the elongated EUV channel-like structure (Zhang et al. 2012 ; Chen et al. 2014 ; Cheng et al. 2014 ) in the high-temperature passbands (e.g., 94 and 131 Å) of the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012 ). More recently, the detailed structure and evolution of flux ropes in the low solar atmosphere were presented by Wang et al. ( 2015 ) and Kumar et al. ( 2015 ). The flux ropes in the low solar atmosphere show some similarities in the morphology of the filaments but have not been confirmed. The relationship between the filaments and the sigmoids and the elongated EUV channel-like structure are still unknown. However, they show some common characteristics in the formation process. For instance, in the framework of magnetic field reconnection, an increasing number of observations suggested that magnetic flux ropes are created either via flux cancellation in the photosphere (Green Kliem 2009 ; Tripathi et al. 2009b ; Green et al. 2011 ; Savcheva et al. 2012 ; Wang et al. 2015 ) or the tether-cutting reconnection in the corona (Moore et al. 2001 ; Kim et al. 2008 ; Liu et al. 2010 ; Chen et al. 2014 ; Cheng et al. 2015 ). Therefore, the study of the evolution and formation of the filament may shed new light on the evolution and formation of the flux rope. At the chromospheric level, observations always show that the dark, loop-like threadlike structures are the most prominent features observed in H α images. Those threadlike structures that mark the emergence of the new magnetic flux are called an arch filament system (Bruzek 1969 ), and those that span and transverse to older PILs of active region are called field transition arches (FTAs; Prata 1971 ). In addition, other kinds of loop-like threadlike structures are nearly parallel to the PILs. However, both of them connect with opposite polarities and trace out the magnetic line of force. In this study, employing the excellent observations from the AIA and the Helioseismic and Magnetic Imager (HMI; Schou et al. 2012 ) on board the Solar Dynamics Observatory ( SDO ; Pesnell et al. 2012 ), we present the rapid formation of a filament via magnetic reconnection between two sets of threadlike structures on 2013 May 29. In the photosphere, at a region where some ends of the two sets of threadlike structures are close to each other, magnetic flux convergence and cancellation occur. This provided us with a good opportunity to detail the evolution and formation of the filament. Detailed observations and methods are presented in Section 2 . The results are shown in Section 3 . The conclusion and the discussion are given in Section 4 . 2. OBSERVATIONS AND METHODS The event was well-observed by the SDO /AIA and HMI, as well as the Global Oscillation Network Group (GONG) at the National Solar Observatory (NSO). AIA takes full-disk images in 10 ultraviolet (UV) and EUV wavelengths covering a wide temperature range, with a pixel size of 06 at a high cadence of up to 12 s. We mainly used the Level

O O B-Wavelength 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 B-Wavelength O B-Wavelength I-Wavelength O O B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObjectRegion I-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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation 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 B-Telescope O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O B-Observatory I-Observatory I-Observatory O B-Observatory 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 B-Observatory B-Telescope O B-Telescope O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O O B-Observatory I-Observatory I-Observatory B-Observatory B-Telescope 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 O


GI surveys mainly focus on the XMM-LSS area. The XXL-S field is fully covered by GALEX GR6/7 with AIS, Medium Imaging Survey (MIS), and/or GI programs. VISTA Three public European Southern Observatory (ESO) large programme surveys have observed the XXL field in the near infrared (, , , , filters: ) with the Visible and Infrared Survey Telescope for Astronomy 6 (VISTA) in various depths. XXL-N is covered by all three surveys: VISTA Hemisphere Survey (VHS, PI: R., McMahon), VISTA Kilo-degree Infrared Galaxy Survey(VIKING, PI: W. Sutherland), and VISTA Deep Extragalactic Observations Survey (VIDEO, PI: M. Jarvis), while the XXL-S is covered only by the VHS survey. IRAC Both XXL fields have been targeted with the Infrared Array Camera (IRAC) on board the Spitzer Space Telescope 7 providing imaging at and over the whole area (XXL-N; PI: M. Bremer, XXL-S; SPT- Spitzer Deep Field, SSDF, Ashby et al. 2014 ). WISE The Wide-field Infrared Survey Explorer 8 (WISE) is an all-sky mission observing the sky from to . In this work we use the ALLWISE data release 9 , which provides imaging for the whole XXL field in all four WISE filters. 3.2. XXL-N Observations covering exclusively the XXL-N area: CFHT The Canada-France-HawaiiTelescope 10 (CFHT) hasobserved the parts of the XXL-N area as part of the CHFT-LegacySurvey 11 (CFHTLS) in two configurations a) wide area ( W1 field) and b)deep field (D1 field) observed with MEGACam, providingimaging in the filters: , , , , (). In this work we use the T0007 data release downloaded from Terapix 12 . We complemented the coverage of CFHT with three additional fields to the north of W1 . The WA and WB fields were observed in the , , filters while the WC field was observed in the filter (PI: M. Pierre). Additionally, XXL-N has been observed with the WIRcam camera on CFHT in the band (, VIPERS-Multi-Lambda Survey). Details on the observations and data reduction are provided in Moutard et al. (2016a , b) . SDSS The Sloan Digital Sky Survey 13 (SDSS) provides observations in the whole XXL-N area in the filters: , , , , (). In this work we use the DR10 data release ( Ahn et al. 2014 ). UKIDSS The UKIRT Infrared Deep Sky Survey 14 (UKIDSS, Dye et al. 2006 ) has two fields overlapping with XXL-N: the Ultra Deep Survey (UDS), and the Deep Extragalactic Survey (DXS) targeting the XMM-LSS area in , , and , bands, respectively. Here we use the DR10 data release downloaded from the WFCAM Science Archive 15 . 3.3. XXL-S Observations covering exclusively the XXL-S area: BCS The Blanco Cosmology Survey 16 (BCS; Desaiet al. 2012 ) has targeted an area of which overlaps with the XXL-S field using the MOSAIC II imager at the Cerro Tololo Inter-American Observatory 17 (CTIO). The observations cover the , , , bands (). The images used in this work were analysed as described in Menanteau et al. (2009) . DECam The Dark Energy Camera 18 (DECam) is the successor of the MOSAIC II camera at CTIO. We observed the XXL-S field (PI: C. Lidman) in

