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

arises due to propagating fluctuations in the accretion flow. In this picture, slower fluctuations arise in the outer regions of the flow, and as they propagate inwards, more rapid fluctuations are added. Variability at a given frequency is produced at a characteristic radius, so includes the spectrum produced at that radius, but then it propagates inwards so it is the sum of different spectral components at all radii interior to that where the characteristic frequency of the component is generated. This is shown schematically shown in Fig. 5 , where the sketch is of a gradually stratified flow, with each region contributing a harder spectrum as the radius decreases, rather than the two component model used above. A fundamental assumption of this picture is that smaller radii correspond to harder spectra. We will discuss this in Section 4 . Figure 5. Cartoon picture showing the disc (grey) and regions of the inner accretion flow contributing to each variability component. The cartoon image of Fig. 5 reveals a model-independent way to extract the spectra as a function of radius. By studying the difference between the variability spectra, we can attempt to isolate the spectrum which is characteristic of the radius at which each variability component is produced. As described above, the highest frequencies are expected to be the ‘cleanest’, i.e. only present in the innermost region and thereby modulating the emission from the fewest emission components. This is supported by our result that the spectrum of L 3 is well-fit by a single pure Comptonization component. L 2 has a lower frequency, and it should therefore contain the same contributions as L 3 , as well as emission from larger radii. To isolate the emission in the regions successively further out, we rescaled the L 3 spectrum to match that from L 2 in the highest energy bin (where the contribution is dominated by the innermost region), and then subtracted the L 3 spectrum. This is the maximum contribution from the hard innermost region, so this spectrum is the softest that can be characteristic of the region where L 2 is produced. Similarly, we rescaled and subtracted the spectrum of L 2 from L 1 . The results are shown in Fig. 6 . Figure 6. Spectra of each variability component after subtracting the contribution from higher frequencies (smaller radii). Colours and symbols are the same as in Fig. 2 . While the data points have large uncertainties, some general features can still be distinguished. The spectrum characteristic of the largest radii (red squares) is the softest, and is subtly different to the shape of the soft Comptonization in our two-component fits. The spectrum which can be associated with L 2 (green circles) is appreciably harder than that of L 1 , while that of L 3 is well described by a single hard Comptonization component with high electron temperature and seed photons around a few keV (as above). These results suggest a more complex flow than in our two component model


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

al. 2002 ). In their consideration of the maser data on the turbulence in the flows from the massive YSOs, Strelnitski et al. ( 2002 ) proposed that “the maser hot spots originate at the sites of ultimate dissipation of highly supersonic turbulence.” This assertion finds support in a well-ordered spatio-kinematical pattern in the small-scale water maser features reported in Cepheus A HW2 by Uscanga et al. ( 2003 ), in W75N by Uscanga et al. ( 2005 ), and in W49N by Gwinn ( 1994b ). Observations of Uscanga et al. ( 2005 ) suggested microstructure with a size about 1 au. This structure had a short lifetime supposedly on the order of a month. All information on the known examples of the structures with an “eddy-like” spatio-kinematical pattern does not contain evolutionary information and has a form of snapshots, although the other maser structures in Cepheus A HW2 show persistence on the timescales of years (Torrelles et al. 2001 ). Uscanga et al. ( 2005 ) speculated that these short-lived kinds of spatio-kinematical microstructures are either produced by fluid instabilities within the shocked material or correspond to nearly round cloudlets (turbulent eddies?) in the ambient medium. In the sections below, we discuss a spectroscopic origin for our observations as well as three dynamical phenomena that may explain them. 4.1. Spectroscopic Origin: Hyperfine Splitting The velocity separation of 0.54 km s −1 between the components in Figure 6 is close to the velocity separations of the H 2 O hyperfine splittings of 0.45 km s −1 between the F = 7–6 and F = 6–5 transitions and 0.58 km s −1 between F = 6–5 and F = 5–4. However, there are several problems with this spectroscopic hypothesis. First, the components of the double-peaked spectrum in Figure 6 are not spatially coincident, so they would have to be associated with different hyperfine components. Second, the F = 7–6 hyperfine transition has the lowest frequency (and F = 5–4 the highest) of the three strong transitions (Kukolich 1969 ), while the strength order is F = 7–6, F = 6–5, then F = 5–4 (Deguchi Watson 1986 ). We would therefore expect the strongest peak at the lowest frequency (most positive Doppler shift) in our spectrum, but the opposite is seen in Figure 6 . Moreover, all three of the hyperfine transitions introduced above have comparable line strengths (see Figure 1 of Deguchi Watson 1986 ), so a triplet spectrum would be expected rather than a doublet in the case of hyperfine intensity anomalies. We think this explanation is unlikely because it would require some complicated combination of hyperfine-specific pumping and/or competitive gain effects to generate the observed spectrum. 4.2. Keplerian Rotation For the first dynamical interpretation, the maser hot spots (see Figure 9 ) might be amplifying along chords (i.e., filaments) in the plane of a Keplerian disk, orbiting a protostellar or protoplanetary object, viewed approximately edge-on. In this case, the length of the filaments


O O O O O B-Tag O O O B-Instrument O O O B-Wavelength O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 O O O O O O O O B-Telescope 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 O O O O O O O O O O O O O O O O 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 B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O B-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Survey I-Survey O O B-Telescope B-Observatory B-Proposal I-Proposal O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Instrument O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O B-Survey O B-Survey 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 B-Wavelength O O O O O O O O O

