Liao et al. 2015 ; Bonvin et al. 2017 ). Similarly, the ongoing public time-delay lens-modelling challenge (TDLMC; Ding et al. 2018 ) aims to test the accuracy of lens imaging modelling algorithms based on different source reconstruction techniques (e.g. Warren Dye 2003 ; Koopmans 2005 ; Vegetti Koopmans 2009 ; Oguri 2010 ; Birrer, Amara Refregier 2015 ; Nightingale Dye 2015 ). Additionally, the TDLMC may shed light on how critical the mass-sheet transformation (MST), a special case of source-position transformation, is (Falco, Gorenstein Shapiro 1985 ; Schneider Sluse 2013 , 2014 ; Xu et al. 2016 ; Birrer et al. 2017 ). All in all, the goal of the TDLMC is to understand how well we can control the systematic effects on σ κ . In addition, Birrer et al. ( 2015 ) used mock data to study whether we can use lens imaging to detect small perturbations on σ κ , while Chen et al. ( 2016 ) used mock data to study the impact of the unstable point spread function on σ κ when using adaptive optics imaging to study H 0 . However, it is difficult for mock data set challenges to reveal the systematics caused by unknown physical phenomena because the mock data only include known processes. The second method to assess systematic effects is to study physical processes that have not been previously considered. For example, Tie Kochanek ( 2018 ; hereafter TK18 ) have questioned the use of measured time delays in cosmography, by showing that, under the assumption of the ‘lamp-post’ model for accretion discs and differential magnification of the disc stars in the lensing galaxy (i.e. microlensing; Wambsganss 2006 ), the measured time delays may introduce a bias in the inferred value of H 0 . Under this assumed disc model, regions of the accretion disc that are separated by distances of the order of of light days vary in a coherent manner in response to activity in the centre of the disc. Differential magnification of portions of such a disc can introduce a phase delay due to the distance from the centre of the disc, and can shift the time-delay light curves by up to days depending on the accretion disk configuration and the microlensing pattern (see more description in Section 2 ). Since each lensed image has a different microlensing pattern, the sum of this proposed microlensing time-delay effect for any pair of lensed images can be non-zero. Therefore, the time delays we measure are not only the cosmological time delays but a combination of cosmological time delays and microlensing time delays, This effect, under certain assumptions, can significantly broaden the uncertainty on time-delay measurements, since it is embedded in the time-delay light curves (see fig. 10 in TK18 ). Although long-term monitoring can partially average out and mitigate this microlensing effect on time delays, the non-zero mean cannot be removed (see table 2 in TK18 ). Thus, TK18 have claimed that the current uncertainty of H 0 measurements from TDSL could potentially be underestimated

B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Event I-Event I-Event I-Event B-Event B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O B-Event O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Event O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O B-Citation O O O O O O O O O O O B-EntityOfFutureInterest O O O O


et al. ( 2012 ) applied the one-dimensional scan observation at two different frequency channels, and estimated that the temporal change of plasma density contributed 4 GHz and 6 GHz to the frequency drifts in two microwave type III bursts, respectively. However, in our work we found that most microwave type III pairs have frequency drifts 4 GHz . Only 3 among the 11 events have absolute frequency drifts >4 GHz ; see in Table 1 . Actually, in the framework of the PE mechanism the separate frequency ( f x ) reflects the plasma density in the flare energy release site, and the temporal variation of f x may reveal the plasma density change during the microwave type III burst pair train. Table 1 lists the temporal change of separate frequencies, and most of them are very slow, even close to zero. Among the 11 type III pair events, the maximum occurred in the event on 2006 December 13, which is about 10 MHz s −1 , and s −1 . Then s −1 . The observation shows that the relative frequency drift () is from 0.3 s −1 to 5.3 s −1 , which is three orders bigger than that caused by the plasma density temporal variation. It seems that the plasma density temporal variation does not contribute to the formation of frequency drift in type III pairs as much as in microwave type III bursts reported by Altyntsev et al. ( 2007 ) and Meshalkina et al. ( 2012 ). The plasma density gradient dominates the frequency drifts of type III pairs. Therefore, we have the relations and . With these approximations, the velocity can be expressed as The frequency gap () between the normal and RS branches is seldom mentioned in the previous literature. This work shows that the observed results of are ranging from 10 MHz to 1700 MHz, and are different from event to event. Then, what factors do dominate the frequency gap? Li et al. ( 2011 ) simulated the generation and propagation of type III bursts based on the assumption of a power-law model (PL; Allen 1947 ) and offset power-law model (OPL; Aschwanden Benz 1995 ), respectively. They find that frequency gaps may be very large ( MHz) when electron beams propagate in offset power law plasma, and relatively small ( MHz) in power law plasma. It seems that the frequency gap may be related to the distribution of plasma density. According to the PE mechanism, the frequency gap means a density difference between the start sites of normal and RS type III bursts. With a density scale length H n , a space length can be derived: L c can be regarded as an estimation of the length of acceleration regions. The electrons are accelerated in this region and get a relatively high energy, then trigger microwave type III bursts outside this region. It is possible that L c is only an upper limit of the acceleration region. Panel (4) of Figure 5 show that the frequency gap has no dependence on the separate frequency. This fact implies that the length of the acceleration region is possibly irrelevant to the plasma density. It is possible that the

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


Cyan and brown lines represent MI and MG, respectively, with v ∞ ≃ v flat = v tot ( r cut ), where r cut denotes the radii at which the integrals are cut. The inset is a magnification of N range = [0, 10]. Right panel : Δ Q MI − Δ Q MG as a function of radial range. The error bars are smaller than the points. From the left panel of Fig. 3 it is clear that MI and MG drift similarly as the range is decreased. As long as the drifts of MI and MG are approximately equal, the measured Q can be corrected similarly to the case of the acceleration scale in the previous section. The right panel of Fig. 3 shows Δ Q MI − Δ Q MG in the context of varying range. |Δ Q MI − Δ Q MG |≲0.01 ≃ const for N range ≳ 3, meaning that the measured Q can be corrected with Δ Q (range) = Δ Q MI ≃ Δ Q MG for galaxies which fulfill max[ r ] ≳ 3 r d . Table 2 lists Δ Q (range) for different ranges. The approach to the theoretical limit for increasing range is slow for the Kuzmin disk. For this reason Δ Q (range) = 0 is only reached for N range > 55 in this case. The corrections in Table 2 isolate the range effect from the acceleration effect. To mimick the observational situation, however, we have repeated the same exercise considering galaxies with max( g obs ) 0.15 a 0 , applying the corrections in Table 1 . We find that the corresponding corrections due to N range are very similar to those given in Table 2 . Table 2. Range corrections. Notes. The uncertainty on Δ Q (range) is negligible. 2.3. Sampling resolution In order to gauge the effect of the spatial resolution of the observations, Q is calculated as a function of the spacing between sampled points in units of r d . The sampling for each galaxy is performed in the range r j ∈ [0.01, 200] r d . In order to compute Q from a discrete set of points, the integral of Eq. ( 2 ) is discretized viz with where v f ≃ v ∞ being the asymptotically flat velocity which is determined as the arithmetic mean between the chain of points that are within 5% of the arithmetic mean of the two outermost points (similarly to Lelli et al. 2016 ). If the third outermost point is not within 5% of the arithmetic mean of the two outermost points, the galaxy is not assigned an asymptotically flat velocity. The left panel of Fig. 4 shows the arithmetic mean of Q calculated via Eq. ( 7 ) – as predicted by MI (black) and MG (blue) – of the mock data for which max( g obs )≤0.01 a 0 as a function of the spacing between the sampled points in units of r d . As expected, Q approaches the theoretical value for extremely small spacings ( r 0.1 r d ) and progressively increases for larger spacing between the sampled points. Fig. 4. Left panel : arithmetic mean of Q for all mock galaxies with max[ g obs ]≤0.01 a 0 as a function of spacing between sampled points. Black and blue lines represent MI and MG, respectively. Right panel : Δ Q MI − Δ Q MG as a function of spacing between sampled points. From the right panel of Fig. 4 it is clear that the increase for

