O O O B-Observatory I-Observatory O O O O B-Instrument O B-Instrument O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O B-Database I-Database O O O B-Organization B-Location I-Location O O O O O O O O O O B-Database I-Database I-Database O O O O O O O O O B-Person O O O O B-Organization I-Organization I-Organization I-Organization

We thank the ESO Paranal team for supporting our SPHERE and AMBER observations. We are also grateful to the referee Susanne Höfner for her valuable comments, particularly on the interpretation of the extended H emission. This research made use of the SIMBAD database, operated at the CDS, Strasbourg, France. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. K.O. acknowledges a grant from Universidad Católical del Norte.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject O O O O O O O O O O O O O B-Telescope O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O

source at its given velocity (within 15 km s −1 ), position (within 5 arcmin), and derived a velocity width and size within our cuts used in Section 2.2 . We recovered every injected source at high velocities, where Galactic emission is the weakest, and nearly every source at low velocities and Leo T velocities (97% and 82%, respectively), the latter of which is lower because Leo T’s velocity is often within the region of average Galactic emission >1 K which we purposely ignored. Nevertheless, we can confidently say that SoFiA would successfully detect Leo T at its actual distance in the vast majority of our search area. We next wanted to determine how accurate our detection limit of Leo T-like objects was, based on our observed flux distribution. To do this, we performed the same procedure as before with two alterations; we scaled the peak flux of the injected source to a larger distance (from 0.5 to 1 Mpc), and we reduced the size of the injected source to better correspond to a more distant galaxy. At high velocities, the detection fraction dropped to its lowest value of 86% at 1 Mpc, but the difference at low and Leo T velocities is much more drastic, as shown in the first three rows of Table 3 (with Mass = 1 Leo T). Note, however, that a typical local group galaxy that is 1 Mpc away has a velocity closer to our high-velocity case than either of the lower-velocity cases. In other words, the region of distance-velocity space where our detection fraction is lowest also probably contains the smallest number of dwarf galaxies. We also tried reducing the injected sources’ size, which results in a ∼10% drop in the detection fraction at lower velocities compared to the same test without changing the size, meaning the dominant reason for the overall drop is the reduction in flux caused by increasing distance. In the bottom three rows of Table 3 we inject sources with successively larger multiples of Leo T’s mass to determine how complete we are out to 1 Mpc. We note that we would detect ≈50% of galaxies at lower velocities with only 2 times Leo T’s mass, and ≈66% of those with 3 times Leo T’s mass. 6 6 At 4 times Leo T’s mass we naturally recover the same detection fractions as the first row of Table 3 , because multiplying the mass of the third row by 4 is equivalent to halving the third row’s distance in terms of H i flux. Table 3 Detection Fraction of Sources Injected at or beyond a Distance of 500 Note. The H i mass of Leo T is . The last row of 10 times Leo T’s mass is an exception to the previous rows in that the size and w 50 cuts we apply are the dominant cause for reduction in recovered sources in regions significantly contaminated by Galactic emission at low velocities. Without the size and w 50 cuts, the detection fractions are all >92%. The higher level of background noise at low latitude causes SoFiA to chop off the outer regions of the object in its size calculation. Therefore our size cut may lead us to miss some dwarf galaxies


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O B-Survey O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

background magnetic field than those observed in the synthetic observations (slight preference of perpendicular alignment; Fig. 6 ), which were generated from a trans- to super-Alfvénic simulation. Combined with other polarimetric properties, we suggest that the relative alignment between dense cores and pc-scale magnetic fields depends on the magnetic properties of the cloud, and could potentially provide an alternative approach than the traditional Zeeman observations on investigating the magnetization level of the cloud. APPENDIX A: CORES IDENTIFIED IN GAS DATA AND THEIR RELATIVE ALIGNMENTS Figs A1 – A3 show all subregions observed by GAS overlapped with the core boundaries identified by astrodendro . The relative alignment between cores and background magnetic field (i.e. the angle between core major axis and background magnetic field direction) in each subregion is plotted in Fig. A4 . Figure A1. Cores (red contours) identified in each individual region in the Ophiuchus cloud using NH 3 integrated emission (colour maps, in K km s −1 ) observed by GAS. Note that cores that are more rounded (with minor/major ratio >0.8) are removed from the analysis and not shown here. Dendrogram leaves without obvious central peak emission are also excluded. Figure A2. Same as Fig. A1 , but for the Perseus cloud. Figure A3. Same as Fig. A1 , but for the Taurus cloud. Figure A4. The cumulative distributions of the core–background magnetic field alignment for the subregions within the three clouds: Ophiuchus (left), Perseus (middle), and Taurus (right). APPENDIX B: RELATIVE ANGLES IN 2D AND 3D Here, we briefly describe the difference between measuring relative angle between two random vectors in 3D and 2D spaces. Without loss of generality, we assume both vectors are unit vectors and one is pointing straight up (+ z for 3D case and + y for 2D case). The probability for the second vector to have an angle θ with respect to the first one is therefore proportional to the surface area of the stripe of constant latitude θ on the 3D sphere (), or the arc length at θ of the unit circle ( R dθ). For unit vectors, R = 1, and since we only consider angles within [0, 90] deg, the cumulative probability of the relative angle to be smaller than θ is therefore Note that the probability is normalized by the total surface area of the sphere (in 3D) or the circumference of the whole circle (in 2D). This explains why a set of 3D random vectors will show a linear distribution in cos α instead of α, where α is the relative angle between any two vectors from the set. Equations ( B1 ) and ( B2 ) are illustrated in Fig. B1 as black dotted lines, which also shows that two vectors in 3D are more likely to be perpendicular than parallel if measured in degrees. Figure B1. Comparing the relative angles in 3D (top) and 2D (bottom), for both analytic solutions of equations ( B1 ) and ( B2 ) (black dotted lines) and between two sets of random vectors (solid lines), showing the angle in


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

We thank the anonymous referee for constructive criticism, particularly regarding estimates of the gas density from the observations. This work was supported by NASA Origins of Solar Systems grant NNX10AH37G.


O O O O O O B-Observatory I-Observatory I-Observatory O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O B-Person I-Person I-Person O O O O O O O O B-Telescope B-Person O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant B-Grant I-Grant I-Grant I-Grant B-Grant O O B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank the staff at the Nobeyama Radio Observatory and the National Radio Astronomy Observatory for help with the observations. We thank Dr. David Frayer for his help in the observations at the GBT. M.A. thanks the Grant-in-Aid for Scientific Research on Innovative Areas (Grant No. 25108002), Grant-in-Aid for Scientific Research (C) (Grant No. 15K05395), and the Institute for Quantum Chemical Exploration.


