength calibration in Doppler units is expected to be about 1 km s −1 . Information of the two target lines and their associated calibration lines is listed in Table 2 . After the wavelength calibrations, the Si iv and Mg ii k lines have redshifts of 2.3 km s −1 and 3.1 km s −1 , respectively, in the quiet Sun region. Here, the Doppler shift of Mg ii k line is obtained using the central absorption at k3, and unrelated to the spectroscopic results of coronal rain. Figure 4. Spectral information of the coronal rain observed by IRIS. Maps of intensity (a1)–(a2), Doppler shift (b1)–(b2), and line width (c1)–(c2) of Si iv (1394 Å) (a1)–(c1) and Mg ii k (2796 Å) (a2)–(c2) lines for the IRIS raster scan #3. Like in Figure 2 (a), the blue rectangles and diamond separately indicate the positions of northern and southern parts of the coronal rain, which is enclosed by the blue dashed–dotted lines. The FOV is denoted by the pink rectangle in Figure 2 (a). See Section 4.1 for details. Table 2 Lines of Interest Note. Listed are the lines, the rest wavelengths of the lines, the Doppler shifts (Δ v ) of the rest wavelengths of the lines to the Si iv (upper) and Mg ii k (lower) lines, and the absolute Doppler shifts of the lines in the spectrum averaged over a quiet Sun region after the wavelength calibrations. Positive (negative) values of the Doppler shifts correspond to redshifts (blueshifts). The rest wavelengths of the lines are obtained from the line list of Tian ( 2017 ). Similar spectroscopic results of coronal rain are obtained for the four middle raster scans of IRIS, i.e., from scans number two to five. Among them we take the results for the third raster scan for example, and display them in Figure 4 . The left and right columns of Figure 4 show the maps of intensity, Doppler shift, and line width of the Si iv and Mg ii k lines, respectively. Here, the instrumental line width of about 26 mÅ is subtracted from the Gaussian line width (De Pontieu et al. 2014 ). In these maps, the line fit parameters outside the locations of the coronal rain are not shown as they are not well-fitted because of low count rates. Therefore, we only concentrate on the coronal rain region enclosed by the blue dashed–dotted lines in Figure 4 . Same as in the IRIS 1400 Å SJIs (see Figure 2 (a)), two substructures of the coronal rain are identified, marked separately by the blue square and diamond signs in Figure 4 . This demonstrates that in our observations in the coronal rain, the 1400 Å channel is indeed dominated by the transition region Si iv line. Comparing the Si iv and Mg ii k intensity maps, we find that the coronal rain seen in the Mg ii k line is located mostly at the same locations as the Si iv coronal rain; see Figures 4 (a1)–(a2). At the north (south) coronal rain, we measure the intensity, Doppler shift, and line width, and obtain the mean values of 46 (18) DN pixel −1 , 7.5 (5) km s −1 , and 8.6 (7.3) km s −1 for the


models that terminate at values in agreement with the inferred luminosity and temperature for SN 2016gkg (as discussed in Section 3.4.2 ). The best-fitting model has an initial stellar mass of M 15M with a 1.5-M companion. The initial period is 1000d and the primary star explodes with M 5.2M . Two additional examples with initial masses 12M (8.4-M initial mass companion, 160-d period) and 16M (14.4-M initial mass companion, 6.3-d period) are shown with dotted and dashed lines, respectively. All of these models agree with the inferred luminosity and temperature of SN 2016gkg. We find that it is extremely unlikely that SN 2016gkg originated from a single star. Woosley Heger ( 2007 ) and Sukhbold etal. ( 2016 ) have found that, for stars with M ZAMS 30M , the pre-SN iron core is too large for an SN to be successful. Moreover, mass-loss is sufficiently strong so that most of these stars lose their entire hydrogen envelopes and are thought to end their evolution as WolfRayet stars, implying that the subsequent SN would be Type Ib or Ic. SNe IIb require progenitor stars with extended low-mass hydrogen envelopes (Podsiadlowski 1993 ; Woosley etal. 1994 ; Elmhamdi etal. 2006 ), and any single-star model for such a system would require finely tuned mass-loss that would otherwise fail to reproduce the observed range in SN IIb light curves, spectra, and progenitor stars. While the single-star scenario could describe a minority of SNe IIb, it is likely that the majority of these systems come from binary-star systems such as the one observed towards SN 1993J (Maund etal. 2004 ; Fox etal. 2014 ). 3.4.2 Binary-star models We examine evolutionary tracks involving binary stars in order to assess the plausibility of these systems as possible progenitor stars for SN 2016gkg. We obtained our binary-star evolutionary tracks from the Binary Population and Spectral Synthesis ( bpass ) code as described in Eldridge Stanway ( 2009 ). These models provide a range of metallicities ( Z 0.0010.040), primary-star masses ( M /M 0.1300), mass ratios ( q 0.10.9), and initial periods [log( P /1d)04]. We fixed the metallicity of the binary-star models to Z 0.010 in order to provide the best match to the observed metallicity of NGC 613. Otherwise, we examined the full range of parameters provided by bpass . For our fitting scheme, we looked for binary-star models that produced a primary star with terminal luminosity and temperature that minimized Overall, we found that 107 out of 5565 bpass models terminated with primary-star luminosity and temperature within our measurement uncertainties for the SN 2016gkg progenitor star. Of these models, the 2 ranged from 0.11 to 4.01 with a median value of 1.05. In Fig. 4 , we show the stellar evolution of the best-fitting binary-star model on the HR diagram along with the inferred luminosity and temperature of the SN 2016gkg progenitor star. The primary star has an initial mass of 15M while the secondary (accreting) star has an initial


in the strong peaks of emission towards the top and bottom of this figure, at distance of 19 arcsec or 1.8 kpc from the nucleus. The spectrum shows complex nuclear structure, with multiple components, including a very rapidly rotating structure, which we interpret as a star-forming nuclear ring. Between the nuclear and bar-end rings, diffuse emission is apparent, particularly in the upper part of Fig. A2 . Thus, in spite of its peculiarity, we do consider this an example of the SFD phenomen, and it is included as such in this paper. Figure A2. Two-dimensional optical spectrum of NGC 3729, centred on the H α and [N ii ] lines. The emission-line clump is indicated by the arrows. Comparison with the bright H ii region towards the bottom of the frame shows the extended nature of the line emission from the clump. The unusual feature seen in Fig. A2 is the peak of emission seen just below the nuclear ring, 5.7 arcsec (560 pc) from the nucleus. At first sight, this resembles an H ii region, but uniquely, in the current data set at least, it shows clear LINER-type ratios. To illustrate this point, Fig. A3 shows the extracted spectrum of this peak in the lower frame, with an H ii region spectrum from the same long-slit observation shown in the upper frame for comparison. The spectra are clearly different, and argue against ongoing SF in the near-nuclear clump. The clump has [N ii ] and H α EW values of 5.63 and 6.73 Å, respectively, similar to or slightly greater than the values for the two SFD regions in NGC 3729 (4.70 and 3.69 Å for [N ii ], 6.76 and 4.50 Å for H α). These values are all at the high end of the EW distributions for line emission from SFD regions, while the [N ii ]/Hα ratio for the clump, 0.837, is entirely consistent with the distribution of ratios for SFD regions (Fig. 1 , lower panel). Figure A3. Extracted H α and [N ii ] emission for the NGC 3729 clump (bottom) and, for comparison, an H ii region in the same galaxy (top). The high [N ii ]/H α ratio in the clump is clearly apparent. One possibility is that the near-nuclear clump could be the nucleus of the tidally shredded companion that has been drawn towards the centre of NGC 3729 through dynamical friction. One test of this is to look for spatial extent. Visual inspection of Fig. A2 indicates that the clump appears moderately extended, e.g. compared with the most compact H ii region (towards the bottom of the image). Measurements confirm this; along the spatial direction, the clump has a full width at half-maximum (FWHM) of 5.3 pixels, or 2.33 arcsec, compared to 3.7 pixels or 1.63 arcsec for the compact H ii region. As the latter may itself be somewhat extended, we also measured the FWHM of the standard star observation taken closest in time to the NGC 3729 spectra, finding values of 3.2 pixels or 1.4 arcsec. Taking either the star or (conservatively) the H ii region as a measure of the seeing broadening the clump FWHM, the true size of the clump is 1.9 or 1.7 arcsec,