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


Collaboration XXVII 2016 , ESZ, PSZ1, PSZ2, respectively) and ACT ( Hasselfield et al. 2013 ; Hilton et al. 2018 ) surveys. A total of 119 clusters are detected within the ACT footprint by either instrument. Here we focus on the 34 joint detections. We exclude three sources partially covered at the edges of ACT footprint or falling into the mask of Planck point sources (used to construct the PACT y -map). Our final sample is thus comprised of 31 clusters of galaxies, hereafter referred as PACT31, with 18 sources distributed in the equatorial strip and 13 in the southern one. By construction our sample is neither representative nor complete. The clusters range between 0.16 and 0.70 in redshift and from 3.7 × 10 14 to 1.3 × 10 15 M ⊙ in M 500 , where M 500 is the total mass contained within R 500 . The mean signal-to-noise ratio (S/N) of the sample is 6.0 in the Planck catalogues and 6.3 in ACT’s. The range of angular size over the sky is 2.5 θ 500 7.9 arcmin, with a mean value of 4.2 ± 1.1 arcmin. We also consider the sample of 62 massive local clusters used in Planck Collaboration Int. V (2013 , P13 hereafter) to derive the pressure profile of the hot intra-cluster gas from the first Planck all-sky survey. Here the Planck maps used to derive the y -map (see above) are those from the all-sky survey (i.e., 2015 data release Planck Collaboration VIII 2016 ). We therefore use this sample, hereafter PLCK62, in order to compare to the profiles derived from our PACT map (see Sect. 4 ). From the second Planck catalogue, PSZ2, the redshift of the PLCK62 sample ranges between 0.04 to 0.44 and the S/N from 7 to 49. The covered mass interval is 2.4 × 10 14 M 500 2.0 × 10 15 M ⊙ , for an angular size one of 3.7 θ 500 22.8 arcmin with a mean value of 9.8 ± 5.4 arcmin. Masses for the PLCK62 sample are M 500 hydrostatic masses from P13, derived from the XMM-Newton observations. For the PACT31 sample, we make use of the M 500 values provided in the PSZ2 catalogue. The latest are derived from an Y 500 − M 500 relation calibrated with Planck SZ integrated fluxes and XMM-Newton hydrostatic masses ( Planck Collaboration XX 2014 ; Planck Collaboration XXIV 2016 ). We checked the consistency between the P13 hydrostatic mass and the PSZ2 masses for the PLCK62 sample, finding a mean ratio of 0.98 ± 0.11. We provide, in Fig. 1 , the distribution of the two samples in the M 500 − z , M 500 − θ 500 and θ 500 − z plans. Fig. 1. Distribution of the PACT31 (red dots) and PLCK62 (blue dots) in the M 500 − z(left) , M 500 − θ 500 (middle) and θ 500 − z(right) . Crosses picture the median value and associated maximum absolute deviation over each sample. Values for the redshift, masses and angular radii are taken from the PSZ2 catalogue ( Planck Collaboration XXVII 2016 ). 3. Computation of the y and pressure profile To recover the pressure profiles from the SZ y -map, we strictly followed the method described and used by P13. The SZ flux is the product of the SZ spectrum

B-Citation I-Citation I-Citation O B-Dataset B-Dataset B-Dataset O O B-Survey O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O B-Telescope O O O O O O B-Instrument O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Telescope O O O O B-Telescope O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Dataset O O O O O O O O O O B-Instrument O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O B-Citation O O O B-Telescope O O O B-Dataset O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O B-Telescope O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation O O O O B-Dataset O O O B-Dataset O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O


0.6–2.1, corresponding to E ( B − V ) = 0.2 to 0.7. However, the dust maps of Green et al. ( 2015 ) and Lallement et al. ( 2019 ) show E ( B – V ) increasing gradually up to 0.1–0.2 at a distance of 1 kpc and remaining flat at larger distances in the direction of G70.0–21.5. The probable explanation is that Boumis et al. ( 2002 ) assumed the recombination value of about 3 for the Balmer decrement, while collisional excitation produces ratios of 5 to 3.7 for temperatures of 20,000–40,000 K (CHIANTI; Del Zanna et al. 2015 ). Thus, for the temperatures estimated in Table 2 , E ( B – V ) could be overestimated by around 0.4–0.5. Variations in the collisional contribution to the Balmer lines would produce variation in the [N ii ] to H α ratios seen in Table 2 . A complication is that the Hectochelle fibers do not cover the entire postshock cooling region. The 15 in fiber diameter corresponds to about 2.2 × 10 16 cm at a distance of 1 kpc. If the ambient density is on the order of 0.2 cm −3 , as in the NW Balmer line filaments of the halo SNR SN 1006 (Ghavamian et al. 2002 ; Bandiera et al. 2019 ), the cooling distance can be larger than the fiber diameter, though the narrow ionization and cooling zone behind the shock would still fit within a fiber. It is probable that the sharp H α filaments seen in the MDM images are just the high-emissivity region just behind the shock, and a fainter, cooler, more diffuse region trails behind. That could account for some of the variation in the strengths of the [O i ], [N ii ], and [S ii ] lines relative to H α in Figure 7 of Fesen et al. ( 2015 ) and Table 3 of Boumis et al. ( 2002 ). To further investigate the line ratios, we ran models with the code described by Raymond ( 1979 ) and Cox Raymond ( 1985 ). We assume a preshock density of 0.1 cm −3 and a magnetic field of 0.5 μ G, and we consider a range of shock speeds from 50 to 90 km s −1 and preshock neutral fractions from 0.05 to 0.6. The density choice is based on the height in the Galactic halo, and the magnetic field has little effect on the postshock region where the strong lines are produced. The preshock neutral fraction is determined not only by the overall Galactic ionizing UV background, but also by the SNR itself. Cox ( 1972a ) showed that an SNR emits a strong burst of ionizing radiation when it enters the shell formation stage, and the recombination time is longer than the SNR evolution timescale. Thus, the preshock gas will be overionized in the case of G70.0–21.5. We truncate the models at distances corresponding to 125. The density could be higher, however, and that makes the cooling region proportionally thinner, so we also consider models truncated at 25 and 50, which correspond to preshock densities of 0.2 and 0.4 cm −3 . In general, a fairly wide range of parameters can match the observed ratio of [N ii ] to H α . However, we reject shock speeds below 60 km s −1 because they predict line widths smaller than we observe. We find that the

