O O O O O O 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 B-Software 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 B-Citation I-Citation O B-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 O O O O O O O O B-Software O O O O O O O O O O O B-Database B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O O B-Mission O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation 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 B-Instrument I-Instrument O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O B-Wavelength B-Wavelength O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O B-Instrument I-Instrument I-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Observatory O B-Citation I-Citation I-Citation I-Citation 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 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 B-Wavelength O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O

in the ionization balance in photoionization equilibrium (Ferland et al. 1998b ; Ferland 2003 ). In order to provide reliable DR rate coefficients for use in plasma modeling, the storage ring DR experiments combined with the new calculations with the AUTOSTRUCTURE code and the FAC code have made huge progress in the past few decades. Storage ring DR experiments of highly charged iron have been performed with almost all of the charge states for Fe 7+ to Fe 22+ (Savin 2007a ; Schippers 2012 ). Following the first paper to describe the calculation goals and methodology (Badnell et al. 2003 ), a series of the papers have been published based on the calculations by the AUTOSTRUCTURE code, and the calculated data are collected into the recent database CHIANTI (Dere et al. 2009 , 2019 ). By comparison of these calculations and the storage ring experiments, DR rate coefficients for carbon-like and oxygen-like ions have been identified as the most urgent needs for astrophysical applications, and therefore precision measurements of the DR rate coefficients of these ions that are abundant in astrophysical plasmas to benchmark the theories are required. Calcium is an abundant element in the solar corona and also in high-temperature astrophysical plasmas. Emission lines from highly charged calcium ions play an important role for diagnostics and modeling in astrophysical plasmas as well as fusion plasmas (Del Zanna Mason 2018 ; Träbert et al. 2018 ). For a C-like Ca 14+ ion, the previous observations were mostly from solar flare and solar wind based on the lines that are largely in the EUV range. These EUV lines are usually from the transitions within the 2 s 2 2 p 2 –2s 2 2 p 2 and 2 s 2 2 p 2 –2 s 2 p 3 configurations. The spectral lines of 555 Å and 1098 Å from 2 s 2 2 p 2 –2s 2 2 p 2 transitions of Ca xv were measured and identified by the Solar Ultraviolet Measurements of Emitted Radiation spectrometer on the Solar and Heliospheric Observatory (SOHO). With the Skylab observation, the ratios of the 181.90 or 215.37 Å lines versus the resonance EUV line at 200.98 Å are excellent density diagnostics at high densities of solar flares (Dere et al. 1979 ). This Skylab observation of Ca xv emission lines to derive the electron density was later on confirmed by a new data analysis and a measurement from the TEXT tokamak plasma (Keenan et al. 1988 , 2003 ). The Ca xv 181.90/200.98 Å ratio was also investigated by the observations of solar coronal emission lines with the Extreme-Ultraviolet Imaging Spectrometer (Culhane et al. 2007 ) on Hinode spacecraft (Kosugi et al. 2007 ), as discussed by Warren et al. ( 2008 ) and Del Zanna ( 2008 ), and several Ca xv emission lines at EUV range are formed at about 4MK and the electron density measurements at these temperatures are potentially important for understanding the coronal heating mechanism. In addition to the EUV emission lines, transitions of C-like Ca xv within the 2 s 2 2 p 2 –2 s 2 2 p 3 d configurations


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

M.B.S. acknowledges a PhD student fellowship from IISER, Pune. We acknowledge insightful comments from the anonymous referee that has helped us improve the paper.


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

other hand (lower panel), the I b / I n ratio is only slightly dependent on C . 6 APPLICATION TO A REAL CASE: SN 1006 6.1 Why SN 1006 In the following, we shall apply the methods derived so far to a real case, refining them whenever required. The Balmer emission along the northwestern limb of SN 1006 represents for this an almost perfect case: observations with high spatial and/or spectral resolution, on which to test and use our models, are available; a shock velocity () high enough to limit the role of CE processes (this simplifies the models and makes them more reliable); structures near the limb that appear rather well ordered; no evidence of efficient CR acceleration, which justifies neglecting the effect of CRs in the analysis. With reference to the shock speed, Ghavamian et al. ( 2001 ) measured a spectral width of , from which for a low T e / T p ratio they derived a shock speed of . A lower shock velocity, , follows instead from the model of Morlino et al. ( 2013b ): for a more detailed and updated discussion, see Raymond et al. ( 2017 ). In the following analysis, we shall fix V sh to . With reference to CR acceleration, a low efficiency in the northwestern limb can be deduced from several results of observations: (1) the absence of non-thermal X-ray emission (Bamba et al. 2003 ; Winkler et al. 2014 ); (2) a non-detection of TeV (Acero et al. 2010 ) and GeV gamma-rays (Xing et al. 2016 ); moreover, from the analysis of Balmer emission, two additional pieces of information point towards a low CR acceleration efficiency: (3) the FWHM (full width at half-maximum) of the narrow line is (Sollerman et al. 2003 ), compatible with being produced by unperturbed ISM with T = 10 4 K, pointing toward the absence of a CR precursor able to heat the upstream plasma; and (4) an absence of evidence of any Hα precursor in front of the shock ( R + 07 ). 6.2 Some recent high-quality observations In this section we summarize some results of two relevant papers, Raymond et al. ( 2007 , hereafter R + 07 ) and Nikolić et al. ( 2013 , hereafter N + 13 ), in which Balmer emission from some areas along the northwestern limb of SN 1006 has been observed in great detail, and that contain a wealth of information, which will be used in the present work. The former paper is based on a very deep HST /ACS image covering most of the Hα emission from that limb, and the superb spatial resolution of that image (an FWHM of about 0.13 arcsec, corresponding to about , where d 2 is the distance of SN 1006 in units of ) allows one to probe scales shorter than the collisional mean-free paths, and therefore to resolve the physical structure of the filaments. The latter paper, instead, presents a map of a selected portion of the northwestern Hα limb of SN1006, roughly corresponding to ‘Regions 26–29’ (as dubbed by R + 07 ). The instrument used, VIMOS in the IFU mode on the Very Large Telescope (VLT), allows both good spatial resolution (with a pixel size 0.67 arcsec,