ACKNOWLEDGEMENTS Based on observations with the Atacama Pathfinder EXperiment (APEX) telescope. APEX is a collaboration between the Max Planck Institute for radio Astronomy, the European Southern Observatory, and the Onsala Space Observatory. The authors acknowledge support from the UK Science and Technology Facility Council under grant ST/L000768/1. iraf is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under co-operative agreement with the National Science Foundation.


the rise time of the light curve can be also used to estimate the radius of the progenitor of type IIP supernova through the relation between the progenitor radius and the rise time of the light curve, i.e. log R(R ⊙ ) = (1.225 ± 0.178) log t rise (d) + (1.692 ± 0.490) (Morozova et al. 2016 ). For SN 2017eaw, the rise time is estimated to be t rise = 6.81 ± 0.85 d in the g band, which gives an estimate of the radius as 515 ± 180 R ⊙ . The above two estimates of the progenitor radius agree within 1σ error. Figure 6. Constraining the progenitor radius of SN 2017eaw based on the cooling of the photospheric temperature in the early phase after the explosion. The red dots are the temperatures inferred from the blackbody fit to the observed UV and optical photometry; while the red curve represents the best fit of the radius. The green and black curves show the upper and lower limits of the estimates of the radius, respectively. The blue stars show the temperature evolution of SN 1987A, and the blue dashed line shows the corresponding best-fitting radius using the theoretical model (Rabinak Waxman 2011 ). We also try to fit the observed SED of the progenitor star from the prediscovery HST and Spitzer images with synthesized spectra calculated using the stellar evolution code marcs . 4 However, the best-fitting model spectrum has an effective temperature of only about 2500 K [A similar value of 2600 K was also suggested by Kilpatrick Foley ( 2018 )] with A V = 1.83 ± 0.59 mag by including the Spitzer data (Fig. 7 ), much lower than that inferred for the HST data alone. Given the luminosity, the lower temperature would result in an effective radius of 1330 R ⊙ for the progenitor, which is inconsistent with the estimate either from the rise time or temperature evolution of the shock cooling in the early phase. Despite an overall reasonable fit, the measurements in two Spitzer bands may suffer large contaminations of the nearby red sources due to large aperture photometry and/or the presence of circumstellar dust. In the latter case, the light of the progenitor star is scattered/absorbed by the surrounding dust and re-emitted at longer wavelengths [see also the analysis by Kilpatrick Foley ( 2018 )]. We also derive the F606W-band magnitude in 2004 by assuming that the dimming behaviour in F814W-band is totally due to the CSM dust. Taking into account this speculated F606W-band magnitude and the observed F814W-band magnitude obtained in 2004, the SED of the progenitor inferred in 2004 matches with the theoretical stellar spectra model characterized by an effective temperature of 3550 ± 150 K and a radius of 636 ± 155 R ⊙ (see Fig. 7 ). As an alternative, the dimming behaviour in F814W band could be also due to the intrinsic variation of an RSG star, but this explanation is inconsistent with either the observation taken at one year to a few days before the explosion or the theoretical prediction for its final stage evolution (see discussions in


ejects these elements into space where they are then available for the next generation of stars. Common uranium isotopes have half-life decay times of 10 8 to 10 9 years, and had been used to determine the age of the universe by observing ultra-metal-poor stars ( Frebel et al. 2007 ). Gopka et al. (2007) identified Th II 5989.045 Å in the KPNO Arcturus spectrum from Hinkle et al. (2000) . They followed this up by the identification of more such lines from the KPNO atlas ( Gopka et al. 2013 ). The most widely used line is Th II 4019.129 Å. Together with the nearby neodymium line Nd II 4018.8 Å this line is used to form the chronometric ratio Th/Nd, first suggested by Butcher (1987) as an age indicator. However, there is no systematic identification of heavy-element lines in benchmark stars. We have visually searched our library sample for the strong lines of U II at, for example 3859.57 Å and 4241.67 Å as well as Th II at 4019.129 Å and 5989.045 Å, leaning on new oscillator strengths from Nilsson et al. (2002a , b ). Some of these lines are indeed identified, for example the Th II -Nd II line pair at 5989 Å in giant stars like Arcturus, α Ari, or μ Leo or the U II transition at 4241-Å in ε Vir. Figure 7 is a comparison of above three targets with the Sun for the Th 5989-Å region. For many others there is only vague evidence due to blending. Note again that the solar spectrum in this plot was also taken with PEPSI in the same manner as the other stars. It shows a dominant telluric blend on the blue side of the expected Nd II line. Th II 5989.045 may be present in the solar spectrum with an upper limit at the 1 mÅ level. Fig. 7 Th II 5989.045-Å and Nd II 5989.378-Å lines in three RGB stars (full lines, from top to bottom in the Ti I line core; Arcturus, Hamal, Rasalas). The top spectrum shown as dots is a spectrum of the Sun. In connection with chronometry, the s-process elements Ba and Sr (a.o.) are also key elements. The most prominent barium line is the one Ba II transition at 4554.02 Å. Other comparably weaker lines are 3891.78 Å and 4130.64 Å (see, e.g., Siqueira Mello et al. 2014 ).Strontium lines are comparably more prominent than U and Th, for example Sr II at 4077.72 Å or 5215.52 Å. The 4077-Å line is commonly used in the M-K system to classify cool, low-gravity, stellar atmospheres because of its density sensitivity ( Gray Garrison 1989 ). Our library spectra may be used to investigate spectral lines from heavy elements in greater detail than before. 7 Summary We present a library of high-resolution (on average ≈220 000), high-S/N optical spectra of a sample of 48 bright reference stars. The sample includes the northern Gaia benchmark stars and a few well-known M-K standards. Deep spectra are build by average combining individual exposures and reach S/N of many hundreds and, in some cases, even thousands. Continua are set by predetermining synthetic spectra that match the target classification. Continuum adjustments of several tens


We are thankful to the anonymous referee for providing constructive feedback that improved our manuscript. This research is supported by the National Science Foundation (USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the Elements) and by the ERC Consolidator Grant (Hungary) funding scheme (project RADIOSTAR, G.A. n. 724560). K.B. acknowledges support from the NCN grants Sonata Bis 2 (DEC-2012/07/E/ST9/01360), OPUS (2015/19/B/ST9/01099), and OPUS (2015/19/B/ST9/03188). M.M., N.V., and R.S. are supported by the U.S. Department of Energy under contract No. DE-AC52-07NA27344 for the topical collaboration Fission In r -process Elements (FIRE). This work was also supported in part by the U.S. Department of Energy under grant No. DE-SC0013039 (R.S. and T.S.). A portion of this work was also carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under contract No. DE-AC52-06NA25396 (C.F., O.K., R.W., M.M.). This research used resources provided by the Los Alamos National Laboratory Institutional Computing Program (O.K., R.W.). Software: OMEGA (Côté et al. 2017b ), PRISM (Mumpower et al. 2017 ), StarTrack (Belczynski et al. 2002 , 2008 ), Los Alamos suite of statistical Hauser-Feshbach codes (Kawano 2016 ), NumPy (Van Der Walt et al. 2011 ), matplotlib ( https://matplotlib.org ).