O O O O O O B-CelestialRegion I-CelestialRegion O B-CelestialRegion I-CelestialRegion O O O O B-Dataset I-Dataset O B-Telescope B-Survey I-Survey I-Survey B-Survey O O O B-Telescope O O B-Observatory I-Observatory I-Observatory B-Observatory O O O O O O B-CelestialRegion I-CelestialRegion O O B-Wavelength I-Wavelength B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope O B-Telescope O O O B-CelestialRegion O O O O O O B-Survey I-Survey I-Survey B-Survey O B-Person I-Person B-Survey I-Survey I-Survey I-Survey I-Survey O B-Person I-Person O B-Survey I-Survey I-Survey I-Survey I-Survey B-Survey O B-Person I-Person O O B-CelestialRegion O O O O O B-Survey I-Survey B-Instrument O B-CelestialRegion I-CelestialRegion O O O O O B-Instrument I-Instrument I-Instrument B-Instrument O O O B-Telescope I-Telescope I-Telescope O O O O O O O O O B-CelestialRegion O B-Person I-Person B-CelestialRegion B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion B-Citation I-Citation I-Citation I-Citation O B-Telescope O B-Telescope I-Telescope I-Telescope I-Telescope O B-Telescope O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O B-CelestialRegion I-CelestialRegion O O O B-Telescope O O B-CelestialRegion O O O O B-CelestialRegion O B-Telescope O B-Telescope O B-Telescope O O O O O B-CelestialRegion I-CelestialRegion O O O O B-Survey O B-Survey O O O O B-CelestialRegion I-CelestialRegion O B-CelestialRegion I-CelestialRegion O B-CelestialRegion I-CelestialRegion B-CelestialRegion I-CelestialRegion O O B-Instrument O O O O B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage O O O O O O B-Dataset I-Dataset I-Dataset O O B-Organization O O O O O O O B-Telescope O O O O O O O O B-CelestialRegion O O B-CelestialRegion O B-CelestialRegion I-CelestialRegion O O O O B-TextGarbage I-TextGarbage O O O B-CelestialRegion I-CelestialRegion O O O O O O B-Person I-Person O B-CelestialRegion O O O O O B-Instrument O O B-Telescope O O O O B-Survey I-Survey O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Survey O B-Survey I-Survey I-Survey I-Survey O B-Survey O O O O O B-CelestialRegion I-CelestialRegion O O O B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage O O O O O O B-Dataset I-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O B-Survey O B-Survey I-Survey I-Survey I-Survey I-Survey O B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialRegion O B-Survey I-Survey I-Survey B-Survey O O B-Survey I-Survey I-Survey B-Survey O O B-CelestialRegion I-CelestialRegion O B-TextGarbage I-TextGarbage O O O O O O O O B-Dataset I-Dataset I-Dataset O O O B-Archive I-Archive I-Archive O O O B-CelestialRegion O O O O B-CelestialRegion O B-Survey O B-Survey I-Survey I-Survey O B-Survey B-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O B-Instrument I-Instrument O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory O O O O B-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Instrument O B-Instrument I-Instrument I-Instrument O B-Instrument O O O O O B-Instrument I-Instrument O O B-Observatory O O O B-CelestialRegion I-CelestialRegion O B-Person I-Person O


with other studies where an agreement with Shakura Sunyaev ( 1973 ) is reported in appropriate regimes. This is seen, for instance, in the limit of weak wind-driving in the models of Scepi et al. ( 2019 , see their Figure 2) or the outer regions of the semiglobal simulations of Hogg Reynolds ( 2018 ). We note that the level of alignment with the Shakura Sunyaev ( 1973 ) models may change with a more realistic treatment of the system. On one hand, radiative cooling (planned for our future work; see Section 5 ) will introduce nonlocal interactions that may break the locality assumption of α -models. On the other, accretion disks in astrophysical semidetached binaries are colder and geometrically thinner than those presented here (as discussed in Section 1.2 ), which alleviates some of the tension related to large H / R ratio, bringing true accretion disks closer to the Shakura Sunyaev ( 1973 ) solution. 4.3.1. Spiral Structure Drives Accretion at Very Low Mach Numbers As we discussed in Section 1.2 , numerical resources limit our global models to accretion disks that are hotter (of M in = 5, 10) than real astrophysical systems (e.g., CVs, where M in ≳ 50). While the Mach 5 model is unlikely to be realized in nature, it can provide a useful context for the Mach 10 data. With this in mind, we use Figures 7 and 9 to explain the mechanisms driving accretion in our hot-disk model Mach 5. As seen in Figure 9 , the body of the disk (solid brown line, Θ ≲ 2.5 H / R ) dominates the accretion rate for most of the grid. Its has a minimum at r ∼ 0.15, where its impact becomes equal to that of the “corona” (dashed brown line, Θ ∈ [2.5, 5] H / R ), the latter’s being maximal at r ∼ 0.15. This radius also corresponds to the transition from a two-peaked to a triangle-like vertical profile in Maxwell stress (Figure 7 ; see Section 4.2 ), a likely related observation. In Figure 9 we see that Reynolds stress dominates over Maxwell stress both within the main body and the “corona.” In the former, the difference is about a factor of 2–3, comparable with the MHD model of Ju et al. ( 2016 ). The radial velocity slice in Figure 6 associates this Reynolds-stress-driven accretion with the grand-design spiral structure, pointing to it as the main accretion driver in Mach 5. 4.4. Long-term Evolution of the Mach 10 Model Within our current computational limits on the Mach 10 simulation’s run time, the disk is not seen to reach a statistically steady state. However, as we are only able to study a single viscous timescale of the disk (see Section 4.1.1 ), it is entirely possible that such a state would be achieved if the model was allowed to continue. Still, the long timescale (∼10 P orb ) variability observed in our Mach 10 model may be of interest for understanding disk accretion. Not only is it potentially present during a change in disk accretion rate, but there is some indication that it may be recurring in nature (see Section 4.1.1 ). In this section, we attempt to

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ΔΩ j indicates an increase of the quantity with cosmic time. 3 EXPECTED DUST DENSITY The basic ingredient of the calculation is represented by the cosmic star formation history (CSFH), ψ( z ). Adopt the analytical fit to the available data provided by Madau Dickinson ( 2014 ) with ψ 0 = 0.015. We can then compute the stellar mass density at any given redshift, z , by integrating In the previous expression H ( z ) = H 0 [Ω m (1 + z ) 3 + Ω Λ ] 1/2 is the Hubble parameter; for consistency with data, we will adopt the following values of the cosmological parameters (Ω m , Ω Λ , h ) = (0.3, 0.7, 0.7). The return fraction of gas from stars appropriate for a Chabrier initial mass function and instantaneous recycling approximation is R = 0.41. The previous expression can be cast in a more handy form where the is the non-dimensional integral in equation ( 4 ); further define , and note that , and . For the adopted cosmology, the stellar density parameter is . The density of stars formed from z = 1 to the present is ΔΩ * = 1.43 × 10 −3 . The metal density associated with Ω * is we have assumed a metal yield y = 0.033 ± 0.01, with errors accounting for uncertainties in the nucleosynthetic yields (Peeples et al. 2014 ; Vincenzo et al. 2016 ). Finally, the dust mass can be computed by knowing the dust-to-metal ratio, i.e. the fraction of metals locked into dust, , where and Z are the dust-to-gas ratio and gas metallicity, respectively. In the Milky Way, (Zubko, Dwek Arendt 2004 ); assuming solar metallicity, Z = 0.0142 (Asplund et al. 2009 ), then f d = 0.43 (Draine 2011 ). At higher redshifts f d in measured from the gas depletion patterns in, e.g. damped Lyman α (DLA) systems (Péroux Howk 2020 ). In the redshift range 0 z 1, (see Fig. 1 and Table 1 ) in the cold, neutral medium out of which stars form. We note that combines the effects of dust production, growth, and destruction, while we aim here at isolating the first process. Hence, we write the dust density associated with the metal density as where, in general, 2 . To determine f d , we proceed as follows. The minimum value, , is obtained by neglecting growth after grains are injected in the ISM by sources [supernovae (SNe) and asymptotic giant branch (AGB) stars]. SNe with progenitor mass form on average 0.3 M ⊙ of dust, 80 per cent of which is typically destroyed by the reverse shock on site (Todini Ferrara 2001 ; Bianchi Schneider 2007 ; Leśniewska Michałowski 2019 ). The AGB stars (>2 M ⊙ ) contribution per unit stellar mass formed for Z > 0.2–0.3 Z ⊙ is ≈4 times higher than the SN one (Zhukovska, Gail Trieloff 2008 ; Dell’Agli et al. 2017 ; Valiante et al. 2017 ). Hence, the combined effective dust yield per SN is y d = 0.3 M ⊙ , which gives , where is the number of SNe produced per stellar mass formed, according to the adopted Chabrier ( 2003 , equation 17) IMF. Larger values of f d might arise as a result of grain growth, which depends on ambient conditions (Asano et al. 2013 ;