2. Data sets and Mg <sc>ii</sc> absorber detection 2.1. X-shooter spectral samples The GRB afterglow spectra were collected in multiple semesters between 2009 and 2016 taking advantage of the X-shooter guaranteed program and subsequent open time proposals. With a uniform set of selection criteria for target-of-opportunity follow-up adopting the criteria for the low-resolution study of Fynbo et al. (2009) , that is, mainly avoiding regions with high Galactic extinction and bursts near to the Sun, the total number of obtained afterglow spectra is 116 until October, 2016. All spectra were obtained with VLT/X-shooter, which provides intermediate spectral resolutions of measured from UV to near-IR wavelengths. The S/N of the spectra vary as some afterglow spectra were obtained several hours to a few days after the GRB trigger, when only host spectral signatures and no characteristic power-law afterglow signature was visible. Removing these from the sample leaves 81 afterglow spectra, again with varying S/N between 1 and 50 per pixel for different bursts and wavelength coverage (see Selsing et al., in prep., for details). The data were reduced with the ESO VLT/X-shooter pipeline ( Modigliani et al. 2010 ) managed by Reflex ( Freudling et al. 2013 ), and with our own post-processing steps to improve the flux calibration and rejection of bad pixels (Selsing et al., in prep.) with reduction scripts made available online 2 . The redshifts of the GRBs lie in the range . Turning to the quasar sample, the XQ-100 survey is a VLT/X-shooter ESO Large Programme that targeted 100 quasars at with a S/N higher than 20 per pixel over the entire wavelength range (see Lopez et al. 2016 , for details). The quasars were selected without prior knowledge of the presence of strong absorbers along our line of sight. The quasars and a large majority of GRB afterglows were observed with X-shooter slit widths of 1.0, 0.9, and 0.9 arcsec for the UVB, VIS, and NIR-arms, respectively, resulting in similar spectral resolutions between the two samples. The redshift distributions of the GRB and quasar samples are shown in Fig. 1 . By construction the quasars have a quite distinct distribution as high-redshift objects were selected, whereas there are no intrinsic constraints for the GRB redshift selection. To match the redshift distribution of GRBs we could include other quasars observed with X-shooter, using archive data. However, these quasars might have been selected on the basis of the presence or lack of any kind of intervening and intrinsic absorption line systems, so we do not expand the quasar sample beyond the XQ-100 data. Fig. 1 Redshift distributions for the two background source samples (XQ-100 and XSGRB). The 81 GRB afterglows and 100 quasars have median redshifts of and , respectively. 2.2. Additional data sets Since the earlier discrepancy on the incidence of Mg ii absorbers relied on the statistics of GRB absorbers obtained to that date, we also examined another


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JDC thanks J. Peacock, A. Pontzen and J. Whitehouse for suggestions, and especially M. White for numerous discussions. We thank N. Dalal, V. Desjacques, F. Leclercq, M. Neyrinck and the anonymous referee for helpful comments on the draft.


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MDP thanks Lara Nava and Daisuke Kawata for helpful discussions and references, Alice Breeveld for her helping hand, and his friends Marco D'Alessandro, John Moore, Ernesto Amato, Peter Rockhill, Peter Včasný, Alexander J. Zech, and Pierluigi Cox for their encouragement. AR acknowledge support from PRIN-INAF 2012/13 and from Premiale LBT 2013. BG acknowledges financial support of the NASA through the NASA Award NNX13AD28A and the NASA Award NNX15AP95A. Part of this work is under the auspice of the FIGARONet collaborative network, supported by the Agence Nationale de la Recherche, programme ANR-14-CE33. DAK acknowledges support by TLS Tautenburg in form of a research stipend. DM acknowledges support from Ida as well as financial support from Instrument Center for Danish Astrophysics (IDA). GS acknowledge the financial support of the Italian Ministry of Education, University and Research (MIUR) through grant FIRB 2012 RBFR12PM1F. MDP and MJP acknowledge support from the UK Space Agency. SRO acknowledges the support of the Spanish Ministry, Project Number AYA2012-39727-C03-01. ZC gratefully acknowledges financial support from the Icelandic Research Fund (IRF). This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester, and by the Chandra Data Archive.


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δ m ( a i ) = 5 × 10 −5 . Additionally, we insert the initial conditions as follows (see also Batista Pace 2013 ; Malekjani et al. 2017 ) Using these initial values one can be confident that matter perturbations always remain in the linear regime. After finding the evolution of fluctuations (δ m , δ d ), we can calculate the growth rate of large-scale structures in the presence of oscillating DE models considered in this work. The growth rate function can be written as The value of σ 8 (), the matter fluctuation amplitude on scales of 8 Mpch −1 , can also be written as By multiplication of these two functions, one can calculate the value of f ()σ 8 () to compare it with f σ 8 observational data. The growth rate data set were obtained from redshift-space distortions (RSDs) from different galaxy surveys. These data points, when measured using RSDs, are degenerate with the Alcock–Paczynski (AP) effect (Alcock Paczynski 1979 ). Assuming an incorrect cosmological model for the coordinate transformation from redshift space to comoving space leads to residual geometric distortions known as the RSDs. These distortions are induced by the fact that measured distances along and perpendicular to the line of sight are fundamentally different. Measuring the ratio of galaxy clustering in the radial and transverse directions provides a probe of AP effect. However, given high precision clustering measurements over a wide range of scales, this degeneracy can be broken since RSD and AP have different scale dependences (Reid et al. 2012 ). In order to overcome the RSD problem, several methods have been used in the literature to apply the AP test to the large-scale structure (Song Percival 2009 ; Samushia, Percival Raccanelli 2012 ; Blake et al. 2012 ; Blake et al. 2013 ; Hudson Turnbull 2013 ; Feix, Nusser Branchini 2015 ; Howlett et al. 2015 ; Chuang et al. 2016 ; Huterer et al. 2017 ). Since we obtain our growth rate data from the above references; therefore, we can claim that the AP effect has been considered for the growth rate data which we used in our analysis. Nowadays there are more than 30 data points of recent f σ 8 measurements from different surveys. The information in some of these data points overlaps significantly with other data points in this collection. Some of them are updated version of previous measurements either with enhancements in the volume of the survey, during its scheduled run or with different methodologies by various groups. Therefore, the collection of these data points should not be used in its entirety. Therefore, in our analysis we use the ‘Gold-2017’ compilation of robust and independent f σ 8 measurements from different surveys constructed by Nesseris, Pantazis Perivolaropoulos ( 2017 ). We apply these data points to put constraints on model parameters. The likelihood function becomes where the statistical vector p is {Ω DM0 , Ω b0 , h , 0 , A, B , σ 8 } and σ 8 is the present value of σ 8 (). The best-fitting parameters and