1 bursts, and the blue-filled triangles indicate the Class 2 bursts. We find that most of the multiple-peaked bursts are located close to the vertex of the CCD. Figure 2. Colour–colour diagram (CCD) of all RXTE observations of 4U 1636-53. The colours of 4U 1636 − 53 are normalized to the colours of Crab. The grey points represent all available observations with one point per observation. The black crosses stand for all X-ray burst in this source. The red-filled circles and the blue-filled triangles represent Class 1 and Class 2 bursts, respectively. We extracted the 64-s interval spectrum prior to a burst as persistent emission. We generated the instrument response matrix using the tool pcarsp and the instrumental background using the tool pcabackest in heasoft for each spectrum. In this work, we fitted the spectrum in the 3.0−20 keV band using xspec version 12.10.1 (Arnaud 1996 ). We added a systematic error to the pre-burst spectra because of calibration uncertainties. During the fitting process, we included the effect of interstellar absorption using the cross-sections of Balucinska-Church McCammon ( 1992 ) and solar abundances from Anders Grevesse ( 1989 ), with a fixed hydrogen column density, N H , of (Pandel, Kaaret Corbel 2008 ). We used all available PCUs during the X-ray bursts to produce time-resolved spectrum. We corrected every spectrum for dead time according to the methods supplied by the RXTE team. Since the light curve of bursts decay is quite smooth, to compensate the lower count rates, we extracted spectrum over longer intervals in the tail of the bursts. For each multiple-peaked burst, we generated one instrument response matrix using the pcarsp and the instrumental background using the pcabackest in heasoft . For the burst spectral analysis, we initially used a single-temperature blackbody model, tbabs*bbodyrad , to fit the net burst spectra, which is well established as a standard procedure in X-ray burst analysis (Kuulkers et al. 2002 ; Galloway et al. 2008 ). The model provides the blackbody colour temperature, kT bb , and the normalization, K bb , proportional to the square of the blackbody radius of the burst emission surface, and it allows us to estimate the bolometric luminosity as a function of time assuming a distance of 5.95 kpc (Fiocchi et al. 2006 ). The bursts bolometric flux are calculated as where , R km is the effective radius of the emitting surface in km, and D 10 is distance to the source in units of 10 kpc. We defined r 1,2 as the ratio of the first peak to the second peak flux. We note that, to reduce the effect of the instrument, we used the bolometric flux (not the net burst count rate ratio in Fig. 1 ) from the standard approach to calculate the ratio r 1,2 . After subtracting the instrumental background for the time-resolved spectra, we used another model that allows us to vary the pre-burst spectrum by a free scaling factor (Worpel et al. 2013 ). We used two models to describe the persistent


The authors are grateful to Amanda Heiderman and Neal Evans for their useful collaboration and discussion on embedded protostellar environments, and to Mike Dunham for his comments on the paper. Many thanks to the referee, Charles Lada, for his very useful comments and suggestions. Astrochemistry in Leiden is supported by the Netherlands Research School for Astronomy (NOVA), by a Royal Netherlands Academy of Arts and Sciences (KNAW) professor prize, by a Spinoza grant and grant 614.001.008 from the Netherlands Organisation for Scientific Research (NWO). The authors are indebted to the various observers who have collected data for their papers and kindly provided them to be included in the LOMASS database, as well as staff at the JAC. Acknowledgment is given to the following programs and languages for building this database: gildas-class and python for data reduction and format manipulation; python-matplotlib for plotting; MySQL for construction of the database; php and html for the web interface.


be derived. The symbols are the same introduced in the legend of Fig. 8 . In our case, the benefit of using instead of Δα −10, 10 to represent the MFS amplitudes consists of a larger number of useful maps. In Fig. 12 , the versus α 0 plot confirms, based on a larger sample of cases, the trends seen in Fig. 10 . The plot appears less scattered than that of Fig. 10 with regard to positions of Hi-GAL and fBm images, while the positions of the simulations cover a wide range towards larger values. The ‘solenoidal’ and the t 1 , yz maps of both the ‘quasi-hydrodynamical’ and ‘high-magnetization’ scenarios are the closest to the observational points, mostly to the ones corresponding to SPIRE maps of l224 and l217, that is to say that, from the point of view of the MFS amplitude, they show a degree of multifractality similar to that of the most actively star-forming regions in our sample. Figure 12. Plot ot the area A Φ under the MFS and above f = 1.5 versus the peak position α 0 for maps for which A Φ can be derived. The symbols are the same introduced in the legend of Fig. 8 . 4.2.4 Left versus right tail width The diagnostics used in Figs 10 , 11 , and 12 consider the MFS as a whole, neglecting information contained in possible asymmetries. In fact, the left tail of the MFS represents the heterogeneity (broad tail) or uniformity (narrow tail) of the high values distribution, as well as the right tail is related to heterogeneity/uniformity of the low values distribution (e.g. Pavon-Dominguez, Jimenez-Hornero de Rave 2013 ; de Freitas et al. 2017 ). Strong asymmetries are observed in most of the spectra analysed in this paper, with the extreme case represented by PACS 70 maps, discussed above. In order to make use of the MFS asymmetry, single values of α on the two sides of the MFS (for example, α 10 and α −10 , to follow the same approach as above) should be considered (de Freitas et al. 2017 ). In Fig. 13 , the two widths Δα L ≡ α 0 − α 10 and Δα R ≡ α −10 − α 0 , are plotted. First, a strong segregation in abscissa is visible between the group of fBm sets (which are right-skewed and for which the width of the left MFS tail α 10 remains nearly constant, see also Table 3 ) and that of Hi-GAL maps. The latter is internally more composite: the most quiescent, l215, is found on the left while the most active, l224, on the right, as a consequence of the leftward broadening of the MFS in presence of bright compact sources (cf. Fig. 5 ). Along the vertical coordinate, a systematic increase is seen from short to long Herschel wavelengths, while the column density maps appear mixed with SPIRE maps but with no specific trend. Figure 13. Plot ot the MFS left versus right tail amplitude for maps for which it is possible to derive both quantities. The symbols are the same introduced in the legend of Fig. 8 . The dotted line represents the bisector, to facilitate the distinction between left-skewed (below the line) and right-skewed (above the line) MFSs,


The Telescope Array experiment is supported by the Japan Society for the Promotion of Science through Grants-in-Aids for Scientific Research on Specially Promoted Research (21000002) “Extreme Phenomena in the Universe Explored by Highest Energy Cosmic Rays” and for Scientific Research (19104006), and the Inter-University Research Program of the Institute for Cosmic Ray Research; by the U.S. National Science Foundation awards PHY-0307098, PHY-0601915, PHY-0649681, PHY-0703893, PHY-0758342, PHY-0848320, PHY-1069280, PHY-1069286, PHY-1404495 and PHY-1404502; by the National Research Foundation of Korea (2007-0093860, R32-10130, 2012R1A1A2008381, and 2013004883); by the Russian Academy of Sciences, RFBR grants 11-02-01528a and 13-02-01311a (INR), IISN project No. 4.4509.10, and Belgian Science Policy under IUAP VII/37 (ULB). The foundations of Dr. Ezekiel R. and Edna Wattis Dumke, Willard L. Eccles, and the George S. and Dolores Dore Eccles all helped with generous donations. The State of Utah supported the project through its Economic Development Board, and the University of Utah through the Office of the Vice President for Research. The experimental site became available through the cooperation of the Utah School and Institutional Trust Lands Administration (SITLA), U.S. Bureau of Land Management, and the U.S. Air Force. We also wish to thank the people and the officials of Millard County, Utah for their steadfast and warm support. We gratefully acknowledge the contributions from the technical staffs of our home institutions. An allocation of computer time from the Center for High Performance Computing at the University of Utah is gratefully acknowledged.


