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 B-Identifier O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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-Instrument O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O B-Identifier O O O O O B-Instrument O O O O O O O O O O O B-Instrument 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 B-Identifier O B-Identifier 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O B-Instrument O O O O O O O O O O B-Instrument O O B-Identifier O O O 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 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 B-Identifier O O O O O O O

to an injected ν τ flux with E 0 = 1 EeV. Normalized cumulative distributions from secondary τ -leptons are shown in Figure 4 for injected neutrinos at angles corresponding to the best-fit reconstructed direction of AAE-141220. Figure 4. Normalized cumulative distributions for Earth-emerging τ -leptons. Colors correspond to the incoming τ -neutrino energy, and the gray band is the 95% containment on the error of the reconstructed shower energy of AAE-141220. We next inject a flux of EeV tau neutrinos and find the spectral shape of the secondary ν τ flux that would be incident on IceCube. As we observed zero coincident events in the time window of 10 3 s around AAE-141220 in the prompt analysis, we calculate the maximum allowed flux normalization (at a 90% confidence level) on the primary flux that would evade this nonobservation. The results are displayed in Figure 5 . Figure 5. Upper limits (90% C.L.) placed by calculating the secondary neutrino flux (purple histogram) from an incident flux of EeV neutrinos assuming constant emission over 10 3 s and comparing to the nonobservation of IceCube events in the prompt analysis described in Section 3.1 for AAE-141220. The flux implied by the ANITA observations (black), represented in this figure as , using information about ANITA’s acceptance (Romero-Wolf et al. 2019 ) overshoots this upper limit (purple arrow) by many orders of magnitude. For comparison, upper limits on the time-integrated muon neutrino flux from the prompt analysis are shown in blue. All fluxes are per flavor . Figure 6. (Top two rows) Sky maps and TS distributions from all three analyses for AAC-150108. For AAE-061228, IceCube was not in a full detector configuration at the time of the event, and thus only the steady and rolling analyses were used to search for neutrino emission. Sky maps and TS distributions for these analyses are displayed in the bottom two rows. Although IceCube’s sensitivity is peaked many orders of magnitude below the reconstructed energies of the AAEs, the limits set on any potential neutrino source that created AAE-141220 are more constraining by several orders of magnitude than the implied flux by the ANITA observations. If one considers constant emission over the entire live time of the IceCube event selection, then the time-integrated flux limit set by the IceCube nonobservation of AAE-141220 becomes around 1 order of magnitude less constraining, as is apparent in the steady limits in Figure 2 . However, for the implied normalization placed by ANITA observations, this value would increase by approximately 2 orders of magnitude due to the limited live time of the ANITA flight. This has the overall effect of increasing the tension between these two normalizations by approximately 1 more order of magnitude than for the 10 3 s follow-up shown in Figure 5 . It is worth noting that the logic for scaling time-integrated limits also applies to AAE-061228, even though we cannot constrain the shorter


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Software I-Software I-Software I-Software I-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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject B-Citation I-Citation O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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

data point density of a photometric LC (i.e. order of several thousands). However, in order to obtain a more realistic error value for q , the mass function is taken into account using the P orb and K 1 values and their errors: where M 1 , M 2 , K 1 , i , and P orb are explained in Table 1 and G is the gravitational constant. Following the error propagation method and assuming M 1 = 1.6 M ⊙ , then according to the definition of mass ratio (Table 1 ), the error of q is derived as 0.0031, which is adopted as the final value. The parameters of the set (c) were calculated using the software A BS P AR EB ( Liakos 2015 ) in mode 2 and they have the usual meaning. In Fig. 6 , we show the photometric model on one LC and the three-dimensional (3D) Roche geometry representation of the system, while in Fig. 7 (upper and middle panels) and Fig. 8 we illustrate the SC data and their residuals after the subtraction of the theoretical LCs for the two data sets. Fig. 6. Upper panel : theoretical (solid line) over observed (points) LC for KIC 8553788. Lower panel : 3D representation of the Roche geometry of the system at orbital phase 0.75. Fig. 7. Upper panel : short cadence LCs of Q5 for KIC 8553788. Middle panel : LC residuals after the subtraction of the binary models. Bottom panel : LC residuals after the subtraction of the pulsation model. Fig. 8. Upper panel : short cadence LCs of Q14 for KIC 8553788. Bottom panel : LC residuals after the subtraction of the binary models. During the modelling of the individual LCs, it was noticed that the spots migrate from one day to another; although this is a by-product result and a detailed study is not an aim of the present paper, their parameters are listed in Table B.1 . Moreover, in the same appendix, plots are given showing the location changes of the spots as well as their location on the surface of the secondary component on the first and the last days of each data set (Figs. B.1 – B.3 ). The reliability of the solution, especially for the extremely low value of the mass ratio, may be checked in the future using the RVs of the secondary component. However, it should to be noted that according to Kallrath Milone ( 1999 , their Sect. 4.1.1.1) the photometric mass ratio can be determined with great confidence for lobe-filling or overcontact systems when at least one light curve and one RV curve exist. Moreover, another useful and recent example regarding the reliability of the “ q -search” method concerns the semidetached systems KIC 10581918 and KIC 10619109. Liakos (2017) determined their mass ratio values based only on their Kepler LCs and without any use of RVs. These photometric values of q were later seen to be in very close agreement with the spectroscopically determined ones of Matson et al. (2017) . Concluding, KIC 8553788 was found to be in a semi-detached state, with the less massive and cooler component filling its Roche lobe, and to have a very low mass ratio of 0.043. Its primary component is a


O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O 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 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 O O O O 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 O O O O O O O O O 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