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


from the synchrotron emission by accelerated electrons but instead from a thermal process; the low-energy photon index would then relate to the spectral slope in the Rayleigh–Jeans regime of the blackbody component ( α = +1). 5.2. Coarse Time-resolved Spectral Analysis In this section, we describe the spectral evolution with time for the defined time intervals. Values from all fits are shown in Table 1 . As described below, strong spectral evolution is seen in the prompt phase. In the first time interval a , the Band function or a power-law function with exponential cutoff (CUTPL) provides a good fit to the data and there is no statistical difference between Band and CUTPL. This is also consistent with the fact that in the case of fitting the Band function alone the high-energy photon index β is very low ( β −3). Furthermore, when we adopt CUTPL to represent the obtained spectrum there is no need for any additional spectral component, as there is no statistical improvement by adding an extra component such as the blackbody or a power-law function (ΔPGstat ∼ 1) as shown in Table 1 . In the second and third time intervals, b and c , if we choose only the Band function, we find the same residuals as obtained in Section 5.1 (e.g., the low-energy bump). We see that the best-fit model is Band+PL and there is clear statistical improvement with respect to the case of the Band function alone (ΔPGstat = 86 and 157 in intervals b and c , respectively). Compared with the spectrum in the initial interval, the Band component low-energy index becomes harder. Interestingly, in these intervals the obtained low-energy photon indices are too large ( α = +0.2 to +0.4) to be explained by non-thermal synchrotron emission as described in Section 5.1 . Together with the small high-energy photon indices ( β ≤ −3), this indicates a narrow spectral component originating in thermal emission from the photosphere. From the theoretical point of view, Beloborodov ( 2010 ) pointed out that synchrotron emission and temporal variability lead to a softer spectrum ( α = +0.4) than the Rayleigh–Jeans index ( α = +1). In addition, a relativistically expanding conical jet structure implies a dispersion in the Doppler factor, which can broaden the photon spectrum (Asano Mészáros 2013 ). Here, we choose the diskpbb model implemented in XSPEC as a modified blackbody model to reproduce the thermal photospheric emission. The diskpbb model represents a multi-temperature blackbody spectrum where the local disk temperature T ( r ) at a distance r from a compact object is proportional to . While this model describes optically thick radiation from a geometrically thin accretion disk, we introduce this model phenomenologically to reproduce our modified blackbody spectrum. If we adopt this model, the photon index in the Rayleigh–Jeans range is represented as 2–2/ p and the diskpbb model can obtain a broader spectrum than a pure blackbody. The diskpbb model plus the power-law function,

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Recent studies have focused on searching for fast radio bursts at GHz frequencies in the first few minutes of a GRB, associated with the plateau phases (Bannister et al. 2012 ), or a deeper search, ∼ Jy sensitivity, for prompt (minute to hours) radio emission from short GRBs (Kaplan et al. 2016 ; Anderson et al. 2018b ). This was followed by a catalogue of 1 d follow-up observations at 15.7 GHz with the Arcminute Microkelvin Imager which increased the number of radio detections of short and long GRBs (Staley et al. 2013 ; Anderson et al. 2018a ). The new detections spanned 0.3–33 d post-burst, meaning that coverage during the prompt emission itself remains largely unexplored. Recently, a rapid response mode was implemented for the LOw Frequency ARray (LOFAR; Van Haarlem et al. 2013 ). LOFAR operates using either its low band antenna (LBA, 10–90 MHz) or with its high band antenna (HBA, 120–240 MHz) and is capable of responding to transient alerts within 5 min of receiving the trigger notice. Rowlinson et al. ( 2019 ) outline the first LOFAR search for prompt radio emission in long GRB 180706A, beginning 4.5 min after the γ-ray trigger. By utilizing the full capability of LOFAR, the observational constraints for coherent radio emission can now reach mJy sensitivities, revolutionizing the search for this emission from many transient events. In this paper, we explore the detectability of low-frequency radio waves associated with X-ray flares, under the assumptions of a Poynting flux model for the prompt emission mechanism in which X-ray flares are a manifestation of prompt non-thermal pulses. We draw a subset of X-ray flares from an established sample, and apply the model to estimate the fraction of low-frequency waves that would have been detectable by LOFAR for a given set of observational conditions. We discuss the optimal strategy to apply to the current LOFAR triggering and data processing, to find the emission from flares expected within this framework. 2 MODEL Low-frequency waves have been postulated to arise at the shock front of a highly magnetized, relativistic wind (generated by the rotational energy of a compact object) interacting with its surroundings (Smolsky Usov 2000 ; Usov Katz 2000 ). In this model, a variable current flowing between the two media either side of the travelling shock front leads to the generation of low-frequency radio waves in the MHz regime. The radio emission should occur at a peak frequency, ν max , in the observed frame of where z is the redshift of the GRB and we adopt an observer frame value of G for the magnetic field in the wind at the radius of low-frequency wave generation (Usov Katz 2000 ), where ε B is the fraction of the total energy in the magnetic field. We note there are several assumptions embedded within equation ( 1 ), such as the properties of the magnetic wind and the deceleration radius (see Usov Katz 2000 , for further details regarding these assumptions). A delay is expected

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


The GBM targeted search pipeline (Blackburn et al. 2015 ), which operates using a seed time and an optional seed sky map, was updated in preparation for the second observing run of Advanced LIGO (O2) to produce an overall lower false-alarm rate (FAR) and to be more sensitive to sGRB-like signals (Goldstein et al. 2016 ). The improvements implemented include replacing the “hard” spectral template with a more physically and observationally representative cutoff power-law spectrum, increasing the data temporal resolution, improving the background estimation, and utilizing localization information in the ranking statistic. 2.1.2. GBM Results The GBM was observing ∼82% of the LIGO sky map at the time of the LIGO trigger, and no onboard GBM trigger was recorded close in time to GW170104. The nearest triggers were more than 13 hr preceding and more than 10 hr following GW170104, and both of these triggers were due to steep non-astrophysical rate increases near the boundary of the SAA just before the detectors were turned off for passage. The untargeted search did not find any untriggered sGRB candidate on January 4. The nearest candidate preceding GW170104 was more than 15 hr earlier, and the nearest candidate following GW170104 was about 8 days later. The targeted search was run over a 1 minute window centered at t GW , searching for any signal on timescales from 0.256 s, increasing by factors of two up to 8.192 s (six timescales). As reported in Burns et al. ( 2017 ), no credible significant candidate was found. The most significant result from the search was on the longest timescale with the “soft” spectral template, which the search found to be marginally consistent with part of the LIGO sky map. Further inspection of the count-rate light curves for each detector reveal a slow-rising bump that begins ∼100 s before t GW and has a duration of ∼300 s. This bump, which is strongest in the GBM Na i channel 1 (12–25 keV) and does not appear above channel 2 (50 keV), is consistent with a low-level increase in magnetospheric activity as Fermi proceeds through its orbit. Using the GBM, we can set an upper bound on the impulsive flux expected from an sGRB-like signal. The current technique is to estimate the background in the same way that the targeted search does (unbinned Poisson maximum likelihood over a sliding window) and calculate the 3 σ upper bound in the count rate as three times the standard deviation of the background count rate. The count-rate upper bound can then be converted to a flux upper bound by assuming a photon model, folding it through the detector response and fitting the amplitude to determine the associated flux upper bound. We note that this technique produces a conservative upper limit because it utilizes a single GBM detector rather than all detectors over the entire LIGO map, which would be significantly more computationally challenging. We evaluate the limits in this way over the