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2000 ). The long-term X-ray pulse profile and pulsed fraction evolution, such as that presented in Section 4.1 , could be evidence for the slow, plastic deformation of the crust needed to produce slower regions of superfluid (Woods et al. 2004 ; Thompson et al. 2002 ). Alternatively, regions of the outer core could be involved as a result of the strong magnetic fields. Magnetar strength fields provide a strong pinning of vortices to flux tubes in the outer core, which leads to a rotation lag between the normal and superfluid components, which, when relaxed, would lead to a spin-down event (Kantor Gusakov 2014 ). In typical rotation-powered pulsars, the expected internal nature of these spin-up glitches is argued to be indicated by the lack of observed radiative changes. This “radiatively quiet” condition does not hold for many glitches in magnetars. Many magnetar glitches are accompanied by drastic changes in their X-ray flux and pulse profiles (e.g., Kaspi et al. 2003 ; Dib et al. 2009 ). This could indicate that external forces are at play in radiatively loud glitches, and these external forces may lead to the net spin-down events reported in several magnetars, including the new event reported here. We have compiled a list of all published confirmed and candidate net spin-down glitches in Table 3 . In this list, we present the magnitude of the change in spin frequency, . For net spin-down glitches that are due to overrecovering spin-up glitches, the of the glitch is presented. For events where there is no sign of a recovery, we show an upper limit for the time during which the spin-down had to occur. We also note that 6 of the 7 reported net spin-down glitches are accompanied by radiative changes. 8 8 This increases to 6 of 6 if we ignore the disputed event; see Table 3 . This is a much higher fraction of radiative activity than seen in spin-up events, where only 5 of 22 timing anomalies were accompanied by radiative changes (Dib Kaspi 2014 ). Table 3 Reported Net Spin-down Glitches Notes. a Accompanied by decaying spin-up glitch with Δ ν = 10.8(4) × 10 −5 Hz. b Possibly accompanied by second glitch event. c Accompanied by decaying spin-up glitch with Δ ν = 2.0(4) × 10 −7 Hz. d Accompanied by decaying spin-up glitch with Δ ν = 5.1(5) × 10 −8 Hz. e Disputed events, see the notes below. f Not seen in analysis of same data by Dib Kaspi ( 2014 ). For the net spin-down glitches in which the net spin down is measured to be due to an overrecovery, we also report the recovery fraction, Q . Recovering glitches are often classified by their recovery fraction, defined as . In younger pulsars, when recoveries are observed, Q tends to be larger than in older pulsars (Wang et al. 2000 ). For the new glitch we report here, we measure . Glitches with have only been seen twice before: once following the magnetar-like outburst of the pulsar PSR J1846−0258 that is powered by a high magnetic field rotation, which had (Livingstone et al. 2010 ), and once during


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From the ∼56% remaining, 70% of them have a counterpart in either 1RXS or 2RXS catalogs. In this paper, we focus on and perform an extensive visual inspection and literature search of the other 30% of the systems. Of these objects, we describe in detail the analysis and characterization of a pilot sample of 13 candidates. We determined a spectroscopic redshift for each cluster candidate finding that most of them are local systems ( z ≲ 0.05), and are very extended (significant X-ray emission traced out to more than 10 arcmin radius). Moreover, all these objects have fluxes above the limit of the 1RXS and 2RXS catalogs. We argue that they might have been missed because of the source finder used in previous works, that is, the sliding-cell algorithm, which is not optimal for finding such low-flux, very extended objects. Our pilot sample also reveals that the surface-brightness distribution of the systems is flatter than the usual profile, that is β 2/3, and that the missed systems are located in the group regime given the determined masses from galaxy velocity dispersions or a L X − M scaling relation ( M 500 ≲ 10 14 M ⊙ ). In a subsequent paper, we will present and discuss in detail the remaining cluster candidates that we have found. Appendix A: Additional figure Fig. A.1. From left to right : RASS photon images ( left ), optical images, integrated count rates profiles, and spectroscopic redshift histograms ( right ) for the galaxy groups in our pilot sample. The optical images are from ATLAS (composed of g , r , i bands, group 2, 6, 10), SDSS (composed of g , r , i bands, group 1, 3, 7, 8, 9) or DSS ( r band, other groups). The images have a 1 × 1 deg 2 size, except for the ATLAS images, which are 0.30 × 0.30 deg 2 . The red cross shows the position of the group candidate. The magenta plus signs display the location of 1RXS or 2RXS sources. The cyan diamonds show the positions of galaxies used for redshift determination. The white asterisks show the positions of known optical galaxy groups/clusters obtained from NED. The green contours are obtained from the corresponding wavelet-filtered images, and the blue circle shows the extent value (i.e., the core radius) of the group. The integrated count rates profile is background subtracted (solid line). The dashed curves give the 1 σ statistical error of the count rates. The vertical and horizontal dot-dashed lines indicate the aperture radius and the count rates used for the primary photometric results. The dotted curve shows the β model of the cluster modelling used to extrapolate to r 500 (see Sect. 4.3.2 for further details). In the spectroscopic redshift histograms the redshift values are taken for all galaxies within a box of 1 × 1 deg 2 centered on the group position with z 0.10 from NED. The total number of galaxies used in each redshift determination is given by the second number displayed in the upper right corner of each panel (see also Table 3 ). The redshift distribution is fitted


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the point sources matched between the two shortest wavelength IRAC bands. To illustrate the locations of detected sources in our catalog, we present in Figs. 5 through 9 the 3.6 m image of each galaxy with the positions of detected sources overplotted, followed by an image of the galaxy without sources shown. For each galaxy, red points denote the location of point sources not likely to be associated with the galaxy, while green points demarcate the regions inside isophotes for the Kron radius for all galaxies but NGC 2366, where the isophote described in de Vaucouleurs et al. (1991) was used. Consequently, the green points are more probably actual sources associated with each galaxy. Figures 10 through 14 show color-magnitude diagrams (CMDs) of [3.6] versus [3.6][4.5] for each galaxy. The points follow the color scheme from the images showing each galaxy, with green points representing sources within the isophotes for with each galaxy, and red points sources in the field of each galaxy. For each magnitude bin, the average uncertainty was computed for both the [3.6] magnitude and [3.6][4.5] color, and is plotted as an ellipse on the left hand side of the plot. For reference, lines are drawn to show the completeness limit of mag and the color [3.6][4.5] = 0, where most stars lie in the plot. In terms of absolute magnitudes, the [3.6] limit corresponds to detections of all objects brighter than in every galaxy. One other interesting feature in the plot was explained by Khan et al. (2015c) . For both NGC 55 and NGC 253, the two galaxies with the most sources of those studied in this work, one can see a “break” at about the same magnitude as the completeness limit. This feature is representative of the two different populations in the photometry, one physically associated with the galaxy, and another simply sharing the same region of sky. Khan et al. (2015c) calls the second population “contaminants”. This population contains foreground stars near the [3.6][4.5] color of 0, some Milky Way Halo late-type giants and unresolved background galaxies in other regions of the CMD. Red supergiants (RSGs) have been empirically shown to exist in the region of negative color space ( Bonanos et al. 2009 , 2010 ). This is due to a suppression of the flux in the 4.5 m photometry owing to molecular bands, most prominently CO ( Verhoelst et al. 2009 ). However, spectroscopic investigations into the individual stellar components of Local Group dwarf irregular galaxies have discovered 15% of new RSGs at positive colors in CMDs for those galaxies ( Britavskiy et al. 2014 , 2015 ). Fig. 10 Colormagnitude diagram for sources in the field of NGC 55. All photometrically measured sources are marked with a red dot, while those residing within the isophotal limits of the galaxy are represented by green dots. Overplotted are lines denoting the limiting magnitude of 18.0 and a [3.6][4.5] color of 0. On the left are ellipses corresponding to the average uncertainty for


