tips of the H 2 bow shocks, where the shock velocities are high and the gas will be dissociated, rather than behind the H 2 bow shocks (e.g., Davis et al. 1999 , 2000 ; López et al. 2010 ; Lee et al. 2014 ; Bally et al. 2015 ). Detection of further [Fe ii ] emission in G53.11_MM1 with high signal-to-noise ratio requires deeper imaging observations, although the marginal detection of [Fe ii ] emission can be interpreted as intrinsically fainter or absent [Fe ii ] emission compared to H 2 emission. In the outflows from high-mass YSOs, the [Fe ii ] detection rate with respect to the H 2 detection rate tends to be low, ≲50% or much less (Cooper et al. 2013 ; Wolf-Chase et al. 2013 ; Caratti o Garatti et al. 2015 ). The brightness of the [Fe ii ] lines also tend to be weaker than the brightness of the H 2 lines (Caratti o Garatti et al. 2015 ). This can be attributed to the different extinction effect between the two lines but it is more likely to happen because H 2 and [Fe ii ] emission arise from different physical conditions, such as gas density, temperature, or shock velocity. In the G53.11_MM1 outflow, the strong, extended H 2 emission with very weak or negligible [Fe ii ] emission may imply that slow, C-type shocks are dominant in G53.11_MM1. Further spectroscopic observations will be necessary to derive the physical conditions of the environment and confirm the shock’s properties. 5. Central YSOs The core G53.11_MM1 is bright from IR to millimeter, with a large IR-excess emission. The central star (YSO1) was previously identified in the Red MSX Source survey with a bolometric luminosity of (3–4) × 10 3 L ⊙ (G053.1417+00.0705; Mottram et al. 2011 ; Lumsden et al. 2013 ); however, it is in fact composed of two sources, YSO1 and YSO2, which are separated by ∼8′′ in the Spitzer mid-IR images with higher spatial resolution. Both YSOs are saturated in the MIPS 24 μ m image but their SEDs with strong excess in mid-IR and spectral indices derived by using the available photometry from the GLIMPSE and MSX catalogs classify them as Class I YSOs that have a dusty envelope infalling onto a central protostar (Kim et al. 2015 ). The two YSOs are also observed in near-IR wavebands. Both are fairly bright in the K -band, marginally detected in the H -band and are not observed in the J -band, which indicates that they are deeply embedded. The evolutionary stages of the YSOs, with the proximity to the center of the outflow (see Figure 2 ), suggest that one or both can be the driving source of the G53.11_MM1 outflow. The coordinates of YSO1 and YSO2 are ( α 2000 , δ 2000 ) = (19 h 29 m 1760, +17°56′233) and ( α 2000 , δ 2000 ) = (19 h 29 m 1726, +17°56′173), respectively. In the following, we will discuss their photometric variability in near-IR and physical parameters constrained from SED analysis. 5.1. Near-IR Photometric Variability YSOs are known to commonly show variability (e.g., Carpenter et al. 2001 , 2002 ; Morales-Calderón et al. 2011 ; Johnstone et

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


as well (see, e.g., Gromadzki et al. 2013 , for more details about light curves of S-type symbiotics). 3.4. Hot component and outburst activity The most prominent features in the light curves of Gaia18aen (Fig. 7 ) are the outbursts observed in 2018. In Fig. 8 , the part of the light curve showing the active stage is depicted. For clarity, the light curves in various filters were shifted to the same level to study the structure of the active stage. Individual brightenings are labeled by the numbers 0−5. Fig. 7. Light curves of Gaia18aen. Individual light curves in various filters were shifted to the level in the OGLE V filter for clarity; values of shifts are shown in the figure legend. Different colors denote different filters. Fig. 8. Outbursts of Gaia18aen. The colors are the same as in Fig. 7 . The vertical dotted lines indicate the individual brightenings (denoted by numbers 0−5). The arrows show the times when the two spectra were obtained. Fig. 9. Light curves in selected filters phased with the period of P = 486.9 d. Individual datasets were shifted to the level in the OGLE I filter. The first small pre-outburst of about 0.5 mag in V filter (denoted 0) was detected at JD 2 458 089. It was followed by more prominent outburst (1) after approximately 27 d (JD 2 458 116) of gradual decline. The maximal brightness during this outburst was ≈11.2 mag in V filter (JD 2 458 119), thus the amplitude was about 3.3 mag in comparison with the quiescent V magnitude (OGLE V ∼ 14.5). The analysis of the combined light curves constructed from the observations in various filters revealed the complex structure of this outburst with at least two another re-brightnenings that followed the first maximum. Approximately after 47 d (JD 2 458 163) after the first maximum Gaia18aen reached the magnitude similar to the brightness of the pre-outburst 0. The outburst denoted in this paper as 2 started after 57 d of a quasi-steady period (JD 2 458 220) and lasted for 35 d (until JD 2 458 255). The maximal brightness in V filter during this period was ≈12.5 mag. A third, small-scale outburst was detected at JD 2 458 357. The amplitude of the outburst was much smaller than in the previous cases, however, the approximate duration was similar to the outburst 2. Up-to-now, the last two increases in brightness (denoted 4 and 5) were detected at JD 2 458 470 and JD 2 458 503. It is worth noting that both brightenings were much shorter than the previous events, at 12 and 15 d, respectively. Moreover, the shape of at least the first event (4) looks as thought it was suddenly interrupted, which may indicate that both brightenings are part of a single outburst that is apparently interrupted by some obscuration process. Since JD 2 458 518, there were no other significant brightenings detected in the case of Gaia18aen. The amplitude of the outbursts and their duration resemble the behavior of typical classical symbiotic stars (e.g., AG Dra, Z And; see, e.g., Mikołajewska et al.