well as the narrow range of scales involved, we are only able to claim qualitative similarity with the Mallet et al. ( 2017 ) prediction. Figure 2. Spectral index of the dissipation range binned in the (, β e ) plane. The black square marks the region with the steepest spectral indices in the range of 0.1 ≲ β e ≲ 1 and . To resolve the ambiguous results obtained with Figures 1 (d) and (e), we repeat our analysis with the subset of the data within the black square in Figure 2 , which encloses 41% of the total data and is bounded by 0.1 ≲ β e ≲ 1 and . The spectral indices are significantly steeper in this region, and if this is caused by reconnection, then may have significantly better scaling with in the marked region than with ρ c . In Figure 3 (a), the slope of the power-law fit for as a function of closely agrees with the one based on the full distribution. In contrast, in Figure 3 (b), the slope of the power-law fit for as a function of is remarkably close to 0. Based on this, we suggest that at least at low β e magnetic reconnection may control the ion-scale break of the solar wind turbulence. The intercept of the power-law fit is , implying C D = 4.7 (see Equation ( 1 )). Figure 3. (a) and (b) are identical to Figures 1 (e) and (d); however, they present the subset of measurements, which are within the black square in Figure 2 corresponding to 41% of the overall data points. Both and were close to normally distributed in our data, thus we use an F -test to investigate whether they have equal variance. The ratio of the sample variances is with 95% confidence intervals of [0.8328; 0.8468]. Thus we reject the null hypothesis and conclude that predicts the break with smaller spread than ρ c . Finally, the scaling of as a function of β i , while significant over the whole range of β i present in the data, is not particularly strong. With reference to the results of Chen et al. ( 2014 ), Mallet et al. ( 2017 ) pointed out that correlations between and β i could cause the scaling behavior of d i to mimic that of . Neglecting a nearly constant factor ,and so if were anticorrelated with β i , the ratio would scale less strongly with β i than otherwise expected. Figure 4 shows that empirically, such an anticorrelation does in fact exist in the solar wind (at least at low β i ). Assuming that the break scale (as does appear to be the case: see Figures 1 (d) and 3 (b)), this contributes to the rather shallow scaling of in Figure 1 (b). Similar consideration could contribute to the shallow scaling of with . Figure 4. 2D histogram showing the distribution of the measurements in the () plane. The least-square fit is indicated with a black line and the average and standard deviation of each 5% of the data are marked in white. 4. Conclusion In this Letter, we have presented a statistical study of the break scale between the inertial and dissipation ranges of the solar wind turbulence spectrum, and to what extent agrees with the fundamental ion length


We thank the anonymous referee for the thorough review that helped us improve this manuscript. We are grateful to Athanasia Tsatsi for useful comments. This research was supported in part by the Polish National Science Centre under grant 2013/10/A/ST9/00023.


The authors thank Luca Ciotti, Pasquale Londrillo, and Carlo Nipoti for sharing their NMODY code. The authors acknowledge Ortwin Gerhard for sharing the code for generating the self-consistent N -body ICs using Lucy’s method. X.W. thanks for support through NSFC grants 11503025, 11421303, Anhui NSF grant 1708085MA20, and the Fundamental Research Funds for the Central Universities. X.W. thanks for support from the Hundred Talents Project of Anhui Province. This project was partially started when X.W. was an Alexander von Humboldt Fellow at the University of Bonn.


gravity brightening exponent for the radiative, primary component, determined through our models, is ∼1 (von Zeipel 1924 ). For the secondary component, the posterior distribution is a slightly skewed normal distribution. By considering the peak of the skewed distribution (not the Gaussian fit to the posterior distribution), we find the gravity brightening exponent to be β = 0.59 ± 0.08. While this is not in agreement with the value of β = 0.32, suggested by Lucy ( 1967 ), we find our value in close agreement (∼2σ) with that of Claret Bloemen ( 2011 ), who computed β = 0.48 for comparable models. This value was computed using ATLAS models (Castelli Kurucz 2004 ) and the Kepler bandpass, and taking into account local gravity and convection. It is also likely that the tidal distortion affects the gravity darkening exponent, as discussed by Espinosa Lara Rieutord ( 2012 ). In our binary models, we fixed the primary and secondary rotation rates to those obtained through spectral fitting, v sin i 1 = 29(2) km s −1 and v sin i 2 = 9(2) km s −1 . Combining these values with our model-determined orbital inclination (assuming that the orbital and stellar rotational axes are aligned) and radii, for the model with pulsations, we obtained F 1 = 7.1(2) and F 2 = 4.0(1), where F is the ratio of the stellar rotational to orbital period and the subscript denotes the primary and secondary components, respectively. For both models, the one with, and the one without pulsations, we obtained the same values with slightly different uncertainties (see Table 4 ). Interestingly, under the assumption that the stellar rotational and orbital axes are aligned, the primary component is rotating slightly faster than the predicted pseudo-synchronous rotation rate (Hut 1981 ), the stellar rotation synchronous with the orbital velocity at periastron, which was calculated to be F = 5.3(2) for both components; while the secondary component is rotating slightly slower. However, if we relax the assumption that the orbital axes are aligned, it is possible to find configurations where both stars are rotating pseudo-synchronously. 5 SUMMARY AND CONCLUSIONS We have modelled the heartbeat star binary system KIC 3749404 by combining a comprehensive assortment of tools including the binary modelling software, phoebe ; emcee , a python implementation of the affine invariant mcmc techniques; and our own software to fit pulsations and Doppler boosting. With these tools, we were able to obtain two successful fits to the heartbeat star light and radial velocity curves simultaneously: one without pulsations and one with all the tidally induced pulsations greater than 20 μmag (seven pulsations). From these fits, we obtained the fundamental parameters of the binary system (see Table 3 ). The difference between the results of these two models hinges on the different inclination values: 602(1) without pulsations and 62(1)° with pulsations. This 2σ difference subsequently produced a larger


We thank the technical staff of the University of Hawaii 2.2 m telescope, and Dan Birchall for his observing assistance. We recognize the significant cultural role of Maunakea within the indigenous Hawaiian community, and we appreciate the opportunity to conduct observations from this revered site. This work was supported in part by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We thank the Gordon Betty Moore Foundation for their continuing support. X.H. acknowledges the University of San Francisco (USF) Faculty Development Fund. Z.R. was supported in part by a USF Summer Undergraduate Research Fellowship. Support in France was provided by CNRS/IN2P3, CNRS/INSU, and PNC; L.P.N.H.E. acknowledges support from LABEX ILP, supported by French state funds managed by the ANR within the Investissements d’Avenir programme under reference ANR-11-IDEX-0004-02. N.C. is grateful to the LABEX Lyon Institute of Origins (ANR-10-LABX-0066) of the Université de Lyon for its financial support within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) of the French government operated by the National Research Agency (ANR). Support in Germany was provided by the DFG through TRR33 “The Dark Universe;” and in China from Tsinghua University 985 grant and NSFC grant No 11173017. N.S. acknowledges the support from World Premier International Research Center Initiative (WPI), MEXT, Japan, and JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers. This work is partially based on observations made with ESO Telescopes at the La Silla Paranal Observatory, Chile, under program 289.D-5035. Some results were obtained using resources and support from the National Energy Research Scientific Computing Center, supported by the Director, Office of Science, Office of Advanced Scientific Computing Research of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.


this case, the inpainting performances with DP and GAN can be affected by noise, and the reconstruction area can be visually distinguished in the square patch. Figure 12. Thumbnail images of Planck temperature maps at (a) 353 and (b) 857 GHz. The radius of the reconstructed area (black circle) is 15′. Two locations are chosen to highlight different inpainting performances with high and low SNRs of Planck 353 map, respectively, at high Galactic latitude, i.e., and at low Galactic latitude, i.e., . For a more quantitative assessment, we thus estimate the summary statistics shown in Section 4.1 and we show the results in Figure 13 . Figure 13. Summary statistics estimated on Planck dust T maps at (a) 353 and (b) 857 GHz. A clear indication that the thermal dust emission data is contaminated by instrumental noise can be inferred by comparing the shapes of Minkowski functionals estimated for the maps at 353 GHz, with the ones from signal-only simulations (Figure 4 ) or from signal-dominated maps (Figure 13 (b)). The morphology of the Minkowski functionals of the former largely resembles the functionals estimated from a Gaussian signal. Two possible candidates for the Gaussian component are (i) Planck instrumental noise, which can be approximated as white within patches, and (ii) CMB residual emission. DP inpaintings are the most affected ones in the presence of the noise at , e.g., notice how the pixel distribution (top left panel) of Figure 13 (a) noticeably departs from the ground-truth one. However, the KS test p -value performed on the DP and ground-truth samples is , i.e., not significantly low enough to reject the null hypothesis that the two samples are different. On the other hand, inpainting with GAN and NN does not show any dependence with SNR, as the performances with these methodologies are essentially similar to the ones observed with the signal-only simulated maps (e.g., Figures 7 , 8 , and 10 ). Finally, we would like to point out that for the case of inpainting with GAN, we use the weights derived from the training set composed of signal-only dust TQU simulated maps. Looking at Figure 13 we notice that GAN is able to statistically reproduce at 353 GHz the features composed by signal and noise, indicating that the network has correctly learned the features related to the intrinsic signal in the presence of noise, and injects signal plus noise features statistically coherent with the ones outside the masked area. However, when the noise is highly dominating in the patch, we can clearly distinguish smooth artifacts in some cases inpainted with GAN (see Figure 12 (a, bottom)). This is somewhat expected because GAN is trained on signal-only simulated images. Further investigations on training GAN with noisy data are needed, and we will address it in a future work. 4.3. Inpainting Maps with Point Sources In this section, we aim at showing real world applications of the three reconstruction methodologies by inpainting areas in real maps