of Trappist-1f from a magma ocean phase to present assuming the modern surface volatile inventory exceeds 1 GPa (ocean depth >∼100 km). Figure 4. Trappist-1f’s coupled redox–thermal–climate evolution. The model is applied from magma ocean to present with initial water inventories ranging from 30–300 Earth oceans (∼1–10 GPa), and initial CO 2 inventories ranging from 20 to 6000 bar. The lines are median values and shaded regions denote 95% confidence intervals across all model runs. The coupled model includes (a) mantle and surface temperature evolution, (b) the solidification of the magma ocean from core to surface, (c) atmospheric evolution, (d) surface ocean condensation, (e) surface energy budget, (f) CO 2 outgassing and weathering fluxes, (g) crustal production, (h) mantle redox state, and (i) the surface redox budget. Despite the large pressure overburden from the surface ocean, crustal production may persist for billions of years due to mantle hydration suppressing the silicate solidus (g). Nonetheless, Trappist-1f does not experience magmatic outgassing due to the high solubility of volatiles in melt at GPa pressures (f), (i). According to this model, Trappist-1f ought to have experienced a ∼100 Myr magma ocean due to the extended pre-main sequence of Trappist-1 (Figure 4 (b)); absorbed shortwave radiation exceeds the runaway greenhouse limit for the first ∼100 Myr of Trappist-1f’s evolution (Figure 4 (e)). During this long-duration magma ocean phase, loss of hydrogen to space oxidized the mantle (Figure 4 (h)), consistent with previous models of magma ocean evolution on planets around M dwarfs (Schaefer et al. 2016 ; Wordsworth et al. 2018 ; Barth et al. 2020 ). Once absorbed shortwave radiation drops below the runaway greenhouse limit, the magma ocean freezes and a deep liquid water ocean condenses out of the steam atmosphere (Figure 4 (d)). Despite the large pressure overburden from this surface ocean, melt production may persist to the present (Figure 4 (g)). This is because crustal hydration reactions and subduction deliver water to the interior (Figure 4 (i)), suppressing the silicate solidus and hence allowing for partial melting. However, despite high crustal production rates, there is no magmatic outgassing throughout Trappist-1f’s evolution (Figures 4 (f), (i)) due to the high solubility of volatiles at GPa pressures. 4. Discussion To what extent is the simple melt-gas equilibrium partitioning approach described here a reasonable representation of waterworld degassing? Outgassing fluxes from magmatic sources are determined by the integrated loss of volatiles over the decompression path from the mantle to the surface as magma ascends and cools (Edmonds Woods 2018 ). The decompression path reflects changes in volatile solubilities as magma ascends from its mantle source to the surface. Solubilities typically decrease with decreasing pressure, which leads to degassing of volatiles along the decompression path (so-called “first


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

first order in δ n The general solution of Eq. ( A.29 ) then reads where α n ( T 1 ) and β n ( T 1 ) are two functions to be determined with the first-order equation. Using Eq. ( A.31 ) in Eq. ( A.30 ), it is straightforward to show (e.g., via the method of variation of parameters) that, if non-null, the terms in brackets will induce terms proportional to τe ± iτ in the expression of , up to a factor on the order of α n and β n . This will make on the order of up to a timescale on the order of O(1/ δ n ) and, therefore, would break the perturbation ansatz in Eq. ( A.28 ). Therefore, to obtain a uniformly valid expression up to such timescales, the terms in brackets have to vanish. This condition leads to with A n and B n two arbitrary constants. As a consequence, the amplitude is ruled only by the coupling term on the right-hand side of Eq. ( A.30 ), which depends on the leading-order amplitudes with n ′ ≠ n . For n ′ ≠ n , it is obvious that the amplitudes follow the same zeroth-order and first-order equations as in Eqs. ( A.29 ) and ( A.30 ); however, because of the considered scaling, T k for k = 0 or 1 in these equations are replaced by with π = ( ω n ′ / ω n ). As a result, we get where A n ′ and B n ′ are two arbitrary constants. According to Eqs. ( A.30 )–( A.32 ) we thus find that is ruled at leading order by Using again the method of variation of parameters, we can show that the amplitude is equal to a series of terms as a function of n ′ that are ). At this point, we assume that the magnitude of slowly varies with n ′, so that it is for n ′∼ n ; this will be checked a posteriori (see the resulting velocity amplitudes in Fig. 2 ). Provided for n ∼ n ′ and otherwise, as justified in Appendix A.2.3 , the main contribution to results from the terms of the series associated with n ′ ∼ n ; as a result, with Δ ω n = | ω n − ω n − 1 |. Within the asymptotic limit, ω n /Δ ω n ∼ n ≫ 1 and thus in order of magnitude. This highlights afterward that, instead of δ n , it is more appropriate to scale the non-adiabatic perturbation of the mode amplitude by in such a way that the perturbation ansatz becomes and the new first-order perturbation . As a result, the relative error when considering up to a timescale on the order of T damp is on the order of . We check a posteriori at the end of Sect. 3.1 that in the considered asymptotic frequency range. Therefore, all the previous perturbation developments, fortunately, hold true and the coupling terms do not stand for secular terms. These terms thus have no effect on the two-timing solution provided by , and are just responsible for the relative error on the order of . In summary, provided that the mode amplitude slowly varies with the radial order, the solution of the homogeneous equation as a function of the variable t , which is uniformly valid up to a timescale on the order of O( T damp ), takes the form, according to Eqs. ( A.31 ) and ( A.32 ), of the adiabatic solution modulated by an exponential


O O O O O O O B-Organization I-Organization I-Organization O O B-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal O O O O B-Organization B-Grant I-Grant I-Grant I-Grant B-Person O B-Observatory B-Telescope O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O

This work has been supported by the Croatian Science Foundation under the project 7549 “Millimeter and submillimeter observations of the solar chromosphere with ALMA” and also supported by NASA Heliophysics LWS grant NNX16AB79G (SHS). Facility: SDO (AIA) . Software: astropy (Astropy Collaboration et al. 2013 , 2018 ), Period04 (Lenz Breger 2005 ), SunPy (SunPy Community et al. 2015 ).


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

computed by Madau Dickinson ( 2014 ), after we converted it to a Kroupa IMF, and the red curve shows it multiplied by 0.4 to match roughly the SFR density history of the SCUBA-2 sources. However, once we also take into account the different FIR calibrations that were used in this work vs. in Madau Dickinson, we find that the SCUBA-2 data are only 0.29 times the Madau Dickinson curve. The red shaded region shows the 68% confidence range when allowance is made for the systematic uncertainties in the SFR calibrations. (b) Number density per unit comoving volume per unit SFR vs. SFR in five redshift intervals (see legend). The error bars in Figure 25 (a) are purely statistical. However, systematic errors in the SFR conversion and in the redshift estimates may also be important. In order to estimate these potential errors, we recomputed the SFR density history randomly, reassigning the SFRs and redshifts within the potential error ranges. Based on these Monte Carlo calculations, we computed the 68% error range produced by the systematics, which we show as the red shaded region. For the highest and lowest redshifts, where there are fewer objects, the systematic and statistical errors are similar, but for redshifts between 2 and 4, the systematic error dominates. In Figure 25 (b), we show the SCUBA-2 SFR density distribution functions computed for the same redshift intervals versus log SFR. Although the normalizations of the distribution functions are changing—they rise to reach a peak at before dropping at higher redshifts—the shapes over are remarkably similar; that is, the number density of high SFR galaxies relative to that of lower SFR galaxies is about the same in each redshift interval. However, at some point this similarity in shape must break down, as there cannot be large numbers of powerfully star-forming galaxies at very high redshifts. The present data show that this must occur at redshifts higher than . In Figure 26 , we show the SCUBA-2 distribution functions of Figure 25 (b) recomputed for the coarser redshift intervals , and 4–6 (colored circles; note that in the interval there are not enough sources to plot the two highest SFR bins). We compare these functions with those computed at lower SFRs from the extinction-corrected UV samples of Reddy Steidel ( 2009 ) and van der Burg et al. ( 2010 ) (small colored symbols and curves), assuming a Kennicutt ( 1998 ) conversion of UV luminosity to SFR for a Kroupa ( 2001 ) IMF. This emphasizes the disjoint nature of the SFRs of galaxies selected by UV and submillimeter observations (e.g., Barger et al. 2014 ): only submillimeter observations can find the most powerfully star-forming galaxies at redshifts . Both the UV and SCUBA-2 distribution functions have similar shapes in the interval. Thus, the number density of high SFR galaxies measured from the SCUBA-2 sample relative to that of lower SFR galaxies from UV-selected samples is about the same in this redshift interval. However, the


