750 and HARP 1028. These flare-productive active regions produced at least one flare of intensity greater than M5. Middle panel: power index evolution for HARP 1464 and HARP 1621. These flare-productive active regions produced flares of intensity between M1 and M5. Lower panel: power index evolution for HARP 1019 and HARP 1318. These active regions showed no flare productivity. Vertical lines in the graphs indicate the occurrence of flares with intensity greater than M1. In addition to exhibiting, on average, a lower value for the power index, flare-quiet regions tend to show much more variability in the temporal evolution of the index. Figure 5 (bottom) shows one such trend—where the index tends to drop off over several days. A second trend is shown in Figure 7 , where NOAA 11274 shows periods when the power index rises to 1. However, these periods of time are short. In contrast, there is no sudden spike in the index value for any of the flare-productive regions as they track across the solar disk. Instead, flare-productive regions exhibit a large power index for many days, both before and after they produce solar flares. This suggests that the flare potential of any active region could be determined a few days in advance of the production of a large solar flare and the occurrence of solar flares does not reduce the future flare potential. Figure 6 shows the results in the form of histograms for all 53 HARPs. The range of index values (1.0–2.5) is similar to that in previous studies (Abramenko Yurchyshyn 2010 ). The dotted histogram shows the power index values taken by flare-quiet active regions. The power index distribution for these flare-quiet regions is quite broad and peaks around 1.6. The dashed histogram indicates the results for flare-productive active regions that produced flares of magnitude M1–M5. This distribution is much narrower, with fewer values below 1.5, and peaks around 1.8. However, the high-value tail does overlap with the flare-quiet distribution. Finally, the solid histogram shows the power index values taken by flare-productive active regions that produced at least one flare of intensity greater than M5. In this case, the power index mostly lies above 2 with a maximum at around 2.2. Figure 6. Histograms of power index values for all 53 HARPs. The dotted line indicates a histogram for 25 flare-quiet active regions. The dashed line shows a histogram for 19 flare-productive active regions that produced flares of intensity between M1 and M5. The solid line indicates a histogram for nine flare-productive active regions that produced at least one flare with intensity greater than M5. Figure 7. Power index evolution of a non-flaring active region HARP 803 (NOAA 11274). Flare-quiet regions tend to show much variation in the power index values. The above classification of HARPs was performed based on the maximum intensity of any flare from the region. However, the flare productivity can be measured more carefully in terms of


function layers can be concatenated together to form a deep CNN. This is usually followed by a fully connected layer also known as a dense layer, which is then finally connected to the output layer. The output layer for a classification problem is the amount of class labels we have in our data. Additionally for deep CNNs, a dropout layer is typically added after the max-pooling operation, which randomly drops off a certain percentage of the preceding nodes. This is done so that the neural network learns to better generalize its performance across the entire data. This is used as a regularization technique to avoid overfitting. CNNs are also trained using back-propagation. However, in practice, since it is computationally difficult to calculate the gradient of the loss function for all images in the training data, we typically divide the data into mini-batches and use the stochastic gradient descent algorithm. Figure 2. Schematic diagram of a typical CNN. Here the input image is a grey scale image of size 48×48 and the output contains two nodes for the binary class labels. 8 and 16 filters of size 4×4 were used for the convolutional layers. These act as feature extractors that identify import patterns in the input image. This diagram was created using an open source tool called NN-SVG 5 (LeNail 2019 ). 2.4 Generative adversarial network (GAN) GANs are a class of machine learning algorithms (Goodfellow et al. 2014 ) in which two neural networks are trained simultaneously with opposing goals. They act against each other as adversaries in a minmax two-player game. A generative model G is tasked with generating new data that capture the distribution of the input data. A discriminator model D is tasked with classifying samples as either REAL (that belong to the original data distribution) or FAKE (samples generated by G ). Assuming is the value/loss function, we are interested in then the first term in equation ( 2 ), is the expectation of the logarithm of D ’s predictions when an input is from the real data sample. D ’s goal is to maximise this term. The second term represents one minus the expectation of the logarithm of D ’s predictions when data generated by G is passed on to to D . The goal of D is to maximize the second term but the goal of G is to minimize this term. This sets up the adversarial framework. In the ideal case, the generator perfectly samples the distribution of the input data distribution, and the discriminator output equals to 1/2. In practice however, we use a minibatch stochastic gradient descent method and train the generator and the discriminator alternatively. The algorithm and the proof for the convergence of the algorithm can be found in Goodfellow et al. ( 2014 ), however for the benefit of the reader, we briefly summarize the training of this network in algorithm 1 . Algorithm 1: Minibatch stochastic gradient descent algorithm used for training a GAN. GANs have been used successfully in a wide range of tasks ranging