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


filter wheels. The gray cylindrical object below the filter and shutter unit represents the cryogenic camera. Center panel : same view of the T80Cam model after cover removal, showing the two filter wheels and the shutter. Right panel : T80Cam integrated at the Cassegrain focus of the JAST/T80 telescope. A summary of the technical characteristics of T80Cam is presented in Table 2 . In addition, full technical and managerial details on T80Cam can be found in Marín-Franch et al. (2012a , 2015) . Table 2. Main technical performances of the T80Cam panoramic camera at the JAST/T80 telescope. 2.3. J-PLUS filter set The main goals of J-PLUS depend on the accurate determination of SEDs of MW stars and nearby galaxies. It is therefore clear that the J-PLUS filter set must be sensitive to both the optical continuum and the most prominent spectral features. In this context, it has been frequently demonstrated that it is possible to retrieve reliable stellar SEDs with a set of around 10–15 intermediate- to broad-band optical filters centered at key spectral regions (e.g., Bailer-Jones 2004 ; Jordi et al. 2006 ; Carrasco 2006 ). Following this strategy, the J-PLUS filter set consists of the 12 filters defined in Table 3 . Four of these are SDSS filters ( g , r , i , and z ; Fukugita et al. 1996 ) that provide the low-frequency continuum, and six are intermediate-band filters of 200–400 Å width, centered on key absorption features. These are the u filter, in common with J-PAS and located at the blue side of the 3700–4000 Å Balmer-break region, and the filters J 0395 for Ca H+K, J 0410 for H δ , J 0430 for the G band, J 0515 for the Mg b triplet, and J 0861 for the Ca triplet. The J-PLUS filter set is completed with two narrow-band filters, J 0378 and J 0660, also in common with the J-PAS filter set. These two filters are sensitive to the [O II ]/ λ 3727 and H α / λ 6563 emission lines, respectively. The three filters in common with J-PAS are envisioned as an added value for the overall calibration procedure, as they will allow second-order corrections of the ZPs to anchor the J-PAS calibration. Table 3. J-PLUS filter system. Notes. (a) In common with J-PAS; (b) SDSS. Rest-frame key spectral features matching the location of narrow- and intermediate-band filters are also indicated. The J-PLUS filters have been manufactured by Schott (Switzerland). A detailed technical description of the filter requirements and design can be found in Marín-Franch et al. (2012b) . Figure 3 shows the overall efficiency of the transmission curves of the filters, whose tabulated data can be found at the J-PLUS website 4 . Fig. 3. Overall transmission curves measured for the set of 12 J-PLUS filters, including the effect of the entire system (sky, mirrors, lenses, and CCD). The filter arrangement is tuned to provide scientifically valuable data for many fields of Astrophysics. Since the intermediate-band filters are sensitive to the strengths of key features of old stellar

O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O B-Instrument O O O O O O O B-Telescope O O O O O O O O B-Instrument O O O O O O O O O O O O O O B-Instrument O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O B-Instrument O O O O B-Telescope O O B-Survey 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 B-Survey 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 B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O B-Survey O O O O O O O O O O O O O O O O B-Survey O O B-Wavelength O B-Wavelength O B-Wavelength O O B-Wavelength 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 O O O O B-Survey O O O O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O B-Survey O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O B-Survey O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength 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 B-Survey O O O B-Survey O O O O O O O B-Survey O B-Survey O O O O O O O O O O O O O O O O B-Survey O O O O O B-Organization B-Location 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 B-Survey O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


over the whole solar disc. The umbra area is the area of the umbra of the sunspot, and pores are excluded. The total umbra area is the area of the umbrae summed over the whole solar disc. Projected areas are measured in millionths of the solar disc ( md ) and corrected areas in millionths of the solar hemisphere ( mh ). The relationship between the areas of a solar feature in two catalogues (C 1 and C 2 ) is modelled by linear regression in the form A 2 aA 1 , where A 1 and A 2 are the areas in C 1 and in C 2 , respectively. We provide three types of plots to show details of the regression: the scatter plot of the regression, the moving root mean square residual (MRMR) and the moving relative root mean square residual (MRRMR). MRMR measures how the root mean square residual (RMR) relative to the regression line depends on the area. For a given area A , the MRMR is determined from the n -nearest areas to A . Similarly, MRRMR measures how the relative root mean square residual (RRMR) relative to the regression line depends on the area. For a given area A , the MRRMR is determined from the n -nearest areas to A . We choose the value 20 for n . To compile the various sunspot catalogues compared in this paper, we used the software package SAM (Sunspot Automatic Measurement). SAM is a set of cooperative computer programs that embraces every aspect of compiling a sunspot catalogue, from (1) setting up the necessary data base for the observational data of the solar images and the telescopes and (2) automatically detecting sunspots (umbra and penumbra) on solar images and determining their heliographic coordinates and area through (3) to making the catalogue ready for publishing (Gyri 1998 ). To identify sunspots on solar images, we used the method published by Gyri ( 2015 ). A solar image may contain not only features belonging to the Sun but also various artefacts too, such as emulsion deficiency, emulsion abrasion, scratches, dust grains, clouds, inscriptions, patches, orientation markers, and much more. The properties of some of these artefacts are like sunspots (especially when the image quality is not too good), so it is hard to filter them out automatically, but a trained human eye/brain can do this in many cases (not always). Even when the average seeing of the image is good, there are regions with poorer seeing and small sunspots in these regions cannot be surely perceived. However, if, in a close-in-time image, these spots are situated in regions with good seeing, then they will show up clearly and could provide conformation. Near the solar limb, especially when the image quality is not too good, the penumbra and the umbra borders are not too definitive. In this case, the human intervention could increase the accuracy of finding these borders. To cope with these situations and with others not mentioned here, the automated sunspot catalogue created by SAM can be humanly revised by using special software, SAMm (Sunspot Automatic Measurement

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


either N prog 2 or N prog 5, which correspond to at most 10 or 40 per cent probability of being star forming during the mini-halo phase, respectively. We obtained results from this simple approach as an academic exercise, and in order to be able to compare results with previous work by Dijkstra et al. ( 2014 ). In the second approach, instead, which we employ as our fiducial case, we self-consistently account for SF in mini-haloes that can cool via H 2 , and exclude these from the list of candidate DH mini-haloes. For environmental pollution, we follow all haloes able to form stars in our cosmological volume, i.e. mini-haloes not DH and all ACHs, and compute the size of the metal bubble starting from the time of the first SN explosion. Hence, the metal bubbles start to expand in our model Δ t = t ff + Δ t SN after the halo is first declared star-forming. To model SF, we assume that the stellar mass formed in ACHs is f ⋆ = 0.05 of the baryonic mass, translating to M ⋆ = f ⋆ Ω b /Ω m M vir . For mini-haloes, instead, we consider a lower star-forming efficiency f ⋆ = 0.005. In both cases, we assume that SF starts with a burst as soon as one free-fall time (defined at the maximum density achievable via adiabatic contraction ρ gas = η gas ρ max ) has elapsed since (i) dynamical heating conditions have failed or (ii) the ACT has been exceeded (if no previous SF in the mini-halo had already occurred), and then proceeds smoothly following the increase in stellar mass with time in the halo. Following Weaver et al. ( 1977 ) and Madau, Ferrara Rees ( 2001 ), we define the bubble radius as where is the average SN luminosity associated to the stellar population in the halo, t the time since the burst of SF, and n ≡ Δ gas Ω b ρ crit (1 + z ) 3 / m H is the gas density (in cm −3 ) the bubble expands through. Now, we assume for simplicity that L SN ≈ E SN η SN M ⋆ ( t )/ t , where is the energy released per SN, M ⋆ ( t ) = f ⋆ (Ω b /Ω m ) M vir ( t ) is the stellar mass at time t , and is the number of SNe per stellar mass formed, and replace them in the bubble radius equation, we obtain, for t > Δ t SN , We notice that this equation reduces, for t ≫ Δ t SN , to the equation reported in Dijkstra et al. ( 2014 ), apart from the slightly lower normalization. In Dijkstra et al. ( 2014 ), the baryon overdensity through which the bubble expands is assumed to be Δ gas ≈ 60, typical of the overdensities found within haloes (60 ≲ Δ gas ≲ 1000), although the bubble spends most of the time in the intergalactic medium at Δ gas ∼ 1−10. This results in the bubble size being underestimated (Dijkstra et al. 2014 ; Habouzit, Volonteri Dubois 2017 ). In our model, instead, we also account how the overdensity changes outside the halo, by fitting the asymptotic case of an extremely rare halo with from Barkana ( 2004 ), and simply express Δ gas as where x ≡ log 10 ( R / R vir ), R is the bubble radius, and the factor 0.787 has been chosen to join the inner constant value and