O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-CelestialObject O O O O O O O B-Instrument O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O B-CelestialObject B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O B-CelestialObject B-Wavelength I-Wavelength O O O O O O B-CelestialObject O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject B-Wavelength O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O B-CelestialObject O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O

H i Ly α (lower left), low-TZ Si iii 1206 Å (upper left), low-TZ C iii 1175 Å (lower right), and coronal soft X-rays (upper right). These flux–flux diagrams are more populated given the better FUV coverage of the two stars, although the C iii comparison for B is still missing points for epochs when E140H exposures were taken: these cut off just below Si iii 1206 Å, so C iii 1175 Å was excluded. As tentatively seen in the Mg ii panels previously, the A correlations line up nicely with the solar equivalents, although A’s X-rays still are shifted downward, and noisier than the others perhaps partly because of non-simultaneous coverage. Again, there is somewhat disjoint behavior in several of the panels between the A and B relations. Notice also that A’s Ly α slope closely matches that of the solar correlation, but B’s trend is somewhat shallower. Similarly, the Si iii correlation against C ii is noticeably shallower for B, and curiously shifted downward, compared to A or the Sun. At the same time, the C iii behavior of B appears to be steeper. Finally, A’s X-rays (though scattered) seem to show a steeper rise with increasing C ii , as in the lower branch of the Sun’s bent power law, whereas B displays a flatter relation (although still with α ∼ 2). Figure 16 (c) displays correlations between low-TZ Si iii 1206 Å and low-TZ C iii 1175 Å (lower left), mid-TZ Si iv 1400 Å (upper left), mid-TZ C iv 1550 Å (lower right), and mid-TZ N v 1240 Å (upper right). Again, the C iii comparison is lacking a few points for α Cen B, most conspicuously on the low-flux side. Despite that, all four panels have the same general appearance: the A points closely track the translated solar power laws, while B shows universally steeper slopes. Curiously, the B trends have “retreated” backward to the extent that the A and B origins of the four correlations are similar (again taking into account the abbreviated C iii series for B). This is a consequence of the behavior seen in the upper left panel of Figure 16 (b), wherein B’s Si iii points are seen to parallel those of A, but also approach a similar minimum. This behavior is unlike the other diagnostics shown earlier, for which the minimum B value generally was comparable to, or exceeded, that of A’s maximum. The contrary behavior emphasizes the unique position of Si iii 1206 Å in both the Sun and α Cen A, as a “super-active” species, showing the steepest power laws relative to the other FUV features, even including hot N v . In α Cen B, in contrast, the Si iii feature has declined in strength, and shows the expected “stellar” behavior, namely Si iv , C iv , and especially N v all exhibit power laws comparable or steeper than unity against Si iii . The final figure, Figure 16 (d), illustrates a number of miscellaneous, but nonetheless illuminating, comparisons. The lower left panel compares the two Mg ii resonance lines, which are both affected by ISM absorptions, but the k-line more so than the weaker


O O B-Person I-Person O O O O O B-Person I-Person O O O O O B-Observatory I-Observatory O O O O O B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant I-Grant O B-Grant I-Grant I-Grant O O O O O O B-Database I-Database I-Database O O B-Organization B-Location I-Location O O B-Database I-Database I-Database O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O B-Database I-Database I-Database I-Database I-Database I-Database I-Database O O B-URL O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Survey I-Survey I-Survey O O B-URL O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O B-Grant I-Grant O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O B-Location I-Location O O B-Telescope I-Telescope I-Telescope O O B-Telescope I-Telescope I-Telescope


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GMO acknowledges support of the Research Foundation – Flanders under contract G075916N and under grant number V434818N. HvW acknowledges support from the Research Council of the KU Leuven under grant number C14/17/082. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. We thank the anonymous referee for the useful comments that improved the manuscript.


O O O O B-Person I-Person O O O O O O B-Person I-Person O O O O O B-Telescope O B-Person I-Person O O O O O B-Organization O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event O O B-Person I-Person O B-Person I-Person B-Observatory O O O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O B-Person O O O B-Organization O O B-Grant B-Grant O B-Grant O O B-Organization I-Organization O O B-Grant B-Person O O O O O B-Grant I-Grant O O B-Organization I-Organization B-Person O O O B-Organization O O B-Grant O B-Grant O B-Organization O O B-Organization

We thank the referee Durgesh Tripathi for useful suggestions. We also thank Linhua Deng for providing us with the NVST data, Rui Liu for helpful discussions, and the ISSI workshop on “Decoding the Pre-Eruptive Magnetic Configuration of Coronal Mass Ejections” led by S. Patsourakos and A. Vourlidas. SDO is a mission of NASAs Living With a Star Program. X.C. and M.D.D. are supported by NSFC under grants 11722325, 11733003, and 11790303 and by Jiangsu NSF under grant BK20170011. X.C. is also supported by the “Dengfeng B” program of Nanjing University. B.K. acknowledges support by NASA under Grants NNX16AH87G and 80NSSC17K0016, the NSFC, and the DFG.


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

The authors acknowledge Chuck Horowitz, Evan O’Connor, and Todd Thompson for productive conversations, concerning insight into and help with the microphysics, and Ernazar Abdikamalov, Sean M. Couch, Luke F. Roberts, and Christian D. Ott for fruitful discussions on the nature of core-collapse supernovae. Support was provided by the Max-Planck/Princeton Center (MPPC) for Plasma Physics (NSF PHY-1523261). D.R. gratefully acknowledges support from the Schmidt Fellowship. A.B. acknowledges support from the NSF under award number AST-1714267. J.D. acknowledges support from a Laboratory Directed Research and Development Early Career Research award at LANL. The authors employed computational resources provided by the TIGRESS high performance computer center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology and by the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the US Department of Energy (DOE) under contract DE-AC03-76SF00098. The authors express their gratitude to Ted Barnes of the DOE Office of Nuclear Physics for facilitating their use of NERSC. This paper has been assigned a LANL preprint # LA-UR-17-20973.


