the divergence of velocity shown in panels (a) and (b) for a short period of time to display the continuous generation of wave trains. (An animation of this figure is available.) In order to study the dynamical behavior of the wave trains outside the CS, we plot the time–distance diagram of the normalized running difference of the density Δ ρ / ρ along the line x = −0.15 L from t = 857.9 to 2038.6 s in Figure 8 (a). There are violent variations below the edge of the CME, and they may have quasiperiodic behavior indicating the propagation of the coronal wave trains. Since the flux rope keeps rising, it is impossible to fix a point aside to check the periodicity of the wave trains. The estimation of the periodicity is also sensitive to the chosen line, along which the calculation is executed. For instance, we followed the dashed line almost parallel to the edge of the CME from panel (a). The associated distribution shows periodicity in panel (b), and the period is calculated to be ∼76.3 s. Therefore, we directly investigate the evolution of the turbulent region above the upper TS. Figure 8. (a) Normalized running difference of the density along the line x = −0.15 L extracted from t = 857.9 to 2038.6 s. The blue diagonal line corresponds to the low-density wing to the left of the TS in Figure 2 (f), and the red diagonal line is where the density jumps back to the coronal value outside the flux rope. (b) Associated distribution along the dashed line in panel (a). The symbol Δ ρ / ρ is defined as ( ρ ( t ) − ρ ( t − Δ t ))/ ρ ( t ). A typical Δ t ≈ 9.2 s. Takasao Shibata ( 2016 ) described how the CS outflow can form a blob of gas between the sides of a “tuning fork” and how the backflow of the gas drives an oscillation of the magnetic structure. The oscillation can drive waves that propagate well outside the “buffer region” where it occurs. Figures 7 (c) and (d) show the dynamics of the backflow. The relation between the coronal wave trains and the turbulence under the CME is analyzed in Figure 9 . In panel (a), we show the time evolution of the maximum of the horizontal velocity V x of the backflow and the fast magnetosonic Mach number before the upper TS. Note that the Mach number is defined as the ratio of the flow velocity to the fast-mode magnetosonic speed. The max( V x ) decreases in general, indicating that the coronal wave trains may appear at different speeds, which could be caused by variations in the local plasma density and magnetic strength. The peaks reveal the oscillation of the MTF. Interestingly, one can find that the Mach number mainly varies around 2.4, which is larger than that before the TS above the flare loops (1.5–1.8 found in observations and simulations; Chen et al. 2015 ; Ye et al. 2019 ). This reveals that it is easier to form the upper TS than the lower one, and the variation of the Mach number is related to the interplay between plasmoids and the TS (Shen et al. 2018 ). Then, we performed the Morlet transform on

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


morphologies (Brinchmann et al. 2004 ). The number of non-AGN decreases steadily as B/T increases, however, there is a significant population (12 per cent of the non-AGN sample) with B/T = 1, i.e. pure elliptical galaxies. Of the 181 pure ellipticals that we classify as non-AGN, only four are unclassifiable via the BPT analysis. 114 are BPT-classified as composite, AGN(non-LINER), or low S/N LINER implying that there is some AGN component in these galaxies, but the radio emission is not significantly enhanced to be selected by our method. The remaining 63 non-AGN pure ellipticals are classified by the BPT analysis as either star forming or low S/N star forming, which is consistent with these galaxies being truly non-AGN. Figure 6. The distribution of bulge-to-total light ratios, which we use as a proxy for galaxy morphology, for the non-AGN galaxies (blue), all AGN i.e. our faint AGN + the BH12 AGN (red), and the faint AGN sample only (green). Non-AGN galaxies have predominantly low B/T values, i.e. are morphological spirals, while almost all BH12 AGN and the faint identified in this work have B/T = 1, i.e. are morphological elliptical galaxies. For the AGN samples, we find that there are few sources with disc-like morphologies (89 per cent have B/T ⩾ 0.5), and the majority of the galaxies have B/T=1, 78 per cent for the total AGN sample and 73 per cent for the faint AGN sample. This also agrees with previous studies that show that radio-loud AGN are preferentially found in massive elliptical galaxies (Wilson Colbert 1995 ; Dunlop et al. 2003 ; Kauffmann et al. 2003 ; Kauffmann, Heckman Best 2008 ). We complete our analysis by briefly checking our morphological results with the local colour–magnitude relation. Using the k-corrected g-band and r-band magnitudes from the MPA–JHU catalogue, we split the sample into red and blue galaxies. We then recreate Fig. 1 showing the density of red sequence and blue cloud galaxies (Fig. 7 ). Galaxies identified as AGN (both the BH12 AGN and those in our faint AGN sample) are typically found on the red sequence that is dominated by early-type galaxies (e.g. Bower, Lucey Ellis 1992 ; Kodama Arimoto 1997 ; Blanton Moustakas 2009 ), in agreement with our results using the bulge-to-total light ratios that find that the majority of AGN have early-type morphology. In contrast, the non-AGN galaxies cover a much broader region of the colour–magnitude diagram and are predominantly in the blue cloud that is typically dominated by star-forming spiral galaxies (e.g. Tully et al. 1998 ; Baldry et al. 2004 ). This is again in agreement with our morphological results where we find that the non-AGN galaxies are disc-dominated. Figure 7. Comparison of the SFRs obtained via optical spectro-photometric data from the SDSS, with the FIRST 1.4 GHz luminosities as in Fig. 1 but coloured by position in the colour–magnitude diagram. Galaxies that are found in the blue cloud are mostly purely star-forming galaxies (shown in

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


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


took advantage of recent studies that thoroughly examined the LMC cluster population in some selected fields located within the B17 's surveyed area. Fig. 2 shows the distribution of the B17 's objects and the seven well-studied LMC regions considered here overplotted. The large hexagons correspond to DECam fields (∼2° × 2° FOV, pixel size = 0.263 arcsec; Flaugher et al. 2015 ) analysed by Piatti ( 2017c ), while the small rectangles correspond to MOSAIC II fields (36 arcmin×36 arcmin FOV, pixel size = 0.269 arcsec) studied by Piatti ( 2017b ) and Piatti et al. ( 2018 ). The 4-m Blanco telescope at the Cerro Tololo Interamerican Observatory (CTIO) was employed to observe those fields, among others distributed outwards the B17 's surveyed area as part of different photometric surveys aimed at studying the most metal-poor stars outside the Milky Way (rectangles: CTIO 2008B-0296 programme; PI: Cole) and the Magellanic Clouds stellar history (hexagons; Nidever et al. 2017 ). Figure 2. Spatial distribution of B17 's objects with selected LMC fields studied by Piatti ( 2017c ) (hexagons) and Piatti ( 2017b ) and Piatti et al. ( 2018 ) (rectangles) overplotted. These LMC fields were carefully surveyed looking for star clusters by employing the method mentioned above (Piatti et al. 2016 ), i.e. by constraining the search using the known cluster dimension and mean stellar density ranges. The final cluster lists resulted to be statistically complete, because the derived photometry detected any star cluster based on counts of its brightest stars all the way down to the main-sequence turnoff (MSTO) of the oldest LMC clusters. Every catalogued B08 's cluster was recovered, in addition to very few new identified clusters in some of the surveyed fields. The CMDs of the recognized extended objects were then cleaned from field star contamination by using the procedure developed by Piatti Bica ( 2012 ), i.e. by building statistically meaningful star field CMDs that tightly reproduced the luminosity function, colour distribution, and stellar density of the respective star fields, to be subtracted to the cluster CMDs. The resulting cleaned CMDs for some of the objects led to conclude that they are not genuine physical systems, but random fluctuations of the field star density. Table 1 lists the number of entries in the B08 's catalogue for each selected LMC field (field ID is as in Fig. 2 ), and the number of true star clusters confirmed according to the photometric analyses performed by Piatti ( 2017c , 2017b ) and Piatti et al. ( 2018 ). Table 1. Statistics of star clusters in LMC fields. Ref.: 1) Piatti ( 2017c ); 2) Piatti ( 2017b ); 3) Piatti et al. ( 2018 ). For comparison purposes, we extracted the results of Section 2 for the selected LMC fields, namely, the number of B08 's objects matched by the B17 's ones as well as the number of B17 's new detections. They are also listed in Table 1 . For completeness, we included in its last column the deprojected