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


galaxies. These objects were used to draw conclusions about the AGN population that would be missed in optical and X-ray surveys. Of the 30 AGN candidates using the Jarrett et al. ( 2011 ) selection box and presented in Satyapal et al. ( 2014 ), only one object is in the mass and redshift range probed by our analysis here (the others are either at higher masses or higher redshifts), and it is found in our sample of star-forming dwarfs in the Jarrett et al. ( 2011 ) box (NSA ID 93798). Secrest et al. ( 2015 ) measured an X-ray luminosity from XMM-Newton observations (extracted with a ∼15′′ aperture) of L 2–10 keV = 2. 4 × 10 40 erg s −1 for this object, and claim that the W1 − W2 color is strongly indicative of AGN activity. While this object is indeed in the Jarrett et al. ( 2011 ) selection box, given the median uncertainties on the WISE photometry, its infrared colors are consistent with this object potentially being scattered from the primary locus of star-forming galaxies and it does not have a strong power law to longer infrared wavelengths as expected for an AGN. Sartori et al. ( 2015 ) presented a sample of 83 objects with photometry placing them in the Jarrett et al. ( 2011 ) selection box, using data from the older WISE All-sky data release. These authors only required S/N > 2 for detections in the W1 , W2 , and W3 photometric bands. We cross-matched against the more up-to-date AllWISE selection, and using a S/N cut of 3.0, we find that only 34 objects (∼41%) continue to fall inside the Jarrett et al. selection box. 9 9 All 83 of the objects in the Sartori et al. ( 2015 ) sample have updated AllWISE W1 and W2 photometry with S/N > 3.0, but 26 of the objects have W3 photometry with S/N 3, only 10 of which have 2 S/N 3. Of these 34 objects, only 15 are in our parent sample of dwarf galaxies. The remaining 19 objects are either not in the NSA because their redshifts are greater than 0.055, or are in the NSA but not classified as dwarf galaxies by our mass criterion. Looking closer at these 15 dwarf galaxies, 10 are found in Table 1 (NSA IDs 4610, 6205, 10311, 53934, 57649, 93798, 109919, 117162, 118025, and 118523), 4 of the 15 are BPT-selected AGNs or composite galaxies (NSA IDs 10779, 79874, 124050, and 125318), and one is the previously discussed quasar contaminant (NSA ID 110100). One object that was listed as a Stern et al. ( 2012 ) candidate but not a Jarrett et al. ( 2011 ) candidate in Sartori et al. ( 2015 ) moved into the Jarrett et al. ( 2011 ) selection box with the updated AllWISE photometry (NSA ID 98135), and one object we have listed in Table 1 does not appear in Sartori et al. ( 2015 ) (NSA ID 151888). 3.5. The Feasibility of Detecting Supermassive Black Holes in Dwarf Galaxies with WISE Finding evidence for AGNs in dwarf galaxies is challenging as AGNs at a given accretion rate have lower bolometric luminosities due to the smaller masses of the central black holes, making them harder to observe above the emission due

O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-CelestialObject I-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O B-Telescope O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Telescope O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O O O O B-Wavelength O B-Wavelength O O B-Wavelength 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 B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Survey B-Wavelength O B-Wavelength O O B-Formula I-Formula I-Formula O O O O O O B-Wavelength O O B-Formula I-Formula 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-Dataset 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 O O O O O O O O O O O O O O B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Survey O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-CelestialObject I-CelestialObject I-CelestialObject 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


It is defined as the standard deviation of the differential light curve over each of the five rotations (Mathur et al. 2014 ). In the analyses below, all three of these measures were tried and found to be essentially equivalent for the purpose of correlating brightness with variability. The method actually employed in this paper is the re-sampled fit to the smoothed R loc ; we will call this R smo . This leads to a set of both absolute brightness and variability measurements at the same 45 time points in each light curve. A few illustrations of these sets are provided in the upper panel of Figure 11 . A linear fit is made to each set of points, and both the slope and Pearson-r correlation coefficient are computed. For the small and large red asterisks, the [slope, Pearson-r] values are [−0.14, −0.91] and [−0.92, −0.84]; for the small and large pluses, they are [0.16, 0.87] and [0.59, 0.53]; and for the small and large black diamonds, they are [0.00, 0.01] and [−0.20, −0.30]. The KIC numbers for the stars shown (in the same order) are 5302725, 9334867, 8078753, 11014223, 2694810, and 11299398. Shown in aqua in the lower panel are the 12 stars that MTF17 identified as exhibiting clear activity cycles over 4 years of observations (their Figure 5 ). Four of these are very clear-cut cases of spot dominance (those with the most negative r coefficients and slopes), two are unclear (those above the lower dotted line), and the rest are distributed along a continuum of spot dominance. Figure 11. Upper panel: five illustrative sets of brightness vs. variability. They have been scaled and shifted to fit on the plot. Color and symbol size are related to slope (see text). Lower panel: slopes of the linear fits to the brightness vs. variability points for all stars; the ordinate is the Pearson-r coefficient for each star. The colors indicate the designations from MTF17 based on the sign of their correlation slopes (see text). Green points are stars with clear brightness cycles in MTF17. MTF17 divided the sample into three cases: anti-correlated (red), correlated (blue), and not clear (black); the colors in Figure 11 correspond to their classification. As explained in Section 2.1 , the “anti-correlated” label is used for stars that become brighter as they become more variable; they are generally interpreted to be faculae-dominated. The points for such stars have a positive slope, so they should lie in the upper right quadrant of the lower panel of Figure 11 , which shows the results for the full sample. Similarly, the blue (correlated) stars get darker as they get more variable (spot-dominated) and are in the lower left quadrant. Most stars from the sample (320 in MTF17; 322 for us) are in this category. In most cases (310 stars), their sense agrees with ours, although there are a few red points in the lower left quadrant, and stars that they did not classify in either category (black) are found in both quadrants for us. The most likely source of discrepancies

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


O O O O 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-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O B-Tag B-Tag 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-TextGarbage I-TextGarbage O O


of the solar wind at 1au is a few km s −1 ( Němeček et al. 2020 ), which is small compared to the average radial wind speed of 400–600 km s −1 . Despite this, attempts to constrain the solar wind AM flux have been made in the past (e.g. Lazarus Goldstein 1971 ; Pizzo et al. 1983 ; Marsch Richter 1984 ; Finley et al. 2019 ). Though each of these studies suffered from uncertainty, either due to the precision of the spacecraft pointing or the ability of the plasma instruments to detect the small tangential flows. These uncertainties are lessened with Parker Solar Probe (PSP) which samples the solar wind within 0.25 au, where the signal to noise on the tangential wind speed measurements should be increased and the influence of wind-stream interactions reduced. However, during its first few encounters, PSP detected tangential solar wind speeds of up to ~ 50 km s −1 ( Kasper et al. 2019 ). These speeds are far greater than expected from magnetohydrodynamic (MHD) modelling (e.g. Réville et al. 2020 ) and, if they were prevalent throughout the corona, would be incompatible with the AM-loss rate implied by the slope of the rotation-age relation. Finley et al. (2020) analyse the data from the first two orbits of PSP and show these flows to be localised, existing along with wind streams that have large negative tangential speeds. Therefore, the average equatorial solar wind AM flux measured by PSP is similar to observationsfrom previous spacecraft. At present, the mechanism(s) that generate these large tangential solar wind speedshave yet to be determined. One possibility is the motion or circulation of open magnetic flux at the base of the wind ( Crooker et al. 2010 ; Fisk Kasper 2020 ; Macneil et al. 2020 ), though this is also not well understood. During PSP’s first two perihelion passes (E01 and E02, respectively), neither the Solar Probe Cup (SPC, Case et al. 2020 ) or the Solar Probe ANalysers (SPAN; Whittlesey et al. 2020 ; Livi et al. 2020 ) were able to confidently measure the properties of the alpha particles in the solar wind. Previously, Pizzo et al. (1983) used Helios observations to show that the alpha particles contain a large negative contribution to the total AM flux (see also Marsch Richter 1984 ). Though, due to an error in spacecraft pointing, the data from Helios required a significant correction, and more recent measurements of the alpha particle AM flux using the Wind spacecraft at 1au instead suggest a much smaller (but still negative) contribution ( Finley et al. 2019 ). As the alpha particles carry roughly 15− 40% of the linear momentum in the solar wind, it is vital that their contribution to the total solar wind AM flux is better understood in order to further constrain the slope of the rotation-age relation for Sun-like stars. In this work, we analyse more recent SPAN-Ion observations from the third and fourth encounters of PSP (hereafter E03 and E04), which we use to determine the mechanical AM flux of both the solar wind