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discrepancies are caused by differences in how ρ SFR is calculated. A good example of this problem can be illustrated by comparing our estimate of ρ SFR at z ≃ 10 with the results of Oesch et al. ( 2014 ). The headline result from Oesch et al. ( 2014 ) is that log 10 (ρ SFR ) = −3.25 ± 0.35 at z ≃ 10 (lower data point in Fig. 9 ), which is in poor agreement with the value of derived here. However, it is worth noting that the value of log 10 (ρ SFR ) = −3.25 ± 0.35 was calculated by summing the contribution of the five z ≃ 10 candidates found by Oesch et al. ( 2014 ), rather than integrating their estimated z ≃ 10 LF to a consistent UV luminosity limit. Interestingly, Oesch et al. ( 2014 ) also calculate an alternative value of log 10 (ρ SFR ) = −2.80 ± 0.11 (upper data point in Fig. 9 ), based on assuming luminosity evolution of the LF (as adopted here) and integrating to our adopted limit of M 1500 = −17.7. This estimate of ρ SFR is in excellent agreement with both our new determination at z ≃ 10, and our best-fitting linear ρ SFR – z relation. Finally, it is interesting to compare our new observational estimate of the high-redshift evolution of ρ UV with the predictions of recently published models of galaxy evolution. Our data points are plotted against the predictions of seven such models in Fig. 10 . It is important to acknowledge that some of these predictions are at least partly based on hydrodynamic simulations, while others are semi-analytic models, some of which have been effectively tuned to reproduce the UV LF at moderately high redshift (e.g. z ≃ 6). Thus, in a sense, this comparison is not completely fair, and cannot be simply regarded as specifically favouring one form of model over another. Nevertheless, some important general trends can be deduced. In particular, the Illustris (Genel et al. 2014 ) and Munich (Henriques et al. 2015 ) models, while clearly capable of reproducing many (often quite complex) aspects of galaxy evolution, both clearly underpredict ρ UV at redshifts higher than z ≃ 7. We stress that this discrepancy is already clear by z ≃ 8 (where the measured value of ρ UV is well established) and is simply confirmed and strengthened by our new results at z ≃ 9 and ≃ 10. The challenge, then, for such models is to be able to produce star formation activity which extends to higher redshifts than currently predicted. Indeed, the only model shown here that systematically overpredicts ρ UV is that of Behroozi Silk ( 2015 ). We note that the overprediction of raw observed ρ UV at redshifts z ≃ 5–6 by the Illustris and Khochfar et al. simulations is not really a fundamental problem, as both of these models do not include the impact of dust obscuration. Figure 10. Our new measurement of the evolution of the UV luminosity density (ρ UV ) and inferred star-formation rate density (ρ SFR ) at z > 5, compared with the predictions of a range of models and simulations from the literature. The model predictions are as follows:

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cloud temperature is assumed to be 5000 K, the column density, , will be enhanced for a given cloud mass. Therefore, for the initial mass function with α = −1 and adopted in this work, the model will produce more systems and overproduce the gas covering fraction for such systems. On the other hand, by increasing the temperature of clouds to be 20000 K, all the gas clouds become highly ionized with . Such a scenario cannot produce any high column density systems as observed. This suggests that the adopted cloud temperature with 10 4 K is perhaps reasonable for reproducing the gas properties of high gas absorbers. Survival of clouds – One of the key assumptions in our model is that the clouds are not destroyed by the hydrodynamic instability. Although a number of studies have shown that various mechanisms can suppress the effect of hydrodynamical instability (e.g. Vietri et al. 1997 ; McCourt et al. 2015 ; Armillotta et al. 2017 ; Gronke Oh 2018 ), it is still unclear how these mechanisms operate in reality. This problem is related to the problem of entraining the cool gas along with a hot wind (e.g. Zhang et al. 2017 ). However, we argue that the existence of cool gas and the evidence of contribution from outflows in the haloes (e.g. Bordoloi et al. 2011 ; Lan Mo 2018 ) suggest that either the cool gas outflows must survive over the hydrodynamic instability, as we assume in our model, or cool gas is redistributed in the haloes by some other mechanisms associated with outflows (e.g. Thompson et al. 2016 ; Lochhaas et al. 2018 ). Gas properties at large scales – Our model has difficulties in explaining systems with beyond 100 kpc (e.g. Zhu et al. 2014 ; Huang et al. 2016 ; Lan Mo 2018 ) due to the low volume density of the hot ambient gas as shown in Fig. 2 . It is, therefore, likely that some of the systems at large distances are produced by neighbouring haloes due to spatial clustering of haloes. Such ‘two-halo’ term is not included in our current model, but should be modelled. 5 SUMMARY We develop a flexible semi-analytic framework to explore the physical properties of the cool pressure-confined circumgalactic clouds with mass from 10 to . We take into account the effects of gravity and interaction between hot gas and cool gas and model the trajectory, the lifetime, and the observed properties of the cool clouds with cloudy simulations. The ensemble properties of the cool CGM are explored by populating clouds following various mass functions in the haloes with three origins, outflows, inflows, and in situ formation. With this framework, we investigate how different mechanisms affect the observed properties of the cool CGM. Our results are summarized as follows: The pressure-confined cool gas clouds have with sizes about 10–100 pc similar to the properties of strong metal absorbers, sub-DLAs, and DLAs observed towards background spectra. We illustrate the effect of hot gas on the motion and lifetime of cool gas clouds; the ram pressure from the