We thank the anonymous referee for constructive suggestions. We are grateful to Maryam Modjaz and Yuqian Liu for sending us the photospheric velocity data before the publication of their paper. This work is supported by the National Program on Key Research and Development Project of China (Grant No. 2016YFA0400801), the National Basic Research Program of China (“973” Program, Grant No. 2014CB845800), and the National Natural Science Foundation of China (grant Nos. U1331202, 11533033, U1331101, 11673006, 11573014, 11422325, and 11373022). D.X. acknowledges the support of the One-Hundred-Talent Program from the National Astronomical Observatories, Chinese Academy of Sciences), and by the Strategic Priority Research Program “Multi-wavelength Gravitational Wave Universe” of the CAS (No. XDB23040100).


at radial gradients in stellar populations have worked within R e (e.g., Spinrad Taylor 1971 ; Mehlert et al. 2003 ; Annibali et al. 2007 ; Spolaor et al. 2010 ; Jimmy et al. 2013 ; McDermid et al. 2015 ; Goddard et al. 2017 ). In recent years, integral-field spectroscopy (IFS) has enabled stellar population measurements at a large radius (e.g., Greene et al. 2013 , 2015 ; Scott et al. 2013 ; McDermid et al. 2015 ; Boardman et al. 2017 ; Goddard et al. 2017 ; Barone et al. 2018 ; van de Sande et al. 2018 ). Here, we focus on the most massive galaxies in the present-day universe using the MASSIVE survey (Ma et al. 2014 ). We have gathered integral-field data for 90 MASSIVE galaxies and measured their stellar kinematics, including higher-order moments (Veale et al. 2017a , 2017b ), stellar velocity dispersion profiles (Veale et al. 2018 ), and kinemetry (Ene et al. 2018 ). In addition, we have Hubble Space Telescope ( HST )/Wide Field Camera 3 (WFC3) imaging for 30 of the galaxies (Goullaud et al. 2018 ) and uniform Canada–France–Hawai’i Telescope (CFHT) K -band imaging for nearly all objects. 2. Galaxy Sample MASSIVE is a volume-limited survey of 116 galaxies (see details in Veale et al. 2017b ) in the northern hemisphere within D 108 Mpc (i.e., to the distance of the Coma cluster), with K -band magnitudes of M K −25.3 mag (roughly > 10 11.5 M ⊙ ). Details of the target selection are described in Ma et al. ( 2014 ). Briefly, our targets are drawn from the Two Micron All-sky Survey (2MASS; Skrutskie et al. 2006 ) Extended Source Catalog (XSC; Jarrett et al. 2003 ) combined with distances from the high-density contrast (HDC) group catalog from Crook et al. ( 2007 ), supplemented by surface brightness fluctuations when available (Blakeslee et al. 2009 , 2010 ; Blakeslee 2013 ) and with the flow model of Mould et al. ( 2000 ) when needed. We have completed IFS observations for 90 galaxies, including complete coverage of the 75 galaxies that have M K −25.5 mag. We use the Mitchell IFS at the McDonald Observatory (Hill et al. 2008 ), which has a 107 × 107 arcsec 2 field of view, one-third of which is filled by 246 fibers of a 4′′ diameter. Each galaxy is observed at three dither positions with 20-minute exposures, interspersed with 10-minute sky observations. The spectra span 3650–5850 Å, with a spectral resolution of 4.5 Å FWHM. The data are reduced using the custom software Vaccine (Adams et al. 2011 ; Murphy et al. 2011 ). For more details, see Greene et al. ( 2015 ). A primary goal of the MASSIVE survey is to measure spatially resolved stellar kinematics for dynamical modeling (e.g., Thomas et al. 2016 ). To achieve a mean signal-to-noise ratio (S/N) of at least 20 pixel −1 , we group individual fibers into spatial bins and co-add the spectra from fibers in a given bin into a single spectrum. The binning scheme is described in detail in Veale et al. ( 2017a ), but we summarize the procedure here briefly for completeness. Central fibers with S/Ns >


We thank Gary Ferland for helpful suggestions that led to improvement of this paper. We are grateful to Kanti Aggarwal, Guiyun Liang, Brendan McLaughlin, Swaraj Tayal, and Oleg Zatsarinny for providing inelastic cross-section data. This work made use of the references provided in the CHIANTI atomic database (Dere et al. 1997 ; Del Zanna et al. 2015 ). This research was supported in part by NSF grant AST-1408723, and in part by NSF Research Fellowship DGE 1656466 to C.D.K.


CDF acknowledges support from the National Science Foundation collaborative grant ‘Collaborative Research: Accurate cosmology with strong gravitational lens time delays’ (AST-1312329). LVEK is supported in part through an NWO-VICI career grant (project number 639.043.308).


for a different simulation in Schwadron et al. 2014 ). Other intended applications have been mentioned throughout the text. We encourage interested researchers to contact us if they would like to use our simulation data for complementary investigations. Appendix A The MAS Thermodynamic MHD Model The numerical code MAS employed in this article integrates the standard viscous and resistive one-fluid MHD equations in 3D spherical coordinates. For the coronal simulation described in Sections 3.1 – 3.3 and 4 , the so-called “thermodynamic MHD model” was used, in which the standard equations are extended to include parallel electron thermal conduction, radiative losses, and parameterized coronal heating. The MAS thermodynamic MHD model has been used extensively for simulating the global corona and solar wind (e.g., Mikić et al. 1999 , 2007 ; Lionello et al. 2001 , 2009 ; Downs et al. 2013 ; Linker et al. 2017 ; Titov et al. 2017 ) and eruptive phenomena such as soft X-ray jets (Lionello et al. 2016 ; Török et al. 2016 ) and CMEs (e.g., Linker et al. 2001 , 2003 ; Mikić et al. 2013b ). In this article, we use a version of the model in which the solar wind is accelerated with Alfvén waves using a Wentzel–Kramers–Brillouin (WKB) approximation (Jacques 1977 ). A more sophisticated wave-acceleration model is under development (Lionello et al. 2014 ; Downs et al. 2016 ). In the version used here, the governing equations take the following form: where A is the magnetic vector potential, is the magnetic field, is the current density, ρ is the plasma density, T is the temperature, is the plasma pressure, v is the plasma velocity, is the direction of the magnetic field, c is the speed of light, γ = 5/3 is the adiabatic index, m p is the proton mass, k is Boltzmann’s constant, κ 0 is the coefficient of the classical Spitzer thermal conductivity, is a profile that limits the radial extent within which collisional (Spitzer’s law) thermal conduction is active, is the equivalent profile for collisionless thermal conduction, Q ( T ) is the radiative loss function, H is the coronal heating term that typically consists of a sum of empirical heating functions (Lionello et al. 2009 ), is the Alfvén-wave speed, and is the gravitational force. Note that joule heating, , is not included in Equation ( 3 ). While it is implemented in MAS, we switch it off in our simulation, otherwise the insertion of the current-carrying flux rope into the background corona (Section 3.2 ) would lead to an instantaneous, unphysical temperature increase of the rope. The last expression in Equation ( 4 ) is a semi-implicit term that is added to the equations to stabilize the algorithm for time steps larger than the fast magnetosonic wave limit (Lionello et al. 1999 ; Caplan et al. 2017 ). Equations ( 5 ) and ( 6 ) are the WKB approximation for Alfvén-wave pressure advance (Mikić et al. 1999 ), where + and − are the forward and backward Alfvén-wave energy densities. The electron density