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

Acknowledgements We thank the referee for many useful comments and suggestions that helped to improve the paper. We would like to thank all those who are, or have been, associated with BiSON. BiSON is funded by the Science and Technology Facilities Council (STFC). MNL acknowledges the support of The Danish Council for Independent Research | Natural Science (Grant DFF-4181-00415). WJC, SJH, GRD, YPE and RH acknowledge the support of the UK Science and Technology Facilities Council (STFC). Funding for the Stellar Astrophysics Centre (SAC) is provided by The Danish National Research Foundation (Grant DNRF106).


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

of ε Cet are mostly not able to be individually separated, and the use of assumptions are required to untangle them (Docobo Andrade 2013 ). The angular separation of the components was 0.1 arcsec in 2015 (Mason et al. 2001 ). We obtained sixteen polarized spectra for ε Cet over a 6.0 h interval on 2016 September 21, corresponding to 2.5 per cent of the estimated rotational period of 10.2 d. The mean LSD profile (Fig. B4 ) combined 6693 lines, and a magnetic detection was obtained from the mean LSD Stokes V profile. We are unable to determine whether the magnetic detection was on the F5V or F6V components because the two stars could not be separated spectroscopically. We estimated B l at +0.6 ± 0.1 G. Our radial velocity determination +15.81 ± 0.26 km s −1 (Table 5 ) is similar to the value of +15.49 ± 0.19 km s −1 in Anderson Francis ( 2012 ), and our S-index 0.186 ± 0.003 (Table 5 ) was less than 0.219 in Pace ( 2013 ). A4 α Com α Com (HIP 64241) is a triple star consisting of a double-lined spectroscopic binary (Duquennoy, Mayor Halbwachs 1991 ) of F5V and F6V components (Edwards 1976 ; Soubiran et al. 2018 ), and a V magnitude 10.2 component with an angular separation of 85 arcsec in 2014 based on data from the continuously updated Washington Double Star Catalogue (WDS) (Mason et al. 2001 ). The system was first observed by Struve ( 1875 ) who reported that occultations were observed (Muterspaugh et al. 2015 ). Roman ( 1950 ) describes α Com as a close visual binary, with equal F5 components, and showing weak lines. Hartkopf et al. ( 1989 ) describes α Com as a ‘lovely edge-on system’ with an orbital inclination close to 90 deg, and suggested a partial eclipse was possibly missed in early 1990. The eclipsing binary has the third longest period known ( P = 25.85 yr) (Lipunov et al. 2016 ), with only eight eclipsing stars having periods longer than 10 yr. We obtained twenty-seven polarized spectra for α Com over a 3.8 h interval on 2017 February 16, corresponding to 5.3 per cent of the estimated rotational period of 3.0 d. The mean LSD profile (Fig. B5 ) combined 7628 lines, and a magnetic detection is visible in the Stokes V profile. We are unable to determine whether the magnetic detection was on the F5V or F6V components because the two stars could not be separated spectroscopically. We estimated B l at +3.1 ± 0.3 G. Our radial velocity determination −18.02 ± 0.27 km s −1 (Table 5 ) is larger the value of −16.05 ± 0.21 km s −1 in Anderson Francis ( 2012 ), and our S-index 0.272 ± 0.008 (Table 5 ) is smaller than the 0.308 in Pace ( 2013 ). A5 ω Dra ω Dra (HIP 86201) is a triple star system consisting of double-lined spectroscopic binary (Abt Levy 1976 ; Konacki et al. 2010 ), and a V magnitude 13.2 common proper motion companion with an angular separation of 70 arcsec (Abt Levy 1976 ; Fekel, Tomkin Williamson 2009 ). The mases of the primary component are 1.46 M ⊙ and secondary 1.18 M ⊙ (Konacki et al. 2010 ), which corresponds to


O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O O O O O B-Software I-Software I-Software I-Software B-Citation I-Citation O B-Person I-Person I-Person B-Software I-Software O O O O O O O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Person I-Person I-Person O B-Person I-Person I-Person O O O O O O O O O O O O O O O B-Event I-Event I-Event O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event O B-Person O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization B-Organization O B-Organization O O O O O O O O O O O O O

ACKNOWLEDGEMENTS We have used NASA’s ADS Bibliographic Services. Most of the computations that made possible this work were performed with NASA NAIF SPICE Software (Acton 1996 and Jon D. Giorgini), Python 2.7 , and their related tools and libraries, iPython (Pérez Granger 2007 ), Matplotlib (Hunter et al. 2007 ), scipy , and numpy (Van Der Walt, Colbert Varoquaux 2011 ). Special thanks to the reviewers that through their criticism significantly contributed to improve the paper. In particular, we thank Steve Chesley for his in-depth initial review of this work; his comments and observations contributed to improve significantly the quality of the manuscript with respect to its initial versions. We appreciate the assistance of Jon D. Giorgini, senior analyst of the JPL Solar system Dynamics Group. We also thank Professor Ignacio Ferrin and Professor David Asher for useful comments and insightful discussions about this topic. We also thank the organizers of Meteoroid 2016 conference for allowing us to present the initial versions of this work to the meteor and asteroid scientific community. This work is supported by Vicerrectoria de Docencia-UdeA and the Estrategia de Sostenibilidad 2014-2015 de la Universidad de Antioquia . MS is supported by Colciencias, Doctorado Nacional - 647 programme. We thank Universidad Pontificia Bolivariana (UPB-Medellin) and DELL for allowing us to run most of our simulations in their data centres.


O O O O O O O O O B-Observatory I-Observatory O O B-Survey I-Survey I-Survey I-Survey O O B-Observatory O B-Person I-Person O O O O O O O O O B-Database O O O O O B-Organization B-Location I-Location O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Grant B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O O B-Grant

Acknowledgments We gratefully acknowledge the fine support at the MMT Observatory, and the Local Group Galaxy Survey conducted at NOAO by Phil Massey and collaborators. This research has made use of the VizieR catalogue access tool, operated at CDS, Strasbourg, France. This study has been supported in part by the Polish National Science Centre grant DEC-2013/10/M/ST9/00086. KI has been also financed by the Polish Ministry of Science and Higher Education Diamond Grant Programme via grant 0136/DIA/2014/43.


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I thank Miles for significantly delaying this publication (by being born and so completely disrupting my life). I would not have it any other way. I thank the anonymous referee for constructive comments that helped to improve and clarify this manuscript. This research was supported by NASA Astrophysics Theory Program grant NNX17AG25G and made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.