O O O O O O O O O B-CelestialObject O O O O O O O O O B-Citation O O O O O O O O O O B-Citation O O O O O O B-CelestialObject O O O O O O O O O B-Instrument O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Instrument I-Instrument O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Telescope I-Telescope I-Telescope O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory 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 B-CelestialObject I-CelestialObject O B-Proposal I-Proposal I-Proposal O B-Person O O B-CelestialObject I-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject 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 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 B-Citation O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject O O O O O B-Citation O O O O O B-Citation O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O


orbit) and electron (black orbit) are accelerated towards opposing foot-points (as one might expect from the charge difference between the species). Furthermore, while the electron is rapidly accelerated almost all the way to the photospheric boundary, the proton never leaves the (upper) corona, but is ultimately reflected and returns along the initial trajectory. In Fig. 8 c, we see that the electron (diamonds) reaches the photosphere after approximately s. In this time, the proton (plus signs) has barely moved. The proton achieves maximum parallel speed after approximately s and mirrors approximately seven times in s, with the first mirroring taking place after approximately s. To assess the reason for the proton becoming trapped in this way, we once again calculate the loss cone (see discussion in Sect. 4.1 for more details). Along the field line in question, we estimate that initial pitch angles less than and would able particles to escape the trap caused by increasing magnetic field strength. As with the case shown in Sect. 4.1 , repeating this experiment with an initial pitch angle of shows negligible differences in proton/electron behaviour; both the acceleration and trapping behaviour displayed in Fig. 8 are caused by the electric field. In extending the simulation time from s to s, we demonstrate that the electric field continues to trap the proton in the upper atmosphere for all time, while accelerating the electron until it reaches the loop foot-point at the photospheric boundary. All particle orbit calculations are automatically terminated upon reaching a Mm layer above the lower simulation boundary (which results from the limited applicability of our test-particle approach in this region). At termination, the electron has travelled approximately Mm in less than s. By comparison, the distance between mirror points for the proton is approximately Mm. The reason for the differences between the proton and electron results are twofold; from Fig. 8 c, we can see that the proton achieves its peak velocity after approximately s, taking much longer to accelerate. Upon encountering a region of oppositely oriented , the proton is unable to overcome the resulting deceleration, and mirrors. By comparison, the electron is continually accelerated as it plummets towards the photosphere. The sign of the electric field strength is positive throughout the lifetime of the electron orbit (see Fig. 8 b), hence the electric field trapping mechanism plays no role in the electron orbit. Furthermore, the magnetic mirror effect also plays no role in this orbit, as the strong, uni-directional electric field encountered by this electron results in a high parallel velocity ( or ). 5. Discussion We have conducted a survey of test-particle behaviour in an environment which aims to describe the behaviour of a solar AR. From this survey (detailed in Sect. 3 ), it is clear that this environment (at the electric field strengths derived by the MHD model) would

O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion 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


the effects of AGN feedback in the evolution of its host galaxy. The galaxy is an isolated elliptical galaxy, and we assume in this work that the specific angular momentum of the gas is low. Physical processes like star formation and SNe Ia and II are taken into account. The inner boundary of the simulation is chosen so that the Bondi radius is resolved, which is crucial for the precise determination of the mass accretion rate of the AGN. According to the theory of black hole accretion, black hole accretion has two intrinsically different modes: cold and hot. They have quite different radiation and wind outputs and thus naturally correspond to two different feedback modes. They have been carefully discriminated and taken into account in the present work. We consider the feedback effects by both the radiation and wind in each mode. The two feedback modes have quite diverse names in the literature, e.g., the quasar (or radiative) and radio (or kinetic or maintenance) mode. Our present work indicates that these names are not only diverse but sometimes also misleading. For example, in terms of regulating the accretion rate of the black hole and star formation in the galaxy, feedback by the wind is always much more important than that by radiation. So, we suggest simply following the names of the black hole accretion mode and calling them the “cold feedback mode” and “hot feedback mode.” The most important distinctive feature of the present work is that we adopt the most updated AGN physics. This is especially the case for the radiation and wind from hot accretion flows, for which much progress has been made in recent years but has not been taken into account in most AGN feedback works (see a recent review by Yuan Narayan 2014 ). It also includes more precise descriptions of the wind in the cold mode that are obtained from recent new observations. These most updated AGN physics are summarized in the present paper. For the feedback effects, we have investigated the light curve of the AGN, the black hole growth, star formation, the AGN duty cycle, and the surface brightness of the galaxy. We have compared these results with previous works that have a very similar model framework to our work but different AGN physics. Significantly different results have been found in almost every aspect mentioned above. This indicates the crucial importance of having correct AGN physics. The main results obtained in this paper are summarized below. 1. We have compared the energy and momentum fluxes of the wind and radiation in the two feedback modes (Figure 1 ). Roughly speaking, in both modes, the power of radiation is larger than that of the wind, while the momentum flux is the opposite. However, the magnitude of the energy or momentum fluxes is not the only factor to determine which component, radiation or wind, is more important in the feedback. This is because the cross section of photon–particle interaction is orders of magnitude smaller than that of