of three stellar half-mass radii at infall on the individual orbits compared to the isolated run as a function of the central dark matter density slope at infall infall . The different initial dark matter density slope also affects the stellar mass-loss, since the dark matter acts as shield for the stars. In Fig. 16 , we plot the mass-loss as defined in Fig. 15 as function of the initial dark matter profile density slope but this time for stars and dark matter. In order to avoid a too crowded plot, we only show results for orbitIV , which is the most disruptive orbit for which all five satellites still have a well-defined centre. Figure 16. Dark matter (dots) and stellar (stars) mass enclosed in a constant sphere with a radius of three stellar half-mass radii at infall on orbitIV compared to the isolated run as a function of the central dark matter density slope at infall infall . In general stars are more resilient to tidal forces than dark matter, and this is due to their smaller spatial extent and larger stellar density; for example satIII is able to retain 40percent of its stars while it is practically totally stripped of dark matter. Nevertheless there is still a correlation between the stellar mass-loss and the initial dark matter slope. An exception to this relation seems to be given by satI , which has a very strong mass-loss both in the stellar and dark matter components despite having a similar infall as satIII . This is due to the different slope for the stellar density profiles between satI and satIII , while the first satellite has a slope of 1.80 (again evaluated between 1 and 2percent of the virial radius), the stellar slope for satIII (and all the other satellites) it is close to 3.0. This difference in stellar slope is most likely related to a major merger event that occurred for satI shortly before redshift one and strongly reshuffled the stellar particle orbits. Finally, we note that some satellites (especially satI ) are left at z 0 with practically no dark matter in their central region, where they are fully stellar dominated, resembling more an extended globular cluster than a dwarf galaxy, we plan to look more into this issue in a forthcoming paper. 4 DISCUSSION AND CONCLUSIONS This work is the second of a series of papers in which we are trying to understand the formation and evolution of the smallest galaxies in the universe. In the first paper ( Paper I ), we presented a series of 27 cosmological simulations of haloes in the mass range 510 8 to 10 10 , these simulations were run till z 1 and aimed to describe the properties of satellite galaxies before accretion. In this second paper, we used a subsample of these cosmological simulations as initial conditions for a series of binary hydrodynamical simulations (satellite host) with the goal of understanding the effects of accretion and environment on satellite galaxies. More specifically, we used a total of seven haloes (five luminous and two dark) with a virial mass


ACKNOWLEDGEMENTS We would like to thank Sarah Bridle and Nicolas Tessore for bringing this problem to our attention. We also thank them for their helpful comments which greatly contributed to this paper. We would furthermore like to express our thanks to the referee, whose comments were very constructive and helped to improve this paper.


This work was aided greatly by discussions with L. Coogan, N. Cowan, C. Goldblatt, A. Lenardic, L. Schaefer, N. Sleep, and K. Zahnle. We thank the anonymous referee for helpful comments that greatly improved the manuscript. We thank the Kavli Summer Program in Astrophysics for the setting to perform this research and the hospitality of the program members and community at the University of California, Santa Cruz. T.D.K. acknowledges support from NASA headquarters under the NASA Earth and Space Science Fellowship Program Grant PLANET14F-0038. D.S.A. acknowledges support from the NASA Astrobiology Institute Virtual Planetary Laboratory, which is supported by NASA under cooperative agreement NNH05ZDA001C.


we consider, the subhalo and two-halo term contributions are quite negligible. This is also the reason why we cannot place tight constraints on the subhalo fraction and subhalo mass. The contribution of the stellar mass of the BCG is only important at very small scales. Thus, the observed ESDs in this study can mainly provide us with the constraints on the host halo properties. Figure 6. The ESD measurements (shaded area) and the best-fit model predictions (black solid line) for groups in the four different mass bins. The dashed, dotted, dotted–dashed, and blue dashed lines are the contributions of an off-centered NFW profile, subhalo, stellar mass of the galaxy under consideration, and the two-halo term, respectively. Table 3 lists the best-fit parameters for groups in different mass bins. As we have seen from the likelihood distribution of parameters in Figure 5 , we can have a fairly good constraint on the halo mass of the group samples. However, if we compare the halo masses obtained from the ESDs with those obtained from the group catalog (c.f. Table 1 ), they are roughly underestimated by 0.1 to ∼0.2 dex. We will discuss this discrepancy in the following section. The overall off-center distances for our BCGs are quite small, assuring that BCGs are indeed good tracers of halo centers. On the other hand, the concentrations of the halos seem to be somewhat larger than the theoretical predictions (e.g., Zhao et al. 2009 ). However, since the concentration c and the off-center distance R sig are quite tightly correlated, if we adopt the lower value of R sig , the concentration c will drop significantly as well. Table 3 Posteriors of the Parameters We Fitted to Our Group Samples Listed in Table 4 are the best-fit parameters for the groups that are separated into the high and low X-ray luminosity subsamples. Although due to the smaller number of lens systems the error for each data point for our X-ray subsamples is somewhat larger and thus the constraints on the five parameters are somewhat weaker, we do see the prominent feature of the halo masses of the high X-ray luminosity subsamples being higher than their low luminosity counterparts in all mass bins. The difference is to 0.2 to ∼0.3 dex, which means that the high X-ray luminosity subsamples are nearly a factor of 2 more massive than their low X-ray luminosity counterparts. Table 4 Posteriors of the Parameters We Fitted to Our High and Low X-Ray Luminosity Subsamples 4. Eddington Bias of the Halo Mass Estimation Recent studies have shown that the combination of galaxy–galaxy lensing and the clustering of galaxies can be used to constrain cosmology (e.g., Cacciato et al. 2013 ; More et al. 2013 ; van den Bosch et al. 2013 ; Leauthaud et al. 2017 ), and that the halo masses estimated for groups using galaxy–galaxy lensing signals and hence the halo mass function can also be used to constrain the cosmological parameters. However, before doing so, one needs to make a careful study of the


We thank the anonymous referee for constructive comments and suggestions. We thank Dr. Hu Zou (NAOC) for his help on optical photometry. This work is supported by the National Key RD Program of China (No. 2017YFA0402703). We thank the staff of the Nordic ALMA Regional Center (ARC) node for their support and helpful discussions. The Nordic ARC node is based at Onsala Space Observatory and funded through Swedish Research Council grant No. 2017-00648. L.F. acknowledges the support from the National Natural Science Foundation of China (NSFC, grant Nos. 11822303, 11773020, and 11433005) and Shandong Provincial Natural Science Foundation, China (ZR2017QA001, JQ201801). K.K. acknowledges support from the Knut and Alice Wallenberg Foundation and the Swedish Research Council. Y.H. acknowledges the support from NSFC (grant No. 11773063) and Natural Science Foundation of Yunnan Province (grant No. 2017FB007). Q.-H.T. acknowledges the support from the NSFC (grant No. 11803090). This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.00441.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This paper makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This paper used public archival data from the Dark Energy Survey (DES). Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the OzDES Membership Consortium, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University. Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Facilities: ALMA , Herschel (PACS , SPIRE) , WISE , CTIO (DECam).