O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location I-Location I-Location O O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant O O O O O O O B-Organization B-Location O O B-Grant I-Grant O O O O B-Person I-Person O O O O O O O O O O O O O B-Person O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Fellowship B-Fellowship I-Fellowship O O O O O B-Person I-Person I-Person O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O O O O O O B-Database O O O O O B-Person I-Person O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Person I-Person I-Person B-Person I-Person O B-Person I-Person

This work is based on observations with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias on the island of La Palma. This work has been funded by the Spanish Ministry of Economy and Competitiveness (MINECO) under the grant AYA2011-22614 and also received partial support from the DGAPA-UNAM, Mexico under grant PAPIIT IN109614. We thank the referee, G. Stasińska, for her valuable comments that helped to improve the quality of the paper. JGR acknowledges support from the Severo Ochoa excellence programme (SEV-2011-0187) postdoctoral fellowship. We are very grateful to Dr. P. Ventura for providing the tables with the surface abundances of his AGB models, and to Dr. C. Morisset for his invaluable help and comments related to the 3Mdb. We also are grateful to A. Karakas from providing the detailed numbers of the models by Fishlock et al. (2014) . We acknowledge fruitful discussions with D. A. García-Hernández, A. Karakas, and M. Lugaro.


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

in green, candidate members in light grey, members in red, and members with measured radial velocity in black. Figure 4. Differences between structural parameters obtained from Sérsic fits and isophotal ones. (a) Difference between r e calculated by Calderón et al. ( 2015 ) fitting a Sérsic model and the ‘isophotal’ ∼27 mag arcsec −2 ones, versus absolute and apparent T 1 magnitudes (top and bottom axes), respectively. (b) Same as plot (a) but for the difference in effective surface brightness. It is important to remark that for the two brightest galaxies ( mag), the effective radius results underestimated when using a single component profile (for NGC 3268 the difference is even larger than 1 kpc). A similar (although milder) tendency is present for S0s and cEs. It can be seen that, as expected, the confirmed dEs show mostly positive differences, while the new galaxies (mainly candidates) are the ones showing more negative differences. This effect is less noticeable if we consider a similar difference but for the effective surface brightness (Fig. 4b ). In this case, the confirmed dEs are evenly distributed about zero. 6.2 Geometrical parameters at different galactocentric radii In this section, we analyse the geometrical parameters obtained from the ellipse output for the whole sample, considering the four radial ranges (regions 1 to 4) defined in Section 4 . Fig. 5 shows the distribution of the intensity-weighted average ellipticity 〈ε〉 for the four regions, with a cross-hatched (red) histogram for faint galaxies (dEs and dSph) and an open one for the whole sample. We note that the morphological classification was done by visual inspection of each galaxy, following the criteria used in FS90. That is why we do not establish a magnitude limit (usually set around M B = −18 mag); an overlap in luminosity between bright and dwarf ellipticals can thus be seen. Figure 5. Histograms of the mean weighted ellipticity distributions, cross-hatched in red for dE and dSph and open for the whole sample. Number of galaxies in each region is indicated in parentheses. The histograms of mean ellipticity show flatter (although slightly less extended) distributions, as compared to those obtained by Chaware et al. ( 2014 ) and Hao et al. ( 2006 ), where a main peak at 〈ε〉 ∼0.1 → 0.16 is evident in regions 1 to 4, implying a dominant fraction of nearly round galaxies. Besides a similar low 〈ε〉 peak, a second peak at 〈ε〉 ≈0.3 is also evident in region 1 of our sample. This reflects the fact that most of the brighter galaxies in Antlia are lenticulars (S0), while dwarfs also tend to exhibit relatively large flattenings, despite most of them being classified as dE (dS0s are found only among the brighter dwarfs.). Figs 6 and 7 show the distributions of the weighted mean values of the Fourier coefficients 〈 a 3 / a 〉 and 〈 a 4 / a 〉. As usual, they are reasonably fitted with a single Gaussian centred at zero, except in the outermost region, where the


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


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We are grateful to Javier Manzano-Santamaría for his support on the experiments. Special thanks go to Marcelino Agúndez for useful discussions. This research was financed by the Spanish MINECO under projects AYA2011-29375 and AYA2014-60585-P. R.M.D. benefited from a FPI grant from Spanish MINECO.


O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database I-Database I-Database I-Database I-Database I-Database I-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O B-Database I-Database I-Database O O B-Organization I-Organization I-Organization

We are grateful to F. Paresce for carefully reading the paper and useful comments, which improved the final version. We thank the referee for constructive comments and suggestions on the manuscript. This research made use of the NASA/IPAC Infrared Science Archive and Extragalactic Database, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Part of this work is based on archival data, software or online services provided by the Scientific Data Center of the Italian Space Agency.


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This work is part of the VIALACTEA Project, a Collaborative Project under Framework Programme 7 of the European Union, funded under Contract # 607380 that is hereby acknowledged.


O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O

in November 2014 (red; Snodgrass et al. 2016 ). 3.2 Dust coma morphology and activity For each cube in our dataset, we extracted maps over the bandpasses of the V , R , and I Johnson-Cousins filters. All maps in the same bandpass were re-centred and then co-added. The resulting co-added maps are displayed in the top part of Fig. 2 . The dust coma morphology is the same for all three bandpasses. It is asymmetrical, likely due to the presence of dust jets. To investigate the presence of jets further, we divided the dust maps by an azimuthal median profile ( Samarasinha et al. 2013 ). Enhanced maps are displayed on the bottom part of Fig. 2 . Here, we can clearly see two jets, which are most likely the cause of the apparent asymmetry of the dust coma. The first jet is located close to the anti-sunward direction, towards the south-west. The second jet is located about 90° away, towards the south-east. Finally, we see a faint feature towards the sunward direction. Those jets are consistent with what was observed on previous passages and what is reported by Knight et al. (2017) and Snodgrass et al. (2017a ) from observations at the same epoch. They are also consistent with the modelling of the pole orientation and active region location done by Vincent et al. (2013) prior to the Rosetta mission. In addition to the two jets mentioned above, we see an enhancement towards the North-West. This corresponds to the dust trail that was reported to be at least two degrees long at that epoch ( Snodgrass et al. 2017a ; Boehnhardt et al. 2016 ; Knight et al. 2017 ). We do not see changes of the coma morphology over the five nights of our observations, nor over a single night. To constrain the comet activity at that time, we compute the Af ρ value, which is a proxy for dust production, as defined by A’Hearn et al. (1984) . We compute the Af ρ for the V , R , and I bands over a 2500 km physical aperture. We use a 2500 km aperture instead of the more commonly used 10 000 km aperture because the comet signal drops significantly at 10 000 km. We obtain values of 65 ± 4 cm, 75 ± 4 cm, and 82 ± 4 cm in the V , R , and I bands, respectively. Those values have not been corrected for the phase angle effect and are consistent with those reported by Boehnhardt et al. (2016) at the same epoch, and they are comparable (even though slightly lower) to those reported by Knight et al. (2017) once the phase angle effect is taken into account. Using the Af ρ values in the different bands, we can also compute the dust reflectivity gradient defined as ( Jewitt Meech 1986 ): where Af ρ x and the corresponding wavelength λ x are expressed in cm and nm, respectively. For the I – V combination, this gives a reflectivity gradient of 7 ± 1%∕100 nm, while it is of 11 ± 2%∕100 nm for the R – V and 7 ± 1%∕100 nm for the I – R combination. This confirms the trend outlined in Sect. 3.1 of higher reflectivity gradient at lower wavelengths. To check for trends with the aperture size, we


