may be higher given that an unmeasurable component of light is lost during this period. No conclusion can or should be drawn from this point, which is presented only for the sake of completeness. 3.2 He <sc>i</sc> line 3.2.1 Equivalent width The equivalent widths of the He i line around the 2014 periastron are shown in Fig. 4 (b). The closed blue circles denote the equivalent width as measured by integrating from the base of the line, while the open green squares denote the measurement obtained from the Gaussian fit, relative to the continuum. Shown for comparison are the measurements around 2010 reported by Chernyakova et al. ( 2014 ) (red crosses). As with the Hα line, the He i line shows a general increase in the absolute equivalent width which peaks after periastron, though the growth is not as great. The variation in the strength of the line is consistent with the variability observed in the Hα line. 3.2.2 V/R In general, the violet component of the double peaked He i line is more dominant, as is seen in the equivalent width | W λ | of the violet component and the ratio of peaks of the violet to red (V/R) components. The V/R variation (Fig. 4 c) has been measured from the ratio of the heights of the Gaussian fits to the Violet and Red component of the He i line. The height is measured relative to the continuum and the error is given by the statistical error of the fit. Around the first disc plane crossing, there is a marked increase in the asymmetry of the line, while there is a decrease in V/R around periastron and a small increase in the red component around the second disc plane crossing. This clearly illustrates the asymmetry of the He i line and its variation around periastron. The V/R variation lies between 0.93 V/R 1.65 during the observed period. 4 DISCUSSION Around periastron the equivalent width of the Hα line smoothly increased to a maximum of −72.7 ± 0.7 around ∼τ + 13 d, after which it decreased to values consistent with the pre-periastron levels. The equivalent widths after ∼τ + 13 d are consistent with the previous periastron passage (Chernyakova et al. 2014 ) but appear to be consistently lower before this. This is clearly seen before periastron where the average equivalent width (and error) of the Hα line was −62.9 ± 3.1 Å in 2010, but −56.7 ± 0.6 Å in 2014. We interpret this as being due to variability in the Be star circumstellar disc which could well change from periastron to periastron. This may imply that the mass of the circumstellar disc was lower before the 2014 periastron passage (as compared to the 2010 periastron passage). Since the circumstellar disc influences the shock front around the pulsar, the differences in the circumstellar disc properties will be an important contributing factor to the variations in the multiwavelength emission observed around different periastra. There is also a marked change in the disc around the time of the first disc plane crossing (τ − 17.5 d), as is noted by the increase in the


not been identified due to the lack of counterparts in the radio/X-ray or GeV γ -ray bands (Aharonian et al. 2005 , 2008a ). Therefore, searching for the counterparts of these unidentified VHE sources in longer-wavelength bands is very helpful to identify and classify them. In the GeV band, more than 7 years of survey data from the Fermi Large Area Telescope ( Fermi -LAT) provides a good opportunity to hunt for the unidentified VHE sources. Indeed, several unidentified VHE sources have been detected with the Fermi -LAT data (Hui et al. 2016 ). HESS J1427−608 is one of the unidentified VHE sources discovered by the HESS Galactic Plane Survey (Aharonian et al. 2008a ). The TeV image shows that it is only slightly extended with a symmetric Gaussian function with a width of σ = 3′. This source is detected with an integral flux above 1 TeV of F γ (>1 TeV) = 4.0 × 10 −12 erg cm −2 s −1 and a power-law spectrum with an index of Γ = 2.16. No nearby SNR or pulsar was detected in the vicinity of HESS J1427−608 (Green 2014 ). The X-ray counterpart of it, Suzaku J1427−6051, was reported by Fujinaga et al. ( 2013 ). The X-ray spatial morphology is clearly extended with a Gaussian width of σ = 09 ± 01, and the spectrum is well fitted by a power law with an index of Γ = , implying nonthermal X-ray continuum emission. The unabsorbed flux in the 2–10 keV band is . Fujinaga et al. ( 2013 ) have discussed the possible nature of HESS J1427−608 as a PWN or nonthermal SNR. Each one can explain some of the observational facts but face difficulties. No radio counterpart was detected in the direction of HESS J1427−608. In the second Fermi -LAT catalog (2FGL; Nolan et al. 2012 ), a GeV source, 2FGL J1427.6−6048c, which is located in the vicinity of HESS J1427−608, was reported. However, their central positions differ moderately from each other. Furthermore, the power-law spectrum index of 2FGL J1427.6−6048c is Γ = 2.7 (Nolan et al. 2012 ), which cannot connect with the TeV spectrum of HESS J1427−608 well. It is very likely that 2FGL J1427.6−6048c is not associated with HESS J1427−608. Meanwhile, it should be noted that no source in the third Fermi -LAT source catalog (3FGL; Acero et al. 2015 ) is associated with 2FGL J1427.6−6048c. In this paper, we carry out a complete analysis of this region using more than 7 years of Fermi -LAT Pass 8 data to investigate the γ -ray emission of HESS J1427−608. In Section 2 , we describe the data analysis and results, including the spatial, spectral, and timing analyses. The possible nature of HESS J1427−608 based on the multiwavelength spectral energy distribution (SED) fitting is discussed in Section 3 , and the conclusion of this work is presented in Section 4 . 2. DATA ANALYSIS 2.1. Data Reduction The following analysis is performed using the latest Fermi -LAT Pass 8 data with the Source event class from 2008 August 4 (Mission Elapsed Time 239557418) to 2015 November 4 (Mission Elapsed Time 468288004). Considering the impact of


the dynamo action in astronomical bodies. We choose to work with periodic cuboid domains, because it allows us to study the dynamo properties of spatially periodic cellular flows. We vary the scale separation in the system through the reconstruction of the computational domain and the characteristic length-scale of the imposed velocity field. The first flow under consideration is the well-known ABC flow (named after Arnold, Beltrami Childress), recently reviewed by Galloway ( 2012 ). The second is a modulated version of the first, with imposed long-wavelength perturbation on the scale of the system. Such periodic flows are guaranteed to produce dynamo action for a wide range of finite values of R m (Roberts 1970 ). We study the kinematic dynamo action in domains of various aspect ratios, to examine the effect of changing the scale separation of the system as well as the effects of imposing a two-scale perturbed flow on the system in the kinematic regime. The first part (ABC flow) of the problem considered here has recently been investigated in a different way by Cameron Alexakis ( 2016 ), who carried out a theoretical study of kinematic dynamo using the Floquet formulation that was originally devised for the Mathieu equation (Whittaker Watson 1902 ). The authors adopted the concepts in Roberts ( 1970 ) to solve the induction equation in the presence of the ABC flow for arbitrary large-scale separations, showing a transition from a large- to small-scale dynamo through a change in the growth rate. The results from this analysis are in general agreement with the findings presented below as the scale separation becomes arbitrarily large. However, their paper does not include the results for Floquet waves with length-scales comparable to the size of the imposed flow, although Galanti, Sulem Pouquet ( 1992 ) noted that such eigenmodes play a crucial role in maintaining the dynamo for large R m . In this paper, we utilize a discrete wavenumber decomposition that is determined by the aspect ratio of the computational domain. This allows us to investigate the transition from a large- to small-scale dynamo with a special emphasis on the length-scale selection of the fastest growing eigenmode of magnetic field and focus on the comparison of the results from the classic ABC and the modulated perturbed flow cases. Our study is based on the results of numerical simulations using a pseudo-spectral method in a triply periodic domain and analytic estimates based on the scale-separation arguments. The choice of the imposed flows allows for the scenario wherein a large-scale dynamo would be obtained at the onset. We then vary magnetic diffusivity in order to study how the dynamo mechanism changes as we increase R m . There are two possibilities: (i) the large-scale structure is preserved due to either the large aspect ratio of the system or the imposed long-wavelength modulation; or (ii) the energy is passed from the large scales to the small scales as


the result by about a factor of 2. Therefore, the shock width in terms of the pair unloaded Thomson optical depth is Fig. 6 shows , obtained from integration of the full equations (without assuming x l > 1), as a function μΓ u / f for several values of Γ u (i.e. on each curve, Γ u remains constant while f varies). It shows that equation ( 13 ) provides an order of magnitude estimate of the shock width as a function of the photon escape fraction. Fig. 7 shows the Lorentz factor profile as a function of . It shows how the shock becomes narrower when the fraction of escaping photons increases. Once the optical depth to infinity becomes too small and photon escape starts affecting the shock structure, the shock adjusts itself and becomes narrower to match the finite optical depth. This is in contrast to a Newtonian shock that cannot adjust itself, and therefore full shock breakout follows within a dynamical time after photon escape starts becoming non-negligible. Figs 8 – 9 show the mechanism that allows the shock to adjust its width – a rapid buildup of x l within a unit interval of the optical depth τ, which compensates for the lack of backscattered photons at τ > τ ∞ . As can be seen from Figs 7 – 9 , the structures of all shocks with different values of f converge while the flow is still relativistic, before it approaches the downstream (τ ≲ 1), even when photon escape strongly affects the shock width. This result supports our assumption that the conditions in the immediate downstream are similar in all shocks, even in the presence of a significant photon escape. Figure 6. The shock width as a function of μΓ u / f . On each of the four curves, f varies while Γ u = 5, 15, 50 and 150 remains constant. is measured using the full analytic solution with η = 0.5 and a = 2, and is defined as the pair unloaded Thompson optical depth, where Γ = 0.9Γ u . The circles mark the location where , at which equation ( 13 ) predicts a transition in the shock width dependence on f . The solid black line is a plot of , and is given for guidance. This figure indicates that the width is given by equation ( 13 ) to within an order of magnitude. Figure 7. Lorentz factor profiles as a function of for shocks with Γ u = 10 and different f values. Figure 8. Profiles of the loading parameter as a function of for shocks with Γ u = 10 and different f values. Figure 9. Profiles of the loading parameter as a function of τ for shocks with Γ u = 10 and different f values. 4 SHOCK BREAKOUT In the previous section, we derived the steady-state structure of an RRMS with photon escape. In astrophysical settings, the shock propagates in a medium having a finite Thomson depth to infinity . Note that we use to describe the optical depth of the circumstellar medium since no pairs are created before it is encountered by the shock. For typical settings, we expect both Γ sh = Γ u and to vary with time. Then, once , photons starts leaking out. However, since the shock width continuously


