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,


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


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


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:


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


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


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


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


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


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


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


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


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


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


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


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


constraint is nearly same. So, we find that, different choices of the group prior p 0 ( z , Ω) cannot significantly affect the constraint of the Hubble constant. On the other hand, for LHVIK network with SBBH mergers, we find the error bars of H 0 are quite large in both cases. Figure 8. The posterior distributions of Hubble constant H 0 . The upper, middle, and lower panels show the results of for the LHVIK, LHVIKCA, CE2ETD network, respectively. The left-hand panels represent the cases of uniform window function w i = 1, and the right-hand panels represent the cases of w i proportion to the stellar mass of groups. In each panel, there are four lines. The green line is the result in the case of A and the blue one is that of B (see the main text for the details). Similarly, the red line is the result in the case of A, and the black line is that of B. Note that, green line overlaps with blue one, and red line overlaps with black one. For LHVIKCA network with SBBH mergers, we find that 44 events satisfy the criteria and are used for the parameter constraining. The posterior distributions of H 0 derived from this network are given in the middle left-hand panel of Fig. 8 , which are for both case of A and case of B. While for SBBH mergers, we find 21 events can be used for the parameter constraining, and the corresponding result is in the case of A and H 0 = 69.97 ± 0.86 km s −1 Mpc −1 in the case of B. Same to the cases of LHVIK network, we find that the effect of group prior p 0 ( z , Ω) is not significant. In comparison with the corresponding cases with LHVIK network, we find the uncertainties of H 0 are nearly five times smaller. Due to the contribution of the two 8-km detectors in the network, the localization ability for the individual event is significantly improved, which leads to two effects on the H 0 constraining: First, the uncertainties of the redshift distribution of the GW event is reduced. Secondly, the number of the GW events satisfying the criteria is increased. So, we conclude that, if the proposals of 8-km detectors can be realized in the near future, the capabilities of GW cosmological, based on the SBBHs as the standard sirens, will be greatly improved in the 2G detector era. Now, we turn to the 3G detector network CE2ETD. As anticipated, we find that the accuracies of H 0 are much better than that of the 2G detector networks. For mergers, 66 events can be used for the parameter constraining, which follow the result H 0 = 70.000 ± 0.008 km s −1 Mpc −1 for both cases with different prior choices. For SBBH mergers, the constraint of H 0 is 70.000 ± 0.018 km s −1 Mpc −1 , derived from 65 events, which satisfy the selection criteria. The posterior distributions in these cases are presented in the lower left-hand panel of Fig. 8 . We find that, even comparing with the results of 2G LHVIKCA detector network, the uncertainty of H 0 is reduced by a factor of 30. Nair, Bose Siani ( 2018 ) discussed a single ET’s accuracy of H 0


values using least squares. Phase residuals of the cross-correlation spectrum are analysed and additive corrections to the a priori weights are computed on the basis of this analysis. The uncertainties of estimates of group delays are derived from uncertainties of fringe phases and additive weights corrections. The uncertainties of fringe phases depend on fringe amplitudes. The explicit expression can be found on page 233 of Thompson, Moran Swenson ( 2017 ), equation (6.63). Computation of total group delays and phase delay rates. The group delays and phase delay rates derived at the previous step are corrections to the a priori delays and phase delay rates used during correlation. The mathematical model of the a priori group delay and phase delay rate used by the correlator is expanded over polynomials of the fifth order at 2-min long intervals that cover the time range of a VLBI experiment. Using these coefficients, the a priori group delays and phase delay rates are computed to a common epoch within a scan for the event of arriving the wavefront at a reference station of a baseline. Using these a priori group delays and phase delay rates, the total group delays for that epoch are formed. 3.2 Astrometric analysis Total group delay is the main observable for astrometric analysis. During further analysis, the a priori model of group delay, more sophisticated than that used for correlation, is computed, and the differences between observed and theoretical path delays are formed. The partial derivatives of this model over source coordinates, station positions, the Earth ordination parameters, atmosphere path delay in zenith direction, and clock function are also computed. Then, corrections to those parameters are adjusted using least squares. The frequency set-up used for this campaign, selected due to hardware limitation (see as an example the set-up for v271i segment in Fig. 2 ) posed a challenge in data analysis. The Fourier transform over frequency over baselines with atca, ceduna, mopra in this example that uses LBDAR DAS has strong secondary maxima (see Fig. 6 ). The amplitude of the second maximum is 0.98, the third maximum 0.93, and the fourth maximum 0.83 with respect of the global maximum. Due to the noise in data and remaining instrumental phase distortion, the fringe-fitting process cannot reliably distinguish the primary and the secondary maxima, and as a result, group delay is determined with the ambiguity of N × 1/2.56 × 10 8 ≈ 3.9 ns, where N is a random integer number, typically in a range [−2,2]. Figure 6. The normalized fringe amplitude as a function of group delay between stations that had LBDAR recording system. The fringe amplitude is divided by the amplitude at the global maximum. At the first stage of the astrometric data analysis, we processed the so-called narrow-band group delays derived as an arithmetic mean of group delays computed over each IF independently and estimated source positions using least squares. The