B-Person B-Person O B-Person O O O O B-Organization B-Grant I-Grant I-Grant B-Person O O O O O B-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Fellowship B-Fellowship O O O O O O O B-Mission I-Mission O O O B-Mission I-Mission O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive B-Archive B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O B-Archive O O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization B-Mission I-Mission O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Telescope O B-Telescope O B-Telescope O B-Telescope O


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of the field at the cusp with respect to the current sheet axis is zero. The analysis of such irregular cusp structures in the literature were performed either analytically (e.g., Vekstein Priest 1992 , 1993 ; Uzdensky Kulsrud 1997 ; Wiegelmann et al. 1998 , 2000 ) or based on numerical simulations (e.g., Karlický Bárta 2007 ). In all of these investigations, the inner structure of the current distribution was neglected. Figure 1. Sketch of a helmet streamer with cusp point and singular current sheet and zoom to the inner cusp point region within the current sheet. The tiny red box inside the zoom defines the domain of our analysis. In this work, we investigate the internal structure of the current sheet at magnetic cusps. We concentrate on regular, mathematical cusp structures with a finite scale of the current distribution, in contrast to the singular current sheets mentioned before. This means that we are considering regular magnetic flux functions in the very close vicinity of the singular magnetic point, here the cusp point, to characterize the topological connections of the involved physical fields and to allow for transverse components of the magnetic field inside the current sheet (right part of Figure 1 ). 2. Objectives and Methodology The investigation of topological properties not only of the magnetic field , but also of the plasma flow and the non-idealness , requires the violation of ideal Ohm’s law, . The reason is that in 2D, the electric field is , where E z = const in the case of stationary translational invariant MHD. If the electric field component in z -direction does not vanish, i.e., , no regular solutions exist for the velocity field at a magnetic null point, meaning that the velocity field diverges. Therefore, one typically has to use nonideal Ohm’s law,to describe flows around a magnetic null point. In the case of resistive MHD, the nonideal term (or total electric field) is given by where η is the resistivity and is the electric current in the 2D case. In the following, we restrict the analysis to stationary flows. More specifically, we concentrate on the investigation of nonideal Ohm’s law, as it reflects magnetic topology and magnetic flux conservation and their violation. Furthermore, we focus on cusp configurations that are structurally unstable but topologically classifiable magnetic singularities. For structurally stable magnetic null points, an indispensable criterion for magnetic reconnection is that the plasma flow can cross magnetic separatrices, where the plasma flow is usually connected to an X-type stagnation-point flow. Cusp structures are thought to result from reconnection processes. However, as in the strict mathematical sense, no magnetic separatrices exist at or near cusps, the question arises how the plasma streams in the vicinity of such structures. To describe such flows, it is necessary to find solutions of the nonideal Ohm’s law, meaning that the plasma flow and the non-idealness are


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We warmly thank the Swift PI Neil Gehrels and his team for approving our observations and scheduling them. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. We also thank François Teyssier for altering us to the many amateur spectroscopic observations which have been made and we acknowledge and thank François Teyssier, Umberto Sollecchia, Joan Guarro Flo, Jacques Montier, Peter Somogyi, Keith Graham and V Bouttard for use of their spectra. Armagh Observatory is supported by the Northern Ireland Government through the Dept of Culture, Arts and Leisure. GJML and NEN acknowledge support from Argentina grant ANPCYT-PICT 0478/14. GJML and NEN are members of the ‘Carrera del Investigador Cientifico (CIC)’ of CONICET. We thank the referee for a helpful and constructive report.


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We wish to thank The Astrophysical Journal editor Allen Shafter for his promptness in handling the manuscript, and in particular the referee, Ivan Hubeny, for his short, constructive, and encouraging comments and promptness in delivering a report that helped expedite the article. This work was supported by the National Aeronautics and Space Administration (NASA) under grant numbers NNX17AF36G, NNX13AF11G, and NNX13AF12G issued through the Office of Astrophysics Data Analysis Program (ADAP) and grant number NNX13AJ70G issued through the Astrophysics Division Office ( Swift Cycle 8 Guest Investigator Program), all at Villanova University. We have used some of the online data from the AAVSO, and are thankful to the AAVSO and its members worldwide for making this data public and their constant monitoring of cataclysmic variables.