Like black holes, this distribution is relatively flat. Figure 6. Distribution of periods for NSLC binaries detectable by Gaia . Blue is the fiducial model, orange is low αλ, green is the kick model with the same momentum as neutron stars, and red is kicks with the same velocity. For completeness we have also included in Appendix C the distribution of distances from earth (Fig. C1 ), apparent magnitudes of the luminous companions (Fig. C2 ), ratios between the semimajor axes and distances (Fig. C3 ), and radial velocity amplitudes (Fig. C4 ). 5 CONCLUSIONS In this work we give some predictions for the detection of binaries with a single luminous companion with Gaia . Similar endeavours exist in the literature, but two novel ideas that we introduce in this paper are that (i) similar methods can be used to detect neutron star luminous companion systems (which are expected to be more numerous) and (ii) the data from Hipparcos can be used to constrains the theoretical models. Our fiducial model predicts a few dozen BHLC detections with Gaia , and about one detections with Hipparcos . The last result is consistent with non-detection by Hipparcos , due to uncertainties in the models and statistical fluctuations. All other variants of the fiducial model have similar properties. The corresponding predictions for NSLC binaries are hundreds to thousands with Gaia and a few with Hipparcos . We emphasize that the numbers reported here only apply to binaries where the Chandrasekhar mass is beyond the dark companion’s mass error margin. One of the challenges in this kind of work is estimating the uncertainty. This is because this work is largely based on poorly understood physics and empirical models calibrated with incomplete data. One way to get an estimate for the uncertainty is to explore the sensitivity of the results to changes in the different model parameters. This was done in Yamaguchi et al. ( 2018 ), and the conclusion was that while the number of BHLC binaries might change by a factor of order unity, the shapes of the distribution functions do not. The results from Gaia , as well as future observations, are necessary to refine these models and improve their precision. To date, there are no reports of quiescent neutron stars (i.e. neither pulsars nor accreting) in binaries. As for BHLC binaries, there is one reported detection of a ≥2.5 M ⊙ mass black hole candidate with a red giant companion (Thompson et al. 2018 ). We note that another isolated black hole candidate with mass of about four solar masses was detected in the globular cluster NGC 3201 (Giesers et al. 2018 ). This discovery is less relevant to this study, because stars in a cluster are thought to have formed in a relatively short period of star formation, whereas we are interested in the case where star formation proceeds continuously. Another important difference is that we neglect gravitational interaction between stars that are not mutually bound, which is justified