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


Mathematically, this is a two-point boundary problem and it will assure that we have a well-behaved solution in the whole r − θ space. We have tried to obtain such solutions but failed. Therefore, we only require the solution satisfying the boundary condition at θ = 90°. As we will explain in the next section, we think the solution obtained in this way should still be physically meaningful. 3 RESULTS We solve the above equations ( 34 )–( 40 ) numerically. We integrate these equations from the equatorial plane (θ = 90°) towards the rotational axis (θ = 0°). We adopt the values of β θ0 and β φ0 with reference to the numerical simulation data of Yuan et al. ( 2012b ), but our results are not sensitive to the exact values. As we have explained before, the toroidal component of the magnetic field, which is produced by shear, should be negative. We do find that the toroidal component is negative at the beginning of integration. But at a certain critical value of θ, denoted as θ B , we find that it begins to change its sign. At the region of θ θ B , the toroidal component of the magnetic field becomes positive thus the solution is no longer physical so we stop our integration at θ B . We think our solution in the region of θ B θ 90° is still physical. 4 This is because, on the one hand, the solution satisfies the equations and the boundary conditions at θ = 90°. On the other hand, the values of all physical quantities of the accretion flow at θ = θ B are physical. Therefore, we can reasonably treat these values as boundary conditions at θ B . In fact, as we will describe below, the main properties of the solutions we obtain in this way are in good agreement with those obtained in Yuan et al. ( 2015 ) from numerical simulations. From the bottom-right plot of Fig. 2 , it seems that there is a sonic point for v θ / c s and the integration stops when the sonic point is approached because of the singularity there. This is not true. This is because, the value of v θ must be equal to zero at the pole because of the axisymmetric boundary condition there. Therefore, v θ / c s should not pass through a sonic point. We note that Jiao Wu ( 2011 ) obtained a similar result with us, i.e. their solution also has to stop at a certain θ angle. An interesting explanation for such a ‘truncation’ is given in their work. Figure 2. Angular profile of a variety of variables. The up-left plot shows that the radial velocity changes its sign at θ ∼ 47°. 3.1 Overall inflow-wind structure of the solutions Fig. 1 shows the poloidal magnetic field configuration. We emphasize that while the even symmetry of the field is our assumption, the strength of the field is obtained by solving equations ( 34 )–( 40 ). Above the equatorial plane, the radial component of the magnetic field is positive (pointing to large radii). So the toroidal component of the magnetic field, which is produced by shear, is negative. We find that such kind of magnetic field configuration is similar to 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 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 B-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula O O O O O B-Formula I-Formula O B-Formula I-Formula O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


for a standing shock just downstream of the radio core that compresses and aligns the magnetic field (Cawthorne Cobb 1990 ). Figure 5. Variations of the emission parameters of 3C 273 transverse to the jet axis (dashed red line) for slice 6 (shown in Figure 3 ). From top to bottom: total intensity, polarized intensity, fractional polarization, and EVPA. The fractional polarization increasing toward the edges of the jet is a predicted polarimetric signature of a jet sheath (as discussed in Section 1 ), with the EVPA transverse to the axis. The black line in the lower panel delineates EVPAs that are exactly ⊥ to the jet spine. The beam width along this transverse slice is shown in the upper panel to the left. 4.2. 4C 71.07 Figure 6 presents a stacked radio map of the blazar 4C 71.07 (0836+710). A very prominent and continuous polarimetric signature of a jet sheath is evident down the edges of the jet in this stacked radio image. Given the continuous nature of the jet sheath on the image, we can estimate the bolometric luminosity of the sheath. This is accomplished by first using the length of the polarized intensity profile along each of the slices to trace out the shaded gray regions shown in Figure 9 (see also Figure 6 ). The size of the sheath on each side of the slice is arbitrarily set by the location where the polarized flux falls below 0.85 times the peak value. An estimate of the bolometric luminosity () of the sheath is determined by summing up all of the deconvolved “sheath” flux (see Figures 8 and 9 ) contained within the gray shaded regions of our stacked map. We convert this extrapolated sheath flux at 43 GHz into a spectral luminosity and assume a power law (), which we then integrate over a range of frequencies that encompass the sheath’s radiation to obtain where we have adopted a spectral index of and limits of integration of and . Our estimate indicates that the jet sheath can potentially provide a substantial source of seed photons even at parsec scales along the jet. It should be pointed out, however, that the beam width is ∼0.2 mas along our transverse slices and that the sheath region we detect is within ∼0.05–0.15 mas of the jet spine. Convolution with the beam, therefore, adds a significant contribution of flux from the spine to our nominal sheath region. As illustrated in Figures 8 and 9 (solid red lines) we attempt to remove this contaminating spine flux from our estimate. The bolometric luminosity given in Equation ( 1 ), however, should only be regarded as a rough estimate of the actual sheath luminosity. Figure 6. Stacked map of 43 GHz images of 4C 71.07 spanning 20 epochs of observation from 2008 to 2016. As in Figure 3 , the black contours correspond to total intensity (contour levels are: 0.9, 1.9, 3.9, 7.9, 15.8, 31.7, 63.4, 126.9, 253.9, 507.8 mJy beam −1 ), whereas the underlying color scheme corresponds to polarized intensity (see the color bar to the right for the flux levels), with the EVPAs denoted by the