0.18, respectively, for the 80 per cent/20 per cent train/test split (right-hand panels in Figs 4 and 5 ). Given more training data for the final model, these hyperparameters should deliver an appropriate model complexity that does not overfit the data. As before, I train 100 models with different random states to avoid being biased by the random components in the fitting process. Henceforth, I will report the median value of the predictions from the 100 models. In Fig. 7 , I compare input T e metallicities with those predicted by the MLP model from strong lines. The error bars show the 1σ standard deviations of the 100 predictions. In general, the spread in metallicity due to the random components in the fitting process is much smaller than the dispersion of the calibration. Fig. 7 suggests that the best MLP model performs reasonably well over a wide range of metallicity. Figure 7. Comparison between oxygen abundances from the best MLP model (Section 2.3.4) and the T e method. The data points are the working sample described in Section 2.1 . The error bars are the standard deviations of the 100 predictions from the 100 model realizations. The dashed line is the one-to-one line. 2.3.5 Feature sensitivity Extracting physical interpretation from neuron weights and biases is known to be difficult. However, it is worth investigating how sensitive different features are to the output to understand their importance to the network. The sensitivity analysis can be achieved by computing the partial derivative of the output with respect to the input features. Using the best MLP model, I perturb one feature at a time while keeping the other features unchanged and compute the changes in the output metallicity. The small perturbation is set to 3 per cent of the standard deviation of the input feature of the working sample. The response of the model to the perturbations is calculated for the entire working sample. Fig. 8 presents histograms of the resulting changes in the output metallicities in the form of a ‘violin’ plot. The top three features that the network output is most sensitive to are [S ii ]/[N ii ], [N ii ]/[O ii ], and [N ii ] (deviate most from zero). Interestingly, photoionization models have demonstrated that the [N ii ]/[O ii ] ratio is a good metallicity diagnostic (at above 0.2 solar) due to its insensitivity to ionization parameter (Kewley Dopita 2002 ; Dopita et al. 2013 ). The combination of [N ii ]/[S ii ] and [N ii ]/H α is also suggested by Dopita et al. ( 2016 ) to be an excellent diagnostic that is insensitive to ISM pressure and ionization parameter. The neural network appears to rely more heavily on features that are also important in diagnostics developed from photoionization models, despite that this information is not given a priori. This demonstrates the ability of the neural network to directly ‘learn’ from the data. Figure 8. Feature sensitivity of the best MLP model, as measured by perturbing one feature at a time and