show evidence of hydrogen (i.e. longer durations). The fact that in 4U 1728–34 bursts with oscillations happen more often in the high/soft state, while PRE burst happen mostly in the low/hard state, suggests that the oscillations and the PRE phenomenon are both correlated with accretion rate and geometry, as proposed by Franco ( 2001 ), van Straaten et al. ( 2001 ) and Muno et al. ( 2004 ); however, the presence of bursts with oscillations in the low/hard state in 4U 1728–34 (and 4U 1636–53; Zhang et al. 2013 ) indicates that oscillations are not only driven by either mass accretion rate or whether the burst shows PRE or not, although mass accretion rate (and perhaps PRE) has an influence on the presence of oscillations. 4.2 X-ray spectral properties and burst oscillations We find a strong evidence for a link between burst oscillations and the spectral properties during the burst in 4U 1728–34, more specifically between the presence of burst oscillations and the changes in the apparent emission area during the decay of the burst. The left-hand panels of Figs 2(a) and (b) , and the discussion in Section 3.1 , show that oscillations in Type-I X-ray bursts in 4U 1728–34 are always associated with a blackbody radius that remains more or less constant for at least ∼2–8 s. A similar trend has also been found in the LMXB system 4U 1636–53 (Zhang et al. 2013 ). The changes of the blackbody radius could be due to either changes in the apparent emitting area of the NS during this phase, or to changes in the colour correction factor, f c . In the case of changes of the apparent emitting area of the NS, Spitkovsky et al. ( 2002 ) and Zhang et al. ( 2013 ) suggested that tail oscillations could be due to the spread of a cooling wake, which is formed by vortices during the cooling of the NS atmosphere. In this scenario, the speed of the cooling wake depends upon the latitude at which the burst ignite, since the speed of the cooling front near the equator is higher than that near the poles (Spitkovsky et al. 2002 ). If the bursts ignite at high latitude on the NS surface, during the burst decay time the front speed of the cooling wake is slow, the emission area changes slowly, and the asymmetric emission during the burst lasts long. These bursts would have oscillations and the blackbody radius remains constant for a while (see the left-hand panels of Fig. 2a ). If the bursts ignite at low latitude, during the decay time the front speed of the cooling wake is fast, the emission area, and hence the blackbody radius, changes fast, and the asymmetric emission is short lived. These bursts would not show oscillations and the blackbody radius evolves very fast. We note that this interpretation has not been calculated in detail. We also note that burst oscillations also appear in the rising phase of the bursts (e.g. left-hand panels of Fig. 2b ). The mechanism of burst oscillations might be different between the rising and decaying phase. The burst oscillations


not directly calculated. Instead, Equations ( 6 ) and ( 7 ) are combined by using the posterior samples: to define the likelihood that one then draws from:Performing these two steps repeatedly produces an ensemble of data sets drawn from Equation ( 6 ). Applying Equation ( 8 ) to our M–R relation requires evaluating the lower levels of the forward model described in Equation ( 4 ). Part of the subtlety of checking data-model consistency arises from the hierarchical nature of our model. In particular, of Equation ( 8 ) includes both the population-wide parameters C , γ , σ M and the individual parameters we can use the posterior samples of either of these groups of parameters to calculate . We show the result of both choices in Figure 5 , using the posterior samples from the baseline M–R relation (second line of Table 1 ). Conceptually, using samples from the individual true mass and radius posteriors () evaluates the fit of the model to the currently observed set of planets (the green histograms on the left), while using posterior samples for the M–R relation parameters () evaluates the fit of the model to altogether new sets of planets (the blue histograms on the right). For the former case, the same and as the observed data set are used; for the latter case, is drawn from the distribution of for the observed planets that have a similar mass, and is drawn from the observed data set’s full distribution of without controlling for radius (the size of the radius error bars are fairly constant across the data set). The second aspect of hierarchical model-checking which requires some effort is the identification of a robust statistic to quantify the discrepancy between the observed data and the model-generated data. Optimally this statistic would test the fit of every part of the modeled probability distribution, including the “average” behavior of the model, the “extreme” behavior out on the tails of the distribution, and for hierarchical models, the accuracy of the grouping and relational structure that is illustrated by graphs like Figure 1 . Due to high dimensional parameter space, this proves to be very difficult, so one must identify several statistics which test such aspects separately. To illustrate the problem, we choose two: f 1 σ , the fraction of a given data set’s simulated mass, radius observations which fall within the 68% coverage interval of our probabilistic, baseline M–R relation (blue region in Figure 4 ), and f μ , the fraction of a given data set’s mass measurements whose 1 σ error bars cross the mean relation μ (see Equation ( 2 )) of that same model. Therefore, f 1 σ tests how well the width of our probabilistic M–R relation fits the data, and f μ tests how tightly grouped the data are around the mean compared to the normal distribution of our model. The results of these tests are displayed in Figure 5 . The observed data’s f 1 σ statistic (top) falls at the 63rd and 83rd percentiles (i.e., within “one sigma”) of the


main age periods in the ring. Age, mass, and Av inferred from the fit are indicated. The data are circles, model is the line, squares are the model after convolution with the filter width used for the data, the horizontal bar indicates the width of the filter. The red point is the photometric emission in the HST /Ha + [N ii ] filter, which includes the line and continuum emission; the yellow point on the vertical grey line is the predicted H α emission from the ionizing budget of the cluster and added up to the continuum prediction, which includes the photosphere contribution, all convolved with the shape of the HST filter (hence the grey line in the younger clusters). The cluster number and its relative coordinates – left corner of each plot – are to be used to find its location in any of the images in this work. To illustrate the range of extinctions and its effect, for each age period two distinct clusters, one requiring minimum Av, other requiring larger Av, are shown. The discrepancy between the predicted H α emission and the data for the youngest 4 Myr burst (illustrated with the clusters 30 y 138), which is due to the diffuse nature of the nebular gas in the ring (discussed in Section 3 ), can be noticed. The cluster no 145 is an example of the few in which the measured emission is in line with the prediction. The simultaneous inclusion of UV, optical, and IR data in the fit was found to be critical for the age determination in the particular range covered in the ring, in the 1 Myr to a few 100 Myr (see below). Moreover, the moderate extinction at the clusters location (Section 5 ) also helped in better constraining ages as the observed SED is close to its intrinsic shape and minimum correction due to dust is required in the fit. On this basis, special features in the SED that were found determinant for the age estimates are: the steep UV–optical–IR spectral slope for assuring the ages of the younger, less than 10 Myr old population (in this case the cluster H α emission cannot be used (Section 3.1 ) but the wide wavelength coverage up to and minimum dust extinction makes the result very solid); the Balmer break for ages older than 20 Myr; the near-IR bands helped to constrain the oldest population beyond 60 Myr because of the progressive curvature of the SED, simultaneously, towards the UV and IR bands. Dating of the clusters detected only from onwards was found largely uncertain: the SSP fits are based on four spectral bins only and the rather featureless shape of the continuum in the workable range, , is alone insufficient to properly constrain the age. For this reason, these clusters are not further analysed in this work. The denser dusty environment of these clusters is evidenced by comparing the UV - with the K -band image of the ring (Fig. 1 ), to see that these clusters are often located behind the thicker dust filaments. Putting in context the cluster properties of NGC 1097’s ring as compared with those of massive young star


energy redistribution, and the absorption lines of these individual elements dominate different regions of the spectrum, the shape of the bright and dark spots on the stellar surface varies with wavelength. Figure 3. Time evolution of the emergent flux from the surface of the star at different rotational phases in a Gaussian passband centred at 1700 Å with a standard deviation of 50 Å (upper panel) and the TESS passband (lower panel). Predicted flux distribution for reference abundances agrees reasonably with the IUE observations (SWP 19761 and LWR 15774) 2 in Fig. 2 . Small differences are most likely caused by missing opacity in model atmospheres. 3.2 Effect of the individual elements The inhomogeneous distribution of flux in most spectral bands, together with stellar rotation, leads to periodic photometric variability of the star. Fig. 4 shows the overall modelled photometric variability of the star, together with the photometric variability computed only taking into account the effect of each individual chemical element separately, to show the contribution of each element to the overall variability of the star. The central wavelengths and half-widths of the filters used in the plots are taken from Prvák et al. ( 2015 ). While the shape of the curves of the individual elements remains roughly the same at all wavelengths, being ‘composed’ in different ratios results in a curve of varying shape. Figure 4. Light curves of φ Phe computed using only the abundance maps of the individual elements (2010 January), along with the overall variability of the star (solid line) in different passbands. The light curves have been shifted vertically to better demonstrate the variability and marked by central wavelengths of the corresponding filters. Note the different vertical scale of the two panels. Fig. 5 shows the dependence of the amplitude of the photometric variability on wavelength. Again, the amplitude of the overall variability, defined as one-half of the difference between the maximum and the minimum magnitude of the star, is plotted together with the amplitude of the variability computed only taking into account the influence of the four chemical elements, one at a time. The variability of the star is largest in the far-UV part of the spectrum, especially around 1300–1400 Å, mainly because of the very low overall flux in this region. In the near-UV and the optical region up to about 6000 Å, the amplitude in narrow passbands varies significantly with wavelength due to the significant absorption in lines. In the red and the infrared, the variability is mostly governed by re-emission in continuum and the amplitude is relatively constant throughout the region. Figure 5. Amplitude of the photometric variability of φ Phe (2010 January) computed as a function of wavelength in Gaussian passbands with a standard deviation of 50 Å. Yttrium, which shows the most pronounced abundance variation, seems to also have the strongest effect on the variability,


Double Star Catalog (WDS; Mason et al. 2001 ), a compilation of all published astrometric measurements of visual binaries. In response, the USNO group assembled all of the data on 40 Eri BC contained in the WDS. We also provided them with a precise measurement based on archival Hubble Space Telescope ( HST ) images obtained in 2006. Moreover, and crucially, in early 2017 they obtained two new high-precision observations with the speckle camera on the 26 inch telescope at the USNO in Washington, D.C. From these sources, there are 22 new measurements since the last one listed by H74 , covering 1974.8 to 2017.2—as well as 158 earlier observations between 1851.1 and 1973.8. Using these data, Mason et al. ( 2017 , hereafter MHM17 ) have computed updated elements for the 40 Eri BC orbit, leading to a significant revision of the dynamical masses. Although the semimajor axis is nearly unchanged from H74 , the new elements lead to a reduction in the orbital period to P = 230.29 ± 0.68 year—a 20% increase in P −2 , and thus in the masses, compared to H74 . The new dynamical mass for 40 Eri B based on the MHM17 analysis and the 2007 Hipparcos parallax is 0.573 ± 0.018 M . In the remainder of this paper, we will also re-evaluate other parameters of the WD, and then discuss the astrophysical implications of these new results. 4. Astrophysical Parameters of 40 Eri B The most precise method to determine the atmospheric parameters ( T eff and log g ) of DA WDs is the spectroscopic technique (Bergeron et al. 1992 ; hereafter BSL92 ; Liebert et al. 2005 ; hereafter LBH05 ; GBR11 ), wherein the observed Balmer line profiles are compared with predictions of modern model atmospheres using χ 2 minimization. The model atmospheres and synthetic spectra we use are similar to the pure-hydrogen LTE models described in Tremblay Bergeron ( 2009 , and references therein). In the case of 40 Eri B, the atmosphere is purely radiative, and thus the solution does not depend on uncertainties in the treatment of convective energy transport. As described in Section 2 (and in BSL92 , their Section 6.4 ), 40 Eri B, with a directly measured dynamical mass, is a key object to test the validity of the spectroscopic technique. We have available nine high signal-to-noise, medium-resolution (∼6 Å FWHM) spectra of 40 Eri B obtained over the past 25 years, mostly with the Steward Observatory 2.3 m telescope at Kitt Peak; details of these spectra are given by GBR11 . The individual spectroscopic determinations of T eff and log g from these spectra are plotted in Figure 1 . The standard deviations (combined in quadrature with the formal internal errors of the fits) are σ ( T eff ) = 220 K and σ (log g ) = 0.036, which are represented by the 1 σ and 2 σ ellipses in Figure 1 . These dispersions are similar to the typical external errors of 1.4% in T eff and 0.042 dex in log g found by LBH05 in fitting DA spectra (values corrected by Bédard et al. 2017 for a minor error in LBH05 ). By