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X-ray emitting e + e − pairs are fast cooling, which allows us to write their detailed energy balance. This results in a lower limit on , which is the ratio of the magnetar's long-term mean energy output in outflows (quiescent MHD wind + sporadic outbursts), , to its spin-down luminosity. This clearly implies that the MWN is not powered predominantly by the magnetar's spin-down-powered wind, and an alternative dominant energy source is required, most likely the decay of the magnetar's magnetic field. We show that the decay of its dipole field alone is not enough, and a significantly larger (by a factor of ∼10 2 –10 3 ) energy reservoir is needed. The most plausible candidate is the magnetar's internal magnetic field, which has to be ≳ 10 − 30 times larger than its dipole field. Finally, by assuming a maximum allowed initial internal field strength (on theoretical grounds) of B int, max ∼ 10 16 –10 16.5 G we obtain an upper limit on g ≲ 5 × (10 2 –10 3 ). In Section 7 we consider the possible origin of the GeV/TeV emission observed by Fermi /LAT and H.E.S.S. In Section 7.1 we consider the possibility of a hadronic origin for the GeV/TeV emission. While inverse-Compton emission by electrons in the MWN is energetically very challenging, we find a much more plausible and energetically reasonable alternative to be the decay of neutral pions that are produced by the interaction of cosmic rays (CR) accelerated in the shock driven by the SNR into the external medium, with nuclei in the nearby giant molecular cloud (GMC). In Section 7.2 , we consider the possibility of inverse-Compton emission by relativistic electrons in the MWN that upscatter seed photons from the NIR Galactic background and the CMB. For Galactic NIR seed photons we find it extremely difficult to account for the observed GeV/TeV luminosity. For CMB seed photons it is also very difficult to account for the GeV/TeV luminosity, and moreover, together with the power-law MWN electron energy distribution (as reflected by their X-ray synchrotron emission) one would expect a much broader spectral peak at TeV energies, which is hard to reconcile with the Fermi /LAT and H.E.S.S. observations. Therefore, we find this option implausible. Finally, we also consider emission from relativistic non-thermal bremsstrahlung from electrons accelerated at the SNR forward shock. Our conclusions are discussed in Section 8 . Our main findings are that the MWN is powered predominantly by outflows from the magnetar, whose main energy source is most likely the decay of its strong internal magnetic field. These conclusions became possible because of the discovery of this first MWN. The outflows from the magnetar accumulate inside the MWN, which therefore serves as a calorimeter that helps us study the system's history. 2 IMPLICATIONS OF THE ASSOCIATION WITH THE SNR The location of Swift J1834 at the very centre of the SNR W41 strongly supports their association. Moreover, it can also constrain the SGR's proper


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ACKNOWLEDGEMENTS MRK acknowledges support from the Australian Research Council’s Discovery Projects funding scheme (project DP160100695). BB is supported by the NASA Einstein Postdoctoral Fellowship and an Institute for Theory and Computation Fellowship. JCF is supported by an Institute for Theory and Computation Fellowship. We thank S. Oh for helpful discussions of bar surveys, and the referee, A. Dekel, for helpful comments.


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

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 127229 to C.J.V. This material is also based on work partially supported by the National Science Foundation under Grant No. AST-1616513 to R.J.R. and Grant Nos. AST-0908126 and AST-1615594 to R.A.M.W. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 679627). We would like to thank the anonymous referee for insightful and helpful comments that led to the overall improvement of this work.


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

not particularly affect the results. Missed associations in this case are due the fact that the light curve iPTF 17cw is not well sampled at early times. Our discussion in Section 4.1.1 clarifies this point. In the case of sources with redshift randomly distributed between 0.01 and 0.1 our results are, as expected, in between the two previously described cases. Specifically, 92% of all simulated sources are detected, and 87% of the detected sources are uniquely and correctly associated. In particular, 100% of the targets simulated from the templates of SN 1998bw and SN 2009bb, 69% of SN 2006aj, and 99% of iPTF 17cw are detected. Of those detected sources, 100% of the targets simulated from the templates of SN 1998bw and SN 2009bb, 48% of SN 2006aj, and 88% of iPTF 17cw are uniquely and correctly associated. For completeness, in Figure 2 we also plot the the efficiency of the optimized observing campaign as a function of total time delay for SN 2006aj-like and PTF17cw-like targets, with redshifts randomly distributed between 0.01 and 0.1. The total time delay is calculated as the sum of the delay between the explosion and the optical detection, and the delay between the optical detection and the first radio observation (which defines the urgency of the radio observing campaign; see Section 3.3 ). In this figure the efficiency (fraction of unique and correct associations) is calculated relative to the number of simulated sources that are detected in each delay bin. We note that for SN 1998bw-like and SN 2009bb-like targets, the efficiency is 100% regardless of the total time delay (and thus, regardless of the adopted observing urgency strategy in the radio). In the case of SN 2006aj-like targets, we completely miss those that are observed with total delays ≳22 days, when SN 2006aj was undetected. Figure 2. Fraction of targets that are uniquely and correctly associated as a function of the total delay between the SN explosion and the first radio observation for sources with z = 0.01–0.1. 4.1.1. Relevance of Early-time Radio Observations for Relativistic SNe In this section we assess the importance of early-time radio observations for correctly and uniquely associating relativistic SNe via an optimized radio follow-up campaign. To this end, we extrapolate the template light curves of SN 2009bb and iPTF 17cw using the early-time behavior of the much better sampled radio light curves of SN 1998bw and SN 2006aj, respectively. We choose to use SN 1998bw to extrapolate the light curve of SN 2009bb, and SN 2006aj to extrapolate the light curve of iPTF 17cw, because they are the most similar to each other. In fact, both SN 1998bw and SN 2009bb were nearby explosions that resulted in a very bright radio signal. On the other hand, both SN 2006aj and iPTF 17cw were very dim and faded away very rapidly. We repeat the simulations and optimization procedure described in the previous section including these early-time extrapolations. Since all sources


O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O B-Instrument B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Identifier O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O B-Instrument O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O B-Instrument O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Instrument B-Identifier O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion B-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O B-Mission O O B-Mission O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-CelestialObjectRegion O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Instrument O B-Instrument 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

minerals that formed in a water-rich environment, including phyllosilicates, sulfates, and hematite, which suggests changes in ancient aqueous environments. After exploring the top of Vera Rubin Ridge (VRR) in 2018, which mostly contains hematite signatures, the rover descended into a trough south of the ridge, dropping as much as 15 meters in elevation during the spring of 2019 to explore part of the clay-bearing unit, and Curiosity is currently investigating the clay-bearing unit on the side of Mount Sharp. Elemental abundances and mineralogical information has been obtained from the ChemCam, APXS, and CheMin instruments, which allows us to directly test the quantitative results from the orbital remote sensing data. Spectral unmixing modelling was performed on the CRISM single scattering albedo spectra to extract the abundances and grain sizes of both hydrous and anhydrous phases. Examples of spectral unmixing results over the hydrated sulfate and phyllosilicate units are shown in Fig. 6 . To investigate the spatial distribution of the secondary mineral abundances, we applied our spectral unmixing model to CRISM image HRL0000BABA to generate the mineral abundance map. Figure 7 a shows the distribution of the secondary phases mapped over Mount Sharp using the CRISM parameter map ( Milliken et al. 2010 ), and Fig. 7 b shows the results of the spectral unmixing analysis over the selected region enclosed in the white box in Fig. 7 a. From Fig. 7 b it is possible to resolve the hematite, phyllosilicate, and hydrated sulfate unit, and these units are consistent with the spatial distribution derived from the CRISM parameter map shown in Fig. 7 a. The spectral unmixing of the CRISM image cube over Gale indicates that there is 30% hematite, 5% phyllosilicates, and 20% hydrated sulfates. We note that the error of the retrieved abundance is around 5% following the error analysis approach used in Liu et al. (2016) . Fig. 7 Panel a : CRISM FRT0000BABA RGB mineral parameter map (red = Fe-minerals, green = Fe/Mg-clay minerals, blue = sulfates) overlain on CTX mosaic. Image adapted from Fig. 3 a of Milliken et al. (2010) . Panel b : Derived mineral abundance map over a region covering Curiosity’s traverse, outlined in the white box in Fig. 7 a. The derived mineral abundances from CRISM observations can be used to compare with the ground-truth data. Vera Rubin ridge (VRR) of Gale crater has the strongest spectral signature consistent with hematite detected from orbit, and the area has been explored by Curiosity rover intensively. Curiosity data show that hematite is present throughout most of the Murry formation and VRR, though it is more abundant in certain drill samples ( Rampe et al. 2019 ). The abundance of these iron oxides are around 20 wt%, as inferred from ChemCam and APXS instruments ( Milliken et al. 2019 ), and the value is slightly lower than what we derived from orbital data. In addition to abundance discrepancies, spatial distribution also