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by the FWHM. Given the nearly symmetric double-peaked profile of A370p_z1 and the small peak separation, we restrict our analysis to relatively small N H i and v exp values because it is well known that high column densities and shell velocities would significantly broaden the line and erase the blue peak, respectively (Verhamme, Schaerer Maselli 2006 ). We perform a quantitative comparison between the observed line profile and the models using the χ 2 statistic. We find that models minimizing the reduced χ 2 preferentially select low N H i (), static geometries ( v exp = 0), low dust content, small b values ( b = 20) and relatively broad input lines (). We show the best-fitting model in Fig. 4 which corresponds to the following parameter set: . We can derive the LyC escape fraction from the best-fitting column density = 99 per cent, where σ 912 = 6.35 × 10 −18 is the H i photoionization cross-section at the Lyman limit. While several models could match the positions of peak emission within the errors, the model is the only one to reproduce the shallow central depression of the profile which is the important signature of a low H i opacity (Fig. 4 ). Searching a finer parameter grid is beyond the scope of this paper, but we note that even when adopting a higher column density cm −2 , the escape fraction remains very high (94 per cent). Figure 4. Comparison of RASCAS models, smoothed by the resolution of X-Shooter, of Lyman α transfer through non-expanding shells of homogeneous gas with the observed Lyman α profile. The best-fitting model (blue) has which correspond to a high LyC escape fractions . We also show examples of models with (dashed orange, dash–dotted green), which would imply . 3.2 Did A370p_z1 self-ionize its local H <sc>ii</sc> bubble? The detection of the blue peak in the Lyman α indicates A370p_z1 sits in a large ionized bubble, otherwise the damping wing of even a partially neutral IGM would have absorbed it. Given its high escape fraction, we now consider whether A370p_z1 could have self-ionized its local H ii bubble. The blue wing extends to λ = 9479.2 Å, from the line centre, corresponding to a physical distance r H ii > 0.26 ± 0.04 pMpc. This estimate neglects any velocity offset between the Lyman α absorption dip from which we have derived the redshift and the systemic redshift as defined by more reliable tracers such as nebular absorption lines. These velocities are however found to be (Gazagnes et al. 2020 ), which, in the worst case, would therefore require a larger ionized bubble for the blue wing to be transmitted (≲ 0.5 pMpc). We also neglect peculiar velocities of the galaxy with respect to the ionized bubble gas which would redshift(blueshift) the Lyman α photons and decrease(increase) the bubble size needed for the blue wing to escape. We now estimate the volume that could have been reionized by A370p_z1 by redshift z = 6.803 and whether its radiation is sufficient to reduce the opacity of the surrounding gas to


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

is a mid-stage merger consisting of two face-on galaxies which appear to overlap and have a projected separation of ∼84 (6.3 kpc). Prominent rings/arms in each galaxy contain the bulk of the visible star clusters (Figure 19 ). The maximum A V adopted for this galaxy is 1.0 mag of visual extinction (see Figure 20 ; Miralles-Caballero et al. 2012 ). The observed and derived properties for the star clusters identified in this galaxy are given in Tables 15 and 16 , respectively. 2MASX J08370182-4954302 2MASX J08370182-4954302 is a mid-stage merger containing two nuclei separated by ∼066 (0.36 kpc). Surrounding the nuclei are multiple bright star clusters in a spiral ridge just northwest and west of the nuclei (Figure 21 ). The maximum A V adopted for this galaxy is 3.7 mag of visual extinction (see Figure 22 ; Rich et al. 2012 ). The observed and derived properties for the star clusters identified in this galaxy are given in Tables 17 and 18 , respectively. NGC 2623 Evans et al. ( 2008 ) discuss the detailed morphology of this galaxy at length. NGC 2623 is a late-stage merger with dust lanes running along its tidal tails into the nucleus. Several bright clusters are distributed throughout the bulge and in a “pie-wedge” concentration south of the nucleus (Figure 23 ). The maximum A V adopted for this galaxy is 1.9 mag of visual extinction (see Figure 24 ; Privon et al. 2013 ). The observed and derived properties for the star clusters identified in this galaxy are given in Tables 19 and 20 , respectively. UGC 04881 UGC 04881 is an early-stage merger containing two nuclei separated by ∼11′′ (9 kpc). Spiral dust lanes and strings of star clusters surround the NE nucleus. In the SW nucleus, a linear distribution of star clusters and a prominent dust lane are seen (Figure 25 ). The maximum A V adopted for this galaxy is 1.9 mag of visual extinction (see Figure 26 ; González-Martín et al. 2009 ). The observed and derived properties for the star clusters identified in this galaxy are given in Tables 21 and 22 , respectively. IC 2545 IC 2545 is a late-stage merger being viewed face on. Dust lanes and strings of star clusters extend from two unresolved nuclei separated by ∼08 (0.54 kpc) in the center of the galaxy. Multiple star clusters are also visible throughout the tidal tails (Figure 27 ). The maximum A V adopted for this galaxy is 4.0 mag of visual extinction (see Figure 28 ; van den Broek et al. 1991 ). The observed and derived properties for the star clusters identified in this galaxy are given in Tables 23 and 24 , respectively. NGC 3256 NGC 3256 is a late-stage merger containing a large number of star clusters along the inner (∼20′′, or 4 kpc) spiral structure of the nuclear region. The spiral dust lanes extending from the nucleus give this galaxy pockets of high and low extinction (Figure 29 ). The maximum A V adopted for this galaxy is 3.3 mag of visual extinction (see Figure 30 ; Rich et al. 2012 ). The observed and derived