gradually distorted until a singular point appears, where the derivative is discontinuous. Further increasing y , the singular point moves at different x positions, thus generating a discontinuity that is also in the derivative . Starting from the position y = 0 where the solution is regular, the singularity develops over a distance ( y ∼ 6), which is of the order of the typical wavelength. This singularity is found also for other values of z , indicating that a singular surface is present in the 3D structure of A z . At the singular surface the components B x and B y are discontinuous, therefore the surface represent a current sheet. In contrast, the component // is regular in the whole domain. In Figure 1 (bottom panel) the profiles of the magnetic field components and of are plotted as functions of x , for y = 6.13 and z = 0.78. The presence of the discontinuity is clearly visible, mainly in the B y profile. The profile of is remarkably constant, except for a dip localized at the singular point. In fact, the constancy of is guaranteed by Equation ( 1 ), while the smoothing procedure, which modifies the “ideal” solution mostly around the singular point, represents an additional element that does not allow the solution A z to exactly satisfy Equation ( 1 ). Figure 1. Case A. Top panel: profiles of as functions of x , for various values of y , and at z = 0.78. Bottom panel: profiles of B x , B y , B z , and as functions of x , at y = 6.13 and z = 0.78. To study a situation that is closer to the solar wind turbulence, in Case B we considered more complex forms for A x ( x , y , z ), A y ( x , y , z ), and a z ( x , z ) that have 3D power-law spectra (2D for a z ). For the evaluation of these quantities, we used a synthetic turbulence model (STM) introduced by Malara et al. ( 2016 ) and already employed in modeling magnetic turbulence (Pucci et al. 2016 ; Perri et al. 2017 ). The STM builds up a turbulent field as a superposition of localized fluctuations with different amplitudes at different logarithmically distributed spatial scales. The model can reproduce an anisotropic spectrum (Malara et al. 2016 ) that follows the critical-balance scaling law (Goldreich Sridhar 1995 ), where and l ⊥ are the perturbation scale lengths parallel and perpendicular to the mean magnetic field , respectively. Using the STM, we generated A x , A y and the boundary condition a z in the scale ranges π ≤ l ⊥ ≤ π /32, . On average, the amplitude of a fluctuation in the spectrum of the vector potential i th component scales as . For h = 1/3 the spectrum of the spatial derivatives of has a Kolmogorov index () in the perpendicular directions, while in the parallel direction. We choose the parallel direction along x , which is approximately the direction of (see below). The STM can also reproduce intermittency through a p -model technique (Meneveau Sreenivasan 1987 ); in the present case we used p = 0.5, corresponding to no intermittency. A more detailed description of


of Sgr in that area of the sky with mean velocities v r 130 and115kms 1 . The position of these peaks are compatible with the ones derived from the velocity distribution of the target stars. According to the classification provided by these models, the bulk of Sgr stars around v r 130kms 1 might belong to the trailing arm of that halo substructure while the less significant peak might correspond to the leading arm. The mean heliocentric distance predicted by PR10 for both wraps in this area of the sky is d 30kpc. On the other hand, LM10 predicts mean distances of d 21 and 28kpc for the leading and trailing arms, respectively. The expected two sections of the Sgr tidal stream along the line of sight to Whiting1 are evident in our spectroscopic results but not in the colourmagnitude diagram (CMD) shown in Fig. 1 . We analyse the distribution of target stars belonging to the Sgr components as a function of g by counting stars associated with the leading [160 v r (kms 1 )100] and trailing [90 v r (kms 1 )150] arms with a bin size of g 0.1. Fig. 3 shows the normalized distribution obtained for both populations and we are not able to determine a shift in the g band between the subsamples of target stars. This might indicate that the leading and trailing arms of Sgr are spatially coincident or have slightly different distances, making it difficult to distinguish the populations in the CMD. Therefore, our results are in good agreement with the predictions made by the PR10 model both for the position and the kinematics of the leading and trailing components of the Sgr tidal stream around Whiting1. Figure 3. Left-hand panel: CMD for stars beyond 10arcmin from the centre of Whiting1. The positions in the diagram of stars belonging to the Sgr trailing and leading wraps are indicated as orange stars and green triangles, respectively. The blue isochrone corresponds to a t 10Gyr and [Fe/H] 1.5 population. Right-hand panel: normalized distribution of stars belonging to both arms as a function of g in the range 19 g 23.5 and following the same colour code as in the left-hand panel. According to the PR10 classification, target stars with radial velocities around v r 120kms 1 might be associated with an old component of the leading arm of Sagittarius, accreted a long time ago (2Gyr). While the northern and southern trailing arms have been well characterized using different tracers such as RRLyrae, blue horizontal branch, sub-giant branch and red clump stars (e.g. Koposov etal. 2012 ; Belokurov etal. 2014 ), the southern leading arm predicted both by PR10 and LM10 , has remained undetected. This might be due to the coincidence of its projected path with that of the trailing arm or to its lower surface brightness. Only tentative detections have been reported using alternative tracers such as carbon stars, with distances and velocities consistent with our results along that line of sight (Huxor Grebel 2015 ). Alternatively, the group of stars with positive radial