As described in Sections 3.6 and 3.7 , the H 2 and PAH emission, indicating the location of the PDR, encircles the western border of the H ii region. A curved morphology of the radio continuum emission in the western periphery further suggests a stalling effect for the ionized gas against the PDR in that direction. As shown by Pellegrini et al. ( 2012 ), the [S ii ]/[O iii ] ratio map can be used to distinguish density-bounded, radiation-bounded, and blister-type H ii regions. Pellegrini et al. ( 2012 ) found that the optically thick nebula with highly ionized gas (low [S ii ]/[O iii ] ratio; appears dark in ratio map) is usually surrounded by an ionization transition zone with a higher [S ii ]/[O iii ] ratio (appears as lighter gray scale). We made an [S ii ]/[O iii ] ratio map of the central part (∼10′ × 10′) of the Sh2-112 H ii region, which is shown in Figure 8 (bottom left panel). The ratio map consists of bright and dark features. We notice a pronounced ionization transition zone (bright region) toward the south of the massive star, where H α emission is traced. This ionization transition zone appears to be surrounded by a relatively diffuse feature in light gray. In the southwestern direction, the ratio of [S ii ]/[O iii ] reveals the presence of ionized gas (dark feature) in the region, which is spatially correlated with the IBL. The distribution of the ionized hydrogen, H 2 , and 13 CO emission indicates that the IBL structure is seen edge-on. An example of this kind of edge-on geometry is the Orion bar, which is located in a blister-type H ii region, the Orion Nebula (Goicoechea et al. 2018 ). In our case, the bright S ii emission could actually be on the surface of the H ii cavity. Therefore, from the above analysis, it seems that Sh2-112 is an example of a blistered H ii region that is ionization-bounded on the high-density sides (western direction) and density-bounded on the low-density sides (eastern direction). The intensity gradient of the radio emission (see 610 MHz emission contours in Figure 7 (b)) supports that the ionized gas is escaping from the H ii region toward the low-density ISM in the eastern direction. Based on radial velocity measurements of the H α (i.e., −9.7 km s −1 ) and CO (i.e., −12.2 km s −1 ) emissions, Israel ( 1978 ) also suggested that the ionized gas in the Sh2-112 region is probably undergoing a champagne flow. Thus, the structure of the radio continuum, dust extinction, 13 CO, and [S ii ]/[O iii ] ratio maps; the spatial distribution of the young stars; and the NIR-to-MIR images of the H ii region indicate that Sh2-112 is a blistered H ii region in which the ionized gas is possibly undergoing a champagne flow. In Figure 9 , we show the AKARI 160 μ m image superimposed by Planck 353 GHz contours (left panel) and a simple geometry of the H ii region (right panel). Based on the distribution of the cold dust emission and young stars, we suggest that the massive star possibly formed on the eastern


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


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


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


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


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


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


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,


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,


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


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


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


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


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


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


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


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


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


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


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


), 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


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


carbon. The luminosity was obtained by interpolating and fitting the optical ( B , V , i ′) and the NIR ( J – H – K s ) fluxes from Fransson et al. ( 2014 ) at several epochs, in addition to the five epochs (days 87, 254, 465, 621, 844) for which we have Spitzer data. Thereafter, the luminosity, L ( t ), was fitted using a power law of time. The exponents are found to be −0.55 and −4.0 with a switch at day 310, as shown in the figure. We also calculate the UVO luminosity in uniform temporal bins in order to reconstruct the UVO light curve. The evolution of L UVO was thereafter fitted using a power law, t − β , with β = 0.55 before day 310 and β = 4.0 thereafter. The best-fit scenario is presented in Figure 1 (top left). The nature of the luminosity, L ( t ), derived in this study compares well with the findings by Fransson et al. ( 2014 ), Jencson et al. ( 2016 ), and Gall et al. ( 2014 ). The rapid decline in luminosity at later times can be attributed to a change in the density profile at the shock front. A similar drop in luminosity is also reflected in the evolution of the X-rays along the line of sight (Chandra et al. 2015 ). 2.1. Possible Source of the IR Emission In this study, good fits to the IR spectra of SN 2010jl, shown in Figure 1 , were achieved using the contribution from any of the three sources (a blackbody, astronomical silicates, amorphous carbon) as the IR component. Therefore, the best-fit models do not have any strong bias toward any of the three sources being the most likely one. A blackbody fit is appropriate when the dusty shell is optically thick. Additionally, the blackbody radius ( R IR ) represents the minimum possible radius of the dusty shell from where the IR emission originates. The NIR fluxes can be fit well using the absorption coefficients of optically thin astronomical silicates. The upper limit on the 9.7 μ m flux at late times was obtained from the SOFIA observations (Williams Fox 2015 ). It indicates the absence of silicate features. Therefore, the presence of silicates is doubtful, unless the grains are large ( a ∼ 5 μ m) or the dusty shell is optically thick. With only photometric data in the 2.2–4.6 μ m region, many featureless dust species can fit the spectrum. We choose carbon as a likely dust type owing to its relatively large abundance in space compared to other metals. Moreover, the studies dealing with the IR spectra from the preexplosion era also hint at the presence of carbon dust in SN 2010jl (Dwek et al. 2017 ). However, the CSM of SN 2010jl is reported to have a N-rich (Fransson et al. 2014 ) C-depleted environment (N/C =25 ± 15, N/O = 0.85 ± 0.15). In such environments, O-rich dust species are known to be the primary dust components and all of the carbon mostly gets locked up in CO molecules (Sarangi Cherchneff 2013 ). To support this argument, the observation of a N-rich dusty shell around massive stars, such as the Homunculus nebula surrounding Eta Carinae, does not show any