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


equation of state (EOS) has been studied for hydrodynamic turbulence and for a polytropic EOS (Federrath Banerjee 2015 ) or an adiabatic EOS (Nolan et al. 2015 ; Mohapatra Sharma 2019 ), indicating additional dependencies, on (for example) the adiabatic index γ , the relation between density fluctuations and . In the magnetized case the majority of studies focus on the isothermal case , finding an additional dependency on the ratio of thermal to magnetic pressure (e.g., Kowal et al. 2007 ; Padoan Nordlund 2011 ; Molina et al. 2012 ). Overall, a highly dynamic picture of turbulence has been found, challenging our ability to examine the general case. In this paper, we present adiabatic magnetohydrodynamic simulations of stationary turbulence in the subsonic ( to 0.6), super-Alfvénic (), and high (ratio of thermal to magnetic pressure with ) regime. This regime approximates the turbulent intracluster medium (ICM; Brunetti Lazarian 2007 ; Brüggen Vazza 2015 ) even though our magnetohydrodynamics (MHD) model neglects effects stemming from low collisionality (Schekochihin Cowley 2006 ; Schekochihin et al. 2008 ). However, studies including effects from low collisionality, e.g., through the Chew–Goldberger–Low MHD model, found that they generally introduce only small differences compared to the MHD model, e.g., a small increase in density fluctuations (Kowal et al. 2011 ; Santos-Lima et al. 2017 ), but leave imprints on Faraday rotation maps (Nakwacki et al. 2016 ). Here, we specifically focus on the effects of departure from an isothermal equation of state by varying the adiabatic index γ and the cooling function between simulations. The rest of this paper is organized as follows. In Section 2 , we introduce the numerical setup and the simulations conducted. In Section 3 , we present results from analyzing the simulations starting with a high-level overview of the energy spectra, to correlations in the stationary regime, to statistics of distribution functions that can potentially be used to break degeneracies between the thermodynamics and sonic Mach number. The results are discussed in Section 4 , and we conclude with a brief outlook in Section 5 on how our findings point the way to future measurements that can be used to better diagnose the properties of turbulence in astrophysical plasmas. 2. Numerical Details In this work we utilize the equations of compressible, ideal MHD equations that are closed by an ideal equation of state , with γ as the ratio of specific heats. The symbols have their usual meaning, i.e., density ρ , velocity , total pressure consisting of thermal pressure and magnetic pressure , and magnetic field , which includes a factor . Cooling is included via and is the total energy density with specific internal energy e . Vector quantities that are not in boldface refer to the L 2 norm of the vector and ⨂ denotes the outer product. The details of the acceleration field that we use to mechanically drive our simulations are

O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation I-Citation O O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation 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 B-Model I-Model 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 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-Model I-Model I-Model O O O O O O O O O O B-TextGarbage 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 O O O B-Model B-Model O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O B-Model I-Model 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 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 B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


again. The velocity is calculated by dividing the distance that the center of the BD moved by the time between recordings. The image was then advanced again and this process is repeated until the BD disappears or merges with another BD. Because the lifetime of the BDs is variable, the time between recordings varies, but as a general rule the number of recordings is maximized (minimizing the time between each recording) but there are at least 11 s between each recording. The average velocity of a BD is the average of these multiple velocity measurements. The speed was measured for only 25 BDs because there were not enough data points for five of the BDs. Figure 3 (i) is a scatterplot between the speed and the ratio of length-to-width of the BDs. We plot this figure in an attempt to find a correlation between how long a BD is relative to how fast it is moving (the thought being that faster BDs might be elongated in the radial direction), but evidently there is no clear relationship; there is perhaps a slight tendency for faster BDs to have less elongation. To investigate the formation mechanism and temperature of these BDs, we obtained their light curves from five AIA channels. Figure 4 shows the light curves of four of our BDs. These light curves are made by tracking the BD from when it first begins to brighten, through peak intensity, and ending when it fades from view or gets dim enough. To measure the intensity, we first find the target BD using the Hi-C 193 Å images and then match the location to the AIA 193 Å images. We center a circle on the BD's brightest part and measure the intensity inside. The frame is advanced and the intensity is measured for the new time, again with the circle centered on the brightest part of the BD. In this way, we track the BD's peak brightness over its lifetime or over its brightest peak during its lifetime. This intensity is then normalized to the highest intensity over the period. Figure 4. Normalized light curves for four example BDs from a set of five AIA bands. Each set of light curves is from tracking the brightest part of the BD as it drifts laterally during its peak brightening. As denoted in each panel by different colored lines, orange is for 193 Å, pink is for 211 Å, yellow is for 171 Å, green is for 1600 Å, and red is for 304 Å. Please note that the time on the x -axis is based on the AIA 193 Å channel; the closest available data in time for other channels is taken at each time step. Therefore, a few seconds’ difference in the observation of different channels is not seen. Asterisks on the 193 Å light curves mark data points. We use four AIA wavelengths in addition to the 193 Å: 211, 171, 1600, and 304 Å. The AIA 171, 193, and 211 Å channels are typically coronal, as their response functions peak at temperatures of roughly 1, 1.5, and 2.5 MK, respectively (Lemen et al. 2012 ). However, all of these channels have cooler-TR lines in the passband and hence have some response in the cooler-TR

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


in the W 1 and W 2 bands and are characterized by W 1 − W 2 0.5 mag. Instead, the red W 1 − W 2 > 1 of our objects imply a considerable contribution of the warm and hot dust to their mid-infrared luminosity (Izotov et al. 2014a ). Three out of five galaxies were detected by WISE in the W 4 band at 22 μm. The estimated ratio of the 22 μm luminosity, which is a characteristic of warm dust, to the luminosity absorbed at 1500 Å in these galaxies is of order of unity (Table 9 ). As the luminosity of the cold dust emitting in the far-infrared range of extreme starbursts (not accessible to WISE ) is less or comparable to the luminosity of the warm dust (Izotov et al. 2014b ), we conclude that the UV luminosity absorbed in visible star-forming regions of our galaxies is consistent with the luminosity emitted by dust in the infrared range. Optical, near- and mid-infrared observations of other low-metallicity SFGs with similar properties suggest that they are relatively transparent (Izotov Thuan 2011 , 2016 ). That there is not much dust-obscured hidden star formation is also implied by the observed thermal free–free cm radio emission in dwarf galaxies with optical and infrared observations. Its flux density is consistent with the value derived from the flux density of the H β emission line (Izotov et al. 2014b ), indicating that there is not a considerable amount of additional star formation, not seen in the UV range, in our galaxies. 10 DISCUSSION To the best of our knowledge, our experiment is the first where compact SFGs with strong emission lines and high [O iii ]λ5007/[O ii ]λ3727 ratios are observed in the LyC. Furthermore, the entire sample (five out of five) at z ∼ 0.3 is found to emit LyC radiation, with absolute escape fractions ranging between 6 per cent and 13 per cent. Our observations thus significantly expand the sample of LyC leakers at low redshift, from four previously known galaxies (Leitet et al. 2013 ; Borthakur et al. 2014 ; Leitherer et al. 2016 ) to nine. The newly discovered sources also show significantly higher LyC escape fractions, compared to f esc (LyC) ≈ (1–4.5) per cent previously found. Apparently, the selection criteria we adopted are very efficient in finding LyC leakers. As such, this finding is probably one of the most important results of our study. Compactness and a peculiar emission line ratio as selection criteria, were previously already suggested to be related to LyC leakage. Jaskot Oey ( 2013 ) and Nakajima Ouchi ( 2014 ) have proposed that extreme [O iii ]λ5007/[O ii ]λ3727 ratios may be due to high escape fractions of ionizing photons and have argued that this could be the case for some ‘GP’ galaxies at z ∼ 0.1–0.3 or in z ∼ 2–3 LAEs. For comparison, Heckman et al. ( 2011 ) examined so-called Lyman-break analogues (LBAs) and suggested that a subset of them, those with a compact massive (∼10 9 M ⊙ ) dominant central object, could be LyC leakers. The LBAs have lower excitation and higher masses compared to