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


Weisz et al. 2011 ). According to numerical simulations, the tidal-driven changes in star formation are rather short-lived, with a typical duration of the activity of about 10 8 yr ( Di Matteo et al. 2008 ). Strong starbursts during which the star formation rate is increased by a factor larger than 5 are rare. IC 1613 is a good example of a dwarf that calmly produces stars over its entire lifetime, while showing also some fluctuations ( Skillman et al. 2014 ). The galaxy has a small H i mass of 8 × 10 7 and a stellar mass of 1.1 × 10 8 ( Woo et al. 2008 ). The current SFR is 0.003 M ⊙ yr −1 ( Mateo 1998 ), but the SFH reveals some episodes in the galaxy life with theSFR enhancement of about threefold ( Skillman et al. 2014 ). Another aspect of evolution of low-mass galaxies not addressed in numerical experiments to date is the often observed irregular distribution of star-forming regions in galactic disks. Such an asymmetric distribution is evident in for example IC 10, dominated by a giant H ii region in its southern part. The observed morphology and the strength of magnetic field are strongly related to the distribution of H ii regions within the galactic disk ( Chyży et al. 2016 ). So as to address the above issues, in this paper a series of 3D simulations of the CR-driven dynamo for low-mass galaxies are performed. In the first place, we simulate a calm evolution of galaxies at different speeds of rotation and different (but constant in time) levels of star formation activity. Below, we introduce a starburst (a rapid enhancement of star formation) and study its impact on magnetic field, while finally investigating how a localised starburst, restricted to just part of the galactic disk, changes the magnetic field topology, and how this is related to the topology for the global starburst. 2 Numerical model and setup 2.1 Cosmic-ray-driven dynamo The CR-driven dynamo model in dwarf/irregular galaxies has been implemented into a numerical code called godunov-mhd ( Kowal et al. 2009 ). The code solves the system of resistive magnetohydrodynamic (MHD) equations in a conservative form in 3D space (e.g. Goedbloed Poedts 2004 ): where ρ , p , and v are the gas density, pressure, and velocity, respectively, p cr is the cosmic-ray pressure, A is the vector potential, B ≡∇× A is the magnetic field, φ is the gravitational potential, η is the magnetic turbulent diffusivity and I is the identity matrix. To close the system an isothermal equation of state is assumed: where c s is the isothermal speed of sound and γ is the adiabatic index of the gas. Cosmic rays form a key component of the model. In our case they are approximated as a fluid, whose evolution is described by the diffusion-advection transport equation following ( Schlickeiser Lerche 1985 ): where e cr is the CR energy density, K̂ is the diffusion tensor, v is the plasma velocity, p cr is the CR pressure, and Q is the source term of e cr . CR pressure is related to the e cr via the adiabatic CR

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


The effect of different thicknesses of H atmosphere is discussed in Section 3.1 . The effect of different values of effective temperature and He layer mass is discussed in Section 3.2 . The effect of different values of total stellar mass are discussed in Section 3.3 . The average period spacing for DAV star models is analysed in Section 4 . In Section 5 , we preliminarily study the dispersion of period spacing for a DAV star KUV03442+0719. In Section 6 , discussion and conclusions are summarized. 2 INPUT PHYSICS AND MODEL CALCULATIONS In this section, we discuss the input physics and model calculations. In Paxton et al. ( 2011 ) reported modules for experiments in stellar astrophysics ( mesa ) which can evolve a star from main sequence (MS) stage to WD stage. mesa is updated quickly on the web site of ‘ http://mesa.sourceforge.net/ ’. The core compositions of a WD star are results of thermonuclear burning. The thermonuclear reaction rates are from Caughlan Fowler ( 1988 ) and Angulo et al. ( 1999 ) for mesa . With mesa version 4298, we evolve a group of MS stars, as shown in the first column in Table 1 , to WD stage by a module named make_co_wd. The input settings in the module are default by mesa . When these progenitor stars evolve to the WD cooling curve on the Hertzsprung-Russell ( H − R ) diagram, the WD models are took out. The core composition structures of these WD models, including mass, radius, luminosity, pressure, temperature, entropy, and carbon profile, are took out together. The location of maximal carbon profile is used as the boundary of the core for approximate calculations. The evolved WD masses in mesa and their core masses are showed in Table 1 . Using the module make_co_wd to evolve WDs is quick but a little rough. In the future work, we will try to evolve WDs in the module named 1M_pre_ms_to_wd and refine the input settings. Table 1. Masses of MS stars, WD stars evolved by mesa , corresponding cores, and corresponding WD stars evolved by wdec . The structure parameters are inserted into white dwarf evolution code ( wdec ). wdec was first written by Schwarzschild and subsequently modified by Kutter Savedoff ( 1969 ) ( wdec 1.0), Lamb van Horn ( 1975 ) ( wdec 2.0), Winget ( wdec 3.0), Kawaler ( wdec 4.0), Wood 1990 ( wdec 5.0), and Bradley ( wdec 6.0). The program is from White Dwarf Research Corporation ( http://whitedwarf.org/ ). wdec can evolve groups of DAV star models. The model parameters are adopted as total stellar mass, effective temperature, He layer mass fraction, and H atmosphere mass fraction. With the core composition structures from WD models evolved by mesa , groups of WD models are evolved by wdec . The He layer and the H atmosphere are very thin for a DAV star. Therefore, we take the total stellar mass of WD models in wdec the same as the WD core masses in mesa , as shown in Table 1 . The carbon profiles of those WD models are results of thermonuclear burning. The element diffusion scheme of Thoul,

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software O O B-Software B-Identifier I-Identifier O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O B-Model I-Model 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-Software O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Software O O O O B-Person O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-Person O B-Software I-Software B-Person O B-Software I-Software B-Citation I-Citation O B-Software I-Software O B-Person O B-Software I-Software O O O O B-Organization I-Organization I-Organization I-Organization O B-URL O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O B-Citation


from the singlet ground state (1 1 S) because radiative transitions between them are strongly suppressed. Due to relativistic and finite-wavelength corrections to the magnetic dipole transition formula, the 2 3 S triplet helium can radiatively decay into the singlet ground state with an exceptionally long lifetime of 2.2 hr (Drake 1971 ). The 2 3 S state can be populated by recombination 4 4 Around 75% of helium recombinations result in the triplet configuration (Osterbrock Ferland 2006 ). or by collisional excitation from the ground state (see Figure 1 ). Depopulation of this state progresses slowly making it metastable, and hence a promising origin of absorption lines. The resonance scattering from the metastable state to the 2 3 P state produces an absorption line at 10830 Å. This transition consists of three lines, two of which—at 10830.34 Å and 10830.25 Å—are practically indistinguishable, whereas the third component is at 10829.09 Å. Figure 1. Atomic structure of the helium atom, indicating the radiative and collisional transitions included in our analysis. The transition shown in red depicts the 10830 Å absorption line. The helium 10830 Å line has been used to probe the dynamics of stellar winds (e.g., Dupree et al. 1992 ; Edwards et al. 2003 ) and outflows from active galactic nuclei (e.g., Leighly et al. 2011 ), as well as the structure of the solar chromosphere and transition region (Avrett et al. 1994 ; Andretta Jones 1997 ; Mauas et al. 2005 ). Even though this line has been identified as one of the most promising spectral signatures of exoplanet atmospheres (Seager Sasselov 2000 ), no firm detections have been reported thus far (see, e.g., Moutou et al. 2003 ). Most previous models of escaping atmospheres have focused on hydrogen or tracked helium only in terms of neutrals and ions, without modeling the metastable state. Turner et al. ( 2016 ) used cloudy to compile a list of ∼60 potentially interesting absorption lines for probing upper exoplanet atmospheres, including the 10830 Å line. 3. Methods and Results 3.1. Isothermal Parker Wind Our model is based on the assumption that upper layers of a hydrodynamically escaping atmosphere can be described by an isothermal Parker wind driven by gas pressure (Parker 1958 ; Watson et al. 1981 ). Winds in which heating and cooling are due to radiative processes are close to being isothermal (Lamers Cassinelli 1999 ). If the radiative heating/cooling processes operate on short timescales compared to the dynamical time of the system, the gas can self-regulate at a constant temperature. A time-independent and spherically symmetric wind has a constant mass-loss rate determined by the equation of mass conservation:For an isothermal wind, the energy equation iswhereas the momentum equation is given byWe ignore the gravitational influence of the star and the Coriolis force. The momentum equation has a singularity at the so-called critical point, which in our case coincides with the sonic point,