values of the parameters varied here, and we refer the reader to Appendix A for the parameters that remain constant in our simulations, including the initial orbital elements for the planets. We tested the three different prescriptions of the general relativity introduced in Sect. 2.3 . They gave very similar results so that in the following we compare the other effects with respect to the simulations performed using the prescription of Kidder (1995) . The planetary reference values were taken to be representative of the Earth; in particular, the quantity k 2,p Δ τ p is equal to 213 s ( Neron de Surgy Laskar 1997 ). The stellar reference values were chosen to be representative of fully convective M dwarfs ( Bolmont et al. 2015 ). For all the simulations we performed, we calculated the transit timing variations ( Agol Fabrycky 2018 ) as follows: (i) for each transit we find the time of the transit mid-time by performing an interpolation to find the precise time a given planet crosses a reference direction. This corresponds to the “Observed transit time” O ; (ii) we evaluate the “Calculated transit times” C by performing a linear fit 2 of the transit times calculated in step i) over the total number of transits; (iii) we calculate the difference O – C to obtain the TTVs as a function of the epoch (or transit number). To quantify the impact of each additional effect on the simulated TTVs, we compute the difference between the TTVs calculated taking into account an additional effect and the TTVs obtained for a Newtonian N -body integration. Table 1 Reference values for the parameters we vary in this study. Notes. We assume that all planets in the system have the same potential Love number of degree-2 k 2 f ,p , fluid Love number k 2,p , and time lag Δ τ p . 4 Influence of each effect on the TTVs We performed a set of six simulations of the TRAPPIST-1 system to test the impact of the additional effects listed in Sect. 2 , and we compare each with a Newtonian N -body simulation. One after another, we explored the effect of each parameter using the reference values in Table 1 and general relativity. We tested the influence of the dissipative part of the planetary tide by assuming for all planets, with all the other parameters set to zero. We repeated the operation for the non-dissipative part of the planetary tide (through k 2,p , equal for all planets), the rotational flattening of the planets (through k 2 f ,p , equal for all planets), the non-dissipative part of the stellar tide (through k 2,⋆ ), the rotational flattening of the star (through k 2 f ,⋆ ), and for general relativity. Figure 1 shows the results for planets b to d. The top panels of Fig. 1 show the transit timing variations for the three planets for the seven simulations, and the bottom panels show the difference between the TTVs and the TTVs corresponding to the pure N -body simulation. The different additional effects have a very limited impact on the shape of the TTVs, but computing


of 2 mbar ambient pressure. The light intensity is ∼10 kW m −2 . The erosion of the dust starts milliseconds after the laser is turned on and is observed by a camera from the side. The measurements are based on the thermal creep of gas, which occurs if a temperature gradient is present along capillaries if the mean-free path of the ambient gas molecules is on the order of the size of the capillaries (Knudsen 1909 ). Pores in a dust bed act like capillaries. The basic setting is therefore a dust bed consisting of the sample material set in a vacuum chamber at a few mbar ambient pressure. A temperature gradient is generated by illuminating the surface of the sample. The resulting temperature profile is flat over the topmost dust layer but then decreases further down into the dust bed (de Beule et al. 2015 ). It leads to a gas flow by thermal creep from the cool deeper layers upwards toward the warm surface. The thermal creep flow itself is independent of a pressure and does not induce an overpressure. However, in the top layer without temperature gradient, a pressure is needed to maintain this flow (de Beule et al. 2015 ). Therefore, a pressure maximum evolves and the top layer of about 200 μ m is subject to an internal overpressure. If this stress is larger than the tensile strength, parts of a dust layer will be ejected. In recent work by de Beule et al. ( 2013 ), it was shown that the mass ejection rate N is inversely proportional to the cohesion per mass F and gravity g as In general, the idea is that a temperature gradient grows with time, the pressure takes some time to build up to the level of tensile strength and if a particle layer is ejected, the process starts all over again. This way, the time interval for particle ejections and therefore the ejection rates are coupled to the cohesive strength or tensile strength of the sample. The lower the cohesion, the smaller the time interval needed to build up the necessary pressure, and less cohesive samples result in higher ejection rates. In the case of this experimental setup and dust samples, the time span is on the order of milliseconds. de Beule et al. ( 2013 ) also showed that the brightness of the recorded frames of the erosion is a measure for the ejection rate. Hence, comparing the inverse of the brightness of the pictures in Figure 3 gives a relative value for the cohesion force (plus gravity) of the different dust samples. Figure 3. Overlay of ejected dust for different tempered samples. The overlay contains 2000 frames, which is a record time of 4 s. The laser intensity is ∼12 kW m −2 and the time of illumination is the same for each sample. Based on work by Muntz et al. ( 2002 ) and Sone Itakura ( 1990 ), de Beule et al. ( 2015 ) find for the overpressurewhere L x 1 marks the length (thickness) of dust layers with a temperature gradient and L x 2 is the active depth with constant temperature below the surface. On short timescales of milliseconds, the established temperature


quantities ( α , δ , , μ δ , D (SpT), v rad ) by adopting their uncertainties and relevant correlations. We drew 10 000 initial conditions, which were evolved for 10 Gyr in the future and traced back in the past for a sufficiently long time (i.e., up to τ evo ). For each star, we note the rest-frame velocity, v rf , the past and future Galactic Cartesian coordinates, and the corresponding velocity components. We estimated the escape probability from the Milky Way, P esc , for each star as the fraction of initial conditions where ( v rf − v esc ) > 0. We determined the vertical component of the angular momentum, L Z , which indicates the direction towards which the star has been ejected. We also numerically estimated the eccentricity, e , the median orbital apocenter and pericenter, R apo and R peri , and the maximum vertical displacement, Z max . The most recent Galactic plane crossings, R ( Z = 0), were recorded and used to determine the flight time from such locations, τ flight . The ejection velocity, v ej , was determined as the velocity possessed by the star at R ( Z = 0), which was corrected for the solar motion and the Galactic rotation. Table 5 lists the relevant orbital quantities for the 12 MS runaway candidates in a Galactocentric reference system that is left-handed, that is, with the x - and y -axis pointing, respectively, from the Milky Way’s center towards the Sun and along the direction of the Galactic rotation. Table 5. Orbital parameters of our MS candidates. Notes. The meaning of the columns from left to right is as follows: current X Y Z Galactocentric Cartesian coordinates, vertical component of Galactocentric rest-frame velocity, Galactocentric rest-frame velocity, escape probability, orbit eccentricity, vertical component of the angular momentum, median pericenter and apocenter, maximum vertical displacement from the plane, Galactocentric radius at the most recent intersection of past trajectories with the Z = 0 plane, ejection velocity from Z = 0, and flight time from Z = 0. 6. Properties of the runaway candidates 6.1. Orbit analysis As expected for nearby runaway MS stars, all but one candidate are bound to the Milky Way’s potential, since they have v rf that is on average two times smaller than v esc at their Galactic coordinates. The only exception is 2207−4329 that has an escape probability of P esc = 0.4, which is defined as the fraction of simulated trajectories with v rest > v esc . Due to our selection cut of v tan > 150 km s −1 (Eq. ( 1 )), all stars in our sample (both the MS and BHB candidates) ended up having | v rad |≲ v tan within the error bars. Three stars, 2034−5307, 2207−4329, and 2259−4931, have the largest v tan ≳ 450 km s −1 of all MS candidates. This unusual feature can also be noted in the Toomre diagram of Fig. 11 , where the three stars have large negative Galactic Cartesian V components (i.e., they lag behind the Milky Way’s rotation), as it is more typically seen for the majority of BHB


for their stellar halos from the Galaxy Halos, Outer disks, Substructure, Thick disks and Star clusters (GHOSTS) survey ( http://vo.aip.de/ghosts/survey.html ; Radburn-Smith et al. 2011 ; Monachesi et al. 2016a ). RGB star counts allowed GHOSTS to reach V -band (Vega) surface brightness sensitivities of ∼33 mag arcsec −2 , revealing roughly power-law stellar halos between minor axis distances of 10 kpc to >50 kpc. These profiles were integrated within the observed range of radii and extrapolated to total stellar halo mass as discussed above. The RGB color is sensitive to stellar halo metallicity (Monachesi et al. 2016a ), and we adopt a derived [Fe/H] value at 30 kpc along the minor axis following the observational calibration of [Fe/H] as a function of RGB colors for globular clusters (Streich et al. 2014 ) assuming . We add stellar halo masses and metallicities at 30 kpc along the minor axis for the MW (Sesar et al. 2011 ; Xue et al. 2015 ; Bland-Hawthorn Gerhard 2016 ), M31 (Gilbert et al. 2014 ; Ibata et al. 2014 ), and NGC 3115 (Peacock et al. 2015 ). Peacock et al. ( 2015 ) estimated a mass in low-metallicity stars in NGC 3115 of , which they adopted as an estimate of the stellar halo mass. As there is a considerable population of high-metallicity stars at large radii in NGC 3115, which could be argued to legitimately belong to its stellar halo, we choose to adopt as a lower limit to its halo mass. No published estimate of stellar halo mass exists for Cen A; we adopt the metallicity along the minor axis at 30 kpc from Rejkuba et al. ( 2014 ). Stellar halo masses (for UGC 180, NGC 1084, NGC 2903, and NGC 4220) or upper limits (for NGC 3351, NGC 3368, NGC 4258, and M101; galaxies that were either presented as upper limits or detections with 1 σ error bars overlapping with zero) are adopted from Trujillo Fliri ( 2016 ; UGC 180) and Merritt et al. ( 2016 ). The stellar halo masses from Merritt et al. ( 2016 ) are extrapolated to total stellar mass as described above and as tabulated by Harmsen et al. ( 2017 ). As these halo masses were constrained using integrated light, these galaxies have no stellar halo metallicity estimates. Total stellar masses were adopted from the source papers, adjusted to a universally applicable Chabrier ( 2003 ) stellar IMF. Bulge-to-total ratios were derived from near-IR ( K -band or longer) photometry from a variety of sources (described in Table 1 ; for Cen A we assume and UGC 180's B / T was roughly estimated to be ). Typical differences between independent estimates for the same galaxies are , comparable to the quoted uncertainties. BH masses and uncertainties (or limits) were adopted primarily from Kormendy Ho ( 2013 ), where again the source papers are tabulated in Table 1 . Table 1 Galaxy Properties Note. Stellar masses are assumed to have an uncertainty of 0.15 dex. a Galaxies with dominant classical bulges. References. (1) Licquia Newman ( 2015 ), (2) Bland-Hawthorn Gerhard ( 2016 ), (3) Sesar