The authors benefited greatly from participation in the International Team 276 funded by the International Space Science Institute (ISSI) in Bern, Switzerland. E.D. was supported by the Grant Agency of the Czech Republic under Grant No. P209/12/1652.


continuum of depths and durations from the many different scales of planetesimal impacts that would occur. The clustering of dips at D1500 also points to these events being correlated which is hard to reconcile with this scenario, though the planetesimals in the belts could be shepherded by planets into confined azimuthal regions (e.g. Wyatt 2003 ; Nesvorný, Vokrouhlický Morbidelli 2013 ). 5.2 Aftermath of giant impact in planetary system A possible way around the issues in Section 5.1 is to invoke dust thrown off in a single collision, perhaps analogous to the Earth–Moon system forming event (Jackson Wyatt 2012 ). In this case there need not be an underlying asteroid belt, as the collision could be between planets whose orbits recently became unstable, or between growing planetary embryos. Such events are expected to result in strong IR excesses (e.g. Jackson Wyatt 2012 ; Genda, Kobayashi Kokubo 2015 ), and are indeed seen in systems such as HD 172555 where giant impacts are the favoured explanation (Lisse et al. 2009 ). In this scenario, the putative collision would need to have occurred between the WISE observation taken in Kepler Q5 and the first large dip at D800. The dip at D1500 is then interpreted as the same material seen one orbit later, with the ∼750 d period implying an orbit at ∼1.6 au. The difference in the dip structure from D800 to D1500 could arise because the clump(s) created in the original impact are expanding and shearing out. This scenario therefore predicts that KIC 8462852 may now have a large mid-IR excess, but the most recent IR observations taken in 2015 January with Spitzer IRAC show no significant excess for KIC 8462852 (Marengo et al. 2015 ). However, non-detection of an excess would not necessarily rule this scenario out, as the dust levels derived in Section 4 (which account for the dust seen passing in front of the star) were shown to be consistent with a non-detection. A more robust prediction is that future dimming events should occur roughly every 750 d, with one in 2015 April and another in 2017 May. Two new issues arise with this scenario however. First, if the period of the orbiting material is a few years, what is the origin of the two small 0.5 per cent dips seen in the first few hundred days (D140 and D260; Table 1 ), and why did they not repeat 750 d later? It is a concern that these could require the existence of an outer planetesimal belt, which may contradict the lack of infrared emission to this star. Perhaps more problematic is the probability that this star (of unknown age) should suffer such an event that occurs within a few-year window between the WISE observation and the end of the prime Kepler mission, and that the geometry of the system is such that material orbiting at ∼1.6 au lies almost exactly between us and the star. Taking this few year window, the main-sequence lifetime, and an optimistic estimate for the scale height of giant impact debris, and the number of Kepler stars observed,


[α/Fe] = +0.4 Dartmouth isochrone. The dashed outline is the final adopted selection window as discussed in Section 2.2 . The agreement between the observations and the theoretical isochrone is good: for 0.6 ≤ ( g − i ) 0 ≤ 0.8 where the isochrone is approximately constant at m i = 0.029 mag, the mean of the globular cluster stars is m i = 0.033 with a standard deviation σ = 0.040 mag. The observed scatter in the globular cluster m i values is large but there is no obvious indication of a systematic offset between the observations and the theoretical isochrone. The scatter is presumably driven by uncertainties in the v magnitudes as the corresponding i 0 , ( g − i ) 0 combined colour–magnitude diagram (generated using an appropriate relative distance modulus offset) shows only a small scatter in ( g − i ) 0 : σ( g − i ) 0 = 0.021 mag about the mean RGB locus. 2.1.2 Known EMP stars An alternative approach is to investigate the location of known EMP stars in the metallicity-sensitive diagram. To perform this task we have compiled from the literature a list of stars with [Fe/H] ≤ −2.5, as determined from high-dispersion spectroscopy. The list was then cross-matched with the SkyMapper DR1.1 data base. In carrying out the match-up we have used tighter limits on the SkyMapper photometry in order to reduce the effects of photometric uncertainty on the location of the stars in the metallicity-sensitive diagram. Specifically, we required e_g_psf AND e_i_psf ≤ 0.02, e_v_psf ≤ 0.03, and E( B − V ) SFD 0.1 mag, and this resulted in a sample of 294 stars. The majority of the stars are drawn from Yong et al. ( 2013 ), Jacobson et al. ( 2015 ), Barklem et al. ( 2005 ), Roederer et al. ( 2014 ), and Cohen et al. ( 2013 ); the effective temperatures, gravities, and metallicities from the latter two sources have been adjusted to ensure consistency with the other sources. The location of the known abundance stars in the metallicity-sensitive diagram is shown in Fig. 3 . We note that the most iron-poor star known, star SMSS J031300.36−670839.3, is the dark coloured five-point star symbol at (( g − i ) 0 , m i ) = (0.62, −0.09) in the figure, while the star HE 0107−5240, which has [Fe/H] ≈ −5.4, is the dark coloured five-point star symbol at (0.59, −0.135). The subgiant star HE 1327−2326 ([Fe/H] ≈ −5.7) is located at (0.29, 0.19), and is also plotted as a dark coloured five-point star symbol in Fig. 3 . In general, the majority of the stars plotted are consistent with expectations in that they lie at notably bluer m i values at a given ( g − i ) 0 than the bulk of the population. However, this is clearly not the case for a small number of known EMP stars that fall well below their ‘expected’ location in the metallicity-sensitive diagram. As will be discussed in more detail in Section 4.1 , generally these stars are strongly enhanced in carbon. Figure 3. SkyMapper metallicity-sensitive diagram for all objects satisfying the basic selection criteria. Overplotted


Additional details of our numerical set-up are described in Appendix A . Mass-loss is a key ingredient in novae, which plays an important role in setting the time-scale of the eruption by removing mass from the white dwarf envelope (Livio et al. 1990 ; Kato Hachisu 1994 ). However, the exact mechanisms giving rise to the unbound outflows, as needed to produce variable internal shocks, are uncertain and not addressed in this work. Relatively slow outflows, of up to several hundreds of km s −1 , may be launched from near the binary L 2 Lagrange point. These could be driven for instance by frictional drag (e.g. Livio et al. 1990 ; Shankar, Livio Truran 1991 ; Lloyd, O’Brien Bode 1997 ; however, see Kato Hachisu 1991 ), non-axisymmetric gravitational torques from the binary (Pejcha, Metzger Tomida 2016a ), or in the outflow of a circumbinary disc formed from matter ejected from L 2 that initially remains gravitationally bound (Pejcha, Metzger Tomida 2016b ). These slow outflows, with velocities of order the binary escape speed, would plausibly be concentrated in the binary equatorial plane. Outflows can also occur from the white dwarf directly, with little or no influence from the binary. These could be driven by radiation pressure acting on the iron opacity bump (e.g. Kato Hachisu 1994 ), or by any large (near- or super-Eddington) localized energy deposition in the white dwarf envelope, e.g. from radioactive heating or damping of convectively excited waves (e.g. Quataert et al. 2016 ). Outflows launched from deeper locations in the potential well of the white dwarf would be expected to possess higher velocities ∼2000–5000 km s −1 and a more spherical geometry than the slower outflows from L 2 . Lacking a first principles model, we are motivated on phenomenological grounds to consider two outflow modes characterized by distinct mass-loss rates, , and asymptotic velocities, v w . Somewhat arbitrarily (as the precise values will vary between novae), we assume a ‘fast’ mode outflow with and a ‘slow’ outflow mode with These are spherically equivalent mass-loss rates. To obtain the true value, must be multiplied by the fraction of the total solid angle covered by each outflow component, f Ω . For instance, f Ω ≈ 1 for the fast spherical outflow, while f Ω ≈ 0.3 for the slow equatorially focused outflow. 1 The top panel of Fig. 2 shows the chosen time evolution of and v w for our two fiducial models (‘single transition’ and ‘multiple transition’). In the single-transition model (red lines in Fig. 2 ), the outflow velocity is increased from slow ( v w = v s ) to fast ( v w = v f ) only once at t ≈ 0, while in the multiple-transition model (blue lines in Fig. 2 ) the outflow velocity fluctuates between slow and fast modes several times. Local maxima (‘flares’) are observed in classical nova light curves on time-scales ranging from hours to weeks (e.g. Strope et al. 2010 ; Walter et al. 2012 ; Henze et al. 2018 ; Aydi et al. 2019 ). To generate