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The anonymous referee is thanked for their very insightful and constructive comments and suggestions, which allowed us to improve the manuscript significantly. We are very grateful to the Tibet AS- γ collaboration for providing their CR maps in electronic format and especially Dr. Yi Zhang for helping us in understanding the data. We acknowledge the use of LAMBDA, support for which is provided by the NASA/GSFC, the software packages HEALPix ( http://healpix.sourceforge.net/ ), developed by A.J. Banday, M. Barthelmann, K.M. Gorski, F.K. Hansen, E. Hivon, and B.D. Wandelt, and CAMB ( http://camb.info ), developed by A. Challinor and A. Lewis. SNZ acknowledges partial funding support by Directional Research Project of the Chinese Academy of Sciences under project No. KJCX2-YW-T03 and by the National Natural Science Foundation of China under grant Nos. 10821061, 10733010, 10725313, and by 973 Program of China under grant 2009CB824800.


O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O

(black circles), and He i λ 3889 (red diamonds). Bottom panel: EW of the same emission lines (with the same color and marker combination as the top panel). The dotted blue lines indicate the value of the He ii line measured from the STIS spectra of 2000 February 09 (MJD 51584). The He i lines were not detected in that spectrum. On the X -axis we plot the Modified Julian Date of the observations. The FWHM and EW of the He ii line show a gradual decrease over the duration of our follow-up campaign: the FWHM decreases from ≈2700 km s −1 to ≈1350 km s −1 and the EW from ≈ 14 Å to ≈7 Å . Neither the FWHM nor the EW have returned to the values measured during the STIS spectrum. The evolution in the EW and FWHM of the He i lines is less clear, but especially that of the λ5876 line seems to follow a similar trend as that of He ii . In contrast, the other lines of similar width, that is, the broad bases of the other emission lines, do not show significant evolution with time in their FWHM, while the EW of some of them (mainly H β and [O iii ] λ 4959, λ 5007) show an increase between MJD 57280 and 58345 to subsequently decay back to the initial value (see Table 2 ). Table 2 Results of the Line Fitting of the Most Prominent Broad Lines Note. With ellipsis dots we indicate an epoch in which the line in question could not be fit. For the He i λ 5876, the values marked with an asterisk are the combination of the values measured for the narrow and broad component. We measure the offset of the lines with respect to their rest-frame wavelength. It is important to note that in good observing conditions (i.e., when the value of the seeing in arcseconds is smaller than the slit width, which is the case for many of our observations, see Table 1 ), the wavelength calibration of the source spectrum could be slightly shifted with respect to that derived by the arc lines (as the latter do fill the whole slit), due to possible imperfections in centering of the source in the slit. This in turn can affect the velocity offset measurements by a few times 100 km s −1 . However, the narrow lines do not show a significant offset with respect to their rest-frame wavelength (its absolute value is always below 200 km s −1 ), implying that the shifts in the wavelength scale caused by the potential imperfect centering of the source in the slit are smaller than a few hundred km s −1 . This is in line with the fact that the extended nature of the source acts as a mitigating factor for any small imperfect centering of the source in the slit. The broad bases of the emission lines are all blueshifted. We measure the shift of the broad bases with respect to the central wavelength of the narrow lines, assuming that these are at their rest-frame wavelength. Each broad line has a different blueshift, but none of them show a clear evolution with time. The velocity offset values are all ≲10 3 km s −1 . For the He i λ 5876 lines, we only separate the narrow and broader component of the


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

grid cell, and then integrate the total photon flux density as in the photon energy range. We use 0.01 keV as , meaning 90 bins in total in the energy range. This process leads to the images shown in Figure 1 , right column. 3. RESULTS AND DISCUSSION 3.1. Asymmetric Footpoint Heating Inducing KHI The temporal evolution of the number density (left column), temperature (middle column), and synthesized SXR photon fluxes (right column) are shown in Figure 1 , covering a timespan of about 4.15 minutes. As described in Section 2.2 , we use H 1 to mimic the flare energy deposited in the upper chromosphere, and the consequent overpressure resulting from H 1 drives upward mass flows at a speed up to 700 km s −1 . We also witness a rapid thermodynamic change (due to thermal conduction) in the loop, reaching an extremely hot temperature around 18 MK. These upward chromospheric evaporation flows have been detected directly in imaging sequences as SXR emission propagating toward the loop-top sources (Silva et al. 1997 ; Liu et al. 2006 ; Nitta et al. 2012 ). This is also seen in our simulation, as in panel (f) of Figure 1 (and in the time period before this image, for which we refer to the corresponding movie). In the last several decades, simulations of chromospheric evaporation have been mostly carried out with symmetric energy input assumptions on both loop footpoints and these focused mainly on the UV-SXR spectral lines produced by the evaporated plasma (Fisher et al. 1985 ; Mariska et al. 1989 ; Yokoyama Shibata 2001 ; Allred et al. 2005 ; Liu et al. 2009 ). However, asymmetric energy deposition at footpoints is a much more likely scenario, and could be intrinsic to the acceleration process as pursued by McClements Alexander ( 2005 ). So, in our simulation we assume that the deposition of flare energy at two footpoints is slightly asymmetric, with a ratio of 0.8 as described in Equation ( 5 ). As a result, the right evaporation flow rises quicker and is hotter than the left one as shown in panel (e). Asymmetric energy deposition guarantees that the two evaporation flows will not merely collide at the apex, a situation known to only generate reflected shocks. Panel (e) indeed shows that when our two evaporation flows run into each other asymmetrically, the right one has already crossed the loop apex. In addition, the hotter, right evaporation flow causes a bigger expansion of the loop cross-section in the right half of the loop. This configuration provides the conditions for the formation of shear flows, the trigger of KHI. As shown in panel (e), right after the collision of both flows, KHI begins to develop immediately, and the typical vortical structures of the KHI appear and grow up quickly from panels (e) to (g). The development of vortices in a magnetized plasma can further induce small-scale structure to develop, with a potential cascade of energy to establish a turbulent plasma state (Keppens et al. 1999 ; Baty et al. 2003 ; Elmegreen