the models relax during 200 T cr (about a Hubble time); the final snapshot was again rotated using the moments of the inertia tensor of the 80 per cent most tightly bound particles. These last systems (one for each model) were evolved during an additional interval of 300 T cr in order to verify their stability. For each of the two models, the snapshot corresponding to 100 T cr of this last evolution was the one used to study and classify the respective orbital contents; we call them E2af and E5af, respectively, for brevity. Fig. 1 shows the kinematic and structural characteristics of the E2af model. In this figure, the abscisae q stands for the ellipsoidal radius where a , b and c are the semi axes of the model, computed following the method of Dubinski Carlberg ( 1991 ), as adapted by Holley-Bockelmann et al. ( 2001 ); Q , on the other hand, is the same as q but projected on to the coordinate planes. The abscisae M ( r )/ M is the mass interior to radius r in units of the total mass of the model. The upper-left panel shows the density profile of the model, computed using ellipsoidal shells with constant axial ratios taken at the half-mass radius. As can be seen, the rotation has not substantially affected the cusp of the model (γ = −1.023 ± 0.020, computed from the densities of the 10 000 innermost particles binned in 100 intervals of distance to the centre). The upper-right panel shows the axial ratios, computed in shells each containing 3 per cent of the particles, previously sorted by energy. The ratios of the semi axes of the shell containing 81 per cent of the mass in its interior are b / a = 0.939 and c / a = 0.791, in good agreement with the values that correspond to the 80 per cent most tightly bound bodies ( b / a = 0.925, c / a = 0.823, T = 0.447), i.e. the parameters used in our previous works. Comparing these values with those of the original E2a model, we can see that the b / a ratio has increased, whereas the c / a ratio and the triaxiality have decreased. The bottom panels show the kinematical profiles, in which , where i is a Cartesian direction x , y or z in the left-hand panel, and r (radial) or t (tangential) direction in the right-hand panel. The anisotropy parameter . Fig. 2 shows the same characteristics but for the E5af model. Again, the cusp is well preserved (γ = −0.956 ± 0.023). In this case, for the same shell as before, b / a = 0.916, c / a = 0.602, while for the 80 per cent most tightly bound particles, b / a = 0.896, c / a = 0.641 and T = 0.335, i.e. both axial ratios have increased and the triaxiality decreased with respect to the E5a model. It might seem odd that rotation has not made the model flatter, but it should be recalled that the process that led from the non-rotating to the rotating model implied considerable changes in structure of the former. For example, about 30 per cent of the original particles were eliminated because they increased their energies beyond the established limits, and the a semi


flux toward the Lyman limit. The consequence of this is that at high redshift (), SLSNe-I have a characteristic red observer-frame color and long-duration light curves. The identification of SLSNe-I at requires information on the UV spectrum and evolution. As highlighted in Section 3.5 , data in this wavelength range are sparse, with only DES16C2nm, Gaia16apd, PS1-11bam, and DES15E2mlf having data that extend to . Figure 9 shows the luminosity and color evolution of SLSNe-I at maximum light inferred from these spectra as a function of redshift. The spectra have been normalized and adjusted to the peak magnitude and color of each event. These spectra are then redshifted between 0 and 4, and integrated through the DECam r and z passbands. Figure 9 shows the evolution in luminosity and color for these spectra, along with other events in the literature. Where required, K -corrections have been determined from the spectrum of Gaia16apd. The single-epoch 5 σ magnitude limits of the DES deep and shallow fields are shown along with those expected for LSST wide-field and deep-drilling fields (Scovacricchi et al. 2016 ; D. Scolnic 2017, private communication). These limits suggest that in a single epoch, DES can detect SLSNe-I that are spectroscopically similar to Gaia16apd and DES16C2nm, to z = 3.2 in z -band observations of its deep fields or z = 3.8 for objects that are spectroscopically similar to DES15E2mlf. For the LSST deep-drilling fields, the maximum redshifts in the z band are 3.5 for the DES16C2nm spectrum and 4.3 when considering the DES15E2mlf spectrum. Figure 9. Observer-frame evolution of SLSNe-I. Upper panel: the apparent r -band evolution of SLSNe-I as a function of redshift. DES16C2nm is shown as a purple star, with literature SLSNe-I in orange and the photometrically confirmed objects of Cooke et al. ( 2012 ) shown as black crosses. Values determined from the maximum-light spectrum of Gaia16apd, normalized to the peak magnitude of Gaia16apd, are shown in blue, with the corresponding DES16C2nm spectrum from VLT in red and DES15E2mlf in green. K -corrections for literature events have been determined using the Gaia16apd spectrum. The magnitude limits for the DES deep and shallow fields and LSST wide-field and deep-drilling fields are also shown. Second panel: as above, only for the z band. Third panel: the J -band evolution of SLSNe-I as a function of redshift. The magnitude limits for the Euclid and WFIRST shallow, medium, and deep surveys are also shown. Lower panel: the r − z color evolution of SLSNe-I as a function of redshift as inferred from the upper two panels. A horizontal line of mag highlights the difference between low () and high () redshift events. This analysis can be extended to the observer-frame NIR, where surveys such as Euclid (with 5 σ limiting magnitude per visit in the deep fields and an irregular cadence of 10 visits to each of the two fields in a 6-month observing window for 5 years; Inserra et al. 2018a )