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 B-Wavelength I-Wavelength B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O B-Dataset 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-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion 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 B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Survey 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 B-Citation I-Citation 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 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-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 O O O O O O B-Dataset O O O O O O O O O O O O B-Wavelength O O O O O O O B-Software I-Software O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software B-Software I-Software I-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

fields to search for weak diffuse emission from the targets (e.g. Cook et al. 2020 ). For this work, we have used data from the 150 MHz TIFR GMRT Sky Survey (TGSS). The first alternative data release (TGSS-ADR1) of this survey (Intema et al. 2017 ) provides the continuum Stokes I images of 99.5 per cent of the sky area north of declination δ = −53° (i.e. ∼90 per cent of the full sky), at a resolution of 25 × 25 arcsec 2 for fields that are north of 19° declination, and 25 × 25 arcsec 2 /cos (δ − 19°) for fields south of 19°. The median value of RMS noise is 3.5 mJy beam −1 for the survey. Out of around 65 dSph galaxies of Milky way and Local Group (McConnachie 2012 ; Drlica-Wagner et al. 2020 ), 23 are found to be within the TGSS footprint. There were five more targets observed in the TGSS, but are not included in this analysis due to presence of image artifacts in those fields. The target coordinates, their half-light radius and distance (McConnachie 2012 ; Koposov et al. 2015 ; Laevens et al. 2015 ; Martin et al. 2015 ; Martínez-Vázquez et al. 2019 ; Cook et al. 2020 ) are tabulated in Table 1 , and the half-light radius distribution is shown in Fig. 1 . Note that the unique hybrid array configuration of the GMRT implies that the telescope has sensitivity to both small-scale compact structures as well as large-scale diffuse emission, with the largest detectable structure (corresponding to the shortest baselines) being 68 arcmin. If the diffuse emission from these targets have angular extent ∼few × r h , there will not be any significant missing flux issue in this analysis. Figure 1. Histogram of the half-light radii, r h of the sample of 23 dSph galaxies used in this study. Table 1. List of the dSph galaxies used in this analysis, with their J2000.0 coordinates, half-light radius ( r h ), and distance ( D ). 3 DATA ANALYSIS For the 23 dSph galaxies, we have used the TGSS-ADR image archive to extract the image of a region centred around the optical position of each of the galaxies in FITS format combining data from multiple overlapping TGSS pointing. For the first part of our analysis, we have extracted 1° × 1° region for each of the target dSph galaxies. Further analysis was done using the casa (Common Astronomy Software Applications) package. We have visually inspected each field to identify and blank all the compact sources (unresolved and marginally resolved) using a 5 σ cut off. These compact sources are unrelated to the expected faint diffuse emission (originating from processes directly involving the DM annihilation/decay) at the galaxy-wide scale, that is of our interest. This will also filter out any plausible unidentified imaging artefact present in the field. We then shift the central coordinate of all the fields, regrid and convolve the data to exactly same pixel size and same synthesized beam before combining to create a stacked image from all 23 dSph target field. We have also selected 23 ‘control’ regions, located close to


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

such quartet at 173.2 GHz that corresponds to the transitions gave us an opportunity to assign the whole series of this kind of transitions and get an initial approximation for the rotational constants of CHNH (at this stage the tunneling parameters were kept fixed at the values of the main methylamine isotopologue, Motiyenko et al. 2014 ). Obtained in this way, the initial model allowed us to continue assigning the spectra in a usual iterative manner by adding new assigned lines to the fit, refining the Hamiltonian model, and producing new predictions. The Doppler-limited resolution of our spectrometers provided an opportunity to resolve nuclear quadrupole hyperfine splittings for 898 rotational transitions. Typically, as for the main methylamine isotopologue, a resolved pattern of the hyperfine structure was observed as a doublet with an approximately 2-to-1 ratio in intensities. The stronger doublet component contains unresolved hyperfine transitions with selection rules and , whereas the weaker doublet component corresponds to the transition. At the same time, a number of hyperfine components with selection rules were also assigned. To provide the hyperfine-free frequencies we used in our analysis of the rotation-torsion-wagging spectrum of the ground state of C methylamine, we fitted the frequencies of the individual hyperfine components using the model described above. The quadrupole hyperfine parameters , and that we obtained from the fitting of the hyperfine patterns of the rotational transitions are presented in Table 1 . Table 2 Main rotational and torsion-wagging splitting parameters (all in MHz except of which is unitless) of the ground torsional state of C and C methylamines. Notes. (a) . Fig. 1 Predicted (in red) and observed (in blue) rotational spectrum of C methylamine between 882 and 908 GHz dominated by -type series of transitions with . A slight inconsistency between predicted and observed spectrum, which may be visible for some strong lines, is due to source power and detector sensitivity variations. Weak unassigned lines are due to higher excited vibrational states. In total, the dataset for the rotational spectra of CHNH in the ground vibrational state includes 2721 rotational transitions with an upper value of . This set of rotational transitions was fitted to the effective Hamiltonian of the group-theoretical high-barrier tunneling formalism that was developed for methylamine by Ohashi Hougen (1987) . The fit adopted in the present study as the “best” achieved the root-mean-square (rms) deviation of 0.039 MHz that corresponds to the weighted rms deviation of 0.73. The Hamiltonian model includes 75 parameters. The values of the molecular parameters obtained from the final fit are presented in Table 1 . In Table 2 , the main rotational and torsion-wagging splitting parameters for CHNH and CHNH ( Motiyenko et al. 2014 ) are compared. From the comparison we see that the values of the main tunneling splitting parameters in


O 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-Instrument O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O 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 B-Telescope O O 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 O O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject O O O O O B-Software 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O 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 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 B-Model I-Model 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 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 B-CelestialObject O B-Telescope O B-Telescope O O O O O O O O O O B-Instrument 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 B-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O B-Telescope O O O B-Wavelength I-Wavelength I-Wavelength O O B-CelestialObject I-CelestialObject 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 B-Telescope B-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag O O O O B-Wavelength I-Wavelength I-Wavelength O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O


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

ACKNOWLEDGEMENTS We would like to thank the anonymous referee for his/her very useful comments that have allowed us to improve our paper. We thank Yi-Jung Yang for useful discussions. This work is supported by the National Natural Science Foundation of China (Grant No. 11703098, Grant No. 11275247, and Grant No. 11335012) and a 985 grant at Sun Yat-Sen University. YMH gratefully acknowledges the support of the National Natural Science Foundation of China (1170030038). FKP acknowledges support from the Doctoral Starting up Foundation of Guizhou Normal University 2017 (GZNUD[2017] 33).