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

of the cores, and as such, our results are limited by our model. We note that spdust does not incorporate some important effects, such as internal thermal fluctuations, impulsive excitation due to high-impact ion collisions, and irregular dust grain shapes, all of which produce an increase in the emissivity of the spinning dust emission. Nevertheless, spdust is the only publicly available spinning dust model, and it has been shown to accurately fit observations of spinning dust emission (e.g. Tibbs et al. 2012 ; Planck Collaboration XV 2014 ; Génova-Santos et al. 2015 ). In addition to the limitations of spdust , we are also dependent on the parametrization of our adopted size distribution. For example, we assume that the size distribution varies only with b C , and that the other parameters, such as a 0, i and σ are fixed. Although Weingartner Draine ( 2001 ) were able to fit extinction curves for a range of R V values with these parameters fixed to the values used in this analysis, it is possible that these parameters will vary. For instance, if grain growth is occurring, then this will likely lead to an increase in a 0, i , which would have an impact on the amplitude of the spinning dust emission. However, in this analysis we follow the example of Weingartner Draine ( 2001 ) in assuming that these parameters are fixed, which enables us to compare our constrained value of b C with the value obtained by Li Draine ( 2001 ) for the diffuse ISM. Additionally, varying the electric dipole moment of the grains will also affect the result. Increasing or decreasing this parameter will result in a corresponding increase or decrease in the spinning dust emission. However, as discussed in Section 3.2 , our adopted dipole moment is rather conservative, and any such increase in this value would result in an increase in the predicted spinning dust curves, which would produce a corresponding decrease in the constrained b C values, therefore not affecting the results of the analysis. Throughout this analysis, we assume that all of the cm emission ( S 1 cm observed ) is due to spinning dust emission. However, as mentioned in Section 3 , it is possible that there may be a contribution from magnetic dipole emission. If this is the case, then this will decrease the contribution of spinning dust emission to the total cm emission, thereby further enhancing the observed deficit of very small grains. Therefore, ignoring magnetic dipole emission throughout this analysis is a conservative approach, and does not impact our results. Finally, we stress that this analysis is the first attempt to use spinning dust emission to characterize the properties of interstellar dust grains, and even with these limitations, this work demonstrates the possibilities of this new method, and as such we hope that it will be included in future studies of interstellar dust. 5 CONCLUSIONS By combining 1 cm CARMA measurements, with far-IR Herschel observations, we have constrained the


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Acknowledgments This work has been carried out with the financial support of Basic Research Program of the Presidium of the Russian Academy of Sciences Transitional and Explosive Processes in Astrophysics (P-41) and Russian Foundation for Basic Research (grant 16-02-00954). The author thanks the referee for the very useful comments and corrections and L. B. Potapova for the help with the preparation of the manuscript.


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

28, 40, 56, 79, 111, 155, and where is the rms noise in Stokes I . Green line segments: magnetic field orientation (perpendicular to polarization orientation). Grayscale background: polarization fraction (%) shown with a power law (). The orange double-headed arrow shows the outflow orientation. The small, black, double-headed arrow in the bottom-right of each synthetic observation (right-hand panels) indicates the average (unweighted) magnetic field orientation. In the top row of Figure 2 , which shows the face-on view of the magnetic field, there is no clear overall magnetic field orientation. In contrast, edge-on views from the y - and x -directions (middle and bottom rows of Figure 2 , respectively) show that the magnetic field morphology is vertical when viewed from both of these orthogonal edge-on views. We have produced additional edge-on synthetic observations using intermediate values of θ (not pictured here). Due to the initial azimuthal symmetry of the simulation and the fact that the initial magnetic field is in the z -direction, we find that all edge-on views look very similar. There are also hints of the characteristic “hourglass” morphology in the edge-on views. This is similar to observations of hourglass-shaped fields in sources such as NGC 1333-IRAS 4A (Girart et al. 2006 ) and L1157 (Stephens et al. 2013 ; Hull et al. 2014 ), where gravitational collapse of a strongly magnetized protostellar core is expected to pinch magnetic field lines. 3.1. Polarization Fraction To explore projection effects, we render projected energy density maps and synthetic polarization maps at viewing angles and , where corresponds to the face-on view and corresponds to the edge-on view from the y -direction. Figure 3 shows the orthogonal viewing angles along and z . Figure 4 shows the views from , , and (top to bottom). We present the synthetic dust polarization maps in the left panel with their corresponding energy density projections on the right. Figure 3. From top to bottom: the x – y plane (face-on), x – z plane, and y – z plane (both edge-on) viewed from z , y , and x directions respectively. Left: synthetic dust polarization maps of S2.5 at , plotted in the same manner as the right-hand panels in Figure 2 . The outflow direction was not discernible in the face-on view. Right: the corresponding energy density, where high energy densities in pink indicate the location of the outflow. Figure 4. Same as Figure 3 , but for intermediate viewing angles , and , where where corresponds to the face-on view from the z -direction, and corresponds to the edge-on view from the y -direction. We calculate the average value of polarization fraction for each dust polarization map by averaging the magnitude of the polarized intensity. The average polarization fraction, , is sensitive to the weighting scheme used to derive it. Also, the locations of the peak intensities of the total and polarized emission are not the same for every source (this is the case for


O O O O O O O O O B-Collaboration I-Collaboration O O O O O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O B-CelestialRegion I-CelestialRegion B-Person O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O B-Person O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant O O O O O B-Software O O O B-Software O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Survey I-Survey O O O O O B-Location B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O B-Location O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization O O B-Survey I-Survey I-Survey O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Software I-Software I-Software I-Software O O O O B-Organization I-Organization I-Organization O O O B-Grant O B-Survey O O B-Location O O O O O B-Organization O O B-Grant B-Grant B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O B-Organization O O B-Grant B-Grant O B-Grant

This paper has gone through internal review by the DES collaboration. We thank the anonymous referee for comments and suggestions that improved the paper. We also thank Helmut Jerjen and Marcel Pawlowski for providing the original VPOS coordinates. T.S.L. thanks Jonathan Hargis, Steven Boada, Daniel Nagasawa, and Katelyn Stringer for very helpful conversations. E.Ba. acknowledges financial support from the European Research Council (ERC-StG-335936, CLUSTERS). This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013 ). 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 University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ESP2013-48274, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234. Research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013), including ERC grant agreements 240672, 291329, and 306478.


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This work has been supported by the project LG 14013 of the Ministry of Education, Youth and Sports of the Czech republic, the grant project 15-06012S of the Czech Science Foundation, and the institutional research project RVO:67985815. M.S. thanks the support provided by the National Aeronautics and Space Administration through Chandra Award Number GO6-17111X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. We thank Hector Bravo-Alfaro for re-reducing existing VLA data. Based in part on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We further acknowledge the usage of the HyperLeda database ( http://leda.univ-lyon1.fr ). Facility: IRAM 30 m .