; Livadiotis McComas 2012 , 2013b ; Livadiotis 2016 ). Therefore, the IBEX maps may be consistent with the radial trend in γ sw detected with NH -SWAP. If we find that γ sw behaves in a systematic way using Voyager 2 observations, we may be able to monitor γ sw with NH and forecast when NH will reach the termination shock or at least determine if the location of the termination shock is moving dramatically inward or outward. Many theoretical and simulation studies have explored how the process of the solar wind picking up interstellar material can heat the solar wind (Matthaeus et al. 1999 ; Smith et al. 2001 ; Isenberg et al. 2003 ; Adhikari et al. 2017 ; Zank et al. 2018 ). Given that when we account for the radial variation of γ sw , we are then able to obtain excellent agreement between the inferred slowing from the amount of pickup and the amount of observed slowing, we conclude our work provides further observational evidence that the solar wind picking up interstellar pickup ions likely plays a role in heating the solar wind and altering the T – n relationship with increasing radial distance. However, additional work combining simulations and data should be performed to determine exactly why the solar wind T – n relationship systematically varies in a way that produces a linear decrease in γ sw with increasing distance from the Sun. Possibly, solar wind turbulence or wave particle interactions generated by the pickup process heat the solar wind altering the T – n relationship with increasing radial distance. In the inner heliosphere compressions, shocks, and shears are strong, but in the outer heliosphere all of those are much weaker. Therefore, those are not likely to impact the changes in the T – n relationship to the degree that waves and turbulence related to the waves could in the outer heliosphere. Our solar wind polytropic index radial profile γ sw ( r ) for the outer heliosphere, our initial analysis of the evolution of the total polytropic index ( γ ) from the inner to outer heliosphere, and the total polytropic index ( γ ) in the heliosheath from IBEX provide substantial metrics for outer heliospheric simulations. This work will become more relevant as NH gets closer to the termination shock heading in the direction of the ribbon and higher-resolution maps of the ENA ribbon from the Interstellar Mapping and Acceleration Probe ( IMAP ) mission become available (McComas et al. 2018 ). Below, we summarize our main findings and conclusions. 1. In the outer heliosphere (21–43 au), we found the density radial profile to decrease at either nearly or slightly less than the spherical expansion rate. 2. As NH moves farther away from the Sun, we can assess if picking up of interstellar material hinders the expansion of the solar wind altering the solar wind density profile. 3. In the outer heliosphere (21–43 au), the temperature profile is well above what is expected for an adiabatic profile. 4. The relationship between the solar wind