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


CP problem in particle physics, as was first proposed by Peccei Quinn ( 1977 ), Wilczek ( 1978 ), and Weinberg ( 1978 ). Ultralight axions are an extrapolation of the QCD axions (with expected masses in the range eV) to much smaller masses eV (Press et al. 1990 ; Hu et al. 2000 ; Peebles 2000 ). At low redshift, they form a Bose–Einstein condensate that oscillates coherently (unlike a stochastic background) on a timescale (e.g., Sikivie Yang 2009 ; Marsh 2016 ; Hui et al. 2017 ; Grin et al. 2019 ; Niemeyer 2019 , and references therein). Constraints on their mass m a have been set using Ly α forest measurements (Armengaud et al. 2017 ; Iršič et al. 2017 ; Kobayashi et al. 2017 ) and cosmic microwave background lensing (Hlozek et al. 2018 ) on megaparsec scales, dwarf spheroidals (Marsh Pop 2015 ; González-Morales et al. 2017 ; Broadhurst et al. 2019 ; Marsh Niemeyer 2019 ; Safarzadeh Spergel 2019 ) and ultradiffuse galaxies (Wasserman et al. 2019 ) on kiloparsec scales, and galactic core observations on (sub)parsec scales (Bar et al. 2019 ; Desjacques Nusser 2019 ; Davies Mocz 2020 ). Pulsar timing offers another avenue to probe the existence of coherent oscillations induced by ultralight scalar fields (Khmelnitsky Rubakov 2014 ; Blas et al. 2017 ; de Martino et al. 2017 ). Upper limits on the amplitude of such an oscillating gravitational potential in the Milky Way halo have already been derived from pulsar timing arrays (Porayko Postnov 2014 ; Porayko et al. 2018 ). Cross-correlation of residuals from different pulsars should improve these constraints (Hellings Downs 1983 ). Axion coherent oscillations also resonate with binary pulsars (Blas et al. 2017 ). While the effect is strongest near resonance, the very small width of the latter (when the coupling is purely gravitational) implies that one shall monitor instantaneous variations (Rozner et al. 2019 ) or the secular drift of orbital elements (Blas et al. 2019 ) away from resonances. Mashhoon ( 1978 ) used Lagrange’s planetary equations to develop an approximate theory of the interaction of a weak gravitational wave with a Keplerian binary. In this paper, we use angle-action variables to investigate the instantaneous variations (that is, not averaged over one orbital time) of a Keplerian system produced by an oscillating background of axion dark matter. We refer the reader to Binney Tremaine ( 1987 ) for an overview of the angle-action formalism. The paper is organized as follows. After a brief presentation of the astrophysical/cosmological context and our numerical implementation in Section 2 , we solve for the time evolution of the perturbed binary system using angle-action variables in Section 3 . We explore the instantaneous variations of the Roemer time delay as a function of orbital parameters, etc., in Section 4 . We conclude in Section 5 . 2. Setup We will use the numerical simulations of Rozner et al. ( 2019 ) to validate our theoretical predictions. We consider a binary

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


of toroidal field, attributable to a magnetic buoyancy instability (see for e.g., Vasil Brummell 2008 ; Guerrero Käpylä 2011 ). If this were to be the case, we might then expect multiple flux structures to be formed at the same time in a turbulent environment, and such structures would most likely possess random strengths, twists, and separations drawn from some distribution. We therefore choose each of our simulations in the MC series for a particular background field strength to start with five flux concentrations, with random initial twists (−5 ≤ q ≤ 5), and random distance, d , between them (with the constraint, d ≥ 2 R , so that they do not overlap), embedded initially at the same (canonical) height in the prescribed overlying large-scale background field. The random values are drawn from a uniform distribution over the range given. Our setup certainly has some significant degree of arbitrariness, owing to the limitations in our quantitative understanding of the amount of twist in flux tubes, the distance between them, and their strengths at their origination in the deep solar interior. For example, our choice of drawing the random values of twist from a uniform distribution might not be very realistic, and a Gaussian with a larger range might be better (or perhaps even a skewed distribution, to account for the effects in the formation of tubes not included in our model, e.g., rotation: see Chatterjee et al. 2011 ). However, as mentioned above, there are some constraints on the value of ∣ q ∣. Firstly, ∣ q ∣ ≳ 12 (the dashed line in Figure 8 , which is actually a very weakly decreasing function of B s ) is unphysical, since in this case the azimuthal field is sufficiently strong to induce a negative density in the structure. Secondly, structures where ∣ q ∣ ≳ 8 are unstable to kink instabilities (according to Linton et al. ( 1996 ), which does not fit our model exactly, but is probably a reasonable guide). Therefore, our chosen distribution (uniform, ∣ q ∣ ≤ 5) seems reasonable, in that it makes it likely that the initial simulation setup has a mixture of weak and reasonably strong concentrations of both helicities, and, if anything, overemphasizes the stronger twists (i.e., those more likely to violate the SHHR). An MC series of this type (fifty simulations, five random tubes each) is reported for four different background field strengths, ranging from relatively weak to relatively influential (0.01 ≤ B s ≤ 0.10). We identify the weak background field with the beginning and end of the cycle, and the stronger background with the peak of the cycle, although we have no direct observational evidence from the deep solar interior of the relative strengths of these fields from which to set their values. Figure 13 shows the results of the MC simulations for each of the four different background field strengths. Each circle in the plot represents an accumulation over a specified time interval [ t 0 , t 1 ] in the simulation of the absolute value

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; Jess et al. 2012 ; Krishna Prasad et al. 2015 , to name but a few). Wang et al. ( 2013 ) employed simulations to indicate that PDs, which are ubiquitously observed in coronal SDO /AIA observations, may be produced by small-scale impulsive heating events (e.g., nanoflares) at the loop footpoints. However, the models employed by Wang et al. ( 2013 ) utilize a more straightforward cosine-based impulsive functional form, rather than the traditional impulsive rise and gradual decay found in many small-scale flare studies. Furthermore, since Keys et al. ( 2011 ) also documented how the velocity evolution of small-amplitude flares closely matches the intensity fluctuations, the Monte Carlo–based nanoflare time series presented here could equally be employed to model intensity or velocity impulses at the base of coronal loops. These more traditional impulsive rises and exponential decays could then be fed into magnetohydrodynamic modeling codes, such as that used by Wang et al. ( 2013 ), to investigate in more detail whether nanoflares can contribute to the creation of PDs in coronal loops, fans, and plumes. Additionally, Hudson Warmuth ( 2004 ) revealed evidence to support the earlier work of Uchida ( 1968 ), whereby wave motion in coronal loops can be associated with weakly nonlinear effects originating in metric Type II bursts. Therefore, the inherent “sawtooth” shape of the nanoflare light curves may be able to help probe some of the weakest oscillating structures, especially since chromospheric and coronal fluctuations are becoming increasingly ubiquitous with continual improvements in instrument spatial and temporal resolutions (Jess et al. 2015 ; Grant et al. 2018 ; Houston et al. 2018 ). Finally, the nanoflare characterization approaches described here can also be directly applied to high time resolution observations of stellar sources (e.g., modernizing the work of Audard et al. 1999 ; Kashyap et al. 2002 ). For example, the photometric precision of high-cadence Kepler observations (Koch et al. 2010 ), or those taken through an assortment of optical filters by ULTRACAM (Dhillon et al. 2007 ) at very high cadences, would be ideal to test the nanoflare signatures on variable dwarf stars. Indeed, developing from the work of Hawley et al. ( 2014 ), Pitkin et al. ( 2014 ), Balona ( 2015 ), and Lurie et al. ( 2015 ), the initial Monte Carlo simulations could be extended to larger-amplitude values to expand the “nanoflare” coverage into more macroscopic sources that demonstrate intensity fluctuations exceeding 3 σ N . With larger-scale impulsive events being much more evident in the resulting light curves, the user would have a much better grasp of the e -folding timescales associated with the flaring activity. As a result, the occurrence rates of (quasi-)periodic activity could be much more reliably constrained, thus better revealing the energy output of such flaring events on distant stellar sources. In addition, high temporal resolution (∼0.1 s)