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

history. On the other hand, galaxies MW c and M31 c are the MW and M31 candidates of Nuza et al. ( 2014 ) (see also Scannapieco et al. 2015 ) that were extracted from a WMAP -5 cosmological simulation of the Local Group. As a result, these galaxies reside in an environment more similar to the actual one. The main properties of each model galaxy at = 0 are shown in Table 1 . The latter also includes a scaled-down version of g106, referred to as g106r, that was used as an MW candidate by MCM13 and MCM14 in their Galactic chemodynamical model. More details concerning the galaxies, as well as the main assumptions and techniques adopted to perform each simulation, can be found below. Table 1. Properties of the simulated galaxies at = 0. The columns show virial mass, virial radius, stellar mass (within optical radius), optical radius, bulge-to-total ratio, and references. Note . a Rescaled g106 used as an MW proxy by MCM13 and MCM14 (see Section 4.3 ). 2.1 g37 and g106 These galaxies are selected from the larger galaxy sample of Martig et al. ( 2012 ). The simulation technique involves basically two steps (see Martig et al. 2009 , for technical details). First, a dark-matter-only simulation is performed in a box of Mpc on a side using the adaptive mesh refinement RAMSES code (Teyssier 2002 ) to extract merger and accretion histories for the target haloes. Some properties such as time, mass, velocity, and spin of incoming satellites are then stored. In the second step, a new simulation is performed in which each halo recorded in the dark-matter-only run is replaced by a model galaxy made up of gas, stars, and dark-matter particles. Similarly, each diffuse particle of the cosmological simulation is replaced with a blob of higher-resolution gas and dark-matter particles. These model ‘seed’ galaxies are made up of a disc containing gas and stars, a stellar bulge, and a dark-matter halo following analytical prescriptions for the profiles in each case. The stellar mass of a galaxy in the simulation is set according to the Moster et al. ( 2010 ) relation as a function of halo mass and redshift. All model galaxies are assumed to be disc galaxies without a bulge, except for the most massive haloes with M ⊙ at 1, in which case the mass of the bulge is set to of the stellar mass. The gas content in the disc is also set according to an analytical scheme: at 1, the gas fraction (with respect to the total baryonic mass) is 0.3 for small galaxies ( M ⊙ ) and 0.15 for the massive ones. At higher redshifts, the gas fraction is chosen independently of the total mass, and is set to 0.5 for 1 3 and 0.7 for > 3. No hot gas halo is included, which should be a sensible approximation only for halo masses lower than a critical mass of M ⊙ , which is required for virial shocks to be stable (e.g. Birnboim Dekel 2003 ). The resimulation starts at = 5 inside a region of radius 800 kpc, i.e. spanning a few times the virial radius value of the main galaxy at = 0, and follows its


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Acknowledgements We thank the referee, Ruobing Dong, for constructive comments that helped improve the manuscript. We are thankful to A. Triaud, Z. Zhu, R. Nealon, C. Manara, and J. Huang for insightful discussions. We thank S. Barenfeld for sharing his ALMA data of HD 143006. M.B. and M.V. acknowledge funding from ANR of France under contract No. ANR-16-CE31-0013 (Planet Forming disks). This work has been supported by the diskSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG. P.P. acknowledges support by NASA through Hubble Fellowship grant HST-HF2-51380.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. The figures were generated with the python -based package matplotlib ( Hunter 2007 ).


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BL thanks Alex I. Maltz and David Hogg for useful discussions. BL and HVP were supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007- 2013)/ERC grant agreement no 306478-CosmicDawn. BL was also supported by the Simons Foundation and DJM by the STFC.


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Acknowledgments The author is indebted to Sverre Aarseth of the Institute of Astronomy, Cambridge, for his continuous efforts in improving nbody6/7 , without which this study would not have been possible. SB is thankful to Jarrod Hurley of the Swinburne University of Technology for reviewing the changes made in the BSE s routines for this work, testing them independently, and also for interesting discussions. SB is thankful to Chris Belczynski of the Astronomical Observatory, University of Warsaw, for supplying the data corresponding to the ZAMS massremnant mass relations, as obtained from the StarTrack program (Fig. 1 ), and also for useful discussions. SB is thankful to the anonymous referee for helpful comments that improved some of the descriptions of the paper. Finally, but not the least, SB is indebted to the computing team of the Argelander-Institut fr Astronomie, University of Bonn, for their support and efficient maintenance of the workstations on which all the computations have been performed.


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The scientific results reported in this article are based on observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programmes 077.D-0764(A) and 297.D-5042(A). PE and ADL acknowledge funding in the framework of the project ULTraS (ASI–INAF contract N. 2017-14-H.0). FCZ is supported by a Juan de la Cierva fellowship.


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

in their terms) appearing at approximately Σ ≳ 100 ⟨Σ⟩ with a slope ≈−1 ± 0.2. Similarly, Lin et al. ( 2017 ) see in the survey of clouds that the PDF becomes systematically shallower, approaching −1, as clouds (or cloud regions) become more actively star forming. We should also note that similar results have been seen in other numerical simulations (e.g. Burkhart, Collins Lazarian 2015 ). 4.4 Cluster mass profile Let us assume that some fraction of objects formed remain gravitationally bound to each other. We expect that the clustered substructures that formed from fragmentation will eventually merge together into a cluster with a density profile that decreases monotonically. Let us derive the power-law index of this profile. Using our model we can calculate the relation between the densities and the survivor masses before the objects rearrange themselves into clusters. For density, take their at-formation value (ρ n ). We can express the index n as which leads to Let us assume (for now) that after formation the objects rearrange themselves to form clusters, while preserving the local volume density – i.e. the local density (of stars) around a star does not change dramatically before/after the re-arrangement. This is motivated by the fact that during mergers, tidal shredding of an object with density ρ occurs at an orbital radius R , where the mean density enclosed within R is approximately ρ. This means that the amount of mass at different density levels must be the same as before the rearrangement, thus Let us assume the relaxed cluster has a power-law density profile: ρ cl ∝ R β − 3 . Also, ε ≪ 1 thus the right hand side of equation ( 25 ) is zero. This leads to thus β = 0, so the mass profile of a bound cluster that results from the assembly of substructures formed in a scale-free fragmentation cascade is ρ cl ∝ R −3 . We can repeat the same exercise while assuming that phase space density (ρ p ) is conserved instead of real space density, as per Liouville’s theorem. This is only true however if ρ p is resolved on infinitely fine scales, as elements of higher phase space density effectively get stretched out and diluted in phase space so that the final observed coarse-grained phase space density is generally lesser than the initial (Lynden-Bell 1967 ). However, we may still suppose that our self-similarity condition means that the evolution operator on the coarse-grained phase space density can only map an initially flat (d M /dln ρ p ∼ 0) phase space distribution into another flat distribution. We can approximate the phase space density as where σ is the velocity dispersion. Assuming that the collapsing clouds are virialized, we can write which leads to From here we can formulate the surviving mass per phase density (similar to equation 25 ): where, in the last step, we used the assumption that ε ≪ 1. Since we are interested in the asymptotic case at large radii. the mass enclosed is approximately converged ( M ≈ const.), thus so we get