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

Time-averaged LW escape fractions in the near-field, averaged over the first two Myr. All values are given in per cent. The structure of the rows is given as in Table 3 . Most LW escape fractions averaged over 2Myr are high; for SFEs with a flat IMF in Halo B, this behaviour is most pronounced. The four outbreaking I-front cases show slightly reduced LW escape fractions, but only down to 97percent. This change occurs because the initial few time-steps, until an outbreak with escape fractions smaller than 100percent, now carry a slightly larger weight. For the slowly moving I-fronts, the LW escape fraction decreases (with the exception of a 0.1 SFE flat IMF in Halo A). Here, the LW escape fraction slowly increases over time as the I-front moves through the halo. These last results need to be taken as lower limits as we have to run the slowing moving I-front simulations with higher resolution, but can do so only after 1Myr (0.18Myr for the Salpeter IMF) due to the high computational costs of the required refinement technique. LW escape fractions of returning I-fronts decrease or increase depending on when the I-front first breaks out (in the case of a quiet late Kroupa IMF) and starts to return. We therefore cannot give a general trend. 4.3 LW flux-averaged escape fractions in the near-field The LW flux of the SED is decreasing over time (compare Fig. 3 ) by factors of up to 410 4 in the case of the flat IMF. We therefore provide the LW escape fraction weighted by the LW flux emitted by the stellar source rather than averaged over time. We list these values in Table 5 and show them in Fig. 10 . Except for an SFE of 0.1percent, the escape fraction is always larger than 75percent. The difference to the time-averaged LW escape fraction from Section 3.2 is most significant for the flat IMF, as in that case, the LW escape fraction drops when the LW flux drops and the overall contribution is small. Additional shielding by atomic hydrogen does not decrease the LW escape fraction in this limit by more than 0.5percent. Therefore, we only provide the escape fraction obtained by considering both H 2 and H shielding together. Figure 10. Flux-averaged LW escape fractions in the near-field for our parameter space. Different SEDs are shown by different symbols, Halo A is colour-coded in light blue, and Halo B is colour-coded in black. Table 5. LW flux-averaged LW escape fractions in the near-field, averaged over the total LW flux of the simulation. All values are given in per cent. The upper three rows refer to Halo A, and the lower three rows refer to Halo B. Shielding by H 2 only and by the combination of H and H 2 yields the same results. 4.4 Time-averaged escape fractions in the far-field In the far-field, the LW escape fractions are generally larger than in the near-field, varying from 59percent to 100percent. Our values are listed in Table 6 . Including shielding by neutral hydrogen can reduce the LW escape fraction by up to 29percent (comparing


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S.X. acknowledges the support for Program number HST-HF2-51400.001-A provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. S.X. also thanks Chris McKee for useful conversations. S.J. acknowledges the support from the Sherman Fairchild Fellowship at Caltech. A.L. acknowledges the support from grant NSF DMS 1622353. Simulations were performed on Blue Waters supercomputer at NCSA, under the allocation PRAC NSF.1713353 supported by NSF. We have made use of NASA’s Astrophysics Data System and the yt astrophysics analysis software suite (Turk et al. 2010 ).


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S. Choudhuri would like to acknowledge the University Grants Commission, India for providing financial support through a Senior Research Fellowship. S. Chatterjee is supported by a University Grants Commission Research Fellowship. SSA would like to acknowledge CTS, IIT Kharagpur for the use of its facilities and to thank the authorities of the IUCAA, Pune, India for providing the Visiting Associateship programme.


B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-Telescope O O B-CelestialObject I-CelestialObject O B-Telescope O B-Identifier O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Telescope O B-Identifier O O O O O O O O O O O O O O O O B-Survey O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O B-Telescope O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey O B-Telescope O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory O B-Location I-Location O O O O O O O O O O B-Instrument O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Survey I-Survey I-Survey I-Survey O O O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Survey I-Survey I-Survey I-Survey O

δ Tau, 2RXS J042836.6+191036 with ε Tau and 2RXS J042834.7+155721 with θ 1 Tau, respectively, which were observed with count rates of 0.44 ± 0.04, 0.03 ± 0.01, 0.02 ± 0.01, and 0.81 ± 0.04 cts s −1 , respectively. Hence, the dichotomy between γ Tau and θ 1 Tau (HD 27371 and HD 28307) on the one hand, and δ Tau and ε Tau (HD 27697 and HD 28305) on the other hand is immediately apparent in the observed RASS rates, with clear detections for the former (active) pair, and almost marginal detections for the latter pair of Hyades K giants. However, later pointed ROSAT observations of δ Tau (in ROSAT sequence RP200442) with a count rate of 0.0250 ± 0.0012 cts s −1 and of ε Tau (in ROSAT sequence RP200576) with a count rate of 0.0101 ± 0.0007 cts s −1 provided clear confirmations of all RASS detections. Using these count rates we can compute X-ray fluxes, X-ray luminosities, and X-ray surface fluxes, using the count-flux-conversion by Schmitt, Fleming Giampapa ( 1995 ), and thus arrive at the numbers quoted in Table 1 . It is important to keep in mind that detailed spectral information is not available from the ROSAT data, the flux conversion is therefore fraught with considerable uncertainty, which we estimate to be on the order of 50 per cent. And we need to keep in mind that, while active stars are variable, these X-ray detections are based on only a small number of visits. Nevertheless, a bifurcation is clearly seen into two active and two inactive K giants, very much like (as shown below) is the result of chromospheric activity monitoring, even though X-ray data do not yield any significant ranking order within each of these two pairs. 3.2 Chromospheric activity 3.2.1 Ca <sc>ii</sc> HK emission: the S-index For this paper, we use the results of spectral monitoring with our TIGRE facility (Schmitt et al. 2014 ), as well as the S -index time series obtained in the framework of the Mount Wilson HK project. The TIGRE facility is a fully robotic telescope with a 1.2 m aperture, located at the La Luz Observatory near Guanajuato, Mexico. Its only instrument is the two channel fiber-fed Échelle spectrograph HEROS with the wavelength range from 3800 to 8800 Å with a 100 Å gap at 5800 Å and a spectral resolution of, according to our recent performance measurements, R ≈ 21 000; a detailed description of TIGRE is given by Schmitt et al. ( 2014 ). In addition, we use data obtained by the Mount Wilson HK Project, which have been made available to the public and can be downloaded from ftp://solis.nso.edu/MountWilson_HK/ ; a detailed description of the data is also provided at this web site. The available data specifically include the star identification; the calibrated S index, which we use in this paper as the basis for our analysis; a code indicating with which instrument the data was taken; as well as the date of the observation and other material. It is important to keep in mind that the hardware used by the TIGRE and Mount Wilson HK Projects is