of freedom is 1. The errors on the elements of the Hessian matrix are propagated to . Since Eq. ( 9 ) is non-linear, we compute the error map on from Gaussian realizations of the errors on the coefficients of the matrix. The uncertainty in , computed within bins of values of the map, is , independent of the intensity at 353 GHz (Fig. A.1 ). Fig. A.1 Two independent estimates of the uncertainties in the determination of angles from the Hessian analysis, computed within bins of values of the map. The red squares represent the noise obtained by propagation of the errors on the coefficients of the Hessian matrix. The noise computed with the toy model (Sect. A.2 ) is plotted with black squares. Fig. A.2 Distribution functions of orientation angles for the selected ridges derived from the Hessian analysis on . They are computed within three bins of Galactic latitudes with equal numbers of data points. The mean absolute latitudes are , , and for the DFs plotted in black, orange and red, respectively. The image shows that the method does not introduce any bias as a function of Galactic latitude in estimating . Appendix A.2: Test on a toy model of the sky We have tested the Hessian algorithm on a toy model of the full sky built from a realization of a Gaussian map, , with an angular power spectrum, equal to a power law of index , computed with the procedure SYNFAST of HEALPix . The spectral index used is within the range of values found for power spectra of dust maps ( Miville-Deschênes et al. 2007 ). The mean value of is 0. We form, where , , , and are four factors chosen to fit the latitude profile, and the longitude profile at Galactic latitude , measured on the map. The values of these factors, including their sign, depend on the realization of . The toy model matches the large-scale structure of the Galactic dust emission, but it does not have its filamentary structure because it is computed from an isotropic Gaussian map. It assumes that the amplitude of the brightness fluctuations at a given scale is proportional to the brightness. This is in agreement with what has been reported for the emission at 100 m of the diffuse ISM ( Miville-Deschênes et al. 2007 ). We use the toy model to quantify the impact of the structure of the diffuse Galactic emission and data noise on the Hessian analysis. We run the Hessian analysis on the map with and without data noise computed as a Gaussian realization of the noise map on . The DFs of orientation angles, computed for the model with added noise, are flat at all Galactic latitudes, as shown in Fig. A.2 . We find no bias on the angle introduced by the large-scale gradient of the emission with Galactic latitude. We use the difference between the two angle maps computed on the map, with and without noise, to estimate the contribution of the data noise to the uncertainty in the Hessian angle (black dots in Fig. A.1 ). This uncertainty decreases for increasing values of (i.e. increasing signal-to-noise ratio).


the cascade emission is shown. The magnetic field in the comoving frame is then . Basically, a higher B leads to a more important synchrotron radiation, while a smaller B leads to a more important IC radiation. Since electrons usually emit higher-energy photons via IC radiation than via synchrotron radiation, the flux of the cascade emission at high energies becomes higher for a smaller B . On the other hand, more high-energy photons in turn produce more e ± pairs at high energies, making a harder electron spectrum than that in the case of a large B , as is shown in Figure 7 . This explains why the spectrum is also harder in the case of B = 0.01 than in the case of B = 1 at keV energies, where the emission is dominated by synchrotron radiation of these (relatively) low-energy electrons in both cases. One can see that the gamma-ray flux around 100 MeV is not very sensitive to the value of B . This is because the injection rate of the secondary electrons that emit 100 MeV photons is dominated by the γγ -annihilation process (i.e., in the right-hand side of Equation ( 3 )), mainly relies on the photon field, and does not change with the magnetic field. On the other hand, the jet is already an electron calorimeter even if only considering IC radiation under the benchmark parameters. Therefore, we expect the total photon production rate at a certain energy is roughly equal to the energy injection rate of the electrons that emit these photons (i.e., L γ ∼ L e ). A large B only changes the way the electrons radiate their energy away but does not increase the photon production rate. Although the energy of the gamma-ray-emitting electrons is different in the IC-dominated case with a small B from that in a synchrotron-dominated case with a large B , the resultant gamma-ray flux is at the the same level, since the energy injection rate of electrons in the relevant energy range is roughly constant with respect to electron energy (i.e., ). Figure 6. Same as Figure 3 , but for the equipartition coefficient for the magnetic field in the GRB jet B . The dashed and dotted lines correspond to the IC and synchrotron radiation, respectively. Figure 7. Quasi-steady-state spectrum of the cascaded electrons in the comoving frame of the GRB jet with fiducial parameters (except for the equipartition coefficient of the magnetic field). Purple, blue, and red curves are for B = 1, 0.1, and 0.01, respectively, while solid and dashed curves are the contribution by the BH and photomeson processes, respectively. 3. Application to LAT GRBs In this section, we apply our calculations to explain the high-energy spectrum of GRB 090926A, GRB 090902B, and GRB 080916C, which represent three different types of spectral feature. The origin of prompt keV/MeV emission is beyond the scope of this work, and we just regard it as a preexisting target photon field for the BH and photomeson processes. In our calculations below, we employ a flat spectrum for the injected proton spectrum ( s =


a revised model for a He shell detonation Type Ia SN. In any case, we think it is likely that the Mn/Fe, Ni/Fe, Cu/Fe, and Zn/Fe enhancements in G 112-43/44 and the three α -poor stars are caused by element contribution from a special kind of SN to pockets of gas from which these stars were formed. Such inhomogeneous mixing of SN products is more likely to affect the chemical evolution of dwarf galaxies than higher-mass systems because in lower-mass galaxies the gas has a relatively long cooling time, resulting in episodic star-formation bursts ( Revaz et al. 2009 ; Venn et al. 2012 ). In view of this, it is interesting that G 112-43/44, as a member of the Helmi streams, was probably born in a dwarf galaxy and that one of the three α -poor halo stars with enhancements of Mn/Fe, Ni/Fe, and Zn/Fe also has Helmi stream kinematics 6 , as seen from Fig. 1 . G 4-36 and BPS BS 16920-17 have kinematics similar to stars belonging to the Gaia -Enceladus population, but BPS CS 22966-43 lies in the Helmi box with positive V Z . Not all stars belonging to the Helmi streams have unusual abundances. Roederer et al. (2010) made a detailed abundance analysis of 12 subgiant and giant stars with Helmi stream kinematics, and Gull et al. (2021) recently added seven stars to this work. Within the typical errors of the abundance determinations (0.10–0.15 dex), [Mn/Fe], [Ni/Fe], [Cu/Fe], and [Zn/Fe] agree with the [X/Fe]-[Fe/H] trends of Galactic halo stars. The stars investigated, however, have [Fe/H] ≲ −1.5 and high [ α /Fe] ratios (e.g., [Mg/Fe] ∼ 0.3), so it remains to be seen if the Helmi streams contain a population of low- α stars at higher metallicities and if some of these stars have over-abundances of Mn, Ni, Cu, and Zn relative to Fe. Low- α stars are well known in dwarf galaxies (see the review by Tolstoy et al. 2009 ). In the Sculptor dSph galaxy, for example, [Mg/Fe] shows a declining metallicity trend from [Mg/Fe] ≃ 0.4 at [Fe/H] = −1.8 to [Mg/Fe] ≃ −0.2 at [Fe/H] = −1.0. Interestingly, Skúladóttir et al. (2017) find indications of a cosmic scatter in [Zn/Fe] of the Sculptor stars (i.e., from about −0.6 dex to +0.4 dex) and a positive correlation between [Ni/Fe] and [Zn/Fe]. At a distance of ∼85 kpc, the giants observed in Sculptor are, however, faint (17.0 V 18.5), and the errors of [Zn/Fe] are of the order of ±0.3 dex. It will require more precise [Ni/Fe] and [Zn/Fe] values as well as an improved precision of [Mn/Fe] values ( North et al. 2012 ) to verify if stars with enhanced Mn/Fe, Ni/Fe, and Zn/Fe ratios are present in Sculptor. Another interesting case is the ultra-faint dwarf galaxy Horologium I, in which Nagasawa et al. (2018) found three very metal-poor ([Fe/H] ∼ −2.5) giant stars that are α -poor ([Mg/Fe] and [Ca/Fe] ≃ 0.0) and enhanced in [Mn/Fe] by about 0.4 dex relative to Galactic halo stars. However, their [Ni/Fe] ratios seem to be normal, and their Cu and Zn abundances were not determined. Again, we need more precise abundances,