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


Photoionization is assumed to be negligible (Kozma Fransson 1998 ). Ionization balance is achieved by equating the rate of impact ionization with the recombination rate for each ion. Within each ion, level populations are computed solving the rate equations for each level under the assumption of thermal balance, i.e. equating the non-thermal heating rate and the rate of cooling via line emission. The assumption is made that the nebula is optically thin, and radiation transport in not performed. The emissivity in the various lines is used to compute the emerging spectrum. The code can be run as a simple one-zone code, in which case the line profile is a parabola with characteristic width determined by the speed of expansion of the outer boundary of the nebula (which is input to the code). Alternatively, a stratified version can use a one-dimensional explosion model (i.e. a radially dependent density/abundance profile), in which case energy deposition, ionization balance, level populations, and emissivity are computed for each shell. Each shell then contributes its own emissivity. Line profiles are built by summing truncated parabolae bounded by each shell’s inner and outer boundary velocity. In both cases, the effects of line blending are automatically taken into account in the computation of the emitted spectrum. Our code has been used for a number of SNe Ia (e.g. Mazzali et al. 2011 ; Mazzali Hachinger 2012 ) and Ib/c (e.g. Mazzali et al. 2007b ), and it can yield a description of the inner layers of the SN ejecta. When used in combination with a description of the outer layers, which can be obtained through a study of the early spectra, the mapping of the inner ejecta that results from nebular studies can be used to obtain a full description of the density and abundance distribution in an SN (e.g. Mazzali et al. 2015 ; Ashall et al. 2016 , 2018 ). One aspect our code attempts to treat is clumping of the ejecta. The simple assumption is made that all ejecta reside in clumps, which occupy a fraction of the total volume, as defined by a filling factor. The density in the clumps is then increased following the decrease in volume, and the composition of the clumps is set to be the same as that of the radial ejecta shell they are in, i.e. all clumps are homogeneously and microscopically mixed. The clumps are still assumed to be in thermal equilibrium. These are of course major simplifications, but in the inner layers of an SN Ia only few elements are present, so it is not unreasonable. Strong clumping has been shown to be very useful in order to reproduce the low ionization seen in late-time spectra of SNe Ic (e.g. Mazzali et al. 2001b ), where it may be thought of as a proxy for the non-spherically symmetric distribution of the ejecta. Clumping is used later in this paper to improve our synthetic spectra, especially in the final epoch. 4 SPECTRAL MODELS AND THE EVOLVING PROPERTIES OF SN 2014J We started our analysis by deriving some basic

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


for the BH in each system and could be supernova (SN), direct collapse (DC), or unsure (U). We have stated that just for the central predicted systemic radial velocity. Refer to Sections 7.1 and 7.4 for the explanation of the suggested birth pathway. a This work. b della Valle et al. ( 1994 ). c Cadolle Bel et al. ( 2007 ). d Gaia Collaboration ( 2018 ). e Kirsten et al. ( 2014 ). 5.2 Systemic radial velocity estimates We have four systems with poorly constrained systemic radial velocities ( Swift J1753.5−0127, MAXI J1820+070, VLA J2130+12, and GRS 1716−249). Using the best distance estimates for these systems, we project them on to the Galactic plane. We estimate the expected systemic radial velocity () of the system at this projected distance on to the Galactic plane and assuming that the system is undergoing pure Galactic rotation about the Galactic Centre. We note that this estimated value of systemic radial velocity is not a true indicator of the systemic radial velocity of the system as it might have received kicks, and thus is probably not following a pure Galactic rotation about the Galactic Centre. Thus for each system, we estimate five probable systemic radial velocity Gaussian distributions with medians of , 50 , and 100 (see Table 5 ). We limit our assumed distributions of the systemic radial velocities based on the fact that out of the systems for which systemic radial velocity is measured, the values lie between −142 ± 1.5 for GRO J1655−40 (Shahbaz et al. 1999 ) and 107 ± 2.9 for SAX J1819.3−2525 (Orosz et al. 2001 ). 6 ANALYSIS – POTENTIAL KICK VELOCITY As explained in Section 1.3 , peculiar velocity of a system when it crosses the Galactic plane is a better probe to understand the kick a BHXB received when the BH was born. Since all the parameters, namely proper motion, systemic radial velocity, and parallax (or distance), have error bars associated with them, it is crucial to propagate these errors appropriately to estimate the Galactocentric orbits of the systems. The age of most BHXBs is not known, which makes integrating the Galactocentric orbits back to the time of birth of the BH uncertain. We thus developed an MC methodology that accounts for the errors on the measured quantities and determines the peculiar velocity every time the system crosses the Galactic plane. The code integrates the Galactocentric orbit of every system in our sample back for 10 Gyr and records the velocity of the system at every plane crossing. Instead of a delta function for the measurement, it involves using Gaussian distributions of the measured parameters with reported uncertainties as standard deviation. Random values are picked from these Gaussian distributions as inputs to galpy (Bovy 2014 ) to create instances of Galactocentric orbits for ∼5000 random draws to make sure we have sampled the input distribution properly. We assume a Galactic potential given by the galpy model MWPotential2014 (see Bovy 2014 ). The Galactocentric orbits are

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


FR and SR and high-mass FR and SR are shown. 3 POPULATIONS OF FAST AND SLOW ROTATORS 3.1 Comparing to the ATLAS3D survey The first question we seek to answer is whether the Illustris simulation produces a representative sample of fast and slow rotators. The ATLAS 3D survey provides an excellent set of observational data to compare to Emsellem etal. ( 2011 , hereafter E11 ), examining the distribution of ellipticity and R for 260 ETGs in a volume- and magnitude-limited sample. We reproduce their results in the left-hand panel of Fig. 3 . Figure 3. Distribution of ETGs in the r plane, (a) reproduced from the ATLAS 3D survey ( E11 ) compared to (b) those created in the Illustris simulation, sampled based on the same selection criteria (see the text for more details). The magenta line shows the line on which edge-on elliptical galaxies with the same degree of rotational support would lie, as described in the text and re-derived in Appendix C . The green line follows equation ( 5 ), defining the cutoff below which galaxies are classified as SRs. Each galaxy is represented by a circle whose colour and size scale with the stellar mass. E11 selected ETGs based on whether they could clearly discern spiral arm structures in the galaxy. Taking into account the variation due to projection effects in observed galaxy properties, E11 suggested making a divide between FRs and SRs based on their and R properties using the curve above which galaxies are classified as FRs and below as SRs. Of their sample, 224 galaxies, or 862percent, were classified as FRs and the remaining 36, 142percent, as SRs, using equation( 5 ) to divide the population. They found FRs to be roughly oblate, with the ellipticity of a galaxy correlating linearly with its anisotropy, . In other words, the FRs are roughly rotationally supported with stars on mostly circular orbits. Thus, the motions of stars and the projected shape of the galaxy have a simple, linear correlation. SRs are instead galaxies with low degrees of rotational support, with many stars on radial or generally irregular orbits. Thus, we can identify galaxies whose shape is well represented by the assumption of rotational support, those with ellipticity () proportional to their degree of velocity anisotropy (). Cappellari etal. ( 2007 ) and E11 find an approximate expression for the variation of R with for galaxies with . We detail this expression in Appendix C , and follow their lead in showing the relationship for 0.7 as a magenta line in the left-hand panel of Fig. 3 . The E11 sample of galaxies is volume and magnitude limited to those galaxies within 42Mpc, brighter than mag, which are clearly visible from the William Herschel Telescope (declination 2935) and which are far from the Galactic plane to avoid contamination (galactic latitude b 15). Using the same criteria (arbitrarily setting the equatorial direction aligned with the positive z -axis and the galactic plane relative to that), we