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

a sum over all mass within λ C of the test point. We take for galaxies with NSA information and for those without, where V max is the maximum rotational velocity estimated by correcting the full-width half-max of the radio detection for turbulence and projection effects (Tully Fouque 1985 ). These contributions to the total potential derive primarily from the test galaxy’s dark matter. Note that in the case of cluster galaxies, the potential of the cluster itself is part of the external contribution. We calculate by summing the contributions of all unscreened mass within λ C . We then calculate the equilibrium H i -OC offset predicted for a given galaxy: if it is unscreened and 0 otherwise, where M ( r * ) is the dark matter plus gas mass between the H i and optical centroids. This follows from the requirement that the extra force on the stellar disc due to its offset from the halo centre compensate for its not feeling the fifth force, so that the stars, gas, and dark matter continue to move together (Jain VanderPlas 2011 ). We calculate M ( r * ) by assuming a constant density ρ 0 within r * (justified post-hoc: r * for the fifth-force models we are sensitive to is 10 −2 − 10 −1 kpc, much less than the halo scale radius r s ), and estimate it separately for each galaxy using the empirical relation between central baryonic and dynamical surface mass densities (Lelli 2014 ; Lelli et al. 2016 ; Milgrom 2016 ). This yields As spans a very small angle on the plane of the sky we compare separately its orthogonal RA ( r *, α ) and Dec. ( r *, δ ) components with those of the measured displacement for each galaxy. We feed these calculations into a Bayesian likelihood formalism. First, we generate N MC = 1000 Monte Carlo realizations of the predicted signal for each Alfalfa galaxy, sampling independently for each one the galaxy–halo connection (from 200 independent AM realizations), the distribution of mass in the smooth density field (from 10 particle-mesh BORG realizations), the contribution to Φ ex and from haloes too faint to be recorded in 2M+ + (calibrated with the darksky-400 N -body box), and the Gaussian observational uncertainties on the structural galaxy properties used to derive M ( r * ) and Φ in . The full probability distributions that we marginalize over are given in table 1 of Desmond et al. ( 2018b ). We estimate the probability that a given galaxy is unscreened as f ≡ N (|Φ ex | + |Φ in | |Φ c |)/ N MC . The likelihood function then has separate screened ( r * = 0) and unscreened (equation 4 ) components, with relative weights 1 − f and f , respectively. We model the unscreened component using a normalized histogram of the distributions of r *, α and r *, δ over all N MC realizations, obviating the need for assumptions on the form of the likelihood function such as Gaussianity. We convolve this likelihood with the Gaussian H i measurement uncertainty for each galaxy, θ i , and treat galaxies as uncorrelated and RA and Dec.


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We appreciate Richard N. Manchester, Hao Tong, Shi Dai, Jumei Yao, Wenjun Huang, and Qihui Chen for helpful discussions. This work is supported by National Natural Science Foundation of China (Nos. 11178001, 11573008, U1631106). Hongguang Wang is supported by the 2018 Project of Xinjiang Uygur Autonomous Region of China for Flexibly Fetching in Upscale Talents. Yanrong Zhang appreciates Guangzhou University–University of Padova Joint PhD Program. The Parkes radio telescope is part of the Australia Telescope National Facility which is funded by the Australian Government for operation as a National Facility managed by CSIRO. This paper includes archived data obtained through the Australia Telescope Online Archive and the CSIRO Data Access Portal ( http://data.csiro.au ). We appreciate the anonymous referee for thorough and valuable comments. We thank Richard N. Manchester, Hao Tong, Shi Dai, Jumei Yao, Wenjun Huang, and Qihui Chen for helpful discussions.


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for this drop is that the rcb has been pushed closer to the surface of the underlying rock core, and with the envelope more nearly completely radiative, differences between how we treat the radiative transfer become magnified. Extremely gas-poor environments demand that atmospheric density profiles be sufficiently steep to contain a given amount of gas within the planet's Hill sphere, and this steepening pushes the thermal photosphere deeper into the envelope (compare the black dotted curves in the right-hand and second-from-right panels of Fig. 5 ); the rcb is, of course, pushed inwards as well. For ρ out /ρ MMEN = 10 −8 , the thermal photospheres of the dusty and dust-free optically thin models are only about twice the radius of the rocky core, and the corresponding rcb densities and opacities are 2–10 times larger than those of the radiative diffusion models. These larger rcb densities and opacities lower the radiative luminosities, slowing cooling and by extension accretion – hence the especially low GCRs seen in Fig. 4 characterizing ρ out /ρ MMEN = 10 −8 . At even lower nebular densities (data not shown), the rcb can be pushed all the way to the rocky core – i.e. the envelope becomes purely radiative – at which point the model sequence terminates (see also the isothermal endmember models in Lee Chiang 2015 , their fig. 4 and related discussion). Although the models shown in Fig. 4 are technically those of nebulae whose gas densities are fixed from t = 0 to 1 Myr and drop to zero thereafter, they are still reliable guides for nebulae whose gas densities deplete smoothly over time. The very fact that rates of gas accretion change only by factors of ∼3 when the nebular density varies by four orders of magnitude suggests that the detailed time history of nebular depletion introduces, at most, only order-unity effects. This expectation is confirmed in Fig. 6 , which shows how super-Earths amass ∼4–10 per cent-by-mass gas envelopes in a nebula that decays exponentially with an e-folding time-scale of 0.1 Myr. Figure 6. How 5 M ⊕ cores build their envelopes in an exponentially depleting nebula. The gas-to-core mass ratio (GCR ≡ M gas / M core ; solid and dashed curves using the right-hand axis) are computed by first fitting a scaling relationship to our numerical results for GCR versus nebular density (we find GCR ), and then integrating over the time derivative of GCR as the nebular gas depletes with an e-folding time of 0.1 Myr (grey curve using the left-hand axis). We halt envelope growth once ρ out /ρ MMEN falls below 10 −8 since the rate of gas accretion slows considerably (by about an order of magnitude compared to ρ out /ρ MMEN = 10 −7 ; see Fig. 4 ) at this level of depletion. 4 DISCUSSION 4.1 Creating super-puffs beyond 1 au So far in this paper, we have concentrated exclusively on planets located 0.1 au from their central stars. This restriction is due to our use of opacities generated from the model of Ferguson et al. ( 2005 ), which