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This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 637324 and from the Academy of Finland (projects 258963 and 267186). The calculations were performed using the Finnish Grid Infrastructure (FGI) project (Turku, Finland).


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

We thank Carlos de Breuck, Katharina Immer and APEX operators for their support for the observations. We also thank the referee for helpful comments. The Atacama Pathfinder EXperiment (APEX) is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme 60.A-9341A. We acknowledge financial support from “Programme National de Cosmologie and Galaxies” (PNCG) of CNRS/INSU, France.


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ACKNOWLEDGEMENTS The Westerbork Synthesis Radio Telescope is operated by the Netherlands Institute for Radio Astronomy (ASTRON) with support from The Netherlands Foundation for Scientific Research (NWO). LND and BWS acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 694745). We would like to thank Andrew Lyne, Marten van Kerkwijk, and James McKee for useful and interesting discussions. LND would like to thank the ASTRON/JIVE summer studentship programme for a fellowship in 2014. We thank the referee, assistant editor, and scientific editor for their constructive comments on 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

Residuals are in units of σ as in Fig. B1 . Following the method used in Appendix B1 , it was verified (but not shown here) that the mass gradients towards filaments after randomization of the distances D skel in bins of distances to the nearest wall D wall are substantially reduced. Only a very weak mass gradient (at a 1σ level at most) is detected after randomization even for d skel min = 2.5 Mpc. Similarly to what was found in Section B1 , increasing this parameter does not induce any substantial reduction of the gradient. Thus this distance was chosen as the limit for the exclusion region around filaments. APPENDIX C: SMALL-SCALE DENSITY-COSMIC WEB RELATION In this Appendix, the impact of the small-scale density estimator on the mass and type/colour gradients is presented. The density used here is DTFE, i.e. the density computed at the smallest possible scale. 10 As in Section 6 , the two methods, the reshuffling and density-matching, are applied. Fig. C1 shows the differential distributions of the distances to the nearest filament, D skel (normalized by 〈 D z 〉, for the same selections as in Fig. 12 . The contribution of the nodes to the measured signal is minimized, by removing from the analysis galaxies located closer to a node than 3.5 Mpc. Star-forming and passive galaxies have been matched in mass, as described in Appendix A1 . The vertical lines indicate the medians of the distributions, whose values, together with the error bars, are listed in Table F3 . Figure C1. Top rows: As in Fig. 12 , but using the DTFE density for both methods, reshuffling (Figure a) and density matching (Figure b). The numerical values of medians, shown as vertical lines, are listed in Table F3 . When the small-scale density, DTFE in this case, is used in the reshuffling method, the randomized (dashed lines) and original signal (solid lines) are nearly identical. Similarly, all gradients are almost completely erased, as expected. Bottom rows: Residuals are in unit of σ as in Fig. 12 . (a) Reshuffling. (b) Density matching. In Figure (a), the mass and type gradients are shown before (solid lines, as in 12 ) and after (dashed lines) applying the reshuffling of galaxies in the bins of overdensity (1+δ), where the number density corresponds to the DTFE density. The result conforms to the expectations. The reshuffling does not remove the observed mass and type/colour gradients, i.e. the distributions before and after the reshuffling are almost identical, suggesting that at the small scale, traced by DTFE, the density and cosmic web are closely correlated through the small-scale processes. Figure (b) illustrates the PDFs for samples that have been matched in overdensity (1 + δ), as described in Appendix A2 , where the density considered is DTFE. The density-matching technique yields qualitatively similar result than the above used reshuffling in that almost no mass and type gradients are detected when galaxies matched in the DTFE density. Qualitatively same


B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-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 B-Wavelength B-Wavelength I-Wavelength 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 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 B-Formula I-Formula I-Formula 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 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 B-Survey O O O B-Software I-Software O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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

al. 2004 ; Rahmani et al. 2014 ; Albareti et al. 2015 ) out to redshifts z ∼ 1, where δλ denotes the separation between two spectral lines, and the subscript refers to the redshift. Our results are not in contradiction with this upper limit. The studies of the variation of the fine structure constant use multiplets of a given atomic element. The targeted spectral features, such as the [O iii ] doublet ( λλ 4960, 5008 Å), cover a relative narrow spectral window (Δ λ ≲ 100 Å). In comparison, our study covers a wavelength window at least 30 times larger. In this context, we wonder whether analyses of the variation of the fine structure constant based on absorption lines (e.g., Quast et al. 2004 ) may suffer from similar type of systematic effects. In addition, the use of nebular emission lines might present equivalent systematic complications in the determination of the centroid of the line, this time caused by the gas kinematics, but such musings are beyond the scope of this paper. Is the result shown in this paper an absolute limit to the accuracy one can achieve with galaxy spectra? Although the present data cannot provide an accuracy better than one part in 100,000 out to z ≲ 0.25, we speculate that high S/N spectra at significantly higher resolution— R ≳ 10,000—can be used to probe in detail the effective shapes of the absorption lines, potentially allowing us to break this barrier. The denser sampling at higher resolution will decrease the statistical weight in the methodology due to differences in the number of fitting points between the blue and the red sides of the spectral features, caused by the stretching of the spectra. APPENDIX POTENTIAL SYSTEMATICS A.1. Wavelength Calibration A.1.1. Testing the Wavelength Calibration of SDSS Spectra In addition to the signal found in the simulated data (Section 4 ) one could also consider the possibility of an inaccurate wavelength calibration of the SDSS spectra. The official SDSS pipeline quotes typical errors (Abazajian et al. 2009 ) of order 2 km s −1 , which translates into an uncertainty of δ Δ( z ; λ 0 ) ∼ 7 × 10 −6 for individual spectra. Although this effect should be significantly lower than our measurements, especially if we consider that the whole analysis rests on the determination of approximately 6.8 million individual spectral features, we nevertheless explore below a possible systematic from a wavelength calibration trend. If the observed signal is due to a calibration wavelength problem, then we should not expect the calibration bias to depend on the redshift bin considered. Consequently, we conduct the following test: for each redshift bin we select only those lines within the common observer-frame window, between 4500 and 6800 Å. We calculate in this region how much the observed wavelengths ( λ obs ) depart from the standard (1 + z ) law for each redshift bin. In this test, we hypothesize that such departures are caused by an inaccurate wavelength calibration, so that the