An additional effect, therefore, will be required to explain the orbital variation of the GeV emissions of LMC LP3 and especially for 4FGL J1405.1−6119. In addition to the effect of the anisotropic soft-photon field, we will explore the orbital modulation caused by the dependence of travel distance of the unshocked pulsar wind that moves toward the observer on the orbital phase. This effect is introduced in Sierpowska-Bartosik Bednarek ( 2008 ) for the PSR B1259−63/SS2883 system and in Sierpowska-Bartosik Torres ( 2008 ) and Khangulyan, Aharonian Bosch-Ramon ( 2008 ) for the very high-energy emission (TeV emission) of LS 5039. Since the interaction between the pulsar wind and stellar wind/disc will produce a termination-shock with cone-like structure (Canto, Raga Wilkin 1996 ), the distance from the pulsar to the termination shock ( r s in Fig. 2 ) increases with the angle measured from the axis created by the pulsar and the companion star. This causes a dependence of the distance from the pulsar to the termination shock in the direction of the observer on the orbital phase and results in the orbital dependent intensity of the ICS of the unshocked pulsar wind. For the gamma-ray binary with O-type star, the GeV light curve is not well studied with the effect of the shock geometry and the system parameters. In this paper, therefore, we will perform an investigation for the modulation of the GeV emission with the shock-cone model, and will apply the model to two gamma-ray binaries, LMC P3 and 4FGL J1405.1−6119. LMC P3 is the first gamma-ray binary outside Milky Way and it is discovered in the Large Magellanic Cloud (LMC) (Corbet et al. 2016 ), which is a neighbour galaxy located at about 50 kpc from the Earth (Macri et al. 2006 ; Pietrzyński et al. 2013 ; de Grijs, Wicker Bono 2014 ). The companion star in the LMC P3 system is an O-type star, but the compact object has not been identified yet. In the LMC, ∼50 supernova remnants (SNRs) are known to emit X-rays (Seward et al. 2012 ), and LMC P3 is associated with SNR 0535−67.5 in the H ii region DEM L241 (Davies, Elliott Meaburn 1976 ). Long, Helfand Grabelsky ( 1981 ) report the first detection of the X-ray emission from the SNR 0535−67.5. Seward et al. ( 2012 ) find a compact X-ray source (CXOU J053600.0−673507) with a luminosity of ∼2–3 × 10 35 erg s −1 in 0.3–10 keV energy bands and an optical counterpart, O5III(f) star. They therefore suggest that CXOU J053600.0−673507 is the high-mass X-ray binary hosting neutron star or black hole. Corbet et al. ( 2016 ) analyse the GeV counter part (LMC P3) of CXOU J053600.0−673507 in data of Fermi Large Area Telescope ( Fermi -LAT) and find a 10.3-d periodic modulation, which reveals that LMC P3/ CXOU J053600.0−673507 is the binary system with a orbital period of P orb ∼ 10.3 d. They also confirm the orbital modulation of the X-ray emission. HESS Collaboration et al. ( 2018 ) subsequently detect the TeV emission from LMC P3. van Soelen et al. ( 2019 ) find


is more interesting. Even when the initial photon energy lies well below the first Landau resonance, the scattering cross section spikes (but does not diverge) at a value of ω f (and therefore ω i ) somewhat larger than 2 m . This spike arises from the pole in the matrix element associated with annihilation of the initial electron with a virtual positron into the final-state photon (Herold 1979 ; Daugherty Harding 1986 ). It appears at a lower photon frequency than the first Landau resonance (energy ) if B > 4 B Q . Figure 3. Differential nonresonant electron scattering cross section vs. initial photon frequency ω i (top panels) and final photon direction cosine μ f (bottom panels), in the regime B ≫ B Q . Curves in the top panels represent . Black curves: μ f > 0; blue curve: μ f = 0; red curves: μ f 0. The cross section rises as the scattered photon approaches the threshold for single-photon pair creation. In the bottom panels, the blue curve marks the classical limit, and black and red curves are used for clarity. Dotted curve: the final-state photon rapidly converts to an electron–positron pair. The partial cross section for scattering into non-pair-creating states is shown in Figure 4 . The high-energy behavior of the total cross section is opposite to the Klein–Nishina result for scattering in vacuum: the cross section grows as ω rises above m . Nonetheless, scattering is still suppressed for photons that have a large energy owing to relativistic motion of the scattering charge along B (Lorentz factor γ ≫ 1), because the factor decreases as ∼1/ γ 2 . Figure 4. Integral nonresonant electron scattering cross section plotted vs. initial photon frequency ω i for a range of initial direction cosine μ i , in the regime B ≫ B Q . The high-frequency peak marks the opening up of pair conversion in the final state (see Figure 6 ). The high-frequency dip in the curves shown in Figure 4 represents the opening up of the final-state phase space to pair creation over some range of scattering angles. A scattered photon can convert directly to an electron–positron pair if , meaning that the cross section for scattering-assisted pair creation, e ± + γ → e ± + e + + e − , can substantially exceed the vacuum value. This phenomenon is examined in more detail in Section 4 . More generally, a high-frequency Klein–Nishina scaling for the scattering cross section—which is approached in the case of scattering at high-order Landau resonances in sub-QED magnetic fields (Gonthier et al. 2000 )—loses meaning as B rises above 4 B Q , because the scattered photon has a high probability of converting to a pair (Beloborodov Thompson 2007 ). 3.2. Finite-<italic>B</italic> Correction to the Cross Section A simple correction to the electron–photon scattering cross section representing a finite magnetic field is available. The overlap of the photon wave function (wavevector k μ ) with a pair of harmonic oscillator wave functions, such as appears in the scattering matrix,


function at the low end. If the space density of metal-poor GCs is ∼2 Mpc −3 , as estimated by Boylan-Kolchin ( 2017 ) using the correlation between GCs and dark matter halos, then the associated stellar density is about half the above value, considering also the metal-rich GCs that formed later. Evidently, a high fraction of star-forming regions included at least one GC before about half the age of the universe. A similar calculation illustrates the importance of GC formation to the universal SFR at early times. If we consider that the duration of the star formation event that made a GC was Δ t , and the redshift range over which they formed was from z = 7 to 2, a period of 2.6 Gyr, then the average SFR from GC-forming events with M max ∼ 10 6 M ⊙ is (5 × 10 7 M ⊙ /Δ t ) × (Δ t /2.6 Gyr) × (8 Mpc −3 ), where the second term is the fraction of time each event occupies in the GC-forming era. The resultant average associated SFR is 0.15 M ⊙ yr −1 Mpc −3 , which is the same as the peak value of the comoving cosmic SFR density in the universe that occurs at redshift ∼2 (Madau Dickinson 2014 ). These two calculations suggest that the early universe was filled with star-forming regions containing young massive clusters (YMCs) that ended up as today’s GCs. There was little additional star formation making smaller clusters or OB associations that dispersed, aside from the smaller clusters and associations directly connected with the GCs. Today the mass density of GC stars is their space density times their average mass of ∼2 × 10 5 M ⊙ (Harris 2001 ), or 1.6 × 10 6 M ⊙ Mpc −3 . This is 0.26% of the current total stellar mass density from Madau Dickinson ( 2014 ), a factor of ∼1/380. The first factor of 50 in this 380 is presumably from scattered stars that formed with the GCs, and then the remaining factor of ∼8 would be from stars that formed recently without making massive clusters. We can also learn about early star formation in dwarf galaxies from their old stellar populations. WLM has an old metal-poor GC whose luminosity suggests that it contains ∼10 6 M ⊙ of stars (Elmegreen et al. 2012 ). The mass of other stars at the same age and metallicity is comparable to this (Leaman et al. 2012 ; Larsen et al. 2014 ), suggesting that the GC was a high fraction of the total WLM mass when it formed (Elmegreen et al. 2012 ). Similarly, the GC mass in the Fornax dwarf spheroidal was ∼0.25 of the galaxy stellar mass when the GC formed (Larsen et al. 2012 ). For IKN and NGC 147, these fractions are ∼0.5 and 0.06, respectively (Larsen et al. 2014 , 2018 ). These are enormously high fractions, especially considering the additional cluster mass that might have been present in the full cluster mass function. Perhaps the clustered fraction of stars at birth was larger than the 25% assumed above, even close to 100% as suggested by Messa et al. ( 2018 ) for regions with high SFR densities. In either case, the star formation events that formed the observed


and smaller p -values. Figure 4. The slope of the power-law fit to the d N /d m p mass distributions over time. The power-law index p is calculated according to equation ( 16 ). Top panel: the data for the L02 simulations. Bottom panel: the data for all seven simulations. As in Fig. 3 , when computing the power-law index, every data point in all of the L02 simulations is included in the calculation for p , and the same goes for the L04 data. Both panels: The shaded region represents σ , the error in p , calculated according to equation ( 17 ). In the bottom panel, when the larger domains are considered and the planetesimal populations from the multiple L02 and L04 runs are combined, there is much less variance in the value for p . The steady, decreasing trend with time is readily apparent. At t = 50Ω −1 , when enough planetesimals have formed to compute a reliable value for p , the values range between 1.6 and 2.0 across the different sized simulations, and well after planetesimals have formed, at t = 150Ω −1 , the values are between 1.4 and 1.6. A decrease in p represents a shift towards fewer and more massive planetesimals at late times. A trend toward larger masses with time is somewhat expected. However, a clear demonstration of this trend has not been demonstrated in previous studies. In fig. 3 from Simon et al. ( 2017 ), the authors show data for p over time in their simulations, but only over a relatively narrow range of time. 4 Similarly, Schäfer et al. ( 2017 ) show how the values of their fit parameters change over time, but also only for a narrow window. This decrease in distribution fit parameters emphasizes that care is needed when attempting to extract a single value for the power-law index or a single set of parameters that describes the mass distribution of planetesimals formed by the SI. The mass distribution is transient and should be expected to evolve indefinitely, albeit as a slowing rate, particularly when a larger simulation domain provides for more material as shown in the next section. 3.3 Total mass of dust in planetesimals and the onset of planetesimal formation Fig. 5 shows the total mass of the planetesimals in the simulations over time. As in Fig. 2 , the larger domain simulations are divided into smaller subdomains with the same area as the L02 runs. The L08 run shows the largest variance in these data. After t = 40Ω −1 , the spread in the total dust mass in planetesimals in any of the subdomains from the L08 run spans 5– of the total mass of dust in a single subdomain. The data from the L02 and L04 runs generally fit within the maximum-minimum bounds of the L08 run. Once again we note that simply re-running these simulations with a different random seed leads to significantly different consequences for planetesimals formation, shown here directly by the wide spread denoted by the red shaded region that is quite similar to the region-to-region variation in the larger domains. Figure 5. The total mass of the