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

field is almost horizontal and the field lines are concave-up. These are also locations where plasma can accumulate and eventually form a prominence (Aulanier Demoulin 1998 ; Lionello et al. 2002 ; van Ballegooijen 2004 ; Dudík et al. 2008 , 2012 ; Mackay van Ballegooijen 2009 ; Gibson 2015 ). The orange magnetic field lines extend up to z = 0.01 above the magnetic dips. If we scale our active region to the size of a typical active region hosting quiescent prominences, i.e., about 300 Mm, then orange magnetic field lines extend up to km above the magnetic dips. This is comparable with the (chromospheric) pressure scale height, therefore resulting in a reasonable proxy of quiescent prominences as the ones discussed in Filippov Den ( 2001 ). A comparison between each simulation suggests that different photospheric motions may result in prominences with similar shapes, but different morphologies. The side views of “Run C” show that the prominence is fragmented in its central part, i.e., it has a region devoid of dips at low altitudes, and it is also asymmetric: one of its ends is higher than the other one. This is not the case for “Run D1” where the distribution of the dips seems to follow a more homogeneous circular shape. One difference between the two cases is the asymmetry of the flows that formed the flux rope: the flows in “Run C” have a higher degree of asymmetry compared with “Run D1.” The details of the formation process may therefore influence the exact morphology of the flux rope and that of the dips, with these differences becoming more difficult to detect in the proximity of the flux rope’s axis ( ZAG15 ). The right-hand side panels show the evolution of the system at three different times. The configuration in the top panels is stable, the one in the middle is unstable in the low diffusion regime, but stable in the high diffusion regime, while the configuration in the bottom panel is unstable also in the high diffusion regime. The top-two horizontal yellow lines indicate the critical decay index and critical height for the onset of the instability under “high” and “low” diffusion conditions (see Table 1 ), while the bottom lines in all three models indicate the height where the decay index is n = 1.1. For “Run C” (respectively, “D1,”“D2”) at the time of the onset of the eruption in “low” diffusion regime, the apex of the axis of the MFR, i.e., the location where the stability criteria should be evaluated, has reached a height where the decay index is n = 1.4 (respectively, ) while the highest magnetic dips reach a height where n = 1.1. Interestingly, this value n = 1.1 is independent of the particular formation process in the three cases presented here. This suggests that the apparent instability criterion as evaluated at the location of the prominence is less sensitive to the flux rope formation process compared to when it is evaluated at the axis of the flux rope. Similarly to the flux ropes discussed in ZAG15 , these MFRs are


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We thank Chris Hales, Anita Richards, Neal Jackson, Lee Whittaker and Joe Zuntz for useful discussions. We further thank Chris Hales, Eva Schinnerer and Vernesa Smolcic for providing us with the partially processed VLA data. MLB is an STFC Advanced/Halliday fellow. BT, IH and MLB are supported by an ERC Starting Grant (grant no. 280127 ).


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

components, respectively. The solid red curve is the sum of these two models. Fig. 8 Schematic representation of the spherically symmetric model for the molecular components of Arp 299A showing approximate spatial scales. Most of the molecular absorption is formed in the outer layers of the dense, most compact C component while the HO emission in the submillimeter seems to originate in the more optically thin C component. A tentative inflowing C component is included to account for the redshifted ground state OH doublet at m. Fig. 9 Reduced for the observed high-lying HO lines in our grid of models with . Fig. 10 for the OH at m with different values of applied to the best fit model of the inner component found using the HO lines. 3.3. Outer component Even in the best fit model for the inner component there is flux missing in the low-lying OH and and HO lines detected with PACS and, especially, the low-lying HO lines detected with SPIRE. To account for this missing flux in the models, a less excited and more extended component is required. To constrain the parameters of this outer component we have followed the same general procedure as for the inner component, but now for the low-lying lines normalized to the flux of the HO m line. In this process we have also taken the best fit model for the inner component into account. The observed line ratios are best reproduced with a dust opacity in the range . In this component collisional excitation becomes non-negligible for cm, but in these models the undetected HO m line goes into emission, favoring models with lower where collisional excitation is negligible. The reduced for our grid of models at the preferred dust opacity is presented in Fig. 11 . The line ratios are best reproduced with dust temperatures between and K, and HO columns between and cm. To also account for the absolute fluxes, the component should have a radius of pc. The best fit is achieved with , K, cm and pc. Fig. 11 Reduced for the observed low-lying HO lines in our grid of models with for the outer component, taking the contribution from the inner component into account. In Fig. 12 we present the reduced for the OH doublets in the outer component for different values of applied to the best fit model found for HO, now taking the OH contribution from the inner component into account. The OH m doublet which is redshifted by km s is not included here. The best fit is achieved with a column density of OH in the range to cm, corresponding to an OH/HO ratio in the range to . Applying a similar process to the upper limits of the OH doublets we get an upper limit to the OH column density of cm. Fig. 12 Reduced for the OH doublets, except for OH m , with different values of applied to the best fit model of the outer component found using the HO lines. 3.4. Extended component Most of the flux in both the HO and the OH lines is reproduced with the two components described in Sects. 3.2 and 3.3 . The ground state OH doublet at m is,