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We are grateful to the MPIfR team, as well as the APEX and IRAM 30 m staff for their help and support during and after the observations. We are grateful to C. Brogan for providing the 21 cm map and the data cube of the velocity-resolved optical depth of HI estimated for M17 SW. We thank the referee for the careful reading of the manuscript and constructive comments that helped to improve our work. We are also grateful with the editor, Dr. Malcolm Walmsley, for his timely comments and suggestions that helped to improve even more our work. Molecular Databases that have been helpful include the NASA/JPL spectroscopy line catalog and the University of Leiden’s LAMDA databases.


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

luminosity and thus accretion rate. For this purpose we used the results of our spectral analysis of the emission of the sources in a wide energy range, obtained during previous outbursts with the RXTE and INTEGRAL observatories ( Tsygankov et al. 2006 , 2007 ). It was found that the source flux in the 0.510 keV energy was 50% from the bolometric (i.e. flux in the 0.5100 keV energy range). Based on these results, in the subsequent calculations we used the coefficient 2 for the conversion of fluxes for both sources in the bright (accretion) state. In the propeller state, Swift /XRT energy coverage is sufficient to detect most of the emergent flux and no additional bolometric correction is needed. Indeed, this conclusion is valid both for the black body and power-law models due to the low temperatures ( keV) or steep photon indexes (). The bolometric correction may introduce additional uncertainty because of our ignorance of the broadband source spectrum at luminosities around the transition. We estimated this uncertainty at the level of 1020% and added it to the final uncertainty for the limiting luminosity. Taking all uncertainties into account, we estimate the bolometric limiting luminosities for the onset of the propeller regime at erg s and erg s for 4U 0115+63 and V 0332+53, respectively. Fig. 4 Observed correlation between a combination of the propeller limiting luminosity and the period, , and independently determined magnetic field strength for five pulsars and one accreting magnetar (M82 X-2) is shown with circles with error bars ( Tsygankov et al. 2016 ). The dashed and dash-dotted lines represent the theoretical dependence from Eq. ( 2 ), assuming NS standard parameters (, km) and and , respectively. The red star and open box indicate the positions of 4U 0115+63 and V 0332+53 obtained in this work, respectively. 4.2. “Propeller” effect The “propeller effect” ( Illarionov Sunyaev 1975 ) is caused by a substantial centrifugal barrier produced by the rotating magnetosphere of the neutron star. The matter stopped at the magnetospheric radius can only penetrate the magnetosphere if the velocity of the field lines is lower than the local Keplerian velocity. In other words, the matter will be accreted only in the case when the magnetospheric radius () is smaller than the corotation radius (). The magnetospheric radius depends on the mass accretion rate, and, therefore, one can estimate the limiting luminosity corresponding to the onset of the propeller regime by equating the corotation and magnetospheric radii (see e.g. Campana et al. 2002 ) where is the neutron star mass in units of 1.4 , is neutron star radius in units of cm, its rotational period in seconds, is the magnetic field strength in units of G, and is the mass accretion rate onto the neutron star. Factor relates the magnetospheric radius for disc accretion to the Alfvén radius calculated for spherical accretion and is usually assumed to be ( Ghosh Lamb 1978 ). Because the


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The authors are supported by an ERC Starting Grant (grant no. 280127 ). MLB is an STFC Advanced/Halliday fellow. We wish to thank Tomasz Kacprzak for making the IM3SHAPE simulations available to us and Wendy Williams and Huub Röttgering for useful discussions on the ionosphere. We also thank Robert Braun for help with the SKA sensitivity curves.


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fluctuation in GX 301–2. This implies that the observed fluctuations are highly significant. The source flux was estimated based on Neil GehrelsSwift Burst Alert Telescope (BAT) data (Krimm et al. 2013 ) 2 and the X-ray light curve was folded in the way similar to the frequency derivative to trace the corresponding flux. The flux was transformed to X-ray luminosity using three simultaneous observations by the Nuclear Spectroscopic TelescopeArray ( NuSTAR ). In the full energy band, 3–79 keV, NuSTAR observed absorbed luminosities of (0.24 ± 0.07) × 10 37 , (0.4 ± 0.1) × 10 37 , and (1.2 ± 0.3) × 10 37 erg s −1 on MJD 56959, 57299, and 58545 (Nabizadeh et al. 2019 ). The luminosities corrected for absorption in the interstellar medium and in the system are consistently about 20 per cent higher. The corresponding count rates measured by Swift / BAT on the same dates are 0.017 ± 0.003, 0.020 ± 0.003, and 0.06 ± 0.03 counts cm −2 s −1 , which imply an average conversion factor of (18 ± 1) × 10 37 erg s −1 (counts cm −2 s −1 ) -1 . With the computed luminosity [Fig. 1(b) ], we now obtain variations of the specific accreted angular momentum [Fig. 1(c) ] with the orbital phase using the equation where I = 10 45 g cm 2 is the moment of inertia of the NS and is the mass accretion rate, which is connected to luminosity L through where ε = 0.15 is the assumed efficiency. It is evident that the spin evolution during the preperiaston flare is complex, showing both spin-up and spin-down episodes. If the mass accretion rate was simply correlated with the transported angular momentum, the NS would be expected to strongly spin-up throughout the flare. However, the maximum spin-up is already observed before the observed peak of the flux, when maximal accretion torque is naively expected. The observed spin-up rate, however, starts to steadily decrease several days prior to the flux maximum even though the accretion rate continues to increase. In fact, zero spin-up rate is observed at the peak of the flare, and the NS is already spinning down right after the peak. The maximal spin-down rate is then reached several days after the peak of the flare, still at a high accretion rate. 3 DISCUSSION Here, we would like to focus on the discussion of the spin-frequency changes around the periastron. As discussed in the data analysis section, even considering uncertainties in the orbital parameters determined by Koh et al. ( 1997 ), the observed evolution of the frequency derivative over the orbit has a high statistical significance and therefore requires a physical explanation. First of all, it is important to emphasize that in GX 301–2, the observed orbital flux dependence is neither consistent with accretion from a transient accretion disc, nor from a smooth homogeneous wind. However, in an eccentric binary system, the wind may be enhanced in the periastron due to tidal interaction of the NS with the primary (Stevens 1988 ). Based on this result, the flaring has been