4026, Si iv 4089, He i 4144, He ii 4200, He i 4387, He i 4471, He ii 4542, Si iii 4552, He ii 4686 and He i 4713. From the observed ratio values, we used the tabulated and graphical results of Martins ( 2018 ) to define spectral types and luminosity classes, as well as, if necessary, the associated qualifiers. When most of the measured ratios indicate the same result, the associated spectral type is then assigned to the star. However, when a satisfactory agreement is not obtained, the distinct types are then used as initial estimates, and a better tuning on the spectral type of the star is then obtained from the comparison of the observed spectrum with those of standards. Figure 1. Normalized blue-optical spectra (4000–4950 Å) of the newly identified O-stars in the LAMOST DR3. The main spectral features used in the blue-optical canonical spectral classification process are labelled. LS V +39 27 (O4 V), together with J20261845+4347472 (O5 III) and TYC 3339-851-1 (O5 V) are the earliest exemplars in our sample, which is complemented by several mid- to late-type O-stars. Figure 2. Normalized blue-optical spectra (4000–4950 Å) of the newly identified O-stars in the LAMOST DR3. The main spectral features used in the blue-optical canonical spectral classification process are labelled. LS V +39 27 (O4 V), together with J20261845+4347472 (O4 IV(f)) and TYC 3339-851-1 (O5 v ((f))) are the earliest exemplars in our sample, which is complemented by several mid- to late-type O-stars. 3.1 Spectral types and luminosity classes In order to obtain the EWs and full width at half-maximum (FWHM) of the spectral lines necessary for the spectral typing process, we followed standard procedures briefly described here. The line-profile parameters were measured using several spectroscopic analysis routines available in the iraf 2 splot package. For each spectral line, we performed model fittings using both Voigt and pure Gaussian profiles, with the associated continuum computed from regions far from the observed line wings (in general, several tens of angstroms from the estimated line centres), with the final uncertainty in the EW and FWHM values ranging from about 10 per cent for spectra with the highest S/N (usually above 300–350) to 15–20 per cent for the spectra presenting lower S/N values. Table 2 presents the EW values measured from all spectra of stars in Table 1 , for the following absorption lines: (i) eight He lines corresponding to the He i-ii λ4026, He i λ4121, He ii λ4200, He i λ4387, He i λ4471, He ii λ4542, He ii λ4686 and He ii λ4713 transitions; (ii) two Si lines corresponding (when present) to the Si iv λ4089 and Si iii λ4552 transitions. Table 2. Equivalent widths (Å) and associated errors of selected transition lines measured in the LAMOST DR3 O-star spectra. From inspection of Figs 1 and 2 , and from the measured parameters for the He ii lines, we can see that the earliest O-stars in our sample are stars 10, 24, 3, 8, 14 and 19. By following the


blue dots represent the brightness change during the outburst, while the green dots refer to the brightness outside of the outburst. 3. Discussions and Conclusions During the outburst of J162117, the spectral observations showed some properties of CVs, i.e., the broad, two-peaked emission lines (FWHM corresponding to 1500 km s −1 ), , and He ii 4686. These are indications of the accretion on a white dwarf (Scaringi et al. 2016 ). Moreover, the strong rotational disturbance of the emission lines in the eclipse indicates the presence of a rapidly rotating disk (Thorstensen 2016 ). Therefore, after ruling of the merging of a contact binary as an explanation of the outburst of J162117, this event was attributed to a dwarf nova outburst (Scaringi et al. 2016 ; Kjurkchieva et al. 2017 ). However, in comparison with known CVs, J162117 shows several peculiarities (Kjurkchieva et al. 2017 ), namely a deeper eclipse at the outburst than at the quiescence state (by a factor 2.8) and outburst amplitudes at the lowest limit of dwarf nova eruptions. These properties reveal that J162117 is not a normal CV. The binary system was monitored photometrically from 2016 April 19 to September 14, using several small telescopes in the world. We were lucky to obtain several high-precision light curves before the outburst. As shown in Figure 2 , there are two shoulders around the primary minima in the B - and V -band light curves. The two minima show a clear U-type shape and that their bottoms are nearly flat. The color curves plotted in the figure also show a U-type shape around the primary minima, while the color curves are flat outside the eclipses. All of these properties suggest that there are no accreting disks around the white dwarf and thus, the white dwarf is not accreting material from the cool secondary at the pre-outburst quiescent state. Apart from the eclipse of the white dwarf component, the BVR light curves shown in Figure 2 are dominated by ellipsoidal variability in a binary star as well as the magnetic activity of the K-type secondary. As displayed in Figure 2 , some small flare-like events are visible in the B -band light curves, while these events are not seen in the V and R band light curves. These are general properties of optical flares (e.g., Qian et al. 2012 ). Moreover, as shown in Table 1 , the errors of the B -band magnitudes for J162117 and the comparison star are about ±0.006, indicating that those B -band flares are true. The light curves in the figure are asymmetrical, displaying the O’Connell effect. Meanwhile, the depth of the secondary minimum (at phase 0.5) is deeper than that of the primary one (at phase 0.0). These observed properties could be explained by the secondary being covered by dark spots near the inner Lagrange point L 1 where the mass is expected to flow onto the primary. The fact that regions near the L 1 point are heavily spotted has been observed in the pre-CV V471 Tau and in a few CVs (e.g., Hussain et al. 2006 ;


3 arcmin, and a zoom-in of a 45 arcsec region for closer inspection. The generated image is reasonably convincing as an extragalactic deep field from the point of view of cursory visual inspection, although like many GAN-generated images, on closer inspection there are artefacts (such as low surface brightness features, pixelization, and discontinuities not seen in the real image) that betray the counterfeit. These artefacts are likely caused by a lack of resolution in the GAN generator, and could be remedied through the addition of more layers, or through the use of a larger convolutional kernel. Both of these approaches would increase the receptive field. The GAN also cannot reproduce some of the larger galaxies with the same level of detail as the real image. Nevertheless, the generated image does contains a mixture of early- and late-type galaxies amongst a more numerous field of background sources. The early and late types have the correct colour and morphology, i.e. classic red/elliptical and blue/spiral, respectively, and background sources have the clumpy and disturbed morphology typically seen in the high-redshift galaxy population. Fig. 3 presents single-band ( F 775 W ) thumbnail images of a sample of 100 randomly chosen sources with F 775 W AB magnitudes in the range 21–26 mag. 50 sources are selected from the real image and 50 are selected from the generated images, but the thumbnails have been randomly shuffled in the figure to demonstrate to the reader the visual similarity of individual galaxies in the generated and real data. Figure 2. Example of a generated deep field. The top left panel shows a generated deep field with the RGB channels corresponding to the F 814 W , F 775 W , and F 606 W bands. The size of the generated image was set to 3.2 arcmin, spanning the full XDF (top right), which has a 60 mas pixel −1 scale. The lower panels show 45 arcsec zoom-ins of the generated and real fields. Figure 3. Thumbnail images of real and generated ‘galaxies’. Each image is 7.2 arcsec across and shows the F 775 W channel on an identical linear grey-scale for 100 sources selected in the range 21–26 mag. 50 targets are selected from each of the real and generated catalogues and displayed in random order in row-wise ascending order of magnitude. To test whether the similarity between the generated and real image is more than superficial, we extract ‘galaxies’ from the generated images and compare to those in the real XDF. We use the source finder sextractor (Bertin Arnouts 1996 ) to detect galaxies in the combined F 606 W + F 775 W + F 814 W (pixelwise-mean) images, measuring the corresponding source flux in the individual bands. Sources are identified with the criteria that five contiguous pixels have a signal ≥5σ above the local background. The same detection procedure is applied to the real and generated images, and the photometric zero-points for the generated images are identical to the real data. Fig. 4 compares the magnitude


features and high brightness temperatures of the compact radio core component on pc scales (e.g. Lal, Shastri Gabuzda 2004 ; Giroletti Panessa 2009 ; Doi et al. 2013 , 2015 ). Generally, the X-ray emission in radio-quiet AGNs is believed to be produced in the hot corona by the inverse Compton scattering of the soft photons from the accretion disc (e.g. Haardt Maraschi 1991 , 1993 ; Liu et al. 2002 ), while the origin of the radio emission in the radio-quiet AGNs is still not fully understood, which is suggested to be from jets by some works although not fully proved (e.g. Czerny You 2016 ). It is shown that the study of the relation between the radio luminosity and X-ray luminosity is a very useful tool to investigate the coupling of the accretion and the jet (Merloni, Heinz di Matteo 2003 ). The radio/X-ray correlation has been investigated for different types of AGN, as well as black hole X-ray binaries (BHBs) in the low/hard spectral state (e.g. Merloni et al. 2003 ; Wang et al. 2006 ; Li et al. 2008 ; de Gasperin et al. 2011 ). It is found that in the low-luminosity AGNs (LLAGNs) and in the underluminous low/hard spectral state of BHBs (e.g. Körding, Falcke Corbel 2006 ), while this correlation becomes significantly steeper, i.e. , in the luminous AGNs and the luminous low/hard spectral state of BHBs (e.g. Corbel et al. 2004 ; Rushton et al. 2010 ; Dong, Wu Cao 2014 ). Some NLS1 have been included in previous studies of radio/X-ray correlation. However, as the number of the NLS1 in the sample is very small, their statistical properties are overwhelmed by other types of AGNs (e.g. Merloni et al. 2003 ; Dong et al. 2014 ; Panessa et al. 2015 ). Furthermore, the measurements of their radio luminosities could be severely contaminated by the host galaxies; e.g. if the resolution of the radio observation is not high enough, the star formation activities in their circumnuclear regions can have very strong contributions to the radio luminosity (e.g. Deo, Crenshaw Kraemer 2006 ; Ohta et al. 2007 ; Sani et al. 2010 ). Caccianiga et al. ( 2015 ) found that the star formation activities can contribute a significant fraction of radio emission even in some radio-loud NLS1. In order to reduce the contaminations from the host galaxy as much as possible, in this work we make use of radio fluxes within the central regions () of nearby radio-quiet NLS1 measured from high-resolution radio images to study their nuclear radio/X-ray relation, which was rarely studied before. This could help us understand the physics of the accretion and jet in high Eddington ratio regime. We also explore the mutual relation between the radio luminosity, X-ray luminosity, optical luminosity, and black hole mass. There are several works on the radio images of radio-loud NLS1 on kpc scales or even pc scales recently (e.g. Doi, Asada Nagai 2011 ; Doi et al. 2012 ; Gu et al. 2015 ). But we do not choose the radio-loud ones so as to avoid the relativistically beaming effects.