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

to the GCs in M20, we derive a dynamical mass enclosed within the outermost GC (i.e. 2.2 kpc) of 3.48 (± 0.84) × 10 8 M ⊙ , with the uncertainty given by the range in potential and orbital anisotropy described above. Our TME dynamical mass is larger than the GC-based half mass, but agrees within the uncertainties. Allowing for a reasonable range in γ would increase the uncertainty to around ±50 per cent; where assuming a lower (higher) value of γ would lead to a reduced (increased) TME mass. The resulting mass-to-light ratio from our TME analysis is M 1/2 /L 1/2 = 12.7 ± 3.7. Forbes et al. ( 2019 ) detected 20 GC candidates associated with NGC 5846_UDG1. If we assume the same mean GC luminosity function turnover magnitude (i.e. M V = –7.3) and width as found by Miller Lotz ( 2007 ) for dE galaxies in the Virgo cluster, then the inferred total GC population is around 45. For this count, the Burkert Forbes ( 2020 ) relation between the number of GCs and the halo mass implies a total halo mass of ∼2 × 10 11 M ⊙ . Given that there are several unknowns in translating the detection of GC candidates into an estimate of the total GC system, it is useful to note that M20 confirmed at least a dozen GCs associated with NGC 5846_UDG1. This gives a lower limit on the total halo mass with this relation, of 0.6 × 10 11 M ⊙ . Both of these total halo mass estimates far exceed the total stellar mass of 1.1 × 10 8 M ⊙ . For comparison, M33 has the same inferred total halo mass of 2 × 10 11 M ⊙ (Seigar 2011 ) but its stellar mass is some 50× larger. Thus, NGC 5846_UDG1 can be described as having a dwarf-like stellar mass with an overly massive dark matter halo. Assuming a total halo mass of 2 × 10 11 M ⊙ as described above, we can compare our half mass and TME mass with different halo mass profiles. We chose three profiles, namely the universal NFW profile (Navarro, Frenk White 1996 ), the mass profile resulting from the dwarf galaxy simulations of Di Cintio et al. ( 2014 ), which resembles a core-NFW profile, and the observationally motivated mass profile for dwarf galaxies from Burkert ( 1995 ). For details of the NFW and Di Cintio et al. profiles, see the appendix of Di Cintio et al. ( 2014 ). We show these three profiles, with the same total halo mass, compared to our half and TME masses measured at small radii in Fig. 5 . The plot shows that our mass measurements lie between the Di Cintio and Burkert mass profiles for a total halo mass as given by the total number of GCs. This suggests that NGC 5846_UDG1 may be better represented by a core mass profile as predicted in some simulations (e.g. Carleton et al. 2019 ) than a cuspy one. However, we cannot, at this stage, rule out other mass profiles and/or different total halo masses. Similar conclusions, favouring a cored mass profile, were reached by Gannon et al. ( 2020 ) for VCC 1287, and by Wasserman et al. ( 2019 ) for DF44. Figure 5. Halo mass profiles. Three halo mass profiles (Navarro et al. 1996 ,


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ACKNOWLEDGEMENTS We thank Martin Shepherd, David Hawkins, Russ Keeney, and Erik Leitch for advice and assistance with the design and construction of the backend. The work at the California Institute of Technology and Owens Valley Radio Observatory was supported by National Science Foundation (NSF) awards AST-0607857, AST-1010024, AST-1212217, and AST-1616227, and by NASA award NNX15AF06G. The work at Oxford was supported by funding from STFC, the Royal Society and the University of Oxford. CD acknowledges support from an ERC Grant no. 307209. OGK acknowledges the support of a Dorothy Hodgkin Award in funding his studies while a student at Oxford, and the support of a W.M. Keck Institute for Space Studies Postdoctoral Fellowship at Caltech. This work formed part of MAS’s PhD thesis (Stevenson 2013 ).


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The AGILE Mission is funded by the Italian Space Agency (ASI) with scientific and programmatic participation by the Italian Institute of Astrophysics (INAF) and the Italian Institute of Nuclear Physics (INFN). Investigation supported by the ASI grant I/089/06/2. We thank the ASI management for unfailing support during AGILE operations. We acknowledge the effort of ASI and industry personnel in operating the ASI ground station in Malindi (Kenya), and the data processing done at the ASI/SSDC in Rome: the success of AGILE scientific operations depend on the effectiveness of the data flow from Kenya to SSDC and on the data analysis and software management. We also acknowledge the use of innovative tools that are under development within the United Nations “Open Universe” initiative.


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The authors wish to thank the anonymous referee for a constructive report, which has improved the paper. We also wish to thank the Aspen Center for Physics for hosting two summer workshops, “The Obscured Universe: Dust and Gas in Distant Starburst Galaxies” in summer 2013 and “New Frontiers in Far-infrared and Sub-millimeter Astronomy” in summer 2016, whose stimulating conversations led to this work. The Aspen Center for Physics is supported by National Science Foundation grant PHY-1066293. C.M.C. thanks the National Science Foundation for support through grant AST-1714528. Additionally, C.M.C. and J.A.Z. thank the University of Texas at Austin College of Natural Sciences for support. J.S. thanks the McDonald Observatory at the University of Texas at Austin for support through a Smith Fellowship. E.dC. gratefully acknowledges the Australian Research Council for funding support as the recipient of a Future Fellowship (FT150100079). J.A.H. acknowledges support of the VIDI research programme with project number 639.042.611, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). S.L.F. acknowledges support from an NSF AAG award AST-1518183. This work relies in part on the COSMOS survey data set. COSMOS is based on observations from the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by AURA Inc., under NASA contract NAS 5-26555. It is also based on data collected at: the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan; the XMM-Newton and Herschel Space Observatory , ESA science missions with instruments and contributions directly funded by ESA Member States and NASA; the European Southern Observatory, Chile; Kitt Peak National Observatory, Cerro Tololo Inter-American Observatory, and the National Optical Astronomy Observatory, which are operated by AURA, Inc., under cooperative agreement with the NSF; the National Radio Astronomy Observatory, which is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc.; the Canada–France–Hawaii Telescope operated by the National Research Council of Canada, the Centre National de la Recherche Scientifique de France and the University of Hawaii; and the James Clerk Maxwell Telescope, which is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, the Operation, Maintenance and Upgrading Fund for Astronomical Telescopes and Facility Instruments, budgeted from the Ministry of Finance (MOF) of China and administrated by the Chinese Academy of Sciences (CAS). Many of the data sets this paper and analysis rely on were obtained on the summit of Maunakea on the island of Hawai’i. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.


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ACKNOWLEDGEMENTS MB and FH acknowledge partial financial support from the INFN TEONGRAV specific initiative. MB acknowledges the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support. This work was supported by the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904. AS is supported by a University Research Fellowship of the Royal Society. This work has made use of the Horizon Cluster, hosted by the Institut d’Astrophysique de Paris. We thank Stephane Rouberol for running smoothly this cluster for us.