O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula 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 B-Wavelength O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Telescope 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-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O B-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 B-Wavelength I-Wavelength O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O B-Wavelength O O O O O O O O O B-Formula I-Formula I-Formula O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength 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 B-Wavelength 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula B-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O


and 180° to the phase space densities at 90° are greater than three. It is easy to see that strong depletions occur within the first bar, and the depletion CSE interval was removed when we estimated the percentages of CSEs. One can also see that the bars in the rear half have two short intervals, which are caused by scattering of strahl electrons. We therefore identify the two short intervals as CSE strahls, and the percentage of CSE strahls is about 35%. Fig. 1. Suprathermal electron pitch angle distributions of 272 eV, magnetic field and plasma data measured by ACE during the October 21C22, 1999 ICME passage. The two vertical dashed lines denote the boundaries of the ICME. Furthermore, this study examined all the suprathermal electron PADs of the 272 ICMEs and estimated the percentages of CSEs. The results are listed in the sixth column of Table A.1 . Only 10 (9.9%) of the 101 MCs have no CSE, and the ratio is consistent with the results of Shodhan et al. (2000) , who examined the CSE signatures of 52 MCs and concluded that 6 MCs have no CSEs. As for the other 91 MCs, the percentage of CSEs varies from 6 to 100%, with a mean value of 57%. Meanwhile, 75 of the 171 nonMC ICMEs (43.9%) do not contain CSEs. The fraction of ICMEs without CSEs is thus clearly larger in nonMC ICMEs than in MCs. The extensive difference may imply that the two groups have different magnetic structures. For the other 96 nonMC events, their mean CSE percentage is 45%, which is smaller than for the MCs (57%). Among the 96 nonMC ICMEs, 21 have greater than 70% CSEs. Examination of the magnetic field component curves of these 21 ICMEs reveals that fields of most events have neither apparent smooth rotations nor disorder, but their magnetic field component curves have only slight rotations, and they are relatively stable or even close to the line. It is well known that most MCs can be described with a constant force-free field configuration, for example, the Lundquist solution ( Lepping et al. 1990 ; Feng et al. 2006 ). According to the Lundquist solution, the shapes of measured field component curves depend on the distance d 0 between the spacecraft trajectory and the rope axis (see Figs. 2–4 of Feng et al. 2006 ). The spacecraft will measure center-enhanced and bipolar curves if the spacecraft trajectory is close to the rope axis; otherwise, the bipolar curves will disappear. Figure 2 shows the variations of the magnetic field components for the case of d 0 = 0.9 R 0 , where R 0 is the radius of the flux rope, z is the axial direction, x is the radial direction pointing to the satellite contact position, and the direction y is obtained from the cross product of z and x . In Fig. 2 , all the three magnetic field components are relatively stable and exhibit only slight rotations. These trends indicate that the spacecraft that passes through the flank of a magnetic flux rope will measure relatively stable magnetic field variations. Therefore, the 21 highest percentage (more

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


calculations and the applicability of their formula for C-rich AGB stars with Z ini 10 4 should be checked by using the appropriate values. Also, the dependence of the mass-loss rate on the velocity amplitude of pulsation should be investigated, since the dependence is considered to be more sensitive for stars with larger C and R . The mass-loss rate derived from the DDW model is significantly smaller than the mass-loss rate assumed in stellar evolution calculations. If we use the derived mass-loss formula after the necessary condition for the efficient DDW is satisfied on the TP-AGB, the dredged-up carbon accumulates in the surface regions; accordingly, the effective temperature decreases and the mass-loss rate could increase. Although in the present calculations the derived mass-loss rate is inconsistent with the assumed mass-loss rate, it should be recalled here again that the hydrodynamical model can derive the properties of the DDW by specifying a set of input parameters, being independent of the stellar evolution model. Thus, the derived formulae, together with a necessary condition for the efficient DDW presented in Section 5.1 , could enable us to evaluate the mass-loss rate and dust yield during the C-rich AGB phase of stars with Z ini 10 4 in a manner consistent with stellar evolution, including whether the efficient DDW can operate on the C-rich AGB. 5.3 Implication for evolution of C-rich AGB stars and the dust-driven wind in the early Universe Investigations on the formation of stars in low-metallicity environments have revealed that the critical metallicity Z cri for the transition from Population III to Population II stars is as low as 10 9 10 7.5 , depending on the depletion factor of metal into dust (e.g. Omukai etal. 2005 , Schneider etal. 2006 , Chiaki etal. 2015 ). Although there is no information available for the initial mass function at the present time, intermediate-mass AGB stars with Z ini 10 4 can contribute to the enrichment of dust in the early Universe if the condition for the efficient DDW derived in the previous subsection is satisfied during the TP-AGB phase. However, the possibility of developing dust formation and a resulting DDW on the AGB is strongly influenced by the mass-loss history during the evolution, on which the time evolution of effective temperature as well as the elemental composition and opacity in the surface layer depend strongly through the number of TDU episodes and/or the occurrence of HBB. At present, we have no knowledge of the mass-loss mechanism and mass-loss rate before the onset of the DDW for the extremely low-metallicity stars considered in this article. In recent investigations focused on low-metallicity (1.6[Fe/H] 0.5) AGB stars observed in distant galaxies, Rosenfield etal. ( 2014 , 2016 ) showed that a mass-loss rate higher than SC05 is required during the AGB phases previous to the onset of the DDW, to reproduce the observed TP-AGB luminosity function as well as the number