the combined energy range of 10 eV–6 keV. The lower energy corresponds to proton velocities of about 44 km s −1 . This means that pristine LISM neutral H atoms cannot be seen by IBEX unless it moves in the direction opposite to the LISM (Heerikhuisen Pogorelov 2011 ). The highest energy corresponds to velocities of about 1000 km s −1 . Bulk velocities of this magnitude are not observed during SW–LISM interaction, except perhaps in coronal mass ejections. However, thermal velocities of this order are possible beyond the TS. An interesting feature discovered by IBEX is the narrow region of enhanced ENA flux, which is now referred to as the IBEX ribbon. Before any explanation of this phenomenon was proposed, it was noticed that the directions toward the ribbon correlated with the line-of-sight directions perpendicular to the ISMF lines draping around the HP in the simulation of Pogorelov et al. ( 2009 ). One of the possible explanations of the ribbon flux was mentioned by McComas et al. ( 2009b ) and Schwadron et al. ( 2009 ), and described in more detail by Heerikhuisen et al. ( 2010 ). It is based on the assumption that PUIs born in the LISM region in front of the HP due to charge exchange of the neutral SW H atoms with interstellar ions, if injected with a pitch angle close to 90° to the draped ISMF direction, preserve their anisotropy long enough to produce ENAs propagating toward IBEX in the plane perpendicular to . This scenario is supported by numerical simulations, when anisotropy is assumed. We also note that the relative brightness of the ribbon is highest at energy ∼1.1 keV, which corresponds to the speed of slow SW of roughly 460 km s −1 . In this paper, we test the crucial assumption of this IBEX ribbon scenario, namely that the anisotropy of a realistic PUI distribution can be preserved long enough to experience another charge exchange. We use fully kinetic particle-in-cell (PIC) simulations to investigate the time evolution of the PUI distribution function in the outer heliosheath (outer) just outside of the HP. The initial distribution function is derived from the neutral H simulations performed by Heerikhuisen et al. ( 2016 ) and takes into account PUIs of the neutral SW and IHS. 2. PUIs in the Outer Heliosphere The ribbon mechanism developed by Heerikhuisen et al. ( 2010 ) requires that the PUI distribution function in the OHS preserves a certain degree of anisotropy for a sufficiently long time for a subsequent charge exchange to occur (∼2 yr for 1.1 keV H ions). This is not quite obvious because ring-beam distributions, typical for ions externally inserted into a background plasma, tend to scatter onto a shell distribution (Williams Zank 1994 ). Heerikhuisen et al. ( 2010 ) assumes that the ring-beam distribution is scattered onto a partial shell distribution depending on the injected pitch angle. In contrast, Chalov et al. ( 2010 ) neglects scattering, but appeals to magnetic mirroring effects that ensure spatial localization


( 2011 ) do show the formation of cores within 1 Myr. From Equations ( 31 ) and ( 32 ), is required for km at 5 AU in 10 MMSN. Figure 4 shows (or α for ), which can prepare the conditions for the formation of Jupiter given by –300 km at 5–6 AU in disks with . Saturn’s core forms in the disk after the formation of Jupiter. The gap opening by Jupiter assists the rapid growth of Saturn’s core at the outer edge of the gap, where the radial drift due to gas drag is negligible. The collisional fragments produced during core formation accelerate the growth of the core, and the supply of fragments produced in the outer disk induces further rapid growth. These effects allow the rapid formation of Saturn’s core within years after gap opening by Jupiter, and the rapid formation may explain the massive core of Saturn (Kobayashi et al. 2012 ). For the rapid growth of Saturn’s core in 10 MMSN, 100 km radius or smaller planetesimals are required, which is satisfied for ( for ) in the 10 MMSN disk (see Figure 6 ). This upper limit is similar to the condition for Jupiter. If Jupiter can be formed via other mechanisms in the MMSN disk, then kilometer sized or smaller planetesimals are required for the rapid formation of Saturn’s core, which corresponds to for . Figure 6. Turbulence strength or α , required for the formation of Mars, Jupiter, and Saturn for the MMSN (top panel) and 10 MMSN (bottom panel). The formation of the core required for Jupiter via core accretion is difficult to accomplish with the MMSN. The value of α is estimated under the assumption of . On the other hand, the formation age of Mars estimated from the amount of W isotope in the mantle is 2–4 Myr (Dauphas Pourmand 2011 ). For 10 MMSN (MMSN), the early formation of Mars may be explained by planetesimals with radii of km (5–30 km) (Kobayashi Dauphas 2013 ). The disk inside the snow line ( AU) has (Hayashi 1981 ). From Equations ( 31 ) and ( 32 ), the formation of Mars requires at 1 AU ( at 1.5 AU) in the 10 MMSN disk, while 10 −4 –10 −3 is suitable at 1–1.5 AU in the MMSN (see Figure 6 ). In addition, main-belt asteroids with radii smaller than 50–100 km have a slope of , which is similar to the outcome of collisional cascade (Bottke et al. 2005 ), while larger main-belt asteroids except for the largest bodies (Ceres, Vesta, and Pallas) have shallower slopes. The main-belt asteroids, except for the largest asteroids, have a peak of in the radius range of 50–100 km. The onset of runaway growth causes a similar shaped peak around the runaway radius (see Figures 1 and 5 ). Assuming that the radius of 50–100 km in the main belt corresponds to the planetesimal radius, at 2 AU ( at 3 AU) in the 10 MMSN and at 2 AU ( at 3 AU) in the MMSN. In Figure 6 , the constraints on the turbulence strength ( or α ) are summarized based on these considerations. Jupiter cannot be formed via planetesimal accretion in the MMSN; therefore, there is no hatched region for Jupiter in the MMSN. If the solar system


In contrast, for cycle 22, the south dominates over the north for small sunspots, but gradually the difference minimizes as we reach toward larger sunspots. Though, we must emphasize that there are cycles for which we do not see any large change in the two hemispheres for any sunspot size range. Cycles 16, 17, and 23 are examples of such cases. In order to quantify the asymmetry between the two hemispheres, we use the “north–south asymmetry index” ( A ns ) as ( S an - S as )/( S an + S as ), where S an and S as are the yearly averaged sunspot area values for the northern and the southern hemispheres, respectively. We plot the time variation of A ns for different sunspot sizes in different panels of Figure 4 . At a first glance, we notice that the variation of A ns is very smooth for the smallest sunspot sizes (Figure 4 (b)), as compared to any other size range (Figures 4 (c)–(f)). This can be understood from the definition of A ns , which varies between ±1, depending upon the presence of at least one single sunspot in any of the hemispheres and absence of any spot in the other hemisphere. Since the smaller sunspots occur more frequently at the time of solar minima compared to the appearance of a large sunspot, the variation of A ns is relatively smoother in the former case. We also notice (from Figure 4 (a)) that at the maximum phase of cycle 21, A ns , has values very close to zero as in the case of cycle 23. However, at the cycle 22 maximum, A ns attains a maximum value of ≈−0.5. This is consistent with the results as obtained by Javaraiah ( 2005 ). This scenario changes a little as we move from small to large sunspot sizes. There is a hint of long-term variation in the asymmetry index. For the largest-sized sunspots (Figure 4 (f)), the northern hemisphere dominates in the cycle minima until cycle 20, after which the southern hemisphere dominates. This trend is also visible in Figure 4 (e). Figure 4. Time evolution of the asymmetry index, A ns , for corresponding sunspot sizes. 3.3.1. Periodicities in the N–S Asymmetry Since the solar cycle has a dominant period of 11 years, it is expected that the N–S asymmetry index will also have some periodicity. There has been a lot of work done in order to probe this periodicity (Carbonell et al. 1993 ; Ballester et al. 2005 ; Chang 2009 ; Javaraiah 2015 ; Ravindra Javaraiah 2015 ). Here, we revisit the periodicity in the N–S asymmetry for different sunspot sizes. We use the A ns curves, shown in different panels in Figure 4 , and the wavelet analysis in order to obtain the periodicities in A ns . Results of the wavelet analysis on the different A ns curves is shown in Figure 5 . The global wavelet power (time-averaged power as shown in the “wavelet power spectrum panel”) is calculated along with a significance level of 90%. This significance level is obtained for the white noise (Torrence Compo 1998 ), and contours are overplotted on top of the wavelet spectrum in order to highlight the region


of reionization, then decreases during the late stage. When the IGM global neutral fraction drops below , on the small scales a positive cross-correlation appears. At this stage, most of the IGM has been ionized, while the neutral hydrogen in haloes starts to dominate the cross-power spectrum, producing the positive correlation seen in the small-scale power spectrum. As the remaining neutral islands in the IGM shrink and decrease in number, the halo H i come to dominate the fluctuations on larger and larger scales, as a result this positive-to-negative transition point on the cross-power spectrum moves to larger scales. Figure 4. The cross-power spectrum between the neutral fraction and the dark matter density. The solid and the dashed lines represent positive and negative values, respectively. The cross-power spectrum between the 21cm brightness temperature and the DM density are plotted in Fig. 5 . We use the two panels to show the early and late stages of reionization, respectively. We find that at the very beginning of reionization, the 21cm-DM cross-power spectrum is positive on all scales, implying that the neutral hydrogen density fluctuations still follow the DM density fluctuations, although some rare density peaks have been ionized. As more and more IGM around density peaks becomes ionized, the 21cm-DM cross-power spectrum decreases, and transits to negative starting from the largest scales. Then, the large-scale 21cm-DM cross-power becomes more and more negative. The amplitude reaches its maximum at around , and decreases again. Different from the f H i -DM cross-power, the 21cm-DM cross-power spectrum is always positive at small scales, indicating that when weighted with the local density, the small-scale 21 cm signal is always dominated by the H i in haloes. At the very late stage of reionization, the positive-to-negative transition scale increases rapidly. Figure 5. The 21 cm brightness temperature and the dark matter density cross-power spectrum. Top panel: early EoR; Bottom panel: late EoR. The solid and dashed lines represent the positive and negative values, respectively. In this plot, the 21cm-DM cross-power spectrum at z = 9.90 shows some oscillations, which are likely statistical fluctuations. To check this interpretation, we estimate the errors on cross-power spectra using the jackknife resampling method. In Fig. 5 , we plot the errors for the z = 9.90 and z = 9.00 curves. To avoid clutter, errors of other curves are not shown there. We see that indeed at z = 9.90 the error bars are larger than the oscillation feature on the power spectrum curve, so it is likely that these are just statistical fluctuations. We also check that at z = 9.00 the errors are comparable with the z = 9.90. However, at z = 9.00 the cross-power spectrum is much larger than z = 9.90. In logarithmic axes apparently its errors are less obvious than z = 9.90. We then turn to the individual contribution from the IGM and haloes to the 21cm power