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

) suggest that these events, and hence IMBHs, are not equally distributed amongst galaxies but rather they find that the Milky Way is expected to underproduce these events by a factor of 10 2 compared to compact blue galaxies. This means the number of lower mass IMBHs in the Milky Way could be as low as 10 2 . As these young clusters evaporate, if they evaporate, their IMBHs would be left with at most only the few stars within the IMBHs sphere of influence. If there are such low-mass IMBHs threading their way through the Milky Way then Gaia may provide a unique opportunity to spot them. As Gaia (de Bruijne 2012 ) observes a billion or so stars in the Milky Way, making very high-precision measurements of the peculiar motion of the stars, it should observe some systems for which their motions can only be explained with the addition of an IMBH. However, if there are in fact only 10 2 such IMBHs in the Milky Way, and Gaia is only sampling 1 out of every 10 2 stars in the Milky Way, we would expect to detect on order of 1 of these objects. Of course, as with the rest of this letter, caution must be taken when considering such a low number of statistics. The spatial distribution of these systems should not deviate much from their initial distribution, at least not as a result of dynamical friction since for the 10 3 M case dynamical friction should only result in an inward migration of the black hole of 40pc, and only 0.4kpc even for a 10 5 M black hole in 13Gyr (assuming a value of 6 for the Coulomb logarithm). Additionally, the all-sky, X-ray survey provided by eROSITA (Merloni etal. 2016 ), with an anticipated launch data in 2016, will likely provide many more IMBH candidates with its sensitivity and long expected exposure time. 4.3 IMBHs in relation to other black holes Finally, in Table 1 we compile the number and total mass of different types of massive objects [stars, stellar mass black holes (StMBHs), IMBHs and SMBHs] in both our Galaxy and within a sphere with a radius of 100Mpc. Here, we outline how we arrived at these values: in the Milky Way there is one observed SMBH, Sgr A*, with a mass of 4.110 6 M (Ghez etal. 2008 ). Caramete Biermann ( 2010 ) estimate a total number of SMBHs within 100Mpc with masses 10 7 M to be about 2.410 4 and from the mass density provided therein, we estimate a total mass of 2.810 11 M within the same volume. We must be careful to note that while the number of SMBHs within 100Mpc may be larger due to excluding the SMBHs with masses 10 7 , Caramete Biermann ( 2010 ) claim that the total mass is barely dependent on the cutoff due to a flattening of the integral mass function at lower mass. Table 1. The estimated number and total mass of SMBHs, IMBHs, StMBHs and Stars within the Milky Way (left two columns) and within 100Mpc (right two columns). In this work, we have calculated the values for the number of IMBHs within 100Mpc and within the Milky Way. In order to estimate the total mass of the IMBHs, we used


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

F.S. was supported by the Max Planck Society grant “Science Projects in Preparation for the PLATO Mission.” S.B. acknowledges support from NSF grant AST-1514676 and NASA grant NNX16AI09G.


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

Acknowledgements Based on observations carried out as part of the Large Program ASAI (project number 012-12) with the IRAM 30-m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). This work was supported by the CNRS program”Physique et Chimie du Milieu Interstellaire” (PCMI) and by a grant from LabeX Osug@2020 (Investissements d'avenir - ANR10LABX56). E. M. acknowledges support from the Brazilian agency FAPESP (grant 2014/22095-6 and 2015/22254-0). I.J.-S. acknowledges the financial support received from the STFC through an Ernest Rutherford Fellowship (proposal number ST/L004801/1).


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

K.Z. is supported by Leverhulme Research Project Grant RPG-2015-096 and the HKRGC grant (Project 14306814), D.K. is supported by the NSFC under grant 11473014, and G.S. is supported by the National Science Foundation under grant NSF AST-0909206. The computation made use of the high-performance computing resources in the Core Facility for Advanced Research Computing at Shanghai Astronomical Observatory, Chinese Academy of Sciences.


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

it rises rapidly to a peak at . Bottom: The metallicity distribution function over the entire galaxy. The bottom panel of Fig. 3 shows the metallicity distribution function (MDF) across the model. The model’s MDF peaks at nearly Solar metallicity and has a long tail to low . The MDF is similar to some extent to the MDF of the bulge (e.g. Zoccali et al. 2008 ; Gonzalez et al. 2015 ). 3 KINEMATIC FRACTIONATION Fig. 4 shows the evolution over the last (i.e. since redshift z = 0.4), of the bar amplitude, A 2 , defined as the usual m = 2 amplitude of the Fourier moment measured overall stars (e.g. Debattista Sellwood 2000 ). The bar forms quite late, starting from ( z ≃ 0.19). It reaches a peak amplitude at , and weakens somewhat in the next Gyr, as is often seen in simulations of isolated galaxies. In isolated simulations, bars generally experience renewed growth past this point (e.g. Combes Sanders 1981 ; Sellwood Moore 1999 ; Debattista Sellwood 2000 ; Athanassoula 2002 ; Bournaud Combes 2002 ; O’Neill Dubinski 2003 ; Martinez-Valpuesta et al. 2006 ), but the late bar formation in this simulation does not give the bar time to strengthen again. Figure 4. Bar amplitude evolution in m12m since redshift z = 0.4 (corresponding to of evolution). 3.1 Density separation Fig. 5 shows the mass density distribution at z = 0 in face-on and edge-on projections for the model separated by different stellar populations. As in Debattista et al. ( 2017 ), younger populations exhibit a stronger bar and a more prominent box or peanut (B/P) shape than the older ones. The difference in the B/P strength as a function of age is a signature of kinematic fractionation as discussed in Debattista et al. ( 2017 ). Figure 5. Density distributions in the face-on (top panels) and edge-on (bottom panels) projections. The bottom left panels show the full edge-on projection, while the bottom right panels show a cross-section with particles chosen within . In the top row of each set of panels we show the accreted stars (left) and all the stars (right). The rest of the panels show populations separated by time of formation of the stars, age. Fig. 5 also shows the density distribution of the stellar population that was accreted, which we define as stars that formed at radius . The accreted stars, which account for of all the stars, formed primarily () by redshift z = 1.27 (). They have a density distribution similar to that of the oldest (age now) in situ stars, i.e. those formed at (see also El-Badry et al. 2018b ). Like the oldest bin, no bar or X-shape is present in the accreted population. 3.2 Age and metallicity dependence of bar amplitude Fig. 6 shows the dependence of the usual m = 2 Fourier global bar amplitude on the age and metallicity. As also apparent from the face-on maps in Fig. 5 , the bar is stronger in younger populations than in the older ones. The very oldest populations have quite a weak bar overall, while the youngest populations have a 3.5 times stronger bar.