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 B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O 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 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 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-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O B-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


the tail in the velocity distribution is produced independently of η, with velocities up to ∼1000 km s −1 . However, different eccentricities do not change the shape of the distribution function with respect to the case of the circular orbit. Therefore, these results suggest that the energy exchange between the generic star of the GC and the BHB is almost independent on the eccentricity, depending only on the initial total energy of the binary. Figure 3. Comparison among the velocity distributions of escaping stars for an SMBHB with mass ratio ν = 1/4 and different eccentricities (η = 0, 0.25, 0.75). The distributions are cut on the left side at 212 km s −1 , which corresponds to the escape velocity from the system evaluated at 20 pc. For what regards the branching ratios, Table 2 shows the branching ratios as function of η. From this table, it is clear that the branching ratio remains nearly constant for different eccentricities. Therefore, not only the shape of the velocity distribution is preserved, but also the probability of star ejection. Table 2. The values of the Branching Ratios (BR) for ν = 1/4 and different BHB orbital eccentricities, η. To conclude, the BHB orbital eccentricity does not affect neither the shape of the velocity distribution nor the branching ratio of ejected stars. Therefore, the main features of the ejected stars depend on the binary mass ratio ν, but not on the binary eccentricity. 3.3 The role of the GC orbital inclination In our scattering experiments, the GC orbits are coplanar with the BHB orbital plane. This means that the angular momentum of the GC and that of the BHs are aligned. In order to explore the role of the GC orbital inclination, we performed a set of simulations in the extreme case of GC orbits perpendicular with respect to the BHB orbital plane, in the case of mass ratios ν = (1/20, 1/10, 1/5, 1/3). The results of our scattering experiments reveal that the GC orbital inclination plays an important role both for the branching ratio and the resulting velocity distribution. Fig. 2 shows the branching ratios for both the coplanar and perpendicular cases. In the perpendicular case, the branching ratios of the ejected stars are reduced. Actually, the angle between the two angular momentum vectors results to have an important role in the output of the scattering experiments, as the relative inclination of the angular momenta of the GC and of the test star has. Therefore, the actual value of the branching ratio comes from a combination of two effects due to the two-mentioned relative inclinations. Calling β and γ the angles between the pairs of (GC, BHB) and (test star, GC), respectively, the higher probabilities are obtained when β ∼ 0 and γ ∼ 0. Finally, when ν ≲ 1/20, the branching ratio tends to the value of the single BH case, for which β is not defined and consequently only γ has a role in the output. The effect of the GC orbital inclination is significant also in the velocity distribution of the

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


the numerical code. The second term is the source term, , which describes the injection of new power-law particles into the causal volume. In general, S ′ ( p e ) receives contributions from other processes, such as Compton scattering, pair-production and annihilation. The advection coefficient for the adiabatic cooling of particles is given by Here, we have used the scaling of particle energy with comoving volume due to adiabatic expansion, such that where is the adiabatic index for a relativistic (non-relativistic) particle distribution. In general, the advection coefficient includes contributions from other processes that change the energy of particles, e.g. Compton scattering, synchrotron cooling, Coulomb interactions, and particle heating (as described below). The adiabatic cooling timescale is obtained from the rate of volume expansion, where where ζ = 7/3 for r r s when Γ ∝ r 1/3 , and ζ = 2 for r ≥ r s when Γ = Γ ∞ . By expressing the LHS of equation ( A3 ) using the number density, we find where we have conveniently defined the comoving growth time of the causal volume, , through Next, we use equation ( A2 ) to express the rate of change of the comoving number density with comoving time in terms of and the causal volume , so that which in turn implies where the comoving particle injection time into the causal volume is defined by and is the particle injection rate per unit volume. Note that the causal comoving volume grows faster than the total comoving volume V ′ since it occupies an increasing fraction of it, , where . Now, using equations ( A3 ) and ( A6 ) lead to the equation for the number density evolution where . By integrating the above equation over p e , it can be shown that the adiabatic cooling term vanishes and , where so that the equation reads . The comoving rate of particle injection per unit volume per unit dimensionless momentum comprises of two terms, where a fraction ξ of the total is accelerated into a power-law (non-thermal) distribution and the remaining fraction (1 − ξ) forms a thermal distribution, where represents the normalized momentum distribution. The total energy density per unit rest mass energy of the injected distribution can be expressed as where 〈γ e 〉 th is the mean energy per rest mass energy of the thermal distribution and for the power-law distribution 〈γ e 〉 nth is given in equation ( 10 ). Here, we make the assumption that the injected thermal particles are cold, so that . The momentum distribution of power-law electrons is given by The normalization is obtained by equating the rate of energy injection per unit volume to that given to the electrons due to dissipation, such that which for γ M > γ m ≫ 1 gives where we take γ M = γ max , the maximum LF corresponding to the outer boundary of the particle momentum grid in the simulation. The efficiency of acceleration is controlled by the mean energy of the power-law electrons, which depends on ξ, and ultimately by the minimal energy of power-law

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


in the magnitude range where our analysis is conducted ( g 24). This procedure was repeated 10 4 times and the corresponding distributions of N syn and μ V, syn were computed. The number of stars contained within the same magnitude limits defined above was counted in the observed CMD and the density of stars per square degree Σ obs was calculated by dividing by the sampled area. The fractions f N of random extractions with N syn Σ obs and the fractions with μ V, mod > μ V, max were then computed. If the MS star density estimated around the sample of observed GCs were compatible with that predicted by models, the distribution of percentiles would be uniform. In Fig. 7 , the cumulative distributions of percentiles of the eight GCs at d ⊙ 45 kpc with respect to the N syn distribution of the five Aquarius simulations are shown. On average, the distribution of percentiles is consistent with a uniform distribution (although a vast range of lumpiness is covered by the five considered simulations), indicating a general agreement with model predictions for three out of five simulations. A Kolmogorov-Smirnov (KS) test indicates probabilities 0.1 P 0.2 for these simulations . However, the simulations Aquarius D and Aquarius E show opposite trends with distributions of percentiles that are incompatible with observations. Note that Aquarius D is the most massive halo among the five simulations of the Aquarius sample, with a virial mass M = 2.52 × 10 12 M ⊙ , exceeding the current estimate for the Milky Way (Patel, Besla Mandel 2017 ). It is therefore likely that the number density of the halo is also overestimated in this simulation. On the other hand, simulation Aquarius E is the one with the lowest fraction of stars in the diffuse halo at distances d GC > 20 kpc, with the majority of stars in this distance range contained in bound satellites. For this reason, the number density outside satellites turns out to be lower than those in other haloes. Figure 7. Cumulative distribution of percentiles in the number density domain for the eight GCs at d ⊙ 45 kpc. Different lines refer to the various cosmological simulations. The probabilities associated with the KS test are also indicated. The same conclusion can be drawn when the entire sample of 14 GCs is considered in the μ V space. The distributions of extracted surface brightness from each of the considered simulations are shown as a function of heliocentric distance in Fig. 8 . We note that the background surface brightness distribution is peaked at values in the range 30 μ V, syn 35 mag arcsec −2 following a declining trend with distance. At large distances, the surface brightness distribution becomes skewed with a tail towards bright values at μ V, syn 34 mag arcsec −2 . This is a consequence of the increasing degree of lumpiness of the halo at large distances: GCs forming within satellites in an early stage of dissolution are still surrounded by the compact remnant of their host galaxy. The upper limits