light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The top panel shows the normalized real part of the wave frequency, and the bottom panel shows the normalized imaginary part of the wave frequency as functions of the normalized wavenumber k . The vertical lines in the bottom panel mark the positions of kd e = 1 for the given mass ratios. In Fig. 3 , we show the dispersion relations for the FM/W wave in quasi-parallel direction of propagation. This mode shows the typical quadratic whistler-mode behaviour at . The FM/W wave is dominated by electron dynamics unless kd i ≲ 1. With decreasing m i / m e , ω r /Ω i decreases while | γ |/Ω i increases. We attribute this behaviour to increasing cyclotron damping by electrons, which is, for the quasi-parallel FM/W wave, most efficient when n = −1 in equation ( 17 ). Thermal electrons with v ∥ ≈ − w e thus efficiently resonate with the quasi-parallel FM/W mode when in our normalization. In the electron–positron case with m i / m e = 1, a significant number of electrons resonate with the FM/W mode at ω r /Ω i = ω r /|Ω e | ≲ 1 and at kd i = kd e ≲ 1 (see fig. 2 by Gary Karimabadi 2009 ). Like in the case of the quasi-parallel A/IC wave, the resonant cut-off of the dispersion relation for ω r → |Ω e | is also present in the cold-plasma limit (Stix 1992 ). The quasi-parallel FM/W mode reaches the wavenumber range kd e ≥ 1 with | γ | ω r for all mass ratios shown in Fig. 3 . Figure 3. Dispersion relations of the FM/W wave in quasi-parallel propagation for different values of m i / m e . The light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The plot follows the same format as Fig. 2 . In Fig. 4 , we show the dispersion relations for the FM/W wave in quasi-perpendicular direction of propagation. The dispersion relation does not depend significantly on m i / m e for m i / m e ≳ 10. The quasi-perpendicular FM/W wave reaches the ion-Bernstein regime at ω r /Ω i ≈ 1. In the perpendicular limit ( θ → 90°), the susceptibilities for both ions and electrons include sums over all n of contributions that are each proportional to 1/( ω r − n Ω j ), leading to this resonant behaviour. As long as m i / m e ≫ 1, electron harmonics do not interfere with the ion harmonics since all contributions to decrease with increasing n . For m i / m e = 2, however, the second-order ion resonance makes a contribution to that is comparable with the first-order electron resonance. The quasi-perpendicular FM/W mode reaches the wavenumber range kd e ≥ 1 with | γ | ω r for all shown parameter combinations with m i / m e ≤ 125. Figure 4. Dispersion relations of the FM/W wave in quasi-perpendicular propagation for different values of m i / m e . The light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The plot follows the same format as Fig. 2 . 2.2 Dependence on light-to-Alfvén speed ratio We now investigate the dependence of the dispersion relation on c / v Ai . For this study, we fix the mass ratio at m i / m e = 100


and model-independent approach. To compare e red and l orb with the data, we follow the procedure of Forero-Romero etal. ( 2013 ), drawing contours in the e red l orb plane to identify those regions of the parameter space that are compatible with current observations. The contours are generated through 10 7 Monte Carlo (MC) iterations, where at each step the values of velocity, mass and distance are drawn from a Gaussian distribution within the intervals shown in Table 7 . The value of v rad was taken from van der Marel etal. ( 2012 ), r from van der Marel Guhathakurta ( 2008 ), while M MW and M M31 are consistent with van der Marel etal. ( 2012 ) and Boylan-Kolchin etal. ( 2013 ). Due to the large discrepancy existing among the and the MC was ran twice using the two different estimates. It turns out that the intervals generated with are extremely large and possess no constraining power, so that we do not consider them in the following analysis. Table 7. Values and intervals used to generate MC contours. M MW , M M31 are expressed in 10 12 h 1 M units, interhalo distance r in h 1 kpc while v rad and v tan in kms 1 . The intervals on r and v rad correspond to the 2 values of van der Marel etal. ( 2012 ), while for v tan they were chosen in agreement with (Sohn etal. 2012 ). In Fig. 2 , we bin the Mod1 objects in the e red l orb plane and compare them to the observational 95percent confidence intervals. The fraction of objects f LG that falls within those boundaries is shown in the last column of Table 8 . This quantity allows us to gauge the ability of a model to account for the observed global dynamics of the system disregarding its transient state. We note that the number for CDM varies between 0.15 and 0.19 which is consistent with Forero-Romero etal. ( 2013 ), who found a 0.08 to 0.12 fraction at the 68percent confidence interval. In the case of modified gravity cosmologies, the results largely confirm the conclusions obtained with the previous analyses of velocities. In fact, models such as FofR04, FofR05, SymmB and to a lesser extent FofR06 produce LG-like pairs within the observational boundaries at substantially lower rates than CDM. In particular, the fraction of Mod1 LGs falling within the 95percent confidence level is reduced by a factor of 3 in SymmB and around a factor of 2 in FofR04 and FofR05, showing from another perspective that the LG dynamics can only be poorly accounted for within these models. These discrepancies are explained by the increased velocity of M31, affecting the values of e red [through the kinetic energy term in equation ( 30 ) and l orb , which tend to shift the distribution farther away from the region allowed by the data]. Figure 2. LG-like pairs versus MC contours showing the 1 and 2 confidence levels. Pairs have been chosen and MC intervals have been generated using the low v tan estimate of Sohn etal. ( 2012 ). Table 8. Energy, angular momentum, spin parameter and fraction of Mod1 pairs falling within


changing from the inner to the outer an MC based on the fitting results. There is a roughly increasing trend of the tangential velocity away from the axis of the MC that continues in the ambient solar wind. However, this increase is not strictly monotonous, which may be attributed to fluctuations. 3. Possible Dependence of the Viscosity on Solar Wind Parameters 3.1. Data and Method The above analysis has shown some viscosity signature from a rough statistic. Here we study the role of viscosity further through detailed investigation of the change of the tangential velocity crossing the MC boundaries. By manually checking the change of the 1 minute averaged tangential velocity profile near the front/rear boundaries of the MCs, we further narrow down the sample by selecting the crossings during which the tangential velocity clearly increases from the inner to the outer the MC. Finally, nine crossings that we think represent the picture fairly well in Figure 1 are selected and shown in Figure 3 . A few data points indicated by the red symbols in Figures 3 (a), (b), and (d) are discarded in the following analysis because they deviate significantly away from the main trend of the crossings due to inevitable fluctuations. Figure 3. Change of the tangential velocities with time. Panels (a)–(d) show the change of the tangential velocities at the front boundary of the MC, and (e)–(i) at the rear boundary. The verticle solid line indicates the boundary of the MC. The ordinate axis is the tangential velocity, where the positive value means the anti-clockwise rotation and the negative value means the clockwise rotation. It is not clear how to obtain the viscous coefficient in the solar wind. Alternatively, we use the following formula to roughly assess the strength of the viscosity between the ambient solar wind and MC plasmain which is assumed to be a function of the viscous coefficient , and and are averaged tangential speeds in MC and solar wind, respectively. The formula follows the idea that if there is no viscosity should approach zero as well as , and if there is a strong viscosity should be equal to , leading to be infinitely large. Considering that there is more or less uncertainty in determining the boundary of an MC, we calculate the values of and based on the measurements within one and a half hours next to the boundary with the nearest half an hour ignored. The uncertainty in is propagated from the uncertainties in the averaged tangential velocities and . The averaged solar wind parameters, e.g., density, temperature, and turbulence intensity of the magnetic field, inside and outside of the boundary are also calculated within the same intervals to investigate the possible dependence of the strength of the viscosity between the ambient solar wind and MC plasma. 3.2. Results The scatter plots between and solar wind parameters inside and outside of the MC are shown in Figure 4 . The turbulence intensity of the magnetic field is estimated based on


the following, we summarize the procedures used in this paper to simulate the auroral radio emission arising from a stellar magnetosphere shaped like a non-central dipole. To calculate the magnetic-field vector generated by an offset dipole, the magnetic-dipole moment is located in a generic grid point ( O ) within the star, identified by its spatial coordinates ( x , y , z ) in the native reference frame Oxyz , where the origin O coincides with the centre of the star, the z -axis is parallel or coincident with the dipole axis, and the x -axis lies into the plane parallel to the z -axis and containing the rotation axis. In the reference frame anchored with the offset dipole, the new coordinates ( X , Y , Z ) of the grid points are defined by the simple coordinates translation ( x x , y y , z z ). In the translated O XYZ reference frame, the Z -axis coincides with the dipole axis and the X -axis is located in the plane passing through the Z -axis and parallel to (or containing) the rotation axis. The corresponding magnitude of the magnetic-dipole moment is defined as follows: where r Z is the distance of the offset dipole from the stellar surface along the direction parallel to Z -axis, and B p is the polar magnetic-field strength, that was fixed equal to 3000G. The three components ( B X , B Y , B Z ) of the magnetic-field vector are calculated in each grid point taking into account the non-central position of the magnetic-dipole moment. In the new reference frame O XYZ , the magnetic vector components are easily calculated using the equations of the simple dipole (see appendix A.2 of Trigilio etal. 2004 ). The magnetic vectorial field is then rotated in the observer reference frame Ox y z , where the origin O coincides with the centre of the star, the x -axis is parallel to the line of sight, and the plane y z coincides with the plane of the sky. The method was described in appendix A.3 of Trigilio etal. ( 2004 ). In the reference frame ( O XYZ ) anchored with the offset dipole, it is also possible to locate the grid points falling inside the auroral cavity using the equation of the dipolar magnetic-field lines, defined by using the equation r L cos 2 , where r is the distance of the grid points to the origin O (where is located). Following the method described in Paper I , it is then possible to find those grid points that radiate auroral radio emission within a beam pattern that intercepts the line of sight and that are tuned at the assigned simulation radio frequency . To take into account the non-central position of the magnetic-dipole moment ( O O ), the distance to the centre of the star from the grid points that are able to radiate detectable auroral radio emission has to be larger than the stellar radius. The star shadowing effect has also been taken into account. APPENDIX B: OFFSET DIPOLE: SIMULATIONS The simulations of the auroral radio-emission visibility from a non-central dipolar field were performed assuming the model parameters