Earth) for different ocean coverages. Panel B shows how pCO 2 varies with varied solar luminosity for different ocean coverages. Both Panel A and B assume an Earth-like outgassing rate of CO 2 . We did not plot solar luminosities greater than 1.2 S eff as the weathering rate dependence on CO 2 becomes negligible. Panel C shows how the surface temperature varies with varied CO 2 outgassing rates (relative to modern Earth) for different ocean coverages. And Panel D shows how pCO 2 varies with varied outgassing rates for different ocean coverages. Panel C and D assume a modern Earth solar constant. All panels assume a fixed planetary albedo of α = 0.3. Based on the results from Figure 1 , a planet’s buffering capability changes significantly when seafloor weathering becomes the dominant weathering sink, due to the different pCO 2 dependencies of seafloor versus continental weathering. We therefore determine the critical ocean fraction where weathering behavior switches from being dominated by seafloor weathering to being dominated by continental weathering by setting F cw = F sw , and solving for the ocean fraction: We solve for this critical ocean fraction for a range of solar luminosities, setting the rest of the variables equal to the median values that we used for Figure 1 , as a function of pCO 2 (see Figure 2 ). The solid curves in Figure 2 correspond to the at which the weathering fluxes from continental weathering and seafloor weathering are equal. While we calculated over a range of pCO 2 values, only certain pCO 2 pressures would be physical for a given solar luminosity using our weathering model. The dashed curves with the points are from our previous results, where we calculated the actual pCO 2 of a planet given its solar luminosity and ocean fraction (see Figure 1 ). Figure 2. The solid curve represents the ocean fraction at which seafloor weathering and continental weathering are equal, as a function of pCO 2 . We solved this critical ocean fraction curve for different solar luminosities and found that the difference was negligible (the black curve shown is for an S eff of 1.0). If a planet’s ocean coverage is above the curve, then seafloor weathering is the dominant sink of CO 2 , and if a planet’s ocean coverage is below the curve, then continental weathering is the dominant sink of CO 2 . The colored curves and points are data from Figure 1 , allowing us to constrain this parameter space by plotting the actual pCO 2 values that our model converged toward for a given ocean fraction and solar luminosity. We find that for solar luminosities lower than modern Earth’s, an ocean fraction of greater than 90% is needed for seafloor weathering to equal continental weathering. What we find from Figure 2 is that for relative solar luminosities less than or equal to S eff = 1.0, the planet requires an ocean fraction between 90% and 99% for the CO 2 flux from seafloor weathering to equal the CO 2 flux from continental weathering. This is