B-Citation I-Citation I-Citation I-Citation 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 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 B-Survey 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 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 B-Formula I-Formula I-Formula 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-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 O O O O O O O B-Dataset I-Dataset B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O O O O O O O O O B-Survey I-Survey B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O B-Survey I-Survey O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O B-Dataset O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation I-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 B-Wavelength B-Survey I-Survey O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset 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 B-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 B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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. ( 2014 ) also suspected the existence of tidal tails for NGC 3201, as they found some unbound stars located a few arc minutes outside of the cluster radius. Recently, Anguiano et al. ( 2016 ) reported the presence of tidal debris for the cluster. Their results were based on spectroscopic measurements from RAVE data. NGC 5024 has five extra-tidal RR Lyrae stars mostly concentrated in a region which is at a distance of three times the tidal radius from the centre of the cluster. The presence of these extra-tidal RR Lyrae stars may be an indication of more extra-tidal population which may also belong to the cluster. Beccari et al. ( 2008 ) found that in the case of NGC 5024, the model with lower concentration ( c = 1.45) and large core radius ( r c = 26 arcsec) best reproduced the observed surface density profile in the inner portion of the cluster but this model deviates from observations in the outer region of the cluster. This type of deviation is a signature of the stars that are tidally stripping away from the cluster (Combes et al. 1999 ; Johnston, Sigurdsson Hernquist 1999 ; Leon et al. 2000 ). Kunder et al. ( 2018 ) reported eight extra-tidal RR Lyrae stars belonging to the Galactic globular cluster NGC 6441 but we did not find any in this study. This is due to three reasons: (1) some of the stars reported by them were not observed in Gaia DR2 (OGLE BLG-RRLYR-3774, OGLE BLG-RRLYR-30603, OGLE BLG-RRLYR-30792, OGLE BLG-RRLYR-3168, OGLE BLG-RRLYR-31080); (2) star reported was not marked as variable by Gaia survey [OGLE BLG-RRLYR-30513 ( Gaia DR2 4039957151898674048)] and (3) stars were reported as RRab variable stars by Gaia survey but were not present in Gaia DR2 RR Lyrae catalogue [catalogue: gaiadr2.vari_rrlyrae; stars: OGLE BLG-RRLYR-3613 ( Gaia DR2 4039958564974057984)], [OGLE BLG-RRLYR-30928 ( Gaia DR2 4039978695412672768)]. Minniti et al. ( 2018 ) recently reported the presence of tidal tails in the cluster NGC 6266. These were not found in our analysis due to the fact that they used additional near-IR VVVX survey observations along with Gaia DR2 data. 5 CONCLUSIONS We searched for extra-tidal RR Lyrae stars in 56 Galactic globular clusters based on the available literature data. Gaia DR2 data for RR Lyrae stars from the catalogue of Clementini et al. ( 2018 ) were used along with data from MPV14 and V18 to assign cluster membership to each RR Lyrae star. The extra-tidal RR Lyrae stars were selected based on three criteria: position of the cluster and the star in the sky; proper motion of the cluster and the star; and position of the RR Lyrae star on the CMD of the cluster. All the three criteria are necessary and none of them can be neglected while selecting the extra-tidal RR Lyrae stars. Based on these three criteria we found 30 extra-tidal RR Lyrae stars belonging to 11 globular clusters. The majority of these clusters have only a couple of candidates. We also note that some of those extra stars for halo GCs may also be part


O O O O O O O O B-Organization B-Fellowship I-Fellowship O B-Organization I-Organization I-Organization I-Organization O O B-Organization O O O O B-Organization B-Person O O O O B-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant O O B-Grant O O O O O O O O B-Grant I-Grant I-Grant B-Person O B-Person O O O O B-Telescope O B-Telescope O O B-Organization O O O O O O O B-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Organization O O B-Organization I-Organization I-Organization B-Person O O O B-Organization O B-Grant O O O O O O O O B-Collaboration I-Collaboration O O B-Database I-Database I-Database I-Database I-Database O O O B-Person O B-Person O O O O O O B-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal O B-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal I-Proposal O O O O O O O O O O O O O O O O

G.S.K. was funded by an appointment to the NASA Postdoctoral Program at Goddard Space Flight Center, administered by USRA through a contract with NASA. M.C. acknowledges support from the Research Council of Norway through its Centres of Excellence scheme, project no. 262622, and through grants of computing time from the Programme for Supercomputing. J.C.A. and A.N.D. acknowledge support from the IRIS mission. IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research Center and major contributions to downlink communications funded by ESA and the Norwegian Space Centre. P.R.Y. acknowledges support from NASA grant NNX15AF25G. We appreciate the open data policies of the Opacity Project and the NIST and CHIANTI atomic database. The authors thank ISSI and ISSI-BJ for the support to the teams “Diagnosing Heating Mechanisms in Solar Flares through Spectroscopic Observations of Flare Ribbons” and “New Diagnostics of Particle Acceleration in Solar Coronal Nanoflares from Chromospheric Observations and Modeling.” Finally, we would like to thank the anonymous referee, whose comments helped to improve this work.


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 I-Survey I-Survey I-Survey O B-Survey I-Survey I-Survey I-Survey B-Grant I-Grant O B-Grant O O B-Survey O B-Grant I-Grant O O B-Telescope I-Telescope O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O O O O O B-Organization O O O O O B-Organization O O O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory O B-Grant I-Grant O O O O O O B-Software O O B-Organization I-Organization I-Organization I-Organization O O O O B-Survey O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O B-Observatory I-Observatory I-Observatory B-Location O O O O O O O O O O O O B-Telescope I-Telescope O O O O B-Archive I-Archive I-Archive I-Archive O O O O O B-Telescope I-Telescope O B-Organization I-Organization I-Organization O O B-Observatory I-Observatory I-Observatory O B-Location O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Observatory I-Observatory O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O O B-Location O O O O O O B-Location O O O O O O O O O O O O O O O O O O O O B-Organization O B-Grant I-Grant B-Grant I-Grant O B-Grant I-Grant B-Organization O B-Grant B-Grant I-Grant O B-Organization O B-Grant O B-Telescope B-Instrument O B-Instrument O B-Telescope B-Instrument O B-Telescope O B-Telescope O B-Telescope B-Instrument O B-Telescope B-Instrument O B-Telescope B-Instrument