O O O O O O O O O O O O O O O O O O O O O B-Survey B-Survey O O O O O O O O O O B-Model I-Model O O O O O O O O O O B-Survey I-Survey I-Survey O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey O B-Citation O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O B-TextGarbage B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O


third harmonic. Figure 8 presents the temporal dependence of the radiation field E x in units, recorded at one point on the boundary of the computational domain for run 1. The emission spectra recorded at the points indicated by the star in Figures 4 – 6 are shown in Figure 9 . The emission line width near the second harmonic of the plasma frequency for all regimes is less than or of the order of 2%. Figure 4. Efficient regime. (a) The map of the electric field E x in the moment (b) radiation spectra of electric field components for the entire simulation time at the outer boundary of the vacuum region as functions of the longitudinal coordinate x ; (c) theoretical growth rate along the line of the local maximum. Figure 5. Weak field. . Figure 6. Unmagnetized. . Figure 7. Strong field. t = 728 ω p −1 . (b) Phase space ( x , v x ) of the beam. Figure 8. The temporal dependence of the E x field in the single point indicated by the white star in Figure 4 . Figure 9. The frequency spectrum of the radiation produced in the single point indicated by the white star on the corresponding Figures 4 – 6 and 10 . Figure 10. Eff. regime + ions. . (a) Ion density in plasma column and radiation field E x in vacuum. (b) Frequency spectrum of radiation field along the boundary of the simulation box. (c) Theoretical growth rate along the line of its local maximum. The beam instability becomes purely longitudinal in the strong magnetic field (Figure 7 ). In this regime, we also observe a noticeable extension of the beam relaxation length. Therefore, we have extended the total system length in order to overlap beam relaxation regions more efficiently. The overlapping degree can be estimated from the image of the phase space (Figure 7 (b)). Figure 7 (a) shows that, in the case of a sufficiently strong external magnetic field, EM emission disappears. Let us consider the efficiency of EM radiation generation in these regimes quantitatively. Figure 11 presents the fraction of the total beam power P b converted into the radiation power P rad for run 1 as a function of time (efficient regime). In this graph, we separate contributions from various radiation polarizations (TM or O mode includes the fields E x , E z , and B y ; TE or X mode— B x , B z , E y ). It is seen that the ordinary TM mode dominates and the efficiency of its generation reaches 4% of the beam power. The total beam-to-radiation energy conversion efficiency is ≈10 −2 . The duration of the main emission can be estimated as an FWHM width of the plot shown in Figure 11 . In all simulations performed for the efficient regime, this duration lies in the range . Figure 11. The efficiency of beam-to-radiation power conversion as a function of time for run 1. The radiation efficiency depends not only on the amplitudes of the plasma oscillations excited by the beams, but also on the degree of their overlap. For this reason, the dependence of the emission level on time has a pronounced maximum corresponding to

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


rate of change in the orbital separation:Here the total rate of change in the orbital angular momentum is determined byThe three terms on the right side of Equation ( 6 ) represent angular momentum losses caused by GR, MB, and mass loss, respectively. The GR-induced rate is calculated with the standard formula (Landau Lifshitz 1959 ; Faulkner 1971 )where G and c are the gravitational constant and the speed of light, respectively. The prescription of Verbuant Zwaan ( 1981 ) is adopted to calculate the angular momentum loss due to MB,For IMXBs and wide LMXBs, the mass-transfer rate may be higher than the Eddington-limit accretion rate of the NS. Thus, the accretion rate of the NS is evaluated usingand the mass loss rate from the binary system isIn the case of super-Eddington accretion, we adopt the isotropic reemission model, assuming that the extra material leaves the binary in the form of isotropic wind from the NS. Therefore, the angular momentum loss rate due to mass loss can be derived to bewhere a 1 is the distance between the NS and the center of mass of the binary. 3. Results of Evolution Calculations We have performed calculations of the binary evolution for thousands of I/LMXB systems. We choose the initial NS mass and the initial donor mass , and set the initial orbital period 1.0 day days. We use exponential diffusive overshooting for the donor stars. Note that there exists a bifurcation period for the initial orbital period day (Pylyser Savonije 1988 , 1989 ). If the initial orbital period is below P bf , the binary systems will evolve with shrinking orbits, possibly forming ultra-compact binaries. This kind of evolution cannot reproduce PSR J1640+2224, and will not be considered here. In addition, we exclude the evolutions with the final orbital periods exceeding 500 days. 3.1. A Typical Example for the IMXB Evolution We present the evolutionary sequences for a typical IMXB system that consists of a 1.4 M ⊙ NS and a 3.5 M ⊙ donor star with an initial orbital period P orb = 6 days in Figures 1 and 2 . The donor star starts to fill its RL and commence mass transfer at the age of 240.6 Myr. The mass-transfer process lasts about 1.9 Myr, at a rate higher than the Eddington accretion rate (the maximum mass-transfer rate >10 −5 M ⊙ yr −1 ). In this case, most of the transferred material from the donor is lost from the binary system. Thus, after the mass transfer, the donor evolves into a CO WD of mass 0.543 M ⊙ , while the NS has accreted only 0.034 M ⊙ mass. The orbital period becomes smaller in the former stage of the mass-transfer process due to the relatively high mass ratio (>1); when the mass ratio is reversed, the orbit begins to expand. The final orbital period is P orb = 17.8 days. Figure 1. Example evolution of a typical IMXB consisting of a NS and a donor star with initial masses M 1 = 1.4 M ⊙ and M 2 = 3.5 M ⊙ respectively, and orbital period P orb = 6 days. The blue and red solid curves denote the evolutionary tracks for

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


disk sources in the Perseus molecular cloud with the data collected in 2013, 2014, and 2015 (D. M. Segura-Cox et al. 2016, in preparation). Here we focus on seven of the candidate disks (Table 1 ; Figure 1 , left) which were observed with A-array prior to 2015 and can be well modeled with the prescription described in Section 4 . The observations were made in three-bit correlator mode, with a bandwidth of 8 GHz divided into 64 sub-bands. Each sub-band has 128 MHz bandwidth, 2 MHz channels, and full polarization products. The two 4 GHz basebands are centered at 36.9 GHz (∼8.1 mm) and 29.0 GHz (∼10.5 mm). Three sources were observed in each 3.5 hr block, and two sources were observed in each 2.75 hr block. Some observations were conducted as 1.5 hr blocks. 3C48 served as the flux calibrator, and 3C84 was the bandpass calibrator. The observations were taken in fast-switching mode to account for rapid atmospheric phase variations, with a 2.5 minute total cycle time to switch between the target source and the complex gain calibrator, J0336+3218. The total integration time on each source was ∼30 minutes for both A-array and B-array. We reduced the data with CASA 4.1.0 and the VLA pipeline (version 1.2.2). We executed additional flagging beyond pipeline flagging by inspecting the phase, gain and bandpass calibration solutions. VLA Ka-band data sets have an estimated amplitude calibration uncertainty of ∼10%, but only statistical uncertainties are considered in our analysis. Figure 1. VLA A+B array data (left), q = 0.25 model from u, v -plane best-fit (center), and residual (right). Images were produced with robust = 0.25 weighting. Contours start at 3 σ ( σ ∼15 μ Jy) with a factor of spacing. The synthesized beam is in the lower left. Table 1 Observations Note. Observation dates mark the start of the observations. Combined beam sizes reflect robust = 0.25 weighting. 3. ESTIMATED MASSES Two key quantities that describe disks are their masses and radii. While accurately determining disk radii requires modeling, masses are estimated from flux measurements (Table 2 ). By assuming optically thin emission, we estimate disk masses from the 8 mm dust continuum flux with the relation (Hildebrand 1983 ):where , d , , and , are respectively the total observed flux, distance, grain opacity, and blackbody intensity at dust temperature T d . We estimate at 8.1 mm by normalizing to Ossenkopf Henning ( 1994 ) at 1.3 mm using a dust to gas ratio of 1/100: = cm 2 g −1 . β = 1 is typically assumed for protostellar disks (Andrews et al. 2009 ), giving cm 2 g −1 . Mass estimates are inherently ambiguous within an order of magnitude due to uncertainties in the dust-to-gas ratio, T d , and β ; rather than compute a single mass estimate, we calculate lower and upper mass estimates for each source by varying T d . Lower masses were estimated by assuming T d = 40 K, and we determined upper estimates using T d = 20 K. These candidate disks range in flux from 867.5 to