assumed to be single Gaussians, using photographic density , and solving for , and c from these lines. Then, I was solved at neighboring wavelengths for the Fe x transitions. This procedure slightly reduced the lower intensity values at the base of the lines, without changing the results significantly. We do not know widths of Fe x lines that are unblended, nor do we know the precise wavelength of Fe x lines on the wavelength scale above. Therefore, the unresolved FS can only be derived as an upper limit by comparing the observed data with the two lines, estimating for the FS splitting itself (or by a least-squares optimization outlined below). In making these comparisons, we adopted the optically thin ratio of 2.09 for the two lines from CHIANTI (Young et al. 2016 ). Some typical profiles are illustrated in Figure 3 . Figure 3. Observed profiles and fits are shown for a specified line width of 0.23 Å, of the 1603.2 Å region of the S082B data obtained above the solar limb. The solid line shows the S082B data, the dotted lines show the two components of the Fe x transitions in their optically thin ratio, and the dotted–dashed lines show the total modeled emission for the given FS splitting. The panel labeled “4 cm −1 ” shows an acceptable by-eye fit, yielding an FS splitting close to 4 cm −1 . The other panels show the fits, with residuals at least 10 times higher, for splitting values of 1, 7, and 10 cm −1 . For values of FS splitting near and below the line width ( cm −1 ) there is some redundancy between FS splitting and line width. The figure shows observed profiles over-plotted with models with a given (1/ e ) width of 0.23 Å (taken from the optimization calculation below) for four values of the FS splitting. The figure suggests an FS splitting value of , certainly cm −1 . The variances, sum of model minus data squared evaluated over the fit to a 1 Å wide band centered at the line, are 2.5, 3, and 9 times the optimal value for 1, 7, and 10 cm −1 respectively. A trade-off exists between line width and FS splitting: the larger the width, the lower the splitting needed to fit the same data. Therefore, we can place only an upper limit on the FS splitting from this analysis of cm −1 . However, we can go a step further. While the data are photographic and subject to nonlinearities in photographic density versus intensity, we nevertheless performed a formal analysis of variances by fitting the two lines and varying the strong line's wavelength, line widths and the FS splitting. Both lines were given the same width and the ratio of the intensities was fixed at 2.09. The pikaia genetic algorithm was used (Charbonneau 1995 ). Figure 4 shows the surface as a function of width and FS splitting. We adopted a constant value for the observational error across the line profiles for the calculation, because the photographic densities lie on top of a large pedestal (equivalent to a dark current). We multiplied the errors by Gaussian functions centered near


were mainly from the NEOWISE database ( Mainzer et al. 2011 ) with some values taken also from Akari ( Usui et al. 2011 ) and IRAS ( Tedesco et al. 2004 ) catalogs. 4.1. Pole latitude versus size The distribution of the pole latitude β for main-belt asteroids as a function of asteroid size is shown in Fig. 4 . The distribution is strongly bimodal for asteroids smaller than 20–30 km, which can be satisfactorily explained as an effect of a YORP-driven evolution ( Hanuš et al. 2011 , 2013b ). Due to the YORP effect, small asteroids evolve towards the extreme values of obliquity. In the lower panel of Fig. 4 , we show the fraction N p / N total of the number of prograde ( β > 0) rotators in a running box over N total = 100 asteroids as a function of size. For asteroids larger than 100 km, the number of prograde rotators is statistically higher ( N p = 68, N total = 108, probability of the null hypothesis that N p = N total /2 is p ≃ 0.7% assuming binomial distribution) in accordance with the model of Johansen Lacerda (2010) who suggested that the preferentially prograde rotation of large asteroids is a result of accretion of pebbles on planetesimals in a gaseous environment. On the other hand, for asteroids in the size range 1–10 km, there is an excess of retrograde rotators ( N p = 520, N total = 1276, p ≃ 2 × 10 −11 ). For asteroids between 10 and 100 km, the number of prograde and retrograde rotators is statistically the same ( N p = 441, N total = 919, p ≃ 22%). Because most asteroids smaller than about 30 km have large absolute values of β , the prograde/retrograde analysis is not sensitive to asteroids with | β | 30°. The ratio is almost the same even if we restrict ourselves to | β | > 30° where the distinction between prograde and retrograde rotation is unambiguous even for nonzero inclination. This is not true for asteroids larger than 100 km, where for | β | > 30° we have N p = 34, N total = 55, and p ≃ 8%. Fig. 4. The distribution of pole latitudes β for all full and partial models of main-belt asteroids. The bottom panel shows the running-box (over 100 asteroids) fraction of prograde ( β > 0 deg) models (red curve) and also the fraction of models with β > 30 deg (green curve). The dashed and dotted lines show the 5% and 1% significance levels at which the null hypothesis that the prograde and retrograde asteroids are equally frequent can be rejected. The excess of small retrograde rotators in Fig. 4 is statistically significant, however, it is not clear if the reconstructed distribution of β is the same as the real one. Although we are not aware of any bias in the observations or the method that could cause the asymmetry in ± β , there could still be some nontrivial systematic effect that we have not taken into account. 4.2. Pole latitude distribution across the main belt The distribution of pole latitude β is not only dependent on the size, but also on the proper semimajor axis, namely on the proximity to resonances. For asteroids in


This is due not to continual acceleration, but instead to previously higher velocities and higher mass loss rates earlier in the model’s evolution. In Figure 4 , we show the linear (left-hand plot) and logarithmic (right-hand plot) temporal evolution of our main fiducial model as well as fiducial models with different WD and envelope masses. Black, red, and green lines represent core + envelope masses of , , and , respectively. In each plot, the top panel shows the evolution of the total luminosity, which is the sum of the luminosity at an optical depth of and the power from positron kinetic energy released by decays above the photosphere. We assume the positrons are able to thermalize and deposit their energy locally while the gamma-rays emitted during the and decays escape the wind and the surrounding SN ejecta. In practice, however, the positron kinetic energy in the optically thin region is smaller than the luminosity at the photosphere, so this contribution is not significant. Note that the luminosity from the SN Ia ejecta is not included. For comparison, the dotted line in the top panels represents the total power from radioactive decays of of initially pure under “lab” conditions. Figure 4. Evolution of winds launched from post-SN Ia surviving WD donors with envelope masses determined by the maximum bound ejecta mass. Three different models are shown, with core + envelope masses of (black), (red), and (green). The left-hand and right-hand plots use linear and logarithmic time axes, respectively. The top panel in each plot shows the sum of the luminosity at the photosphere and the luminosity from thermalization of positron kinetic energy from decays above the photosphere. The dotted line represents the total power from radioactive decays of of initially pure under “lab” conditions. Note that the luminosity from the SN Ia ejecta is not included. The middle panels track the effective temperature at the location. The bottom panels show the velocity at the photosphere (solid) and the mass-averaged velocity of material above the photosphere (dashed). The effective temperature, derived from the luminosity and radius at the surface, is shown in the middle panels. The velocity at the location is shown as a solid line in the bottom panels, and the mass-averaged velocity in the optically thin region is shown as a dashed line. The observed quasi-bolometric late-time light curve of the best observed SN Ia to date, SN 2011fe, is shown as bullets (Nugent et al. 2011 ; Tsvetkov et al. 2013 ; Kerzendorf et al. 2014 ; Shappee et al. 2016 ). The late-time flattening of SN 2011fe and other SNe Ia above simple predictions for decay within the SN ejecta has been attributed to light echoes and the decay of long-lived radioactive isotopes such as 57 Co and 55 Fe (Seitenzahl et al. 2009 ; Röpke et al. 2012 ; Kerzendorf et al. 2014 ; Graur et al. 2016 ; Shappee et al. 2016 ). Our models represent an additional contribution to the total luminosity, and


et al. 2018 ). In the X-ray, events up to 10 32 erg (10 32.7 erg bolometric) have been detected (Güdel et al. 2004 ). The Microvariability and Oscillation of Stars ( MOST ) satellite (Walker et al. 2003 ) performed the most comprehensive previous measurement of the Proxima flare rate. MOST observed Proxima for 37.6 days, observing 66 white-light flare events, the largest of which was 10 31.5 erg in the MOST bandpass (∼4500–7500 Å). No superflares were observed; extrapolating the cumulative flare frequency distribution (FFD) obtained by Davenport et al. ( 2016 ) from the MOST flare sample out by 1.5 dex predicts that ∼8 × 10 33+ erg events in the MOST bandpass occur per year. To search for superflares and other short-timescale phenomena, the Evryscope (Law et al. 2015 ) is performing long-term high-cadence monitoring of Proxima, along with every other bright star in the Southern sky. In 2016 March the Evryscope detected the first-known Proxima superflare. Although no M-dwarfs are usually visible to the naked eye (e.g., Shields et al. 2016 ), Proxima briefly became at least a magnitude-6.8 star during this superflare, at the limit of visibility to dark-site naked-eye observers. 2. Evryscope Flare Discovery and Observations We discovered the Proxima superflare as part of the Evryscope survey of all bright southern stars. The Evryscope is an array of small telescopes simultaneously imaging 8000 square degrees of the sky every two minutes (Law et al. 2015 ). The Evryscope observes essentially the entire Southern sky above an airmass of two, at two-minute cadence in g ′ and at a resolution of 13′′ pixel −1 . The system has a typical dark-sky limiting magnitude of g ′ = 16 and tracks the sky for 2 hr at a time before ratcheting back and continuing observations, for an average of ∼6 hr of continuous monitoring each night on each part of the sky. The Evryscope image archive contains 2.5 million raw images, which is ∼350TB of data. A custom pipeline analyzes the Evryscope data set at realtime rates (Law et al. 2016 ). Each image, consisting of a 30 MPix FITS file from one camera, is calibrated using a custom wide-field solver. After careful background modeling and subtraction, forced-aperture photometry is extracted based on known source positions in a reference catalog. Light curves are then generated for approximately 15 million sources across the Southern sky by differential photometry in small sky regions using carefully selected reference stars and a range of apertures; residual systematics are removed using two iterations of the SysRem detrending algorithm (Tamuz et al. 2005 ). In extremely crowded fields, such as for Proxima (−2° galactic latitude), we re-run the pipeline for particular targets, optimizing the aperture sizes to avoid nearby stars. As a very large event, the Proxima Superflare was discovered in routine by-eye checks of interesting targets in the Evryscope data set. Smaller flares are discovered and characterized with an automated