O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O 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-Observatory B-Telescope 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 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 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Telescope O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Instrument 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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


et al. 2014 ). We used the same tools to produce periodograms for our SOAR and McDonald data, whose rapid acquisition cadence allowed us to identify the correct K2 periodogram alias (Figure 1 ). After identifying the true alias, we performed a least squares fit of a sinusoid to the K2 light curve data with the software Period04 (Lenz Breger 2014 ), using the peak frequency of 3152 μ Hz as an initial guess. Our best-fit value for the period of J1252 from K2 is 317.278 ± 0.013 s (3151.807 ± 0.013 μ Hz). When fitting to the ground-based data, we used this period as an initial guess, and performed nonlinear least squares fits to determine if the period was consistent for all data sets (Table 2 ). Table 2 Results of Nonlinear Least Squares Fits of a Sinusoidal Signal to McDonald Observatory Light Curves from 2018 to 2019 Note. The equation used is , where the initial guess for P is the period determined from the K2 data (317.278 ± 0.013 s). We report the time of first photometric maximum in each filter for each set as determined from the phase term. Because white dwarf rotation rates are typically on the order of hours to days (Berger et al. 2005 ; Hermes et al. 2017b ), we were surprised to find that the period of this object was far shorter, falling at over 11 times the Kepler long-cadence Nyquist frequency (283.5 μ Hz). Murphy ( 2014 ) presents the function by which periodogram amplitude diminishes with super-Nyquist signals as , where t exp is the instrument sampling rate, and P is the object period. For J1252, the measured amplitude from the Kepler long-cadence sampling rate is diminished by a factor of 17.79 compared to the intrinsic. The inferred intrinsic amplitude from this is 4.20%, which is comparable to the 4.56% amplitude from the McDonald BG40 data (Figure 1 ). The remaining difference is attributable to the respective Kepler and BG40 filter bandpass shapes and wavelength ranges. We detected a significant difference in color amplitude, with ratio g / i = 2.26 ± 0.22 in our multicolor light curves, but did not detect a significant phase shift between the two colors (Figure 2 ). The individual fits also show evidence of period and phase modulations. The 2018 McDonald BG40 and SDSS filter sets were separated in acquisition by one day, but show a 2–3 σ difference in the object period. In addition, there is significant power asymmetry in the lobes of the primary feature of the Fourier transform for the observational data, indicative of phase modulation. More data are needed to explore these phenomena further. Figure 2. Folded light curves of J1252 in SDSS- g and - i filters from McDonald Observatory in 2018. We note a large ratio (>2) in amplitude between the two filters, and no apparent phase difference. 3.2. Atmospheric Parameters and Magnetism We present the phase-binned 400 l mm −1 SOAR spectra of J1252 in Figure 3 . To produce these, we folded our individual spectra into five equally spaced phase bins, each covering one-fifth of the

O O O O O O O O O O O O O O B-Telescope O B-Observatory O O O O O O O O O O O B-Mission 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 B-Software B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-CelestialObject 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 O O O O O O O O O O O O O O O O O B-Observatory I-Observatory O 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 O O 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 B-Telescope O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject 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 B-Observatory B-Survey O O O O O O O O O O O O B-Telescope O B-Survey 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 B-Observatory B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-Survey B-Wavelength O O B-Wavelength I-Wavelength O B-Observatory I-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O


1982 ; Forbes 2000 ; Vršnak 2008 ; Aulanier 2014 ; Janvier et al. 2015 , for reviews). Characterizing coronal currents before and during eruptions is therefore important to develop a comprehensive understanding of the triggering and acceleration of CMEs, especially in the context of a growing need for accurate and quantitative space weather forecasts. In addition, on a more fundamental basis, specifying the spatiotemporal evolution of eruption-related currents at the Sun’s surface would also bring an unprecedented input to the versus debate (e.g., Melrose 1991 ; Parker 1996 , 2001 ; Heikkila 1997 ; Vasyliunas 2005 ), in particular regarding whether the magnetic field or the electric current should be considered as a prime variable and boundary condition in solar eruption models in particular, and in space plasmas in general. All these considerations have recently led to a renewed interest in studying solar electric currents (see, e.g., Melrose 2017 ; Georgoulis 2018 ; Schmieder Aulanier 2018b ). The paradigm regarding the spatial distribution of currents in solar active regions has evolved over the years. For a long time, the geometrical properties of cylindrical flux ropes naturally led to the view that active region magnetic fields ought to be shielded from their surroundings through external return currents, with a magnitude equal to that of the direct currents. This so-called current neutralization of coronal flux ropes was considered to be a natural prediction of the paradigm, in the context of the MHD twisting of coronal flux-tubes (as explained e.g., in Parker 1996 ; Dalmasse et al. 2015 ). Such neutralized currents in the corona, however, are problematic for several eruption models that rely on the existence of net currents (e.g., van Tend Kuperus 1978 ; Forbes Priest 1995 ; Kliem Török 2006 ; Démoulin Aulanier 2010 ). In addition, the most recent observations of sunspots revealed that many flaring active regions carry a non-neutralized (i.e., a net) current (Ravindra et al. 2011 ; Georgoulis et al. 2012 ; Cheng Ding 2016 ; Zhao et al. 2016 ; Vemareddy 2019 ). These observations could have been considered to support the paradigm, with some circuit models associated with net coronal electric currents directly originating from the depths of the Sun’s interior (Alfvén Carlqvist 1967 ; Melrose 1991 ). However, recent numerical MHD models of magnetic fields in the corona driven by magnetic flux emergence (Török et al. 2014 ) or by line-tied motions (Dalmasse et al. 2015 ) have both unveiled that MHD processes could also generate net coronal currents in pre-eruptive active regions, due to the shear component of the magnetic field across polarity inversion lines (PILs). Two different analytical interpretations have been provided to explain this association, either by invoking Lorentz forces (Georgoulis et al. 2012 ) or a simple property of the integral form of Ampère’s law with force-free fields (Dalmasse et al. 2015 ). In both cases, it was

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


soft X-ray emission towards the south loop. As suggested by Snowden et al. (1995) , we find that significant 0.25 keV emission remains inside the loop after the foreground emission from the Local Bubble and the background intensity are subtracted. The background intensity is the intensity that is expected from the Galactic halo and is modulated by the total gas absorption. Taking the south loop absorption into account, we find no clear spectral difference between the EXE1 region north of the east shell and the EXE2 region towards the south loop. The spectral dichotomy that is visible on the maps is largely induced by the south loop absorption. A single-temperature plasma cannot match the X-ray spectra across the three bands in any of the sampled directions, however. Two hot phases are required, with respective temperatures of 3–9 MK and 0.3–1.2 MK under the assumption of a uniform pressure across both phases. The derived pressure of (3− 8) × 10 4 cm −3 K exceeds the pressure of the Local Bubble of 10 4 cm −3 K ( Puspitarini et al. 2014 ). The need for at least two plasma phases might indicate global plasma oscillations across the superbubble that are caused by its complex interior history ( Krause et al. 2014 ). In addition, the significant emission hardening seen towards the region that is enclosed between the H α arcs A and B corresponds to a higher pressure and hotter temperature that support the hypothesis of a younger age and faster expansion of this sub-region ( Heiles et al. 1999 ). The origin of the south loop ring is unclear. A wind-blown bubble seems unlikely because of the lack of massive stars in this direction ( Burrows et al. 1993 ). We find no gradient in temperature or pressure between the south loop and adjacent regions that would support a cooling flow of hot gas that leaks at the rear of the superbubble ( Heiles et al. 1999 ). The gas ring, filled with plasma that is a few million degrees hot, is consistent with an old supernova remnant. The progenitor star may have belonged to the Cassiopeia-Taurus OB association, which extends from 130 to 300 pc ( de Zeeuw et al. 1999 ; Pellizza et al. 2005 ) in these directions. The more sensitive and refined X-ray maps that will soon be obtained by the extended Roentgen survey with an imaging telescope array (e-ROSITA) will spatially and spectrally constrain the heterogeneity of the hot gas phases that fill the superbubble better. This will enable us to reconstruct the possible sequence of supernovae that have blown this structure. 6.3 Magnetic field in the superbubble We have used Planck polarised dust emission and the gas dynamics information from the H I line decomposition to study the magnetic field in the superbubble. We probed the plane-of-sky magnetic field, B sky , using the modified Davis–Chandrasekhar–Fermi method (DCF method) proposed by Cho Yoo (2016) . We have obtained magnetic strengths 17 times lower than previous estimates along the west rim ( Soler et al. 2018 ). The