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model O B-Model I-Model 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 B-Model I-Model 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 B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 was about 3 per cent) to about 4.5 per cent at the time of our observations. In this spectral region, we have not detected any change between 2015 and 2018, but data obtained in 1995 were in between the values measured in the two epochs. At 6800 Å, data obtained by Putney ( 1995 ) show the lowest values among all data sets (∼1 per cent). Our BBP measurements in the red (4.0 per cent integrated over a R filter) are consistent with the relatively recent BBP measurement of Butters et al. ( 2009 ), who had detected a signal of 4.06 ± 0.16 per cent. In conclusion, we have clearly detected a change of 1.5 per cent over a 40+ yr interval, but found no evidence of change over a time-scale of the order of three years. 8.3 Linear polarization No large changes of the fraction of linear polarization are detected either on a short (3-yr) or long (40-yr) time-scale. However, over a 40–45 yr interval of time, the position angle has definitely changed by more than 10° both in the blue and the red. In the following, we look at the various linear polarization spectra and their differences in more detail. On the long time-scale sampled by the difference between the 1970s data and our recent ISIS spectra (40 yr), there definitely are changes. In particular, below 4000 Å, the recent level of linear polarization sampled by Q / I seems to have decreased, while that sampled by U / I is larger. This corresponds to a very significant rotation of the position angle of the linear polarization away from the value of ∼20° found in the 1970s to about 33° in recent times. We note that the measurement by West ( 1989 ) obtained 1986 suggests also a decrease of linear polarization compared to the 1970s (3.19 per cent in the B filter, for a position angle of 19.1 ± 0.8) but as discussed in Section 4.3 , these kinds of comparison should be made with caution. It is notable that although the circular polarization is quite different from zero throughout the visible spectrum, the non-zero linear polarization is present essentially below 5500 Å, with possible low-level features suggested by the Steward spectrum, but largely absent from the lower resolution MCSP data. The position angle in the red as measured in the 1970s was around 110°, with a fair amount of scatter due to the small but not quite vanishing amplitude of Q and U in that region. In the ISIS data, both Q and U are also close to zero, therefore the position angle has a large uncertainty, but is consistent with a 10°–30° rotation from the value measured in the 1970s. We conclude that linear polarization measurements are certainly variable over a time-scale of decades, mostly in terms of a rotation, while no significant variation has been detected on time-scale of three years. A rotation constant in wavelength provides a first rough description of the change in linear polarization. 9 CONSTRAINTS ON THE ROTATION PERIOD OF Grw+70° 8247 Measurements of the position angle of the broad-band linear polarization of Grw+70°

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


also do not show another source within the NACO FoV, indicating that both BHB2007-2AB and VLT 171104.07-272258.8 are more evolved than BHB2007-1. In the analysis we also calculated the photometry in the K S band of BHB2007-2AB and VLT 171104.07-272258.8, listed in Table 2 . Table 1 Astrometric Measurements of the Components Measured with Respect to the Central Source [BHB2007]-1 Table 2 Apparent Magnitudes of the Components Measured with Respect to the Central Source [BHB2007]-1 3.3. Stellar Properties Here we calculate the stellar properties of [BHB2007]-1 and -2 based on the Gaia EDR3 parallax (see Section 3.2 ) and the notion that [BHB2007]-2 is a binary system. We collected the B-to-W4-band photometry of −1 and −2 from Vizier. We investigated the ASAS-SN light curves (Kochanek et al. 2017 ) finding that the visual brightness of both stars is only moderately variable ( mag over years). We adopted a Phoenix model of the stellar photosphere (Hauschildt et al. 1999 ) with the effective temperature constrained by Covey et al. ( 2010 ) ( K and K, for −1 and −2, respectively, with typical uncertainties of ±300 K) and visual extinction calculated from the observed colors between the R , I , and J bands, and stellar luminosity L * from the integrated photospheric model. For [BHB2007]-1, this yielded mag and . However, the edge-on geometry of the disk (see Section 3.4 ) may in principle yield an underestimation of the luminosity. In fact, stars with very inclined disks appear on average older (since less luminous) than the other stars (see Garufi et al. 2018 ). As for [BHB2007]-2, we first had to consider the visually triple nature of the star (see Section 3.1 ). All three stars sit within the 2MASS beam, meaning that the observed photometry is a contribution of all of them. We computed the actual J -, H -, -, and W 1-band magnitudes through the relative flux ratios measured in our NACO images. We then constrained visual extinction and stellar luminosity of [BHB2007]-2A assuming that the constrained by Covey et al. ( 2010 ) refers to this star since it is significantly brighter than the other two. We found that the is comparable with that of [BHB2007]-1 (1.5 ± 0.4 mag) while the luminosity is . Finally, we constrained stellar mass M * and age t of the two sources through multiple sets of pre-main-sequence tracks (Baraffe, MIST, and Parsec; Baraffe et al. 2015 ; Dotter 2016 ; Bressan et al. 2012 ). Bearing in mind the assumptions and the uncertainties described above, we found and Myr for [BHB2007]-1, and and for [BHB2007]-2. The stellar mass of [BHB2007]-1 is significantly smaller than what was constrained by Alves et al. ( 2020 ) from the position–velocity diagram of the CO emission (2.23 ). Such a large discrepancy cannot be explained by an erroneous estimate of the stellar luminosity alone since the evolutionary tracks corresponding to stars with K are nearly vertical, making the stellar mass only marginally impacted by the luminosity.

O O O O O O O O B-Instrument O O O O B-CelestialObject O B-CelestialObject I-CelestialObject O O O O B-CelestialObject O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Formula O B-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O B-Dataset I-Dataset O O O O O O O O O B-CelestialObject O O O O O O O B-Wavelength O O B-CelestialObject O B-CelestialObject O B-Database O O O B-Survey 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-Model I-Model O O O O B-Citation I-Citation I-Citation I-Citation 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 B-Wavelength O B-Wavelength O O B-Wavelength I-Wavelength 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 B-Citation I-Citation I-Citation I-Citation 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-Survey O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength B-TextGarbage I-TextGarbage O B-Wavelength I-Wavelength O O O O O O O O O B-Instrument O O O O O O O O O O B-CelestialObject 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 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 B-Model B-Model O B-Model B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject O O O B-CelestialObject O O O O B-CelestialObject 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


of 1.5. Convection sets in close to the point where the cold branch of the S-curve ends which leaves this point sensitive to α ml . This effect is even stronger on the critical point where the hot branch starts, as this is where convection is the strongest. Higher values of α ml shift both critical points at which the S-curve bends closer together, leading to a smaller Q Σ crit . This alters the global behaviour of the disc and the outburst properties: the decay from the outburst in a disc with $α ml $ = 6 starts at higher Σ and higher T eff , and less mass is accreted and accumulated in the disc during the outburst cycle. Therefore, more efficient convection produces outbursts that are more frequent and of lower amplitude, and even lack quiescent phases. While it is important to note that this lack of quiescence may be related to uncertainties in the end of the lower branch, there are other ways out. In the discussion below, we examine a few options to restore or modify quiescence. The comparison of DIMRI with $α ml $ = 1.5 and DIMa (Figs 10 and 9 c) highlights the importance of changing the dissipation profile, as this is the only difference between these two models. The main difference is that the outbursts in DIMRI with $α ml $ = 1.5 are wider and the quiescence is longer than in the DIMa light curve. Changing the mixing length parameter is not the only way to increase the outburst amplitude and restore quiescent phases to the DIMRI models. Increasing the mass transfer rate, while all other parameters are fixed, makes the disc hotter and denser. This means that the surface density everywhere in the quiescent disc is closer to the critical value and the disc luminosity is higher. The result is more frequent lower amplitude outbursts for higher mass transfer rate regardless of model, as illustrated by comparing the two mass transfer rates shown in Fig. 9 for each of our three models. Hence, merely reducing the mass transfer rate in the DIMRI model can increase the outburst amplitude and restore quiescent phases. If one sets as low as g s −1 in the DIMRI (with α ml = 6), the elapsed time between two consecutive outbursts starts to be longer and also the outburst amplitude rises (see Table 1 and Fig. 11 ). Note that for such a low , the discs in DIM and DIMa become cold and stable. There is yet another alternative way to restore quiescence in the DIMRI light curves. Observed X-ray fluxes in quiescent dwarf novae are far too large compared to what models predict. A solution to this problem is a truncation of the inner disc. Numerical calculations by Hameury, Lasota Warner ( 2000 ) and Schreiber, Hameury Lasota ( 2003 ) confirm that truncating the inner disc has substantial influence on the dwarf nova light curves and may solve the discrepancy between observations and theory. This truncation may be caused by the magnetic field of the primary white dwarf. A white dwarf magnetic field in the range 10 4 –10 7 G (which translates to a magnetic