O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O B-Telescope O B-Telescope O O O O O B-Software I-Software O O B-Software I-Software B-Identifier I-Identifier O O O O O O O O O O O O O O O O B-Telescope B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Telescope B-Telescope O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Citation I-Citation O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength I-Wavelength O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O


OLR, corotation (CR), as well as the 4:1 and 6:1 resonances from higher order Fourier modes of the bar potential. We define a quasi-isothermal ( Binney 2010 ) unperturbed distribution function in action space to represent a young and cold ( σ R = 30 km s −1 ), as well as a hotter and older ( σ R = 50 km s −1 ) disc stellar population. Then we use a first canonical transformation to move to the slow and fast action-angle variables, which allows us to determine the regions of phase-space where orbits are trapped at resonances. In the vicinity of these resonant regions, and after averaging over the fast angles, the dynamics of the slow variables is that of a pendulum, for which we make a new canonical transformation to pendulum action-angle variables. We then phase-mix the original unperturbed distribution function over the pendulum angles to obtain the perturbed distribution function in the different resonant zones. We can then compute the perturbed distribution function at different positions and velocities, making use of the epicyclic approximation. We refer the reader to Monari et al. (2017a , 2019) for more details of the method. We note that it gives a very good representation of orbits trapped at resonances, but is not the best possible description of the linear deformation zones. In Fig. 2 , we present the variations in density of the v φ − R plane resulting from the response of both the cold (young) and hot (old) stellar populations to the bar potential of Portail et al. (2017) . As expected, the features are marked much more clearly for the dynamically young population. Interestingly, this is particularly true for the 4:1 resonance, which corresponds to the Sirius ridge, which is also seen very prominently in the data as a young feature in a large range of radii. Moreover, the density contrast of the ridge associated with corotation is most prominent for young stars around R ∼ 7 kpc, which is also where the Hercules ridge appears most clearly both in global density and as a young feature in the data. The ‘hat’ feature, which corresponds to the bar’s OLR in this model, appears prominently for the young and cold population at R ∼ 9 kpc, where it also peaks in differential age in the data. This analytical model thus provides a remarkable qualitative match to the trend uncovered in the data. Fig. 2. Normalised perturbed distribution function in the presence of the large bar perturbation of Portail et al. (2017) . Top panel : for an unperturbed distribution function representing a young and cold disc stellar population with σ R = 30 km s −1 at the Galactocentric solar radius R 0 . Bottom panel : for an older and hotter disc population with σ R = 50 km s −1 at the Galactocentric solar radius R 0 . 4. Arcturus and moving groups of the thick disc We note in Sect. 2 that the ridges from Arcturus down to Ella all have stellar ages that appear slightly but systematically younger than the surrounding population, which, combined with the regularity

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


of stars in the K2 samples prevent us from drawing any firm conclusion with regards to the slopes. As for the offsets, the effect of such differences seems to be at the level of ∼ ± 7 μ as at most. In addition, the fairly good agreement between SkyMapper and APOGEE does not exclude the possibility that the photometric T eff and [Fe/H] may be influenced differently in different fields (e.g. C3 and C6) by external factors such as, for instance, the extinction. A further point we would like to raise concerns the apparently larger scatter in the K2 fields. In that respect, we identify the order of magnitude of the Gaia and seismic ( PARAM ) parallax uncertainties (Fig. 12 ). The asteroseismic uncertainties are slightly larger in the case of K2. This can mainly be explained by the fact that the original mission, Kepler , continuously monitored stars for four years, whereas each campaign of K2 is limited to a duration of approximately 80 days ( Howell et al. 2014 ). Despite this, photometric systematics in the K2 data leading to, for instance, spurious frequencies are now well understood, and the pipelines used to produce light curves have been developed over time to remove or mitigate these effects. As a result, we do not expect the global seismic parameters to show any significant bias due to the K2 artefacts (see also Hekker et al. 2012 , and the Kepler and K2 Science Center website 5 ). Nonetheless, the astrometric uncertainties are also substantially larger for K2, almost doubled compared to Kepler . A possible reason for this would be that the regions around the ecliptic plane (such as C3 and C6) are observed less frequently, as a result of the Gaia scanning law, and also under less favourable scanning geometry, with the scan angles not distributed evenly ( Gaia Collaboration 2016b ). To test this hypothesis, we use the quantity visibility_periods_used : the number of visibility periods, that is a group of observations separated from other groups by a gap of at least four days, used in the astrometric solution. This way, we can assess if a source is astrometrically well-observed. This variable exhibits significantly higher values for Kepler , ranging from 12 to 17. The number of visibility periods for K2 are lower or equal to ten, indicating that the parallaxes could be more vulnerable to errors. The predicted uncertainty contrast between the Kepler and K2 fields is about a factor 6 of 1.6, which is indeed consistent with the location of the histogram peaks in the top panel of Fig. 12 . Fig. 12. Distribution of parallax uncertainties in Gaia DR2 ( top ) and in PARAM ( bottom ) for the Kepler (red), C3 (orange), and C6 (purple) fields. 5.2. Quasars and colour-magnitude diagram Lindegren et al. (2018) investigated the parallax offset using quasars, and obtained a global zero-point of about −30 μ as. It is no surprise that this value differs from the ones we obtain in the current work. Indeed, this parallax offset depends on magnitude and