thick disc was assumed to span from 9 to 11 Gyr. We also checked with an age span of 10–12 Gyr for the thick disc and found that it gives the same best-fitting parameters. The slight decrease in the mean metallicity of the thick disc compared to the estimate based on simply measuring the metallicity of stars within 5 R /kpc 11 and 1 | z |/kpc 2, is due to the inclusion of stars lying between 2 | z |/kpc 3 in the fitting process. This suggests that there is a small vertical gradient in the metallicity of the thick disc as found by others previously (Kordopatis et al. 2011 ; Duong et al. 2018 ). Note, stars in 2 | z |/kpc 3 were not included in the former scheme as they could be contaminated with stars from the metal-poor stellar halo and could suffer from volume incompleteness. However, they are included in the later scheme because it takes both these effects into account. In Fig. 12 we show the mean metallicity as function of Galactocentric radius R for different slices in height | z | for all stars with positive rotation about the Galaxy, which should eliminate star belonging to the halo. Results from APOGEE-DR14 and GALAH DR2c are shown separately. We also plot Galaxia predictions from the MP and MR models. The MP model clearly has a thick disc that is too metal poor to fit the observed data for | z | > 1 kpc. The new MR model reproduces the GALAH data very well. It also reproduces the APOGEE data very well, except for the slice closest to the mid-plane and the slice furthest from the mid-plane. Compared to GALAH, stars in APOGEE that are close to the mid-plane are metal rich, but the stars progressively become metal poor with increasing height above the mid-plane. These differences could be due to systematics in abundances between the two surveys, but could also be due to the different selection function of the surveys. The effect of selection function is clearly visible in Fig. 12(f) corresponding to the top most slice (2 | z |/kpc 3). Here, the MR model has a thick disc with a mean metallicity of −0.16. However, the mean metallicity of stars in this slice is −0.2. This is due to two reasons. First, because the metal poor stars are more luminous and are visible furthest in a magnitude-limited survey, we find that this effect decreases the metallicity of thick disc stars in this slice by 0.02 dex. Secondly, the top most slice has a larger contribution from the (metal poor) halo compared to other slices and this contamination decreases the metallicity of stars in this slice by −0.015 dex. Fig. 12 shows that close to the mid-plane there is a strong radial metallicity gradient. As we move away from the mid-plane the gradient diminishes progressively to zero. Close to the plane, a radial gradient of −0.07 (dashed line), as used in the Besançon (MP) and MR models, is roughly consistent with the observed data. Figure 12. Mean metallicity as function of Galactocentric radius R for different slices in height | z | for all stars with positive


like a galaxy cluster creates a small-scale dipole pattern in the direction of the large-scale CMB temperature gradient. The QE (Hu et al. 2007 ) is based on extracting the correlation between the dipole and background gradient to estimate the lensing convergence . Specifically, the lensing convergence can be estimated from a weighted product of filtered versions of a gradient map and small-scale lensing map :Here, is the pointing unit vector, is angular multipole, and A l is a normalization factor. While designed to pull out the lensing-induced correlations between large-scale and small-scale CMB anisotropy, the QE is also sensitive to correlations due to foreground emission. Of particular concern is the cluster’s own SZ emission, which is typically an order of magnitude larger than lensing signal. As pointed out by Hu et al. ( 2007 ), the magnitude of the SZ bias can be lowered by decreasing the characteristic scale of the low-pass filter on the gradient map, which is set to 2000 in the current work. However, a stronger low-pass filter obviously reduces the number of modes used to measure the gradient, and thus decreases the signal-to-noise. The modified QE instead eliminates this bias by using an SZ-cleaned map for the large-scale gradient map. The large-scale gradient map is chosen because the CMB has much more power on large scales, so the noise penalty from SZ removal has minimal impact. Note that while multiple foregrounds can be removed in principle, in practice the focus has been on removing the SZ signal. This is simply because the SZ signal introduces the largest bias. With the SZ signal present in only one of the two maps, there is no SZ-induced correlation between the two maps and no net bias on the reconstruction of the lensing convergence. However the SZ emission in the small-scale lensing map does add noise to the lensing reconstruction. Since under self-similarity the SZ flux (Kaiser 1986 ), y , is expected to scale with cluster mass M as while the lensing signal is linear in mass (in 1-halo regime), the additional SZ variance will generally be more important for high-mass clusters. The SZ variance will also be more important in low-noise surveys, i.e., when it is larger than the instrumental noise in the convergence map. 3.2. Template Fitting to Reduce the SZ Variance An obvious way to eliminate this SZ variance is by using SZ-free maps for both the small-scale and gradient maps. Of course this would undo the advantages of the modified QE for the instrumental noise in the small-scale map. One can also reduce this extra variance by projecting out a model template for the SZ signal, and thereby reducing the total amount of SZ power in the small-scale map. Given the impossibility in creating a “perfect” SZ template, the template fitting will not completely eliminate the SZ signal in the small-scale map. However, template fitting can significantly reduce the SZ power in the small-scale map, and thus reduce the SZ noise penalty