The feedback on our analysis from an anonymous expert referee significantly improved our manuscript. This work is based on observations taken by the CANDELS Multi-Cycle Treasury Program, the 3D- HST Treasury Program (GO 12177 and 12328), and the z9-CANDELS program (GO 13792) with the NASA/ESA HST , which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This work also relies on observations made with the Spitzer Space Telescope , which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. This work relies on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO program ID 179.A-2005 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium. Some of the data utilized in this paper were gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. This paper is also based (in part) on data collected at the Subaru Telescope and retrieved from the HSC data archive system, which is operated by the Subaru Telescope and Astronomy Data Center at the National Astronomical Observatory of Japan. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. 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. We acknowledge the support of NASA grants HST -AR-13252, HST -GO-13872, and HST -GO-13792, NWO grant 600.065.140.11N211 (vrij competitie), and TOP grant TOP1.16.057. Facilities: HST (ACS , WFC3) , Spitzer (IRAC) , CFHT , VISTA , Magellan (FourStar) , Subaru (HSC) , Keck:I (MOSFIRE/U142).


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

; Chen et al. 2016 ; Wu et al. 2017b ). For simulations described in the current work, we apply an HRO formulation whereis the magnitude of the angle between N H isocontours (orthogonal to ∇ N H ) and , the simulated polarization pseudovectors. Here, is defined aswhere p = 0.1 is a set constant polarization fraction and χ is the angle in the plane-of-sky derived from the Stokes parameters (see, e.g., Wu et al. 2017b ): The relative orientation angle Φ is then calculated pixel-by-pixel in a column density map. The lowest column density pixels () are ignored, and a gradient threshold for is applied (similar to, e.g., Planck Collaboration et al. 2016 ), to better separate GMC material from diffuse background fields. The remaining pixels are then separated into 25 bins of equal count based on N H . Note that we assume n He = 0.1 n H , yielding a mass of per H. Figure 2 shows column density maps for the noncolliding and colliding models with B = 10, 30, 50 μ G for the density-regulated model. Their respective HROs are also shown for low, medium, and high column density bins. Here, φ represents the smaller angle between the polarization-inferred magnetic field and N H isocontours. Thus, histograms peaking at φ = 0° indicate inferred B -fields preferentially aligned parallel to filamentary structures, while peaks at φ = 90° indicate a preferentially perpendicular alignment. Figure 2. First and third rows: column density maps with the normalized plane-of-sky magnetic polarization field, p , represented with black pseudovectors. The noncolliding cases for B = 10, 30, and 50 μ G are shown in the first row, while the respective colliding cases are shown in the third row. Gas from the density-regulated SF models is shown in each case at t = 5 Myr. Second and fourth rows: histograms of relative orientations are shown directly below their corresponding column-density maps. HROs compare the angle between p and iso- N H contours pixel-by-pixel. The projected map is divided into 25 column-density bins of equal pixel count. HROs for the lowest (1st bin; black), middle (12th bin; blue), and highest (25th bin; red) N H are shown, using angle bins of 15°. The histogram color corresponds to the regions bounded by low (black), intermediate (blue), and high (red) value iso- N H contours as shown in the respective projection map. The thickness of the data points indicates the variance within each bin. Histograms with peaks at 0° correspond to p predominantly aligned with iso- N H contours (i.e., B -fields parallel to filaments), while peaks at 90° correspond to p predominantly perpendicular to iso- N H contours (i.e., B -fields perpendicular to filaments). Gas in the noncolliding, model is slightly preferentially aligned parallel to filaments at high, medium, and low column densities. At , the low- N H gas retains effectively the same orientation behavior, while the mid- and high- N H bins show an increasing trend toward perpendicular alignment. This trend increases


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Acknowledgements B.B. thanks the European Research Council (ERC Starting Grant 757448-PAMDORA) for their financial support. A.J. was supported by the European Research Council under ERC Consolidator Grant agreement 724687-PLANETESYS, the Swedish Research Council (grant 2014-5775), and the Knut and Alice Wallenberg Foundation (grants 2012.0150, 2014.0017, and 2014.0048). S.N.R. and A.M. thank the Agence Nationale pour la Recherche for support via grant ANR-13-BS05-0003-002 (grant MOJO). A. I. thank FAPESP for support via grants 16/19556-7 and 16/12686-2. We thank the referee John Chambers for his report and comments that helped to improve this article.


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

We thank the anonymous referee for the careful and constructive comments that greatly improved this paper. This paper is based on observations made with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, under NASA Contract NAS 5-26555. These observations are associated with Program 13364 (LEGUS). Support for Program 13364 was provided by NASA through a grant from the Space Telescope Science Institute. This research has made use of the NASA/IPAC Extragalactic Database (NED) operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. D.A.G. acknowledges financial support by the German Research Foundation (DFG) through grant GO 1659/3-2. M.F. acknowledges support by the Science and Technology Facilities Council (grant number ST/L00075X/1).


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

clear difference for the Dark Sage galaxies in Fig. C1 versus Fig. 10 is the upturn in the typical values of centrals at . This is not a sign that the analytic model breaks down; rather, what we are seeing here is a tendency for low- galaxies to have both low and low Σ 0 . This could potentially just be a reflection of the fact that this mass scale is at the simulation’s resolution limit; the median H i mass of Dark Sage galaxies occupying Millennium haloes of 100 particles is . Our Dark Sage galaxy sample with is therefore almost certainly not halo-mass complete. Current results from these galaxies should thus be taken with a grain of salt, but they should mature as Dark Sage is transitioned to higher-resolution simulations. TNG100 does not share the same feature. That is, satellites and centrals follow the same power-law-like relation for the full H i mass range (similar to the top panel of Fig. 11 ). Figure C1. Similar to Figs 10 and 11 (for the right- and left-hand panels, respectively) but now the classical H i radius has been replaced with the H i half-mass radius. For simplicity, we only show the GD14 prescription for the H i /H 2 breakdown for TNG100 (the other prescriptions give effectively the same results). Measurements of individual galaxies from our observed sample are overlaid in the top panels. Thin, dot–dashed lines in the top panel give the best-fitting linear relation to the simulated galaxies, assuming a slope of 0.5. Systematic differences seen between the simulations and observations are consistent with the standard H i size–mass relation results. For Dark Sage , satellites in low-mass haloes behave the same as centrals in their upturn in at low (cf. the top and bottom panels of Fig. C1 ). But for most satellites, i.e. those in haloes of , there is no strong upturn. To explain this, we need to understand how disc truncation would affect the – relation. As pointed out in Section 4.1 , a truncated model-1 or -2 profile with is indistinguishable from a non-truncated profile with . The higher the halo mass, the more truncated the satellite’s H i is, therefore the larger the typical fitted is, meaning the more common it is for , where . Also, because many of these satellites will have had more H i before infall, they are less likely to be biased towards low Σ 0 like Dark Sage centrals of the same current mass; in principle, unlike , truncation should not affect the best-fitting Σ 0 to [or, in this case, ]. Both effects mean satellites at low should typically have lower than centrals. The effect of halo mass on is otherwise the opposite to how it was for . That is, at fixed , satellites in higher halo masses have slightly higher on average. This can again be explained in terms of Σ 0 . Dark Sage satellites in higher-mass haloes tend to have slightly lower Σ 0 ; the medians for those in haloes of and are 10 and , respectively. While there is still a tendency for lower Σ 0 to also mean higher , the specific value of is less