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model fitting is extensively detailed in ( Chen et al. 2016 ). In Table 2 , the refined planet parameters for CoRoT-29b are given. The orbital period and the zero epoch are calculated by fitting a linear function to our two transit epochs together with literature epochs. The rest of parameters are calculated by individually fitting the light curve of each epoch, but also by jointly fitting both transits together. These values are compared to those in the discovery paper by Cabrera et al. (2015) . Fig. 3 White light curve of CoRoT-29b. It is a summation of all the color-shaded passbands as shown in Fig. 2. From top to bottom : (1) normalized flux ratio between CoRoT-29 and its reference star, together with the best-fitting model; (2) white light curve after removing the modeled systematics, for display purpose; (3, 4) best-fitting light-curve residuals. Fig. 4 Color light curves of CoRoT-29b. Left and right panels : data from July 31st, 2014 and July 8th 2015, respectively. The light curves are shown after removing the modeled systematics, and overplotted are the best-fitting light-curve models. Fig. 5 Transmission spectrum of CoRoT-29b. The dashed line indicates the best-fitting derived from the white light curve. Blue and red colors indicate the two observing epochs. The gray-shaded area marks the scale height. Within error bars the spectrum is flat. 4. Discussion and conclusions Figure 3 presents the white light curve for the two datasets. In the top panel the raw flux ratios between CoRoT-29 and the comparison star are shown, where effects of airmass and seeing are still present. In the middle panel of the same figure, the light curves have been normalized and all systematic effects, except the analytic transit model, have been removed. Overplotted to the data are our best fits to each of the transits. It is remarkable that even at the faint magnitude of the CoRoT-29 (), using GTC we are able to reach precisions down to 300 ppm in 5 min exposure time; this is a factor 2.2 above photon noise. The residuals of the transit fit do not show any clearly identifiable features attributable to red noise, or an unaccounted for planetary signal. To be sure that the decorrelation process is not removing real asymmetries in the transit curve, we have generated mock light curves introducing an asymmetry in the form of a stellar spot (not shown). In that case using the same fitting methodology and a symmetric transit, the asymmetry is recovered, and only when using an asymetric transit profile, taking into accout the stellar spot effects, are the residuals of the fit similar to those in Fig. 3 . To further explore possible transit anomalies, we plot in Fig. 4 the color light curves for each of our spectral bins for the two observed epochs. It can be seen that the symmetry of the transit is maintained over all spectral bins and in both epochs. The only exception would be on the bluest light curves from July 8th 2015, where deviations from the transit model

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is , these IC emissions are detectable with CTA, provided that the distance is within a few tens of Mpc and that the dimensionless accretion rate is in the range . If , they are detectable with CTA, provided that the distance is within a few Mpc and that . 6.1. Improvement from H16 In the present work, there are two major improvements from H16 , which formulated the BH gap model and applied it to various BH masses in . First, the distribution functions of electrons and positrons are solved as a function of the Lorentz factor, γ , in the present work, whereas a monoenergetic approximation was adopted in H16 . It is found that the Lorentz factors broadly distribute below the saturated value that was estimated in the monoenergetic approximation. This fact causes an important impact on the gap electrodynamics. Since only the highest-energy IC photons contribute in the gap closure (Section 4.2.5 ), the monoenergetic approximation has overestimated the pair creation in the gap, thereby underestimating the gap width and luminosity (cf. Figure 10 of the present paper and Figure 23 of H16 ). Moreover, the reduced Lorentz factors significantly suppress the curvature process, whose power is proportional to . Also, the primary IC spectrum is softened to peak between 1 and 10 TeV in the present work, whereas it peaked between 10 and 100 TeV in H16 . Since CTA increases its sensitivity with decreasing photon energy around 10 TeV, this result encourages us to observe nearby low-luminosity AGNs in VHE. Second, in the present work, we take into account an anisotropic and inhomogeneous RIAF specific intensity in computing the IC and pair creation. In particular, it is found that the polar region is less efficiently illuminated by the RIAF photon field compared to the middle latitudes . It leads to a harder and stronger VHE emission along the rotation axis than that into the middle latitudes. On the contrary, in H16 it was simply assumed that the RIAF photon field was constant for θ . Thus, although the VHE flux decreased with θ owing to the reduced near the equatorial boundary, it decreased more slowly than the present analysis. 6.2. Comparison with Pulsar Emission Models Let us compare the present BH gap model with the pulsar outer gap model. In both gap models, the gap appears around the null-charge surface where the GJ charge density vanishes, as the stationary solution of the Maxwell–Boltzmann equations. There are, however, differences as described below. In pulsar magnetospheres, the neutron star (NS) emits X-ray photons from its surface, losing its thermal energy. The luminosity of these soft photons decreases as the NS ages. The decreased soft-photon density in the outer magnetosphere results in an extended gap along the magnetic field line. For middle-aged pulsars, w becomes comparable to the radius of the outer light surface, within which the special relativistic GJ charge density changes substantially owing to the convex geometry of the magnetic field

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


predictions. The luminosity of X-ray emissions ( L X ) from pulsars, sometimes mixed with their PWN, has indeed been found to strongly correlate with a pulsar’s spin-down power . In Seward Wang ( 1988 ), with Einstein data for nine pulsars, it was found that L X (0.2–4 keV) is proportional to , where the luminosity L X is contributed from both the pulsars and their nebulae. With ROSAT data of 27 pulsars, Becker Trümper ( 1997 ) reported that L X (0.1–2.4 keV) is about . This luminosity counts only the emissions from the pulsar. To reduce the contribution from surface thermal emissions, Possenti et al. ( 2002 ) considered an energy range of 2–10 keV and reported that , with a sample of 39 pulsars whose PWNe, if present, were not separated from their pulsars. Therefore, in that study, the luminosity includes a contribution from PWNe if they exist. Another relation of (2–10 keV) was reported in Mattana et al. ( 2009 ) for 14 TeV-emitting PWNe, some of which are mixed with the pulsar’s luminosity. In the works mentioned above, there seems to be an indication that the relation between the X-ray luminosity L X and the spin-down power has a larger power index when emissions from PWNe are included and a smaller one when only the emission from the pulsar is considered. Indeed, in Cheng et al. ( 2004 ), with a sample of 23 pulsars in the energy range between 2 and 10 keV, the non-pulsed luminosity was found to be , while the pulsed one was . In Li, Lu Li ( 2008 ), with 24 PWNe and 27 pulsars, it was reported that, at 2–10 keV, and , where L X, pwn is the luminosity from PWNe and L X, psr is that from pulsars. It is one of the purposes of this paper to examine these relations with a larger sample. The spectral photon indices Γ pwn and Γ psr in the power-law spectra of the non-thermal X-ray emissions from PWNe and from pulsars are another important property of the emission. With nine bright Crab-like pulsars, relations between Γ pwn and Γ psr , between Γ pwn and , and between Γ psr and were reported (Gotthelf 2003 ). These relations were, however, not confirmed in Li et al. ( 2008 ) with a larger sample of pulsars and their PWNe. None the less, Cheng et al. ( 2004 ) reported an indication of a positive correlation between Γ pwn and , and Li et al. ( 2008 ) found moderately strong positive correlations between Γ pwn and L X, pwn and between Γ pwn and . On the other hand, Γ psr was not found to correlate with luminosities or other pulsar timing properties (Cheng et al. 2004 ; Li et al. 2008 ). In this paper, we report correlations among properties of the PWN/pulsar power-law component of the X-ray emissions and of pulsar rotations, using a sample of 35 PWNe, all with detected pulsars whose X-ray emission can be separated from that of PWNe. To have a more uniform comparison basis, we consider the flux in the energy range from 0.5–8 keV for all the sources in the sample. This flux is derived from the power-law component of the corresponding best-fitting