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


as well, e.g. CALIFA, MaNGA, and SAMI (Croom et al. 2012 ); but the ∼10 times higher spatial resolution of the MAD data boosts the ability to disentangle the different components, in addition to providing information on scales that are still largely unexplored in terms of a systematic study as a function of the location on the SFMS. 4.1 Resolved BPT diagrams We use the well-known [O iii ]/H β versus [N ii ]/H α Baldwin, Phillips Terlevich (hereafter BPT; Baldwin, Phillips Terlevich 1981 ) diagram to identify regions within the galaxies that are ionized by UV radiation from newly born stars (regions of star formation – hereafter, the SF gas) and regions that are ionized by AGN-emitted radiation, shocks, or AGB stars. In these diagrams (e.g. Fig. 1 ), the upper, solid line is the photoionization model of Kewley et al. ( 2001 ), which defines the upper envelope of the region of parameter space occupied by extreme starbursts; this line is a conservative boundary between SF gas and AGN/shocks. The lower, dashed line shows an equivalent but empirical demarcation derived by Kauffmann et al. ( 2003 ). The area of BPT parameter space that lies between these two lines is regarded as identifying regions of gaseous emission with an intermediate ionization spectrum. Figure 1. BPT diagram of all the spaxels from all the galaxies in the sample. The colour scheme has been selected as a continuous variation from purple/blue (SF) to red (AGN/shock dominated), using the η parameter. To explain how η is defined, we compute the minimum distances ( d 1 , d 2 , and d 3 ) of three general points (P 1 , P 2 , and P 3 , respectively, each one in a different region of the BPT diagram) to the two lines that define the three BPT regions. The spaxels with EW(H α)6 Å lie inside the dash–dot area (see the text). It is also well known that the EW is an extra proxy to constrain the possible ionization source of the ionized gas, restricting the SF regions to those with EW(H α) > 6 Å (e.g. Cid Fernandes et al. 2011 ; Sánchez et al. 2014 ; Barrera-Ballesteros et al. 2016 ; Belfiore et al. 2017 ). The EW(H α) is measured by dividing the H α intensity by the flux density of the underlying continuum of the emission line-free spectra, computed as the mean flux density of two windows of 30 Å wide and centred at ±60 Å from the observed H α wavelength. The spaxels with EW(H α) 6 Å are presented in Fig. 1 as those inside the dash–dotted area. The ratio between all the spaxels with EW(H α) 6 Å and all the spaxels under the empirical SF demarcation of the BPT is 4 per cent. Although this ratio is lower than 2 per cent for 24 out of 38 galaxies, it is significant for some galaxies such as NGC 3521 (23 per cent), IC5273 (11 per cent), or NGC 4941 (8 per cent). To obtain a single-valued continuous parameter that conveys the location of each spaxel on its galaxy’s BPT diagram, we define the variable η as either ( i ) the inward-pointing orthogonal distance from the dashed line, identifying SF

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


‘truncation’ of the disc could have shrunk the dust disc to its tiny radius. On the other hand, the SED is also compatible with some amount of large dust outside of 0.6 au. For this scenario, radial ‘migration’ coupled with fragmentation interior to the H 2 O snowline (located at 0.6 au) result in a cliff in Σ dust of two orders of magnitude and in a sudden increase of grain sizes. Our modelling shows that this scenario matches the observed SED for outer dust disc radii of R dust, 2 ≲ 45 au. In both scenarios, a dust mass inside of 0.6 au bigger than ∼1 M ⊕ is required to match the observed SED, however due to the optically thick nature of the dust, we do not obtain an upper limit on the dust mass. In the ‘migration’ scenario, the dust mass needs to be fine-tuned to ∼1 M ⊕ inside the H 2 O water snowline in order to match the SED as the dust masses inside and outside of 0.6 au are dependent on each other. In order to distinguish further between these scenarios, the gas radius of the disc can offer important information. If it is truncated at very small radii as well, a dynamical truncation of the disc seems likely. If it is more extended, radial drift in combination with dust physics at the water snowline offer a plausible explanation. We present predictions for CO J = 2–1 fluxes, invoking various M gas – R gas combinations, that will enable future observations to potentially distinguish between these two scenarios. Finally, we note that regardless of the underlying mechanism for the small-scale dust disc, its optically thick nature suggests that several M ⊕ of dust can be located within a small radial extent from the central star. Such a configuration suggests that V410 X-ray 1 may be a potential precursor to a system of tightly packed terrestrial planets, such as the recently discovered TRAPPIST-1 system. APPENDIX A: DUST PROCESSING AT THE WATER SNOWLINE In Section 4.2 , we study whether the truncated dust disc could be related to physical processes happening at the water snowline. The key property that changes across the snowline is frag , the maximum collision velocity of grains for which coagulation, rather than fragmentation, is to be expected. Following Blum Wurm ( 2000 ) and Gundlach Blum ( 2015 ), frag is reduced by an order of magnitude interior to the snowline. If grain growth is limited by fragmentation, the local value of frag is linked to the maximum expected grain size through equating the relative collision velocity Δ for the largest grains at any location with frag . Δ for grains that are coupled to a turbulent flow via drag forces is given by (Voelk et al. 1980 ; Ormel Cuzzi 2007 ): where α is the Shakura–Sunyaev viscosity parameter (Shakura Sunyaev 1973 ), c s the sound speed, and St is the local Stokes number (ratio of drag time to dynamical time) for the largest grains. In the Epstein drag regime, the midplane St for grains of size a max is given bywhere we have assumed a Gaussian vertical structure. When growth is