O O O O O O O O O O O O O O O B-Telescope O B-Observatory O O O O O O O O O O O O O O O O O O O B-Person I-Person B-Observatory I-Observatory O O O O O O B-Person O O O B-Organization O B-Grant O B-Grant B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O B-Organization O O B-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O B-Organization O B-Grant I-Grant O O O O O O O O B-Telescope O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software B-Software O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Location O O B-Organization I-Organization I-Organization I-Organization B-Location O O O O O O O B-Software I-Software I-Software I-Software B-Software O O O O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O B-Organization B-Organization I-Organization I-Organization O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Grant O B-Grant

We thank the anonymous referees for useful suggestions on the manuscript. We are grateful to NuSTAR and Swift PIs for approving the ToO observations and to the mission operation teams for quickly executing them. We also thank P. Smith (Steward observatory) for considering our request of observations. V.S.P. acknowledges funding under NASA contracts 80NSSC17K0310 and 80NSSC18K0580. R.A. is a member of the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne. The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include NASA and the Department of Energy in the United States; the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This work performed in part under DOE Contract DE- AC02-76SF00515. This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software, and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). This research has made use of the XRT Data Analysis Software (XRTDAS). This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. This research has made use of data obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Part of this work is based on archival data, software or online services provided by the ASI Data Center (ASDC). Data from the Steward Observatory spectropolarimetric monitoring project were used. This program is supported by Fermi Guest Investigator grants NNX08AW56G, NNX09AU10G, NNX12AO93G, and NNX15AU81G.


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

We thank Boris Leistedt, Hiranya Peiris, Nishant Agarwal, Eduardo Rozo, Shirley Ho, Ashley Ross, and the anonymous referee for useful comments and discussions. We are supported by DOE Grant no. DE-FG02-95ER40899 and NSF Grant no. AST-080764. DH thanks the Aspen Center for Physics, supported by NSF Grant no. 106693, for hospitality.


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

We thank the anonymous referee for helpful comments. M.L.W. and A.I.Z. acknowledge support from NSF grant AST-1211874. M.L.W. also thanks the Technology and Research Initiative Fund (TRIF) Imaging Fellowship program for its support. C.R.K. acknowledges support from NSF grant AST-1211385. K.C.W. is supported by an EACOA Fellowship awarded by the East Asia Core Observatories Association, which consists of the Academia Sinica Institute of Astronomy and Astrophysics, the National Astronomical Observatory of Japan, the National Astronomical Observatories of the Chinese Academy of Sciences, and the Korea Astronomy and Space Science Institute. Facilities: Mayall (Mosaic-I) , Blanco (Mosaic-II) , Magellan-1 (LDSS-2 , LDSS-3) , Magellan-2 (IMACS) , MMT (Hectospec) .


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

This work was supported by NASA under Astrophysics Theory Program grants NNX11AI96G and NNX14AK44G. The authors would like to thank the anonymous referee for very useful comments that have improved the paper.


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

This work is supported in part by the French Agence Nationale de la Recherche under Grant ANR-12-BS05-0002. D.F.M. thanks the support of the Research Council of Norway.


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

This work was partially supported by the Spanish Ministerio de Economía y Competitividad through project AYA2013-43188-P. The author also thanks R. Smith, S. Courtea, S. Zarattini, and T. Lisker for useful discussions during the preparation of this manuscript. The author would like to thank the anonymous referee for the constructive revision of the manuscript.


O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O B-Identifier I-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O B-Organization B-Location B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory B-Organization O B-Observatory O O O O O O O B-Archive I-Archive O B-URL O O O O O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization B-Organization O O O B-Grant

Acknowledgements We thank the referee, Anthony Remijan, for his critical review of our article that helped to clarify several aspects of our analysis. This paper makes use of the following ALMA data: ADS/JAO. ALMA#2016.1.00074.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The interferometric data are available in the ALMA archive at https://almascience.eso.org/aq/ . Part of this work has been carried out within the Collaborative Research Centre 956, sub-project B3, funded by the Deutsche Forschungsgemeinschaft (DFG) – project ID 184018867.


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

an arc and IRS 3 a jet. IRS 3 also exhibits 3–6 cm emission which indicates shock ionization due to the interaction between the jet from IRS 3 and the surrounding gas (Young et al. 2009 ). Finally, in the outflow source L1251A, a collimated molecular outflow was detected with CO J = 2 − 1 line observation by Lee et al. ( 2010 ). The dynamical timescale of this outflow is 5.2 × 10 4 yr assuming an inclination angle of 70° (Lee et al. 2010 ). Spitzer IRAC observations revealed four infrared sources IRS 1–IRS 4. The driving source is IRS 3, a Class 0 object. From this object, a collimated long infrared jet originated. Our observed position is 12 arcsec east and 9 arcsec south to IRS 3 (see Fig. A1 ). The detected strong Spitzer IRAC observations revealed a jet with a bipolar structure extending from north to south though IRS 3. The jet may originate from a paraboloidal shock (Lee et al. 2010 ). About the N-bearing species in these outflows, the average values of x(HC 3 N)/x(HC 5 N) and x(HC 5 N)/x(HC 7 N) are 6.8 and 4.6 respectively, which are both larger than those of the Lup I starless cores and the WCCC source Lup I-1, showing that the abundance of N-bearing species decreases faster with carbon length in these outflows than in starless cores and WCCC sources. The ratio of x(HC 3 N)/x(HC 5 N) is somewhat lower than the median value (8.7) of 16 low-mass protostars detected by Law et al. ( 2018 ). Table 7 shows that in the starless cores, x(C 3 S) is two or more times lower than x(HC 7 N). The x(C 3 S) in the WCCC source Lup I-1 is also three times less than x(HC 7 N). While in the other three outflow sources the x(C 3 S) are 2–5 times of the x(HC 7 N). These results demonstrate that the x(C 3 S)/x(HC 7 N) values for the three outflows are larger than those of starless cores and the WCCC source almost one order of magnitude higher than their average value. 4.3.2 Chemical mechanism of Group JS sources The abnormal high abundance of C 3 S compared with those of nitrogen-bearing CCMs in JS sources has not been seen before. Previous studies revealed that the column densities of C 2 S have good positive correlation with those of HC 3 N and HC 5 N in quiescent dark cores (Suzuki et al. 1992 ). The column densities of C 3 S are 3–5 times lower than those of C 2 S (Suzuki et al. 1992 ; Fuente et al. 1990 ). High C 2 S and C 3 S abundances were found towards Taurus dark clouds, and there is still a good correlation between column densities of C 2 S and HC 5 N. In star formation regions, S-bearing CCMs were at best only marginally detected (Suzuki et al. 1992 ), indicating that the results of our three outflow sources are unusual. WCCC theory was a possible explanation for the large hydrocarbon abundances such as C 4 H and C 6 H present in L1251A (Cordiner et al. 2011 ). However, WCCC cannot explain the abundances of C 3 S in the three outflow sources, since the relative intensities of N- and S-bearing molecules in WCCC sources are close to those in