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


shown to scale. The temperature and abundance maps of the ∇ − T case are almost the same, except the scale height of the atmosphere is smaller. Fig. 5 Abundance profiles for H 2 O and H 2 plotted for a range of temperature between 2000 and 3000 K. At a given pressure, H 2 O and H 2 dissociation depends strongly on the temperature. The higher the temperature, the lower the abundance in the atmosphere. At a fixed temperature the variation of the dissociation rate is a function of P and P 2 , respectively, for H 2 and H 2 O. 2.3 Retrieval model: TauREx The spectral retrievals has been computed with the TauREx retrieval code ( Waldmann et al. 2015b , a ). TauREx consists in aBayesian retrieval code which uses the ExoMol line lists ( Yurchenko et al. 2011 , 2014 ; Tennyson Yurchenko 2012 ; Barton et al. 2013 , 2014 ), HITRAN ( Rothman et al. 2009 ; Gordon et al. 2013 ) and HITEMP ( Gordon et al. 2010 ). TauREx assumes a plane-parallel exoplanetary atmosphere with 1D distribution elements and temperature-pressure profile. We assume the radius at the base of the model of Wasp-121b as the value for which the atmospheric pressure is 10 bar. We simulate the exoplanetary atmosphere assuming a pressure between 10 6 and 10 −4 Pascals. We consider an atmosphere dominated by hydrogen and helium, with a mean molecular weight of 2.3 amu. We also suppose the presence of CO and H 2 O as trace gases. An important assumption is that TauREx does not take into account thermal dissociation of species and assumes that molecular abundances are constant with the atmospheric pressure (see Changeat et al. 2019 for a detailed discussion on the effect of this assumption). We set up the prior range for the molecular volume mixing ratios of CO and H 2 O between 10 −12 and 10 −1 , which allows us to explore a wide range of solutions. Even if we never add clouds in our input simulation, we set up the prior range for clouds between 10 −12 and 10 −1 to allow theretrieval code to have more freedom. We also feel that this better simulates a real situation where clouds would be put in the retrieval without prior knowledge about their occurrence in the real planet. The allowed range for the planetary radius and the atmospheric temperature (assumed constant in the vertical) are, respectively, 1.3 R Jup − 4.0 R Jup and 400−3600 K, with R Jup the radius of Jupiter. The range for the temperature is linked to the minimum and maximum temperature in the GCM simulation of Wasp-121b, as shown in Table 1 . As we simulate JWST observations, we set up the range of wavelengths between 0.6 to 10 μ m. For the non-retrieved parameters such as masses and stellar radius, we use those describe in Table 2 . Table 1 Parameters used in the three simulation configurations of WASP-121b. Table 2 Mass, radius, and temperature parameters of the WASP-121 star (top) and its planet Wasp-121 b (bottom). Notes. They are used for the observable generations and for the retrievals. We note that the TauREx retrieval

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Software O O O O O O O O B-Dataset I-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Database O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Database O B-Citation I-Citation I-Citation I-Citation O B-Software O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-Telescope O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O B-Software O


and the quasi-parallel case for the acceleration of the electrons could better reproduce the observed distribution of the Stokes parameter Q . For another remnant G1.90.1, which also has two opposite protrusions on the X-ray morphology, assuming it has evolved inside an elliptical planetary nebula with ears and clumps, Tsebrenko Soker ( 2015 ) investigated the formation of the shape with two ear-like protrusions using 3D HD simulations, and the interaction of the ejecta with the clumps produces the double-shock structure. SNRs evolved in inhomogeneous mediums have morphologies with interesting signatures. In this paper, we intend to study the formation mechanism of the peculiar structures illustrated by the multiband observations for SN 1006. By introducing an ambient medium with a density discontinuity, we investigate how the substructures of it are produced via numerical simulations. Different from Schneiter etal. ( 2010 ), the HD simulations in this paper are performed in 3D, and the NE and SW protrusions and the NW filament can be reproduced using the model. The model and numerical set-up for SN 1006 are shown in Section 2 . The results are presented in Section 3 . Finally, the discussion and some conclusions are given in Section 4 . 2 THE MODEL AND NUMERICAL SET-UP To investigate the dynamical evolution of the remnant SN 1006 to reproduce the peculiar morphology, we assume the ejecta have evolved in the non-uniform medium with a density discontinuity. As illustrated in Fig. 1 , the plane of the density discontinuity is perpendicular to the z -axis, and the number density of the ambient medium is assumed to be where is the unit vector along the z -axis, n H is the hydrogen number density, 1.4 is the mean atomic mass for a gas of 10:1 H:He ratio, the ratio x 3 is adopted in this paper, which is consistent with that derived from the observations with XMM Newton (Acero, Ballet Decourchelle 2007 ). Figure 1. Scheme of the simulation model. The explosion occurs at the centre, and there is a density discontinuity at the plane . The LoS is in the xz plane with an angle of to the z -axis. After the supernova explosion, the spherical ejecta with a radius of R ej , a mass of M ej , and a kinetic energy of E ej is set at the centre of the simulation. Initially, the material in the ejecta has a velocity of , where v 0 is the velocity at the boundary of the ejecta (Jun Norman 1996 ; Truelove McKee 1999 ). The inner part of the ejecta within a radius of r c is homogenous with a density of c , whereas the outer part has a mass of M ej and a density with a power-law dependence on r with an index of s (Jun Norman 1996 ), i.e. where 0 is the density at r R ej . s 7 and 3/7 are used for the Type Ia SNR in this paper. The other details of the initial condition for the ejecta were shown in the equations(1)(3) in Jun Norman ( 1996 ). Without including the effects of the radiative cooling and the particle acceleration, the dynamical properties of the