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


line profiles. Calculations of lines formed in disc winds from white-dwarf stars have been limited to resonance lines tend to produce absorption profiles for inclinations i ≳ 70° (Proga et al. 2002 ). However, disc-wind models for T Tauri stars can produce similar H α line profiles to those seen in RS Oph (Kurosawa, Harries Symington 2006 ). Polarization measurements may be able to distinguish between inflow and outflow models, since, in the inflow models, the fraction of scattered light contributing to the blue wing is larger. 4 SODIUM ABSORPTION LINES 4.1 Na <sc>i</sc> <sc>D lines in RS Oph</sc> Sodium absorption lines have been suggested as a useful diagnostic of the circumstellar environment in both supernovae and their progenitor systems (Patat et al. 2007 ; Chugai 2008 ; Patat et al. 2011 ). The Na i D lines, together with other strong metal lines such as the Ca ii H K lines, probe the density and ionization conditions in the circumstellar environment. We modelled the line profiles expected from the simulations, with the aim of understanding where the observed features in RS Oph form in the CSM and whether the same circumstellar components can be responsible for metal line variations observed in some SN Ia. We have modelled Na i D absorption line profiles directly from the simulations, using the results from the ionization calculation described above. All neutral sodium atoms are assumed to be in the ground state and contribute to the absorption lines. We present line profiles from calculations in which the mass-loss rate has been scaled to 5 × 10 −7 M ⊙ yr −1 , since this gives better agreement with observations both for the ionization structure and the line profiles. We did not include a detailed treatment for the H ii region in the Na i D line ionization calculation; instead, we neglected the contribution from all material within 3 × 10 13 cm. The results are not particularly sensitive to this choice of radius. We assume that the continuum flux around the Na i D lines is dominated by the RG. The presence of an emission component in RS Oph limits the extent to which this is true (Patat et al. 2011 ). The emission component has a width v ∼ 100 km s −1 , higher than the width of the absorption lines, and is likely associated with emission from the ionized region. The line profiles were derived by calculating the optical depth to the photosphere along lines of sight through the CSM. The photosphere was subdivided into lines of sight to ensure that the substructure along the line of sight is resolved. Finally, the flux from each line of sight was combined and weighted by area. Fig. 6 shows the resulting synthetic line profiles. For inclinations i ≳ 70°, the line profile shows both red and blueshifted components. The redshifted components arise in the wind that is falling back on to the white dwarf and accretion disc, and is therefore strongest when the white dwarf is closest to the observer and the line of sight intersects the most

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


the satellite at two specific times, and where its spin is indicated by a curled arrow. When cold rotationally supported disc galaxies merge they produce complex tidal tails ( Toomre Toomre 1972 ; Eneev et al. 1973 ; Quinn 1984 ; Barnes 1988 ). These tidal tails can be quite different from those originating in spherical dispersion-supported systems. This is also what we find in our simulations, as shown in Fig. 4 . The bottom row of this figure zooms in on the discy satellite and reveals that some of the stars in green (i.e. the ridge in the bottom panel of Fig. 3 ), are lost first. These are followed by some stars in cyan with lower final eccentricity and slightly less retrograde motions since they are part of the ridge in the middle panel of Fig. 3 . We also see that there is some alternation in green and cyan stars amongst the material that becomes unbound slightly later. Since a discy satellite has internal and orbital angular momentum, mass loss depends on the exact configuration of the merger (e.g. inclination, spin) and not only on the internal binding energy of the stars as in the case of a spheroidal system. For example, the presence of a single extended counter-tail can be explained by the alignment of the spins of the two galaxies ( Struck Smith 2012 ), i.e. although the secondary moves on a retrograde orbit, its sense of rotation is prograde with respect to the primary. A difference in eccentricity also arises from these additional degrees of freedom. For a given internal binding energy stars have a range of internal angular momenta, which translates in debris with high and low orbital angular momentum, resulting respectively in more circular and more radial final orbits (the latter being typical of shell-like features). In addition to these effects, dynamical friction causes the satellite’s core to spiral inwards. This enhances the prominence of the only tidal arm apparent in Fig. 4 , which trails behind the core. 3.2. Some implications We have just shown that the stars in the velocity arch constitute debris lost early on in the merger. This probably also has implications for the chemical abundances of its stars since dwarf galaxies are known to possess metallicity gradients. For M ⋆ ∼ 10 9.6 M ⊙ the gradients have an amplitude ∼ − 0.064 dex kpc −1 according to Ho et al. (2015) . Thus, if Gaia -Enceladus had a physical extent of 5 kpc, this could imply a metallicity difference of 0.32 dex between its centre and outskirts. Myeong et al. (2019) studied some of the stars in the velocity arch, and argued that these stars, together with other retrograde stars, were part of a different accreted galaxy that they named Sequoia. These authors have shown that the stars are more metal poor on average than the debris of Gaia -Enceladus by ∼0.30 dex, which suggests they formed in an object that is ten times smaller ( Matsuno et al. 2019 ). However, an alternative explanation supported by our simulations is that these stars (or some of them)

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the Orion disks dust content, as measured with ALMA, are comparable with those measured for Perseus with VLA observations ( Fig. 5 bottom panel): 16 and 45% for Class 0 and Class I, respectively. Figure 6 presents a different visualization of the distribution of exoplanet systems dust masses compared to the range of disk masses observed in Class 0 and Class I disks in Perseus. The conclusions of our work show that for the complete sample of disks in Perseus and with a large sample of known exoplanets, there is enough solid material in the Class 0 stage to explain the solid content in observed exoplanetary systems. This conclusion is consistent with Najita Kenyon (2014) and Greaves Rice (2011) but now with much more robust statistics. In recent years, several studies, specifically with the use of microlensing observations, have estimated that nearly all stars could host a planet of at least 10 M ⊕ ( Cassan et al. 2012 ; Suzuki et al. 2016 ). Very few cases and irreproducibility of microlensing observations suggest caution should be taken when extrapolating the results to all systems. It should be kept in mind that a large population of wide-orbit planets could pose a challenge to efficiency of planet formation even at the Class 0/I stage ( Najita Kenyon 2014 ). Actual timescales for the different phases of low-mass star formation are uncertain. Based on a statistical analysis of a population of protostars, it is estimated that the Class 0 evolutionary phase lasts for ~0.1 Myr after the beginning of the collapse, and the Class I phase ends when the protostar is ~ 0.5 Myr old ( Dunham et al. 2014b ). More recent estimates of the half-lives of the protostellar phases give Class 0 half-life values of ~0.05 Myr and ~0.08 Myr for Class I ( Kristensen Dunham 2018 ). Therefore, our results indicate the start of the planet formation begins less than 0.1 Myr after the beginning of the cloud collapse. This is consistent with the ages of the oldest meteorites in our Solar System ( Connelly et al. 2012 ). 4.3 The context of planet formation models It is worthwhile to put our empirical constraints on the solid mass reservoir in the context of planet formation models. Broadly speaking, planets can either form bottom-up through the assembly of smaller building blocks in the so-called core accretion scenario, or top-down in the gravitational instability scenario via direct gravitational collapse of the disk material. In the latter case (see Kratter Lodato 2016 for a review), planets need not contain rocky cores and we may therefore have overestimated the solid mass locked in planets. In addition, in this view planets form at the very beginning of the disk lifetime when the disk is gravitationally unstable, possibly at even earlier stages than we probe here. If this is the case, our observations do not put constraints on the mass budget required for planet formation since planets would already be formed in the disks we are considering. Our results are instead

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