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


O O O O O O O O O O O O O O B-ObservationalTechniques O O B-CelestialObject I-CelestialObject O O O O O O O O O B-CelestialObject B-ObservationalTechniques 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 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 B-Wavelength B-Wavelength O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O 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 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 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 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 B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-Citation I-Citation I-Citation I-Citation 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 B-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 O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

produce 2 mag of variation in peak luminosity between the polar and equatorial directions. Polarimetric observations of SN 1998bw were also consistent with asymmetry in the ejecta of 1998bw. Polarimetry studies suggest that CCSNe, particularly those with relatively small envelope masses, may exhibit significant asymmetry in their ejecta (see, e.g., Wang et al. 2001 ). If the ejecta of ASASSN-15nx were highly asymmetrical and viewed at a favorable angle, the actual amount of synthesized might be substantially reduced from the current estimate and produce its high peak luminosity. On the other hand, there is no strong evidence of asymmetry in the [O i ] ( 6300, 6364) nebular lines, as suggested by Taubenberger et al. ( 2009 , 2013 ). However, quantitative modeling is needed to investigate whether an asymmetric model could explain the prolonged linear light-curve and spectroscopic features of ASASSN-15nx. Synthesizing a large amount of radioactive normally should also lead to nebular-phase spectra rich with iron-group elements, as seen in Type Ia SNe, but this doesn’t appear to be the case with ASASSN-15nx. This could pose a serious challenge to the high mass scenario, and nebular-phase spectral modeling would be needed to examine it further. 7.2. CSM Interaction An alternative to the radioactive decay model is strong CSM interactions. In these models, the structure and distribution of the CSM can determine the shape of the light curves. As in SNe IIn (Schlegel 1990 ), which are characterized by narrow emission lines (FWHM ∼ few hundreds of ) in the spectra, strong interactions are thought to be responsible for powering their prolonged and often luminous light curves (e.g., Smith et al. 2008a ; Rest et al. 2011 ). Sometimes ejecta–CSM interactions can lead to steeply declining light curves, as has been proposed for SN 2009jp (jet–CSM interaction; Smith et al. 2012a ) and ASASSN-15no (Benetti et al. 2018 ). PTF10iam (Arcavi et al. 2016 ), which has early light curve features similar to ASASSN-15nx, may also be explained by interaction. The density profile of the CSM can be sculpted to produce the observed light curve of ASASSN-15nx. In ASASSN-15nx, we do not see narrow- or intermediate-width emission lines from the expanding shock driving photo-ionization of the remaining CSM. It is possible to miss such emission lines if those were only present before our spectroscopic observations began at 53.0 days. However, this seems unlikely, as the continuous and linear decline of the light curve indicates a single dominant powering source throughout the evolution, which should produce similar narrow emission lines at later phases if they were present earlier. On the other hand, sometimes CSM signatures may also remain hidden if there is asymmetry or the CSM has a velocity of several thousands of . Some of the spectral features in ASASSN-15nx can be attributed to indirect signatures of CSM interaction. The synow model could not reproduce the broad and


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magenta boxes in Figure 3 ). In particular, S3 has a best-fit temperature similar to that of the gas within the interface and is in pressure equilibrium with the external gas. We note that the temperature gradient to the east is much smoother than that in the west (Figure 7 ). This difference may be due to more evident KHI to the east, which may have disrupted a previously existing cold front. KHI accelerates the turbulent mixing of gas of different phases, as we expect from theory and simulations (ZuHone et al. 2011 ; Roediger et al. 2015a , 2015b ). Large KHI rolls (above certain wavelengths, l max ) are expected to be suppressed by gravity (Chandrasekhar 1961 ). We do not expect to observe KHI rolls larger thanwhere U is the shear velocity at the front and g is the gravitational acceleration (Roediger et al. 2012b ). We assume ρ c = 1.5 ρ h and U ( r ) = 0.3 c s ( r ); c s and g ( r ) were calculated from the best-fit deprojected temperature profile and the X-ray hydrostatic mass profile (Paper 1 ). We present the maximum KHI length scale as a function of radius at the cluster center in Figure 10 . The size of these features stays below this upper limit. A potential ghost bubble of ≳5 kpc diameter resides at r = 13 kpc ( r = 10 kpc in projection) to the northwest (Figure 2 , see Paper 1 for details). Interestingly, Walker et al. ( 2017 ) propose that such giant X-ray surface brightness decrement may be due to KHI instead of AGN bubbles. The position and size of this ghost bubble candidate are also in the allowed parameter space for a giant KHI roll. Figure 10. Maximum wavelength for KHI rolls as a function of radius in NGC 1399 (black solid line). Gravity suppresses KHI above this length scale. Blue, green, magenta, and red circles mark the sizes and radii of S1, S2, S3, and a ghost bubble candidate, respectively. Alternatively, S1, S2, and S3 may be thermally unstable X-ray filaments resulting from gas cooling (David et al. 2014 , 2017 ). The growth time of KHI can be estimated from (Roediger et al. 2012a ) We calculate τ KH for the maximum KHI length scale, the maximum growth time, at each radius as shown in Figure 8 . The maximum growth time of KHI is shorter than the cooling time by two orders of magnitude. KHI is thus somewhat favored as their origin. The timescale of KHI is also significantly shorter than the dynamical timescale (free-fall time or buoyant rising time), implying that KHI, coupled with gas sloshing, may have played an important role in regulating the thermal state of the hot plasma at cluster centers. 5. Conclusions The Fornax Cluster is a nearby low-mass cool-core cluster. It displays prominent sloshing structure wrapping around the cluster center. We analyzed a mosaic XMM-Newton observation and a total of 250 ks Chandra observations centered on its BCG NGC 1399. We present the properties of the hot gas over a radial range of 1–250 kpc. We found the following. 1. Four sloshing fronts are visible at radii of 200 kpc,