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


NGC 4449 must have been ongoing for a significant fraction of the burst lifetime. Depending on the 3D distribution of the extended H i , this material may not have been expelled into the IGM, but may instead reside at extended radii around the galaxy and/or recycled back into the galaxy. For NGC 5253, the detected outflow surrounds much of the central star-forming region and is strongest in the south. Marlowe et al. ( 1995 ) measure velocities of the Hα detected shells of 35 km s −1 with physical extents of ∼1 kpc. Summers et al. ( 2004 ) find the extent of the X-ray emission to be somewhat smaller (∼0.5 kpc). However, using combined Chandra observations, we find a more extended region in the south of the galaxy that reaches ∼2.4 kpc in projection that cannot be explained by dynamical arguments and short star formation time-scales. These inconsistencies are alleviated when the longer star formation time-scales from the SFHs are considered. Furthermore, the SFR in NGC 5253 has declined by nearly a factor of 6 over the duration of the burst. The declining SFRs and small-scale outflow in NGC 5253 indicate that we are seeing the end of a wind phase (see also Fig. 7 ), rather than just the beginning of an outflow as has been previously suggested (Summers et al. 2004 ). For NGC 1569, the dynamical age of the outflow was previously estimated to be 10 Myr (Heckman et al. 1995 ; Martin 1998 ). Using this time-scale, Martin et al. ( 2002 ) estimate the amount of oxygen that could be in the wind of NGC 1569 and compare this to the amount of metals produced by star formation over a 10–20 Myr time-scale assuming a nucleosynthesis yield. Based on their best-fitting model of a solar metallicity in the wind, and to maintain consistency with the current gas-phase oxygen abundance in the galaxy, these authors report nearly all metals formed in the recent star formation activity have been expelled in the wind. However, as stated in Martin et al. ( 2002 ), this requires that the present-day gas-phase oxygen content in the galaxy was created in previous episodes of star formation that must have been quiescent (i.e. not energetic enough to drive an outflow). Based on the CMDs and the derived SFHs, there has been significant star formation in the last few 100 Myr in NGC 1569, with the peak star formation occurring 65 Myr. This suggests that the wind has been ongoing. Furthermore, the best-fitting model of a solar oxygen abundance in the hot wind does not take into account the uncertainties; a nearly equal χ 2 is found for 0.25 Z ⊙ , as well as for supersolar abundances for NGC 1569 (Martin et al. 2002 , see their table 5). The amount of metals ejected by the wind in NGC 1569 remains an open question. 6 CONCLUSIONS We have examined the diffuse soft X-ray emission from Chandra observations in six nearby starburst dwarf galaxies from the STARBIRDS sample (McQuinn et al. 2015a ) and compared the X-ray properties with the neutral gas distributions, SFHs quantified from

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


since once the magnetic field twists into an overwhelmingly toroidal configuration, as measured in the comoving jet frame, it is very difficult for it to share additional energy with the particle flow (Begelman Li 1994 ). The above results apply to a pair-dominated jet; the effect of an ion component on radiatively cooled turbulence is outside the scope of this paper. The ions would effectively not cool at all, but would probably receive the majority of dissipated energy (Zhdankin et al. 2019 ), suggesting that the true value of σ could be much lower due to a hot ion component. A self-consistency condition that needs to be met in order for external IC to dominate over synchrotron cooling, , could be violated if δ ph or Γ j is too small. A cooled turbulence model is also attractive for explaining flares from BL Lac-type blazars, which lack an intense ambient radiation field. Here it is plausible that the jet emission is self-contained and likely due to the SSC process, and even larger values of σ (at least the σ associated with the electron or pair content) would be required. 6 CONCLUSION In this work, we conducted and studied the results from a series of PIC simulations of driven turbulence in relativistic collision-less pair plasma with external IC radiation. We focused on understanding the statistical properties of turbulent fluctuations and particle distributions during the statistical steady state, where injected energy from external driving is balanced by radiative energy losses. We performed a parameter scan over the steady-state magnetization 〈σ〉 and system size L /2〈ρ e 〉, to the extent that computational resources allowed. We now summarize our main results: Regardless of initial conditions, turbulence eventually acquires a rigorous statistical steady state (by heating or cooling) with an equilibrium temperature that is close to analytic predictions (equation 7 ) and can be controlled by adjusting the energy density of the external photon bath, U ph . Radiative turbulence thus provides an ideal scenario for studying the fundamental properties of kinetic turbulence. The properties of turbulence change from low 〈σ〉 to high 〈σ〉. The former looks like standard non-relativistic MHD turbulence, apart from the tendency to have rotational magnetic fluctuations. The latter has fluctuations that are highly relativistic, compressible, and electromagnetically dominated. The steady-state particle energy distributions are always close to the thermal (Maxwell–Jüttner) distribution, with only a modest non-thermal population (broadening the tail by a factor of ∼2 in energy). The non-thermal population is more temporally variable and energetically significant at high 〈σ〉. These steady-state particle energy distributions are well fit by analytic solutions to the Fokker–Planck equation describing stochastic particle acceleration, for simple forms of the momentum advection and diffusion coefficients (linear and quadratic in energy, respectively). 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model B-Model O O O O B-Model I-Model O O O O O O O O O O O B-Model I-Model O O O O 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-Model O B-Model O O O O


by these telescopes (e.g., Serabyn Lacy 1985 ; Serabyn et al. 1988 ; Lacy et al. 1991b ; Roberts et al. 1996 ; Zhao et al. 2009 , 2010 ). The stretched appearance and kinematics of the GCMS suggest the models in which the streamers are tentative structures with Keplerian orbits around Sgr A* (e.g., Serabyn et al. 1988 ; Zhao et al. 2009 , 2010 ). There are still alternate models to explain these properties (e.g., one-armed spiral; Lacy et al. 1991b ; Irons et al. 2012 ). The tidal force of Sgr must have a serious effect on the interstellar medium (ISM) in the vicinity of Sgr A*, i.e., the GCMS (e.g., Lacy et al. 1982 ). Furthermore, the strong Lyman continuum radiation from the OB and WR stars in the Central cluster ionizes the ISM rapidly in the region (e.g., Genzel et al. 1996 ; Paumard et al. 2006 ). A recent dust observation of the GCMS with ALMA suggested that there is a possible scenario for the formation of the Central cluster: a star-forming molecular cloud is falling from a region somewhat far from Sgr A* and supplies young stars and the ISM to the vicinity of Sgr A* (e.g., Tsuboi et al. 2016 ). However, it is not clearly demonstrated how the gas is fed to Sgr A* because the innermost part of the ionized gas has very weak intensity and complicated structures. We present new observational results on the ionized gas streams in the vicinity of Sgr A* based on the observation of the H42 α recombination line using the Atacama Large Millimeter/submillimeter Array (ALMA). The distance of the Galactic center is assumed to be 8 kpc in this paper. 2. Observation and Data Reduction We have observed the GCMS in the H42 α recombination line (85.6884 GHz) as a part of the ALMA Cy.1 observation (2012.1.00080.S; PI: M.Tsuboi), which is an ionized gas tracer. The entire ALMA observation consists of a 137-pointing mosaic of the 12 m array and a 52-pointing mosaic of the 7 m array (ACA), covering a area including the “Galactic center 50 km s −1 molecular cloud” and the GCMS in CS (97.980953 GHz), SiO (86.846995 GHz), H 13 CO (86.754288 GHz), and H42 α emission lines. The molecular cloud encompasses the most conspicuous star-forming region in the vicinity of Sgr A*. We will present the detailed description of the analysis and the full results in another paper. We have detected the recombination line in the GCMS and the Sgr A East H ii region, and we concentrate on the GCMS in the H42 α recombination line in this paper. The data of the recombination line have angular resolutions of and using “natural weighting” and “Briggs weighting ( R = 0.5)” as u–v sampling, respectively. The frequency channel width is 244 kHz. The velocity resolution is 1.7 km s −1 (488 kHz). J0006−0623, J1517−2422, J717−3342, J1733−1304, J1743−3058, J1744−3116, and J2148+0657 were used as phase calibrators. The flux density scale was determined using Titan, Neptune, and Mars. Because the observation has a large time span of 19 months, the absolute flux density accuracy may be as