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M V ∼ −13.5 and Carina M V ∼ −9.5) merit a special mention. Although both dwarf galaxies have been quenched fairly recently (∼2.5–3 Gyr ago), there are suggestions that these dwarf galaxies have been orbiting the MW for a much longer time (e.g. Pasetto et al. 2011 ; Rocha et al. 2012 ; Patel et al. 2020 ; Rusakov et al. 2020 ). However, the results are dependent upon a number of model uncertainties and are much debated in the literature (Jahn et al. 2019 ; Pardy et al. 2019 ). We choose to retain Fornax and Carina in our sample. This leaves us with a sample of 13 and 28 satellites for the MW and M31, respectively (see Table 1 ). The lookback time of shutdown in star formation of these dwarf galaxies has been drawn from the literature, and has been estimated from data of varying quality. For 6 M31 dwarfs drawn from the ISLAandS project (Skillman et al. 2017 ), the shutdown time has been estimated from deep CMDs reaching down to the oldest main-sequence turn-off (MSTO). The shutdown time for the vast majority of the M31 dwarfs have been estimated from resolved HST data reaching fainter than the horizontal branch (Weisz et al. 2019b ). A sizeable fraction of the satellites of the MW have their time of their shutdown in star formation estimated from HST data reaching down to the MSTO (Weisz et al. 2014 ). For a few of the nearer MW dwarfs, the star formation has been estimated using ground-based data (e.g. Torrealba et al. 2016 ; Bettinelli et al. 2018 ). In Table 1 , we have included both the systematic and statistical uncertainties of τ 90 . The constraints on τ 90 as well as the ancient star formation history of M31 dwarfs will dramatically improve with observations from the upcoming Cycle 27 HST Treasury survey as part of HST -GO-15902 (PI D. Weisz). Table 1. Star formation shutdown time. Note . Distance of M31 satellites is taken from Conn et al. ( 2012 ) and Weisz et al. ( 2019a ). τ 90 is taken Weisz et al. ( 2014 ), Weisz et al. ( 2019b ), Brown et al. ( 2014 ), Bettinelli et al. ( 2018 ), and Torrealba et al. ( 2016 ). M V taken from McConnachie ( 2012 ). 5.1 Temporal clustering of star formation shutdown The lookback time of shutdown in star formation in the satellites of the MW and M31 is strongly clustred. We demonstrate this by employing a kernel density estimator (KDE) to estimate the mean lookback quenching time of these clusters. In the bottom panel of Fig. 21 , we estimate the probability density function (pdf) of the lookback quenching time. To do this, we select the ‘bandwidth’ (smoothing parameter) for each KDE, such as to to optimize the bias-variance tradeoff (1.29 and 0.98 for the MW and M31, respectively). The pdf of the MW is double humped with prominent peaks at ∼2.5 and ∼11 Gyr ago. The pdf of M31 has a single prominent peak ∼6 Gyr ago. These prominent peaks continue to be significant and stable, even after taking into account the uncertainties in the lookback quenching time of the satellites. The inclusion of the

B-Formula I-Formula I-Formula I-Formula O B-CelestialObject 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 B-CelestialObject O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation 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 B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-Telescope 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-CelestialObject O O O O O O O O O O O B-Telescope O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O B-Grant I-Grant O B-Person I-Person O O O O O O O O O O B-CelestialObject 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O B-CelestialObject 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


subtraction, flat-fielding, cross-talk correction, fringing, etc.). From the CP calibrated frames, we use the Astromatic 5 5 http://www.astromatic.net/ software suite (Source Extractor (SE); SCAMP; SWARP; PSFEx; Bertin Arnouts 1996 ; Bertin et al. 2002 ; Bertin 2006 ) to register frames to a common coordinate system and account for pixel scale distortions across the DECam field of view using the 2MASS astrometric reference star catalog and calibrate our photometry to the Sloan Digital Sky Survey (SDSS) system using frames of the LSE_44 SDSS southern standard star field taken at varying airmass during the observing nights. 3. Analysis 3.1. Dwarf Detection and Photometric Analysis We detect dwarf candidates using a full-color RGB image constructed from our u ′ g ′ z ′ imaging with custom Python image processing scripts. This filter combination samples the full optical spectral energy distribution (SED) and is sensitive to old, metal-poor stellar populations expected of primordial dwarf galaxies, while the inclusion of the u ′-band also serves to sample flux from younger stellar components arising from more recent star formation. Figure 1 shows the RGB image with orange dashed curves indicating NGC 5128-centric iso-radial contours. We visually searched this image for faint, extended sources displaying smooth morphologies with shallow surface-brightness ( μ ) profiles typical of low-luminosity dwarfs. Using this method, we unambiguously find 16 dwarf galaxy candidates, of which a single previously known dwarf is recovered (KK98a 189; Karachentseva Karachentsev 1998 ) and the remaining 15 are reported here for the first time, noting that one dwarf (dw1317-4255) has recently been confirmed to be a true member of the Centaurus A group Crnojević et al. 2018 ). The set of zoom-in images in Figure 1 show the dwarf candidates and measure 2′ on a side, corresponding to physical ∼2.2 × 2.2 kpc 2 regions at the distance of NGC 5128. We point out that by employing a “by eye” detection technique, we are unable to make a robust estimate of the completeness limit to our imaging in a straightforward manner and thus cannot make broad statements on the true total population of dwarfs in this region. We instead defer such an analysis to a future work detailing the overall properties of dwarfs detected throughout our survey region, noting that a lack of completeness estimate does not affect our conclusions. Figure 1. Locations of the new dwarf galaxy candidates on a u ′ g ′ z ′-based RGB color image. White-bordered images show 15 × 15 cutouts centered on the dwarfs, corresponding to ∼1.7 × 1.7 kpc 2 at the distance of NGC 5128. The scale of the background frame is indicated in the lower-left corner. Dashed orange curves show distances corresponding to 100, 150, and 200 kpc from NGC 5128. North is up, east is to the left. We use galfit (v3.0.5; Peng et al. 2010 ) to measure the structural and photometric properties of the dwarfs. We first create 365 × 365 (4 × 4 kpc