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

measure the target power spectrum , and ψ’s PDF, from the SB simulation. In using both from a single realization, the results may depend on peculiarities in that realization. The limitation is due to the lack of an available software to produce accurate fitting functions for the power spectrum and PDF of ψ. This introduced dependence is not a problem, as long as one has the aim of isolating the contribution from the PDF and the correlation of ψ to the specific realization examined, to assess how much information they convey with respect to the exact result. To emulate the final ψ field, we set the phases of the pre-translation Gaussian field to the phases of the initial density field of the realization. We do not smooth the measured ψ field, because both the power spectrum and the PDF are measured at the grid level, and one can check that the ψ field variance is already consistent with its power spectrum variance integrated up to the Nyquist frequency. In Fig. 12 , we can see that the PDF of the ψ realization from ITAM matches the one of the N -body simulation (much better than muscle , and particularly 2LPT), as it should by the virtue of the translation transform equation ( 2 ). Likewise, the Lagrangian-space ψ power spectrum of ITAM matches that of the N -body simulation better than the other prescriptions, as shown in Fig. 13 . The two standard simulation schemes have a mismatch, with 2LPT diverging the most at small scales and muscle departing the most on large scales. This confirms the detailed analysis of the power spectra of Lagrangian schemes conducted by Chan ( 2014 ), where it is also found that these techniques come short of matching the power spectrum measured in N -body simulations. Another benchmark of the goodness of a fast simulation scheme is the similarity between the resulting matter density and the N -body matter density. This is generally quantified by means of the cross-correlation spectrum, which for two fields A and B is Figure 12. PDFs of ψ for various schemes. The peak at ψ ∼ −3 is associated with collapsed halo particles. In muscle , halo particles give a Dirac-delta function at ψ = −3 (see equation 43 ). Figure 13. Transfer function of ψ, defined as the ratio of the power spectrum of ψ generated from the fast simulation scheme over the one measured from the N -body realization. The cross-correlations are plotted in the top panel of Fig. 14 . As we can see, the muscle implementation still performs better than ITAM, which in turn is better than 2LPT, at least on smaller scales. Examining this further, 2LPT is almost a local approach, in the sense that it considers the information of each voxel and its nearest neighbours (equation 37 ). ITAM by construction is non-local, as it involves the two-point correlation function. muscle is also non-local, but the non-locality is coming from a smoothing procedure on various scales centred around each voxel (equation 43 ). Considering that the one-point mapping of ITAM is very


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

host halo mass, and the green valley transition time-scale, τ Green , for both disc and elliptical RS satellite galaxies. We select all = 0 RS satellite galaxies that, at the time the galaxy became green ( t Green ), were also satellites (corresponding to of the satellite sample), and calculate the ratio between the satellite galaxy’s stellar mass and the host halo mass, log 10 M * / M 200 , at t Green . Throughout this section host halo mass refers to the halo mass 1 of the central galaxy within which the satellite galaxies are embedded. Fig. 7 shows the green valley transition time-scale, τ Green , as a function of log 10 M * / M 200 at t Green for RS satellite galaxies that are discs (blue dots) and ellipticals (red dots) at = 0. It can be seen that for both disc and elliptical satellite galaxies, τ Green tends to increase with M * / M 200 . This is highlighted by the best-fitting linear regression of the τ Green −log 10 M * / M 200 relation for elliptical (red dashed line) and disc (blue solid line) satellite galaxies. We find that τ Green correlates more strongly with M 200 than with M * , so that satellite galaxies embedded in cluster-sized haloes transition the green valley faster than their same-stellar mass satellite counterparts residing in lower mass haloes. Figure 7. Green valley transition time-scale, τ Green , of satellite galaxies as a function of the ratio between stellar mass and host halo mass, log 10 M * / M 200 , at the time when the galaxy left the blue cloud, t Green . The data points with error bars show the median τ Green values in bins of log 10 M * / M 200 for galaxies that have been satellites since t Green and at = 0 have κ co ≥ 0.4 (shown as blue dots) or κ co 0.4 (shown as red dots). The error bars correspond to the 25th−75th percentiles of the τ Green distribution in each mass bin. The lines correspond to the best-fitting linear regressions. The red satellite galaxies tend to have quenched more rapidly if they are elliptical and if their stellar mass is smaller relative to the total mass of their host halo. This relation is mostly driven by a dependence on halo mass, rather than on stellar mass. Fig. 7 shows that satellite galaxies embedded in clusters (log 10 M * / M 200 − 4 with haloes more massive than ) tend to cross the green valley over shorter time-scales than satellite galaxies residing in lower mass haloes, regardless of the galaxy’s morphological type. However, the spread in the τ Green distribution is large. In the case of central galaxies, although most of them reside in cluster-sized haloes, we do not find any correlation between τ Green and halo mass or M * / M 200 . This is in agreement with previous studies that suggest that environmental quenching is mostly associated with satellite galaxies rather than centrals (e.g. Peng et al. 2010 ; Darvish et al. 2016 ). Central galaxies show properties that are more associated with the galaxies’ stellar mass (i.e. on average more massive galaxies are


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ACKNOWLEDGEMENTS The authors thank V. Bosch-Ramon and an anonymous referee for their useful comments. DK is supported by the Japan Society for the Promotion of Science KAKENHI Grant Numbers JP18H03722, JP24105007 and JP16H02170. MA is supported by the RIKEN Junior Research Associate Programme.


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 O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O B-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Mission I-Mission O O O O O O B-Telescope I-Telescope B-Telescope O O B-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Citation I-Citation I-Citation O O B-Instrument I-Instrument I-Instrument 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 O O O O O O O O B-Instrument 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 B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-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-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

methane possesses strong and distinctive absorption signatures. An annotated list of these attempts can be found in Zahnle et al. (2011) , Knutsen et al. (2021) , and in tabulated form in Pla-Garcia et al. (2019) . Hitchcock Lovelock (1967) pointed out that the composition of the Martian atmosphere could provide clues as to the possible presence of life on the planet. Therefore, methane has long been seen as the most accessible testimony of potential signs of life ( Atreya et al. 2003 , 2007 ) or of a remnant geophysical activity on Mars. Indeed, the presence of methane has such a strong connotation of Mars being potentially an active or even a life-hosting planet, contrary to all other chemical or geophysical evidence suggesting the opposite, that it has attracted the attention of a wide community extending far beyond those interested in Martian atmospheric composition. However, the succession of failed and successful attempts to detect methane has also created a blurred picture, and a comprehensive understanding of the existence and origin of methane on Mars has remained out of reach. Several attempts that were initially presented as positive detections were later either retracted or questioned. This is the case of the Mariner 7 detection (as explained above) and the Canadian-France-Hawaii Telescope (CFHT) observations of Krasnopolsky et al. (2004) – whose spectrum quality raised the suspicion of Zahnle et al. (2011) , who also questioned the seasonal variations of methane found by Geminale et al. (2008) based on a survey carried out with the Planetary Fourier Spectrometer (PFS). Finally, the methane mapping of Fonti Marzo (2010) using the Thermal Emission Spectrometer (TES) was later retracted by the same authors in Fonti et al. (2015) . Of all the detections made between 2003 and 2010, only a few survived the scrutiny of the community. The PFS 2003 detection reported in Formisano et al. (2004) , while bearing evident shortcomings regarding its resolving power and sensitivity, has resisted criticism and remains to this date the first non-rebutted detection of methane in the Martian atmosphere. In addition, Mumma et al. (2009) published the first ground-based evidence of methane collected the same year as the PFS, the scientific implications of which were bolstered by the revelation of puzzling spatial and seasonal variations attributed to a sudden release from the Nili Fossae region. Several studies have explored the chemical ramifications ( Lefèvre Forget 2009 ) as well as the spectroscopic consistency of these detections ( Zahnle et al. 2011 ). These works converged toward the idea that our current understanding of the physics and chemistry governing the Martian atmosphere is incompatible with the observed variable behaviour of methane, which should rely on an extraordinary, yet undefined mechanism. Together with the fact that detections had long lain on the fringe of the detection capability of all instruments used at that time, the