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 B-Citation O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O B-Model I-Model O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation 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 O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObjectRegion O B-Citation I-Citation I-Citation I-Citation 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 I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObjectRegion O B-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 B-CelestialObject I-CelestialObject O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory 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 B-CelestialObjectRegion O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O B-Observatory O O B-Identifier O B-Person O O O O O O O O B-Observatory O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O O B-Telescope I-Telescope I-Telescope B-Telescope O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O B-CelestialObjectRegion O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O B-CelestialObjectRegion O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O


of the crustal currents and the polar magnetic field. We compute the consequent X-ray luminosities and compare them with the observed values for magnetars. In Section 3 , we examine the dependence of conductivity tensor and Ohmic dissipation time-scale for high magnetic fields. In Sections 4 and 5 , we look at the X-ray and dipolar radiation luminosities, periods, and decay time-scales in the dynamo model and the screened core model. We find that in the screened core model, the ratio of the dipole radiation loss to the X-ray luminosity ( L X ) is a ‘U’ curve as a function of increasing spin-down age and period. Finally, in Section 6 , we try and understand the observed cut-off in the period of magnetars and end with a discussion in Section 7 . 2 CRUSTAL CURRENT AND POLAR MAGNETIC FIELD DISSIPATION AND X-RAY LUMINOSITY FOR SOME MODELS 2.1 Estimation of crustal magnetic field energy decay rate from the magnetar spin-down age Let us first make a simple estimate of the rate of magnetic energy dissipation in the crust. We assume the crust to be a shell of thickness, Δ R cr , in which the magnetic fields diminish with time as the crustal currents dissipate. We shall give some estimates which, though qualitative, capture some of the physics. The amount of magnetic energy stored in the crust is given roughly by the expression where B is the observed surface polar field and V is the volume of the crust. V = 4 R 2 · Δ R cr ∼ 4 × 10 17 cm 3 , where we have taken R ∼ 10 6 cm as the radius of the star and Δ R cr ∼ 1 km as the thickness of the crust. We shall use this definition of the crust for the rest of the paper. As the field drops to a fraction of its original value, we assume this energy will be dissipated and released as X-ray luminosity. We further assume that the typical time-scale in which this happens is given by the spin-down age of the magnetars, Thus, a crude estimate for the ‘average’ X-ray luminosity is given by dividing the stored magnetic energy by the spin-down age, This equation can be found in Dass Soni ( 2012 ). Hence, For , we use the relation below which is based on the dipole formula, As a standard (average) value of the polar field for magnetars we take, B p ∼ 4 × 10 14 G (which is the value of the initial field in the following Section 2.2 ). For such fields, the magnetar data indicates average periods of ∼8 s. On substitution, this yields an average crustal X-ray luminosity: The instantaneous luminosity when the periods reach ∼8 s will, of course, be less than the average. The dipolar spin-down radiation energy loss rate for magnetars with such magnetic fields and periods is then given by: where we have taken, I = 10 45 gm/cc, here and in what follows. 2.2 Estimation of magnetic field energy decay rate due to Ohmic resistance and the Hall effect The work of Gourgouliatos Cumming ( 2014 ) and Wood Hollerbach ( 2015 ) computes the magnetic field evolution in the crust via the Hall effect. In their work, they start with polar fields

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


use the results of a double-Sérsic fitting to the surface density profile of our simulated galaxy, as described in Section 4.2 (the values are given in Table 2 ). Eris BH sits well below both relations, even though the black hole seeds start off close to the extrapolation at lower masses of the MBH-stellar mass relation (coloured bullets in the left-hand panel): this is because the black hole accretion rates are much lower than what would be required to keep up with the star formation rate in the central region (see Fig. 3 ). Figure 7. M BH – M Star and M BH – M Bulge relations. The red and blue symbols are from a compilation of Erwin Gadotti ( 2012 ) for early-type and late-type galaxies, respectively (with fits for the M BH – M Bulge relation shown by the dashed lines). The orange diamond is the location of the Milky Way in the plane as reported by Erwin Gadotti ( 2012 ). The yellow circle indicates the location of Eris BH . The coloured bulletts in the M BH − M Star figure show the location of the seeds, colour-coded as in Fig. 1 Table 2. Summary of global properties of Eris BH and Eris at z = 0. The stellar and gas masses in columns 1 and 2 refer to the total stellar and gas masses within the halo, also used to calculate the baryon fractions given in column 3. The disc and bulge masses have been obtained fitting a double Sérsic profile to the face-on surface density profile, with scale lengths given in columns 8 and 9. The last column gives the Sérsic index for the bulge, while the Sérsic index for the disc has been fixed to unity. Masses are given in solar masses, distances in kpc and velocities in km s − 1 . Having only one simulation, we can not give quantitative predictions on whether black holes in pseudobulges follow a different relation with the properties of the host (or if they do not follow any relation at all). But we note that our results on the M BH –σ and M BH – M Bulge relations are both consistent with what is found by Greene et al. ( 2008 ), and could also fit within the picture drawn by Kormendy et al. ( 2011 ), given the slow Seyfert-like growth of our simulated black hole. 4 BLACK HOLE FEEDBACK AND ITS EFFECTS ON THE HOST GALAXY As described in Section 2.2.2 , the simulation includes also a prescription for black hole feedback: a fraction of the energy extracted in the accretion process couples thermally with the surrounding medium. This standard prescription has been used extensively in other works, and its effects led to the idea of a ‘self-regulation’ of black hole growth to explain the origin of the M BH –σ relation and the ejection of gas from the host galaxy and the resulting quenching of star formation (e.g. Di Matteo et al. 2005 ). Given that the accretion rates are generally quite small for the central black hole of our simulated galaxy, we expect the effects of feedback to be modest. We find, in fact, that the amount of energy released by the black hole is significantly lower than the one released by