O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O B-CelestialRegion O B-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O B-Telescope O O O B-Software O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O B-Telescope O O O O O O O O O O O B-Mission O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O B-Citation I-Citation I-Citation I-Citation O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O B-Mission O O O O B-Telescope O O O O O O O O O O O O O O O O O B-CelestialRegion O B-CelestialRegion O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O B-Software O O O O O B-Telescope O B-CelestialRegion O O B-CelestialRegion O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


radiative losses and energy input per unit mass across the atmosphere due to the most important hydrogen transitions in models with the beam flux equal to 3 × 10 9 erg cm −2 s −1 . The figure shows that beams with a low E C (20 keV) disrupt the top chromosphere, shift the transition region to heights of up to 1500 km, and produce emission in the Lyman continuum and Ly α . The figures also show a peak of absorption in the Lyman continuum at the same height where we can see the maximum of radiative losses in the Balmer and the higher-order continua. This means that the Lyman continuum irradiated downward contributes to hydrogen ionization in the deeper layers. The radiative losses for E C greater than 40 keV do not show any such Lyman emission, but they still show the emission in the higher-order continua that are clearly driven by the particle-beam precipitation. Figure 1. Radiative losses during the flare electron-beam precipitation for E C in the range of 20–120 keV. The beam flux is equal to 3 × 10 9 erg cm −2 s −1 . A positive (negative) corresponds to absorption (emission). The profiles are taken 20 s into the simulations. Table 1 shows the gross radiative losses in the atmosphere due to the free–bound Lyman and Balmer transitions (LyC and BaC, respectively) and the bound–bound Ly α and H α transitions, respectively. The radiative losses were integrated only over the chromosphere and the temperature minimum region—between the height of 300 km above the photospheric floor and the height where the temperature begins to exceed 10 5 K. These numbers do not include any possible reabsorption outside these atmospheric heights; therefore, they do not quantify the radiative output of the atmosphere as seen by an observer. The table shows that there is an overall stronger emission for particle beams with higher flux with the LyC showing the greatest variation. In models with E C = 20 keV the LyC losses reach values of 10 19 –10 20 erg cm s −1 g −1 ; however, models with high E C show that the LyC remains at the quiet level (∼10 16 erg cm s −1 g −1 ). The situation is the same for the Ly α , where the quiet level reaches ∼10 17 erg cm s −1 g −1 . The radiative losses listed in Table 1 show that when the beam flux is increased, the maximum radiative losses in the studied lines and continua occur at higher values of E C . With increasing E C it is the LyC that reaches the peak of the radiative losses first and then the Balmer continuum. This is due to the greater penetration depth of the beams with higher E C and the fact that the LyC originates higher in the atmosphere than the BaC. Table 1 Atmospheric Heating and Radiative Losses Due to the Hydrogen Transitions in Electron-beam-driven Models Note. The radiative losses and the beam heating, as shown in Figure 1 , were integrated over the temperature minimum region and chromosphere. The first row shows the radiative losses for the quiet atmosphere. Figure 2 shows the RH synthetic spectra for the

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


an underlying population with (red lines) and (cyan lines). All results are for the ShGeLMC simulation, with . The discussion above is simplified in a number of ways. First, we assume that the individual members of the galaxy population all have the same escape fraction, i.e., the distribution of is a delta function. As we noted previously, this is not likely to be true. Second, we assumed that all galaxies in our mock samples could be observed at the same signal-to-noise. A realistic sample would contain galaxies with a range of luminosities, and would therefore have a different noise level for each object. Nevertheless, this simple test shows that measuring the mean escape fraction of a large sample is possible even if the errors are large for individual objects. 5. SUMMARY AND DISCUSSION In this paper, we have shown how machine learning algorithms such as lasso regression can be applied to simulated galaxies to obtain a function that maps a spectrum to a Lyman continuum escape fraction. Our method uses the entire observable spectrum, which leads to an increase in performance over, for instance, using only the UV slope and the H β line (Zackrisson et al. 2013 ). We find that using the lowest NIRSpec resolution, R = 100, gives the best results for a given exposure time. Interstellar dust presents a challenge for our method, but it can be dealt with unless the dust attenuation law is very poorly known. Training a model on data with low noise results in a more complicated model that uses a larger number of spectral bins compared to a model trained on data with high noise. The performance of the model is always better when the training and testing data have the same noise level. Therefore, in a real-world situation, a suitable approach might be to train several models using different noise levels, and apply them depending on the noise level for each specific observed galaxy. In a sense, this method represents the reverse of the more traditional approach used when fitting SEDs, which has also been used to constrain (Ono et al. 2010 ). In SED-fitting, one usually generates a large grid of model galaxies, and looks for a model galaxy that looks similar to a given observation. It is then assumed that the properties of the observed galaxy will be similar to that of its closest match in the model grid. The problem with this approach lies in defining “similar.” Typically, the similarity of two SEDs is measured simply as mean of the squared difference between the fluxes in all filters. However, when constraining a single property, such as , not all wavelength regions are equally important. In fact, our results show that most of the information about comes from only a few wavelength bins. The method presented here automatically finds the optimal way of comparing observations to simulations, when the goal is specifically to infer the escape fraction. We emphasize, however, that this is not a model-independent method. Like all other indirect approaches to

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


of single vibrational transitions. Row 1 of Fig. 6 shows the temperature measured by the internal sensor (solid line) and determined by our algorithm (data points). There is a linear offset to the sensor temperature, the molecular temperature being systematically higher. This discrepancy can be corrected by a linear function A least-squares fit yields a = 1.414, T off,1 = 292.2 K, and T off,2 = 290.45 K. The dashed line in row 1 of Fig. 6 shows the corrected sensor temperature. The residuals between corrected sensor temperature and molecular temperature (σ = T measured − T alg ) displayed in row 2 show minor systematics during the unheated phases. The real cell temperature can then be determined from the algorithm output by inverting equation ( 24 ). We consider three cases for the origin of the temperature offset and discuss them in the following sections. Figure 6. Determined parameters of the measurements as a function of time. Shaded grey areas mark the time intervals during which the heating was switched on. Row 1: Data points with error bars represent the temperature of each spectrum as derived by our algorithm. The solid line shows the temperature determined with the gas cell sensor and the dashed line is the linearly corrected sensor temperature. Residuals between the corrected sensor temperature and the molecular temperature are given in row 2. Row 3 shows the determined effective RV/wavelength shift of each spectrum. 5.3.1 Erroneous model We assume the energy levels to include two terms, the vibrational and rotational energy (equation 12 ). In reality, there are several other contributors to the energy levels, such as a translational and an electronic term. We do, however, argue that the omission of these terms cannot lead to a bias in temperature determination, since the temperature determination is only dependent on the difference between energy levels Δ E ; hence, any term independent of the quantum numbers ν and J is cancelled out in equation ( 18 ). 5.3.2 Heating by the source lamp The source lamp in our setup is located relatively close to the iodine cell, so heating of the gas cannot be dismissed outright. As can be seen in the lower panel of Fig. 3 , the absorption is in fact temperature dependent. The lamp therefore heats the gas and causes a temperature gradient between the cell centre and the cell wall, where the temperature sensor is located. But if this effect were large enough to be present in the data, the temperature offset would not drop to zero at lower temperatures (see upper panel of Fig. 6 and equation ( 24 )), which is why we can rule it out as the underlying cause. 5.3.3 Heat sensor Equation ( 24 ) shows that the difference between the sensor and algorithm temperatures drops to zero at a temperature of 290.45 K, which was in fact the room temperature inside the laboratory at the time of the measurements. Furthermore, the residuals between corrected sensor temperature and the one determined via our algorithm show

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