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we take the average over contributions from all pairs of cells (and the third associated cell that is uniquely determined by the triangular condition) that fall into that bin. We do not look at the bispectrum bins unless at least some combination of the wave numbers in that bin satisfies a triangular condition. To avoid counting equivalent triplets multiple times, we impose a condition k 1 > k 2 > k 3 . Fig. A1 shows the average nonlinear and linear power spectra of matter particles from Quijote simulations. We rescaled the linear power spectrum to have a matching amplitude at small wave numbers. The two are reasonably close for large-scale modes (up to k ∼ 0.1 h Mpc −1 after which the additional power in the nonlinear power spectrum becomes visible. The partial erasure of the BAO signal is also visible by eye. Fig. A2 shows the average bispectrum of matter particles from Quijote simulations at z = 0 as a function of the longest wave number. Features in the shape of this three-dimensional function provide additional opportunities for the standard ruler test. Figure A1. Non-linear power spectrum at z = 0 (blue) and a linear power spectrum (black) of Quijote matter particles. The linear power spectrum is measured from particles at z = 99 and rescaled to have a matching amplitude on large scales. Figure A2. Bispectrum of Quijote matter particles at z = 0 as a function of the largest wave number k 1 . Multiple points at the same abscissa show all bispectrum bins that share that value of k 1 but have different values of k 2 and k 3 . We multiply the bispectrum by a factor of k 1 k 2 k 3 . This factor is proportional to the number of fundamental triangles in the bin and separates different points for better visibility. To estimate the covariance of these measurements, , by computing the sample covariance over 8,000 Quijote simulations, X i l are the power spectrum and bispectrum measurements, where the first index goes over the bins and the second index goes over simulations. N sim is the number of simulations. Fig. A3 shows the correlation matrix of these measurements defined as We ordered the measurements so that the first 50 elements are binned P ( k ) up to k max = 0.5 h Mpc −1 . They are followed by binned B ( k 1 , k 2 , k 3 ) arranged in such a way that the bispectrum bin with smaller k 1 goes first (smaller k 2 when k 1 are equal, and smaller k 3 when both k 1 and k 2 are equal). The first 150 bins arranged in this way accommodate all bispectra up to k 1, max = 0.1 h Mpc −1 . The correlation between power spectra at high wave numbers is clearly visible in this plot. The bispectrum measurements are also correlated between themselves and the power spectra but to a lesser extent. Figure A3. Correlation coefficient of the power spectrum (first 50 bins, goes up to k max = 0.5 h Mpc −1 ) and the bispectrum (last 150 bins, goes up to k 1, max = 0.1 h Mpc −1 ) measurements. Colourmap is adjusted in such a way that red, blue, and white cells


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We thank Andrei Mesinger for useful comments on the manuscript. AP gratefully acknowledges the use of facilities at ETH, Zürich during the early phases of this work. The research of HP is supported by the Shyama Prasad Mukherjee Fellowship of CSIR, India.


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

→ ∞. This arises from the fact that the gravitational restoring force contains an imaginary component, which acts as an anti-damping (growth) term and dominates the Chandrasekhar dynamical friction when the angular velocity is sufficiently large. Order-of-magnitude estimates for the various time-scales (damping and oscillation) were computed, and their ramifications in the context of this rotating system were explored. We also demonstrated a formal equivalence between Eddington black hole accretion and dynamical friction, thereby ensuring that both these problems can be treated in a unified manner. Through a comparison of the time-scales, it was shown that the Eddington accretion time-scale is faster in some instances, thereby constituting the more dominant effect. However, as black holes cannot accrete matter in such a fashion indefinitely, the limitations of this paradigm were also duly indicated. We have discussed some of the limitations of our formalism in Sections 1 and 5 , since some of the inherent assumptions are not accurate over the entire domain of the galaxy. However, it may be possible to use some of the results obtained herein to study the dynamics near the Galactic Centre (Genzel et al. 2010 ). For instance, recent numerical simulations of supermassive black hole binaries, with Galactic rotation taken into account, suggest that they can be significantly displaced from the Galactic Centre (Awais Mirza et al. 2017 ). Hence, the formalism developed in this paper may provide a heuristic explanation for such phenomena (although we have considered only single black holes in our analysis). Additionally, as the solutions obtained are analytical in nature, the main purpose of the paper is to arguably provide a benchmark solution against which numerical simulations can be compared. Lastly, we note that our treatment is quite general as it is Newtonian in nature, and does not invoke any of the specific features of black holes – it is equally applicable to a massive object in a sea of light particles. For instance, it may be possible to consider Saturn as our massive object, and the (moonlets that constitute) rings of Saturn as the lighter particles, analogous to the works of Griv et al. ( 2000 ) and Griv, Gedalin Yuan ( 2003 ). Moreover, it might be possible to also model axisymmetric systems via this formalism, in the regimes specified herein, such as discs with a Miyamoto–Nagai gravitational potential (Miyamoto Nagai 1975 ). By employing the same mathematical methods employed herein, we can also model the dynamics of a Reissner–Nordström (charged) black hole interacting with a constant galactic magnetic field via the Lorentz force. APPENDIX A: DYNAMICAL FRICTION IN A ROTATING ISOTROPIC CLUSTER Consider a cluster described by a potential–density pair together with an ergodic distribution function (DF) . If we introduce an overall rotation to the cluster, then it was argued in Lynden-Bell ( 1967 ) that the new DF can be obtained by the