SEDs from Abdo et al. ( 2010a ), a time-scale of one day due to the lack of variability data and γ min = 200 (Zhang et al. 2012 ). 4 RESULTS We used three types of EEDs to fit the SEDs of TeV BL Lacs. The SEDs for the maximum probability and the 1σ error band are shown in Fig. 1 . The one-dimensional (1D) probability distributions and the two-dimensional (2D) confidence contours of the model parameters are shown in Figs 2 – 5 . In the 1D distributions, the dotted lines show the maximum likelihood distributions and the solid lines show the marginalized distributions. In the 2D distributions, the inner contour denotes the 68 per cent CL, while the outer contour represents the 95 per cent CL. The model parameters are listed in Tables 1 – 3 . Figure 1. Left-hand panels: SEDs of the three objects fitted by three types of EEDs, where the solid black, blue dash-dot and magenta dash-dot-dot lines represent the SEDs given by the BPL, PLLP and PLC EEDs, respectively. Right-hand panels: SED contours of the three objects in γ-ray bands with the 1σ error bands, where the shaded areas in grey, blue and orange represent the SED contours given by the BPL, PLLP and PLC EEDs, respectively. Figure 2. 3C66A. Left-hand panels: Distributions of the parameters given by the three types of EEDs, where the dotted lines show the maximum likelihood distributions and the solid lines show the marginalized probability distributions. Right-hand panels: 2D confidence contours of the parameter correlations for the three types of EEDs, where the contours of the parameters with larger correlations are shown. The inner contours denote the 68 per cent CL, while the outer contours represent the 95 per cent CL. Figure 3. As Fig. 2 , but for PKS1424+240. Figure 4. As Fig. 2 , but for PKS1424+240 in the flare state. Figure 5. As Fig. 2 , but for PG1553+113. Table 1. Model parameters of the best fits and the marginalized 68 per cent confidence intervals (CI) for BPL EEDs. Table 2. The model parameters of the best fits and the marginalized 68 per cent confidence intervals (CI) for PLLP EEDs. Table 3. The model parameters of the best fits and the marginalized 68 per cent confidence intervals (CI) are listed for PLC EEDs. 4.1 3C66A The SED fitted by the PLC EED does not cover the Fermi /LAT bands, and χ 2 /dof is worse than that of the other two EEDs. It is found that the SED fitted by the PLC EED within the 68 per cent CL does not cover the Fermi band well compared with the other two EEDs. Hence, the PLC EED was ruled out in modelling the SEDs. We obtain that χ 2 /dof values are 1.22 and 1.20 for BPL and PLLP EEDs, and the parameters are well constrained except for α in both models. However, the flux in the 20–50 keV bands given by the PLLP EED is higher than that for the BPL EEDs, indicating that hard X-ray observations could distinguish between the two types of EED. In summary, the red shift of 3C66A is 0.16 and 0.24 from the BPL and PLLC models, respectively, and the red shift of the