O O O O O O O O O O O O O O B-Software O O B-URL B-Software I-Software B-Software I-Software B-Software B-Software B-Software B-Software B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O B-Instrument O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O O O O B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O B-Software 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 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-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 O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Software B-Identifier 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


to the study would be to ensure that observations of a given object on all telescope configurations are all carried out well within the expected Keplerian orbital time at the inner rim. This would allow a possible smoothing out of the asymmetric emission to be lifted. A second improvement would be to push for a higher angular resolution at VLTI using the longest baseline (≈ 200 m). This implementation is currently under study at the European Southern Observatory (ESO). Finally we note that some objects are sufficiently to the north so that they could be observed with VLTI and the Center for High Angular Resolution Astronomy (CHARA), which would provide a remarkable ( u , v ) coverage and angular resolution. Table 5 Sizes of the stellar environments: theoretical sublimation radius ( θ sub ) and the measured half-flux radius ( θ 1∕2 ). 5.5 Comparing the images to the theoretical dust sublimation radius We can measure the sizes of circumstellar emission from the images by taking the half-light radius corrected for the disk orientation (see Appendix D ). We assessed the accuracy of the size measurement against the true sizes from radiative transfer models in Appendix F by reconstructing images on the synthetic data generated from those models. The recovered sizes match the true sizes of the models with a sharp inner rim as long as the inner rim is resolved enough (i.e., θ 1∕2 ∕ θ res ≥ 1.2). However, we find a bias for sizes from extended inner rim models (see Appendix F ). We tend to recover sizes that are smaller than the true sizes for very resolved targets (i.e., θ 1∕2 ∕ θ res ≥ 2.5). Most of the targets (12/15) are relatively well resolved (i.e., θ 1∕2 ∕ θ res ≥ 1.3). In Fig. 8 , we plotted the sizes of the targets against their luminosity for both this work and L17. For the imaged object, we see good agreement between both size determinations, that is, using parametric models and image reconstruction. For some targets (HD 145718 and R CrA), the difference is significant (ratio larger than 1.5 between the two sizes) and this is likely due to model bias (as the parameteric model for R CrA was an ellipsoid instead of a ring and the stellar-to-total flux ratios are different for HD 145718). We note that the size difference is in the opposite direction of the size bias from image reconstruction that we identified in Appendix F . Fig. 8 Size-luminosity relation. The green circles are the sizes measured from images, red crosses are the sizes from parametric models as determined in L17, and cyan triangles are the physical spatial resolution reached by our observations. The two size estimations and the spatial resolution are linked by a vertical dotted line. The dashed gray line represents the theoretical sublimation radius. In order to have a reference to interpret the sizes of the circumstellar emission from the reconstructed images, we computed the theoretical dust sublimation radii using: (see, e.g., Monnier Millan-Gabet 2002 ; Kama et al.

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


of the log N –log S distribution in this region were found to be in very good agreement with that predicted for CV populations (Fornasini et al. 2014 ). The NuSTAR survey of this region measured a log N –log S distribution that is consistent with Chandra sources if the average source spectrum is thermal with kT ≈ 15 keV (Fornasini et al. 2017 ). This is significantly harder than the kT ≈ 8 keV spectrum derived by previous soft X-ray measurements of the Galactic center (Muno et al. 2004 ; Heard Warwick 2013 ) but softer than NuSTAR measurements of the Galactic center, thus possibly indicating a lower fraction of IPs relative to other types of CVs in this region. 3. <italic>NuSTAR</italic> Data Preparation 3.1. Introduction to Zero- and Two-bounce Photons To obtain the wide solid-angle aperture necessary to study the diffuse X-ray emission from the Galactic bulge, we exploit NuSTAR ’s ability to measure unfocused, or “zero-bounce,” X-rays from an ∼1°–3° radius field of view (FOV). The details of the NuSTAR instrument relevant for this analysis are summarized here. NuSTAR has two identical telescopes, each consisting of an independent optic and focal-plane detector, referred to as FPMA and FPMB. The optics use a conical approximation to the grazing incidence Wolter I design, in which X-rays are focused by reflection from an upper parabolic mirror section and then a lower hyperbolic mirror section. The FOV for these focused, or “two-bounce,” photons is ∼13′ × 13′. To block unfocused X-rays from reaching the NuSTAR detectors, a series of aperture stops are attached to each focal-plane bench. However, this shielding is not complete, and there remains an ∼35 radius aperture, partially blocked by the optics bench, from which totally unfocused, or zero-bounce, photons can reach the detectors. The solid-angle aperture for zero-bounce photons is over 2 orders of magnitude larger than the FOV for focused photons, even after accounting for blocking by the optics and vignetting effects due to the aperture stop. This large solid angle for zero-bounce photons allows us to study the diffuse emission of the Galactic bulge. In this analysis, we construct a spectrum using photons from the full detector plane, which are a combination of photons from the zero-bounce aperture, two-bounce FOV, and instrument background (similar to the technique used in Ng et al. 2019 ). Via this technique, we lose the imaging capabilities of the NuSTAR optics but gain spectral information from a large region of the sky. Although the aperture for zero-bounce photons is much larger, the two-bounce FOV is not entirely negligible due to the increasing intensity of the Galactic diffuse flux in the two-bounce FOV of our observations. Using the mass model of the nuclear stellar disk and bulge, as described in Section 4.3 , we estimate that the two-bounce count rate from the Galactic center in our spectrum is ∼20%–25% as high as the zero-bounce count rate from the bulge. We thus need to

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


versus dust-corrected O 32 values (a proxy for ionization parameter) for our galaxies (blue circles), colour-coded by absolute i ′-band magnitude. We plot as black points the XMPs uncovered uniformly from the SDSS spectroscopic sample by Sánchez Almeida et al. ( 2016 ). The uncertainties (1σ) are plotted for our galaxies, and are hidden by the markers in several cases. The vast majority of SDSS XMPs are clustered at Hβ EWs 50 Å and O 32 3. Relatively few previously identified XMPs extend into the high-sSFR region of this diagram at Hβ EWs >50 where our objects reside. The gas in the XMPs presented here is also more highly ionized than in most XMPs from the SDSS spectroscopic sample, consistent with substantially different stellar populations and resulting ionizing radiation fields. The O 32 ratio is commonly used as a proxy for the ionization parameter, or the density of ionizing radiation relative to the gas density. Fig. 9 reveals that indeed, the XMPs presented here host more highly ionized gas than most XMPs from the SDSS spectroscopic sample. Our XMPs have O 32 ratios ranging as high as 10, with median O 32 = 4.1 (and an even higher median O 32 = 6.4 for the subset with Hβ equivalent widths above 100 Å). This is substantially higher than the majority of SDSS XMPs shown, which have median O 32 = 1.2. This indicates that the gas in the galaxies we have uncovered is more highly ionized than in most previously known XMPs, consistent with these systems hosting harder ionizing radiation fields. The offset towards higher Hβ equivalent widths and O 32 ratios in our XMPs suggests that these systems host significantly more prominent young massive stellar populations than typical previously known XMPs. Fig. 9 indicates that the average XMP from the SDSS spectroscopic sample has undergone a more extended star formation history, resulting in an optical spectrum with a substantial contribution from stars formed >10 Myr ago and less highly ionized gas. The EUV and X-ray radiation powered by a typical nearby XMP with a Hβ equivalent width of 30 Å (sSFR ≃ 1 under constant star formation) is potentially very different from that of a reionization-era galaxy which has formed essentially all of its stars in the last 100 Myr (sSFR ≃ 5–10 ). Future studies targeting these high-sSFR XMPs will provide a new window on to the massive stars and X-ray populations that likely dominate the early universe. As a first step towards constraining their EUV ionizing spectra, we examine high-ionization nebular He ii emission in our galaxies. The He ii λ4686 nebular emission line is a recombination line powered by extremely energetic photons >54.4 eV. This line is commonly observed in low-metallicity star-forming dwarf galaxies (e.g. Garnett et al. 1991 ; Brinchmann, Kunth Durret 2008 ; Shirazi Brinchmann 2012 ; Senchyna et al. 2017 ), but the origin of the necessary >54.4 eV photons is still a matter of debate. The commonly cited candidate sources of narrow He ii are very

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