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

If the synchrotron losses dominate as a radiative cooling channel, the product of the maximum attainable energy and the square root of the magnetic field strength, , can be taken as a measure of the accelerator efficiency. The extension of the electron spectrum to PeV energies in the magnetic field exceeding , tells us that in the Crab Nebula we deal with an acceleration efficiency approaching the ideal MHD limit (i.e. the strength of the accelerating electric field gets close to the strength of the magnetic field). Another important issue of the spectral modelling of the Crab Nebula is related to the so-called Crab flares – intense flashes of synchrotron radiation extending to GeV energies (Abdo et al. 2011 ; Tavani et al. 2011 ). The short variability time-scale and the distinct spectral shape of the flaring component require a magnetic field that is significantly larger than the average nebular field, , a non-ideal MHD configuration, and/or relativistic motions with a large bulk Lorentz factor (see Bühler Blandford 2014 , and references therein). Even under these extreme conditions, the Crab flares require the presence of electrons with energy exceeding a few PeV. The Crab flares are likely to be formed in a region(s) quite different from the site(s) where the steady component of radiation is produced. In both cases, the acceleration of electrons proceeds with efficiency close to or even beyond the ideal MHD limit. The tough efficiency requirement for the acceleration of the wind electrons can be significantly relaxed assuming that another component of electrons is responsible for the multi-MeV gamma-rays. This hypothesis is supported by a non-smooth transition between the spectra of the INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL ) and the Imaging Compton Telescope ( COMPTEL ). If this spectral feature is real, then it is better to reproduce the spectral structure at multi-MeV energies by invoking an additional component of electrons with a hard energy distribution (Aharonian Atoyan 1998 ). The currently available data do not exclude a significantly stronger magnetic field in the regions where this hypothetical hard distribution is localized (Aharonian Atoyan 1998 ). Therefore, the IC emission produced by electrons from the hard component could be suppressed compared with the IC radiation associated with the standard wind electron component. The synchrotron radiation alone does not allow us to infer information about the electrons and magnetic fields in this most critical – for highest energy electrons – MeV/GeV energy region. For any reasonable magnetic field, the MeV synchrotron radiation is produced by electrons of many hundreds of TeV. Therefore, the UHE gamma-rays produced by the same electrons through the IC scattering contain information that can shed light on both the electron energy distribution and the magnetic field strength. In this regard, the recently reported detection of gamma-ray fluxes above 100 TeV


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We are grateful to the anonymous referee for valuable comments, which improved the analysis and the presentation of the results. We gratefully acknowledge Knut Olsen for providing the ATCA/Parkes H i data in a preferred format and for useful suggestions. We are grateful to Smitha Subramanian and C. S. Stalin for the remarks and suggestions, which improved the presentation of the paper. We thank Gurtina Besla for her comments on the paper. Thanks to Arun Surya and Rathnakumar for the valuable support in matlab programming.


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(cf. Equation ( 1 )). Note that the ionization fractions derived in Ghavamian et al. ( 2002 ) are insensitive to the total preshock gas density n 0 . 2.2.2. Magellanic Supernova Remnants Ghavamian et al. ( 2003 ) study the entire remnant of DEM L71 using Fabry–Perot imaging spectroscopy, with preshock densities inferred from Chandra ACIS-S spectra modeled by Rakowski et al. ( 2003 ). The latter find a range of preshock densities along different regions of the rim of the remnant, roughly bounded by the range ≈0.5–1.5 cm −3 . In particular, n 0 ≈ 0.5 cm −3 is consistent with the majority of the eastern rim of the remnant, while in portions of the northwest rim, n 0 ≈ 1.5 cm −3 . Modeling the observed collisionally excited hydrogen-Balmer emission, Ghavamian et al. ( 2003 ) conclude that a wide range in neutral fraction may be plausible, but that would be necessary in order to produce detectable H α emission. Ghavamian et al. ( 2007 ) revisited DEM L71 in the far-UV, as well as the LMC remnants 0509-67.5, 0519-69.0, and 0548-70.4, using spectra obtained from the Far Ultraviolet Spectroscopic Explorer . The ratio of fluxes in Ly β and O VI 1032 Å depends linearly on the preshock neutral fraction; the observed ratio in DEM L71 requires a hydrogen neutral fraction of 20–40%, consistent with previous limits. No UV lines were found for the remnant 0548-70.4. For the remnants 0509-67.5 and 0519-69.0, the same method constrains the neutral hydrogen fraction in the surrounding ISM to >40%. The best-fitting ambient densities can be found by comparing the present size and ionization state of the remnant with hydrodynamical models: recently, Kosenko et al. ( 2014 ) found n 0 = 0.1–0.3 cm −3 for 0509-67.5, and n 0 = 1.0–2.0 cm −3 for 0519-69.0, although Kosenko et al. ( 2010 ) report densities as high as 2.4 cm −3 . As a conservative estimate, we adopt 0.3 cm −3 and 2.4 cm −3 as our fiducial ISM densities for 0509-67.5 and 0519-69.0, respectively. The radius of the forward shock for both remnants is ∼4 pc, for an LMC distance of 50 kpc. 3. Constraints on the Nature of the Progenitors of Nearby SNe Ia 3.1. Flash Ionization We may now investigate the extent to which the presence of neutral hydrogen at the present radii of all remnants considered above constrains the release of ionizing photons in the last τ rec ≈ 100,000 years. Chevalier Raymond ( 1978 ) were the first to consider the simplest case, a “burst” of ionizing photons from the supernova itself. For a present shock radius R and mean ambient density n , the total number of hydrogen-ionizing photons emitted in such a burst must have been fewer than 4 π R 3 n /3 ≈ (0.2–6) × 10 58 for SN 1006, 0509-67.5, 0519-69.0, and DEM L71 (see Table 1 ). Notably, this upper bound applies not only to the shock breakout from the supernova itself, but to any short-lived phase that the progenitor or its companion underwent immediately preceding or following the explosion, such as any briefly hot, luminous surviving WD


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We thank Calcul Québec for computational resources. This research was partially supported by the Natural Sciences and Engineering Research Council of Canada and the Faculté des Études Supérieures et de la Recherche de l'Université de Moncton. This paper is based on: (1) observations obtained at the CFHT which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii; and (2) data obtained from the ESO Science Archive Facility under request number 72877.