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O

density in this domain becomes comparable to the previously introduced offset. Finally, the most interesting result revealed by these plots is that during phase 2 the velocity profiles are most often located very close together and are, moreover, in a good correspondence with the macrospicules’ leading edge trajectories (black line in Fig. 8 ) discussed in the next section. Fig. 7 Reconstructed evolution of the macrospicule’s one-dimensional velocity field as projected on the vertical axis. Upward velocities are shown in blue and downward in red. Fig. 8 Velocity profiles at varied heights from 15 to 40 Mm (coloured lines). The straight black line corresponds to the parabolic fit of the macrospicule’s leading edge trajectory. Table 1 Obtained parameters of the macrospicules. Notes. Here, deceleration is the actual value measured from the parabolic fit, while ballistic deceleration is calculated based on Eq. ( 13 ). Beyond that, for one of the macrospicules (No. 10 in Table 1 , which was chosen for illustration in Figs. 4 – 8 , and 10 ) we identified a train of three compression waves which start to propagate upwards from the macrospicule’s base in the early phase of its motion. The waves are scarcely seen in the initial density map, but are clearly identifiable in the subtracted high-frequency component (Fig. 5 c) as a set of fringes. They arise mainly from intensity variations, and we are inclined to interpret them as the magneto-acoustic waves since the intensity change is more likely to result from the density oscillations, rather than from a change in temperature or in ionisation degree. The inclination of the fringes and the distance between them yields a varying propagation velocity, which gradually decreases from km s for the first wave to km s for the last one, and a wave period of roughly s. Most probably, the leftovers of these waves in the filtered density map are responsible for the quasi-periodic disturbances in the velocity field, seen in Fig. 8 at , , and min. 3.2. Leading edge trajectories Along with the reconstruction of the velocity field, we studied trajectories of the apparent end points of the same 18 macrospicules, and for 15 of them we found these points to follow parabolic trajectories with high precision (Fig. 4 d). The obtained trajectory parameters corrected for the inclination angle are presented in Table 1 . The decelerations typically range from 160 to 230 m s and initial velocities (defined as the extrapolated velocity at zero height) from 80 to 130 km s. Two macrospicules, however (Nos. 2 and 4), have significantly higher decelerations, which are even larger than gravity on the solar surface m s, and correspondingly have significantly higher initial velocities. Also, the maximum heights reached by the macrospicules are typically from 30 to 45 Mm, and the lifetimes are in the range of 10–20 min, which is in a good agreement with earlier studies ( Withbroe et al. 1976 ; Dere et al. 1989 ; Karovska Habbal 1994 ).


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ACKNOWLEDGEMENTS We like to thank the referee Prof. Mathias Steinmetz for a constructive and insightful report. Software credit : astropy (Astropy Collaboration 2013 ), bmcmc (Sharma 2017a ), chainconsumer (Hinton 2016 ), daft https://github.com/dfm/daft , ipython (Pérez Granger 2007 ), matplotlib (Hunter 2007 ), numpy (van der Walt, Colbert Varoquaux 2011 ), pandas (McKinney 2012 ), and scipy (Jones et al. 2001 ).


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et al. ( 1994 ), 17 = period redetermined by combining Catchpole Feast ( 1981 ), and WBF, 18 = OMC (Mas-Hesse et al. 2003 ), 19 = various literature -band data. The full table is available at the CDS. Appendix B: Mass-loss rates, luminosities, and fits to the SEDs Tables B.1 and B.2 list the parameters of the models which best fit the observed data. These include the identifier, information on the atmospheric model used (effective temperature, , and for the C stars, C/O ratio), grain size and dust type, luminosity, dust optical depth in the -band, mass-loss rate, whether was fitted (1) or fixed (0), , whether was fitted or fixed, the slope of the denisity law, whether was fitted or fixed, outer radius (in units of inner radius), and the reduced . These tables are published in its entirety at the CDS; a portion is shown here for guidance regarding its form and content. The reduced chi-square value is given for reference only. There is a large range in values, and sometimes the values are far larger than unity. This is in part related to the construction of the SED and the available photometery (and error) which can be very different across sources, and the role of variability. Figures B.1 and B.2 show the best-fitting models, and give a subjective indication of the quality of the fits. The top panel shows the observed SED and IRS spectrum and the fitted model on an absolute scale, while the bottom panel shows the IRS spectrum and the model (the blue line), scaled to a quasi-continuum point based on the average flux in the 6.35–6.55 m region. Horizontal lines near the bottom indicate wavelength regions excluded from the fit. Table B.1 Fit results of the C-star sample. Notes. Column 1 lists the identifier. Column 2 lists the information on the model atmosphere that is used as (in K)/((C/O)). Column 3 indicates the grain size and type: The number after the indicates the grain size in m. Then follows the proportion of AMC (zubko): SiC (Pitm): MgS (Hofm) = 100 : x : y. Column 4 lists the luminosity. Column 5 lists the dust optical depth at 0.5 m, and Col. 6 lists the total mass-loss rate (assuming an expansion velocity of 10 km s, and a dust-to-gas ratio of 0.005). Column 7 indicates if the optical depth was fitted (, or fixed ). Column 8 lists the temperature at the inner dust radius, and Col. 9 indicates if this temperature was fitted (, or fixed ). Column 10 lists the slope of the density law, and Col. 11 indicates if this temperature was fitted (, or fixed ). Column 12 lists the outer radius in units of the inner dust radius. Column 13 lists the reduced of the fit. The full table is available at the CDS. Table B.2 Fit results of the M-star sample. Notes. Column 1 lists the identifier. Column 2 lists the information on the model atmosphere that is used as (in K)/. Column 3 indicates the grain size and type: The number after the indicates the grain size in m. Then follows the proportion of olivine (MgFeSiO), corundum, metallic iron, and


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We thank the anonymous referee for valuable feedback that helped improve the paper. The research leading to these results was funded by the Spanish Ministerio de Economía y Competitividad (MINECO) under grants AYA2012-32295, ESP2015-68964-P, AYA2016-76682-C3-2-P, and AYA2015-54346-C2-1-P. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, progs. 077.B-0151A and 081.B-0042A. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA), and the Canadian Astronomy Data Centre (CADC/NRC/CSA). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.