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


2003 ). Its depletion covers a relatively narrow range of values ( Fig. 1 ) showing that it is not a strong function of environmental density. It has been hypothesized that the majority of carbon should be locked in graphite grains, as a likely explanation for the 2175 Å emission feature ( Draine 1989 , 2003 , and references therein). Graphite has been commonly adopted in ID models (e.g., Mathis et al. 1977 ). However, observational evidence pointed out that graphite cannot explain the variability of the 2175 Å feature ( Fitzpatrick Massa 2007 ). Furthermore, in analogy with the silicates, which are found to be amorphous, also graphite was deemed unlikely to survive in large quantities in the harsh environment of the ISM. Graphite should therefore face a natural process of amorphization ( Compiègne et al. 2011 ). The idea of carbon as a single and separate phase from the silicate population does not agree with a scenario of a constantly evolving and mixing medium ( Jones et al. 2017 ). Hydrogenated amorphous carbon (HAC) may indeed coat the silicate grains, forming a single population (e.g., Duley et al. 1989 ) with different characteristics with respect to the environment in which they reside and depending on the particle size (e.g., Jones et al. 2017 , and references therein). Polarization studies however have so far not confirmed this scenario. The carbon feature at 3.4 μ m shows a negligible degree of polarization with respect to the silicate feature at 9.7 μ m, pointing to two distinct grain populations ( Whittet 2011 ). Finally, under special condition of high pressure, for instance in a shocked environment, graphite and amorphous carbon can turn into nano-diamonds, which can constitute as much as 5% of the amount of C in the ISM ( Tielens et al. 1987 ), possibly with H and N inclusion ( Van Kerckhoven et al. 2002 ; Bilalbegović et al. 2018 ). Diamonds of possible ISM origin have been found in meteorites ( Lewis et al. 1987 ). An important carbon carrier are polycyclic aromatic hydrocarbons (PAH), large molecules (Ångstrom-sized) formed by carbon and hydrogen in a honeycomb structure. These molecules constitute up to about 10% of the carbon abundance (e.g., Tielens 2013 ). PAHs are very sensitive to ionizing radiation from far-ultraviolet to X-rays and they are easily destroyed near star formation sites at AU distance scale (e.g., Siebenmorgen Krügel 2010 ), up to kiloparsec scale, for active galaxies ( Voit 1992 ). Apart from C, other constituents can be studied in detail by future generation telescopes. Sulfur in the dust phase seems to be absent from the diffuse ISM ( Sembach Savage 1996 ). However, a relative fast transition to a depletion approaching −1 dex is reported in dense media, such as molecular clouds ( Joseph et al. 1986 ). In molecular clouds, sulfur can be included in aggregates such as H 2 S, SO 2 , OCS, SO, H 2 CS, NS SiS, CS, HNCS CH 3 SH ( Duley et al. 1980 , and references therein) as well as other

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


), the inner radius of the disc is 0.06 au. Additionally, the disc is in hydrostatic equilibrium in the vertical direction and its density profile ρ( r , θ) is given by the equation from Dullemond ( 2000 ): Here, Σ 0 is the superficial density at the outer edge of the disc, R 0 is the external radius of the disc and H ( r ) is the disc scaleheight. The last variable is defined from the self-irradiated passive disc proposed by Chiang Goldreich ( 1997 ) and is given by H ( r ) = r H 0 / R 0 ( r / R 0 ) 2/7 . The ratio H 0 / R 0 0.1 defines cold discs whereas H 0 / R 0 > 0.1 defines hot discs according to Faure, Fromang Latter ( 2014 ). Additionally, typical values for protoplanetary discs range from 0.1 to 0.3 (Ono, Nomura Takeuchi 2014 ). Hence, for a generic case, we adopted the value of 0.17. 4.2 Dust and ice model Because the interaction between light and matter in astrophysical environments is regulated by absorption and scattering processes, we calculated the opacity for a core of silicate 1 (Weingartner Draine 2001 ) with the inclusion of amorphous carbon and ice (H 2 O:NH 3 :CO 2 :CH 4 ) to simulate the presence of a mantle. The carbon inclusion was assumed to be 0.15 (Pontoppidan et al. 2005 ), and the abundances of ice relative to H 2 were 10 −4 for water and 10 −5 for CO 2 , CH 4 and NH 3 . To perform the mixing rule, we adopted the Maxwell–Garnett effective medium theory (Bohren Huffman 1983 ) to calculate the effective CRI for the grains. Considering that the relation between the complex dielectric function () and CRI () for non-magnetic materials is given by , the equation for the effective CRI () is given by where and are the CRI for the silicates and for inclusions, which can be carbonaceous material or ices, respectively. The opacity for the grains was calculated employing the Mie theory (Mie 1908 ), assuming spherical grains with a single grain size of 0.3 μm. Figs 6(a) –(c) show the opacities for the grains considering the Fluence 0, Fluence I (10 11 ions cm −2 ) and Fluence II (10 12 ions cm −2 ). As can be seen in Fig. 6 , the CRI presented in this paper allows us to calculate an opacity data base to be used in astrophysical models. This type of data base has been created by Ossenkopf Henning ( 1994 ), although such data are consistent only for non-processed regions in the ISM. However, the processing of the ice is a common scenario and the opacities from Ossenkopf Henning ( 1994 ) lead to wrong conclusions about the chemical evolution of the ice. In this way, the data base presented in this paper can be used to calculate new opacity tables, by using realistic data of processed ices, as well as realistic grain geometry. Figure 6. Absorption and scattering opacities of astrophysical grains employed in this paper. Panel (a) presents the opacities of bare silicate and panels (b) and (c) present the opacities of silicate with ice at Fluence 0, I and II. The lines were moved arbitrarily to highlight differences due to energetic

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g is the gravitational acceleration. We can use the velocity profile of the shock to calculate the surface density profile of the ejecta blanket Energy and momentum conservation yield limits on the slope of the surface density distribution −2.5 > dln σ/dln r > −3. If we assume a constant density for the settled ejecta, then the thickness of the ejecta blanket scales the same way as the surface density. Most ejecta blankets around craters on the Moon are within this range (Zhu et al. 2015 , 2017 ; Raggio et al. 2016 ). In contrast, ejecta blankets from chemical and nuclear explosions on Earth are slightly steeper −3 > dln σ/dln r > −4, due to air drag (Carlson Jones 1965 ). Using the same shock trajectory we can make a theoretical prediction for the density slope we numerically calculated in the previous section. We saw that ∝ m −β . At distances much larger than the radius of the impactor, the velocity profile is roughly homologous ≈ d / t , where d is the distance from the impact site and t is the time since the impact. Combining these relations with the definition of density m ≈ ρ d 3 we find a scaling relation for the density profile ρ ∝ r −3 − 1/β . For β = 2/3 we obtain dln ρ/dln r = −4.5, which is close to the value obtained in the numeric simulation dln ρ/dln r = −4.1. Eventually, the shock stops and the crater reaches its final size. There are two criteria that can determine the final size of the crater (which will always be the smaller of the two). One possibility is that the shock stops when the shock pressure drops below the elastic modulus of the soil Y , so the final shock radius is where R i ≈ ( m i /ρ 0 ) 1/3 is the radius of the impactor. The second possibility is that the shock stops when the shock pressure drops below the hydrostatic pressure g ρ R , and so In the case of the lunar regolith, this is the deciding condition. 3.2 Craters from PBHs The density of PBHs is much higher than that of meteors, so instead of transferring all of their energy to the target at the impact site, the impactor just passes through and deposits roughly the same amount of energy per unit length along its trajectory inside the target. For this reason, above some critical threshold, the evolution of the shock wave is independent of the density of the impactor. To understand how the shock wave will behave in this case, one can think about this problem as a series of point explosions, where the energy of each explosion scales with its depth E ∝ x . If the mass of the BH is m i , then the effective cross-section is determined by the Bondi radius , and so . For a uniform density soil, the mass in a sphere of radius x around the hotspot is m ≈ ρ 0 x 3 . Hence, . We thus obtain a new power-law relation between the shock velocity and the swept up mass, which is shallower than that obtained for classical craters, i.e. β = 1/3. Using the same reasoning as in the previous section, we find the slopes of ejecta blanket surface density profile As was done

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