and H i emission of several radio source populations. Assuming a luminosity dependence for the fractional polarization, O’Sullivan et al. ( 2008 ) realized a simulated polarized image based on the radio source catalogue of Wilman et al. ( 2008 ). Very recently a new simulated catalogue was produced (T-RECS; Bonaldi et al. 2019 ) based on cosmological dark matter simulations to reproduce the clustering of sources and it models the radio sky both in total intensity and polarization with updated information on radio sources. Our simulation, like the above simulations, aims at giving useful information for the advent of the SKA. Similarly, it is based on cosmological RLFs integrated over cosmological volumes but the models adopted to reproduce the characteristics of the radio sources and also the procedure are in general different. In addition, alternative to the previous works, we use observed high-quality images of extended radio sources to reproduce the morphology and the spectro-polarimetric properties of the simulated radio sources. This is especially important as these simulations will be used to study magnetic fields in galaxy clusters (Loi et al. in preparation). For each simulated radio source, our catalogue lists the following parameters: type , in principle we can classify our sources in several subclasses, radio-loud or radio-quiet AGN, SFG, quasar etc. Following Novak et al. ( 2017 ) and Smolčić et al. ( 2017a ) we consider two main families depending on the mechanism that triggers the radio emission: SFG and AGN; redshift , z; size , we used the relations adopted by Wilman et al. ( 2008 ) for radio-loud AGN and SFGs. The size model are redshift-dependent and in particular the SFG size depends also on luminosity; luminosity at 1.4 GHz , we extract this information from the RLFs of Novak et al. ( 2017 ) and Smolčić et al. ( 2017a ) for the SFGs and AGNs, respectively, based on the results of the VLA−COSMOS 3 GHz Large Project (Smolčić et al. 2017b ), extrapolated to 1.4 GHz assuming the spectral index derived in combination with the the VLA−COSMOS 1.4 GHz Large and Deep Projects (Schinnerer et al. 2010 , 2007 , 2004 ); coordinates , (x, y); morphology and spectro-polarimetry properties , we select a model of radio source from a dictionary depending on its luminosity and type. Each model of this dictionary consists of four 1.4 GHz images: the surface brightness I ν in total intensity; the spectral index distribution α determined by assuming that the flux density S ν at a frequency ν is S ν ∝ ν − α ; the fractional polarization defined as the ratio between the polarized intensity and the total intensity FPOL = P / I ; the intrinsic polarization angle which is defined with respect to the Q , and U Stokes parameters as: The images of the dictionary are real high-quality high-resolution images performed at high frequency. In particular, we used VLA images at C and X bands at arcsecond resolution so that the polarization properties


and GRMHD models, as well as from measurements of the ring diameter in the image domain. Our measurements remain consistent across methodologies, algorithms, data representations, and observed data sets. Motivated by the asymmetric emission ring structures seen in the reconstructed images (Section 5 ) and the similar emission structures seen in the images from GRMHD simulations (Section 6 ), we developed a family of geometric crescent models (see, e.g., Kamruddin Dexter 2013 ) to compare directly to the visibility data. We used two distinct Bayesian-inference algorithms and demonstrate that such crescent models are statistically preferred over other comparably complex geometric models that we have explored. We find that the crescent models provide fits to the data that are statistically comparable to those of the reconstructed images presented in Section 5 , allowing us to determine the basic parameters of the crescents. The best-fit models for the asymmetric emission ring have diameters of 43 ± 0.9 μ as and fractional widths relative to the diameter of 0.5. The emission drops sharply interior to the asymmetric emission ring with the central depression having a brightness 10% of the average brightness in the ring. The diameters of the geometric crescent models measure the characteristic sizes of the emitting regions that surround the shadows and not the sizes of the shadows themselves (see, e.g., Psaltis et al. 2015 ; Johannsen et al. 2016 ; Kuramochi et al. 2018 , for potential biases). We model the crescent angular diameter d in terms of the gravitational radius and distance, , as d = αθ g , where α is a function of spin, inclination, and R high ( α ≃ 9.6–10.4 corresponds to emission from the lensed photon ring only). We calibrate α by fitting the geometric crescent models to a large number of visibility data generated from the Image Library. We can also fit the model visibilities generated from the Image Library to the M87* data, which allows us to measure θ g directly. However, such a procedure is complicated by the stochastic nature of the emission in the accretion flow (see, e.g., Kim et al. 2016 ). To account for this turbulent structure, we developed a formalism and multiple algorithms that estimate the statistics of the stochastic components using ensembles of images from individual GRMHD simulations. We find that the visibility data are not inconsistent with being a realization of many of the GRMHD simulations. We conclude that the recovered model parameters are consistent across algorithms. Finally, we extract ring diameter, width, and shape directly from reconstructed images (see Section 5 ). The results are consistent with the parameter estimates from geometric crescent models. Following the same GRMHD calibration procedure, we infer values of θ g and α for regularized maximum likelihood and CLEAN reconstructed images. Combining results from all methods, we measure emission region diameters of 42 ± 3 μ as, angular sizes of


3 DM particles (Rasera et al. 2010 ; Alimi et al. 2012 ; Bouillot et al. 2015 ). For the flat ΛCDM model, the six key cosmological parameters were set at the central values determined by the Wilkinson Microwave Anisotropy Probe Seven Year data (WMAP7) (Spergel et al. 2007 ; Komatsu et al. 2011 ). For the other two DE models, the values of the seven cosmological parameters (the six key parameters + w ) were chosen to satisfy the same WMAP7 constraints. Table 1 lists the values of the matter density parameter, Ω m , linear power spectrum amplitude on the scale of , σ 8 , dimensionless Hubble parameter, h , dark energy equation of state, w ≡ w 0 + w a (1 − a ) with scale factor a ( t ) (Linder 2003 ), and mass of individual DM particles, m p , for the three DE models. For a more detailed description of the DEUS, we refer the readers to Alimi et al. ( 2012 ) as well as the DEUS webpage. 4 4 All data from the DEUS are publicly available at http://www.deus-consortium.org/ . Table 1 Initial Conditions and the Particle Mass Resolution A phantom DE ( w CDM) is characterized by its negative kinetic energy that exerts stronger repulsive force than Λ (Caldwell et al. 2003 ). Whereas, a quintessence model is characterized by the potential shape of a scalar field DE. For the DEUS, the Ratra–Peebles potential, whose shape is expressed as powers of linear combinations of the exponentials of the scalar field (Ratra Peebles 1988 ), was specifically chosen. Although the distant-field diagnostics based on the linear observables like the CMB temperature spectra and SN Ia luminosity–distance relations cannot distinguish among the three models (Bouillot et al. 2015 ), an efficient near-field probe based on the nonlinear observables might be able to pull it off since the formation and evolution of the nonlinear structures proceed in a different way among them (e.g., see Alimi et al. 2010 ). Table 2 Halo Spin Transition Zones The halo catalog from the DEUS comprises the gravitationally bound objects identified at various redshifts by the Friends-of-Friends (FoF) halo finder with a linkage parameter of 0.2 (Roy et al. 2014 ) and provides information not only on the center of mass position, , and virial mass, M h , of each object but also on the positions and velocities of its constituent DM particles, which allow us to compute its angular momentum vector, . The well-resolved FoF objects in the mass range of at z = 0 are selected for a sample of the galactic halos to be used for the current analysis. The low-mass FoF objects with are excluded from our analysis on the ground that the angular momentum vectors of the halos composed of less than 300 DM particles are likely to suffer from inaccuracy caused by the shot noise (Bett et al. 2007 ). The routine we go through for the investigation of the DE dependence of the halo spin transitions is similar to that described in Lee et al. ( 2020 ), the summary of which is provided in the following. 1. Divide the simulation volume