lower. If the unknown energy is from dark energy, this implies the existence of inhomogeneity of the dark energy (de Putter et al. 2010 ; Blomqvist 2008 , 2010 ). Appendix A NPB Correction for Patches with Beam Convolution Fourier transform presumes that the signal is periodic such that the two ends are continuous; thus, when one deals with real data, it is inevitable to encounter jump discontinuity, which induces extra power in the power spectrum. Although the data are mostly discrete, the NPB effect nevertheless persists and should be taken into account as systematic error. A patch taken from a full-sky map has such an intrinsic effect, which is uncorrectable because NPB is part of the morphology. The effect, however, is further aggravated when there is beam convolution. As the statistics and comparisons in this paper are made between beam-convolved Planck data and simulations with the best-fit ΛCDM model (without beam convolution), it is necessary to study the effect because the power spectrum of a beam-convolved patch has more induced power than the smoothed power spectrum of the nonperiodic patch. To estimate the correction, we simulate 50 full-sky CMB maps and take 30 deg 2 patches centered at the equator (in total 600 patches). We take the central 20 deg 2 part directly from the 30 deg 2 patches and denote their mean power spectrum as . Then we use 5′ to convolve the 30 deg 2 patches and choose the central 20 deg 2 part, the mean power spectrum of which is denoted . The correction is therefore , where b is the beam transfer function. One finds that the extra power due to 5′ beam convolution is a rather smooth curve and can be best fitted to be ( μ K 2 ) from l ≥ 300. And for the 143 GHz band map with beam transfer function 730 (Adam et al. 2016a ) the correction for NPB is ( μ K 2 ). Appendix B XPS on the <italic>Planck</italic> Data Throughout the paper we use XPS on the Planck data: four CMB maps, the 143 GHz channel map, and the foreground-subtracted maps at 100, 143, and 217 GHz from the SEVEM method, to extract the peak position. The XPS is a quadratic estimator between two maps that can provide an unbiased estimate of the underlying power spectrum of the correlated signals and, at the same time, reduce the uncorrelated ones. We take from the Planck Legacy Archive the FULL MISSION RINGHALF1 and FULL MISSION RINGHALF2 maps for SMICA, NILC, SEVEM, Commander, and the 143 GHz map. Since the patches from RINGHALF1 (denoted α ) and RINGHALF2 (denoted β ) contain the same CMB signal but uncorrelated noise, we can employ the XPS on their Fourier modes and ,where ∗ denotes complex conjugate and the angle brackets denote average over all for integer k . However, as Chiang Chen ( 2011 , 2012 ) pointed out, lack of an ensemble and nonzero chance correlation with the so-called “uncorrelated” signal results in some residual from the XPS, which has the following relation:where and are the (uncorrelated) noise power spectrum from RINGHALF1 and


this work we do not see a wedge structure due to the incomplete treatment of instrumental frequency dependence. This will be addressed in future work. We have however included two theoretical lines relating to the wedge limit on all figures – a dashed line which assumes sources in the entire field of view (in our case 10 deg) will leak into the main field and an optimistic solid line which assumes only sources within the chosen central 4 deg (approximately the full width at half-maximum – FWHM – of the station beam) will affect the image. Further work on the contamination within the wedge is ongoing in the literature and as such recovery below the theoretical wedge line should be treated with caution. We refer to the combination of the noise, dirty foregrounds and dirty cosmological signal as the ‘total input signal’. We refer to the foreground model estimated by GMCA as the ‘reconstructed foregrounds’ and the difference between the reconstructed foregrounds and the total input signal as the ‘residuals’, which will contain the cosmological signal, noise and any foreground fitting errors. The foreground fitting errors can be defined as the difference between the simulated foregrounds and the reconstructed foregrounds and will contain any cosmological signal or noise which has been fitted as foregrounds as well as an absence of any foregrounds not modelled. 5 RESULTS Unless otherwise stated we present results for cylindrical power spectrum calculated over a 10 MHz bandwidth segment centred at 165 MHz, where the variance of the cosmological signal peaks in our simulation. This bandwidth is formed using an extended Blackmann–Nuttall window, though other windows are possible, as discussed in Section 5.1 . We 3D Fourier transform the data segment and bin the data according to the values of k perp , k los . The power at any particular k los , k perp , P ( k los , k perp ) = 〈δ( k los , k perp )δ*( k los , k perp )〉 is the average power of all the uv cells in the bin centring on k los , k perp . We choose to plot the ‘dimensionless’ power spectrum, , which has units of mK 2 throughout this paper: where V is the volume of the 10 MHz bandwidth in Mpc. We first construct cylindrical power spectrum for the different signal contributions in order to understand how the EoR window is constructed. In Fig. 1 , we see the Galactic synchrotron, Galactic free–free and unresolved extragalactic foregrounds while in Fig. 2 we see the dirty cosmological signal and dirty foregrounds (with all three foreground contributions summed). The action of the PSF can be clearly seen as a loss of power on scales above this (i.e. for k perp > 0.65 Mpc −1 ). Note that, since we are seeing power spectrum over a 10 MHz bandwidth only we do not see the evolution of the cosmological signal over redshift. We see clearly the area of k -space where the foregrounds appear to be at their strongest is at low k los , however, it should be noted that there is appreciable foreground


of the neck radius, a , determined by the numerical simulation and laboratory experiments. The spring constant increased almost linearly with neck radius, and the results from the numerical simulation (circles) and laboratory experiments (triangles and squares) were observed to overlap. Figure 6. Results of FEM simulation (circles) and laboratory experiments (triangles and cubes) for compression. The solid line denotes the semianalytical formula (Equation ( 4 )). Triangles and cubes are determined using the data between 90 to 95 and 40 to 90 N, respectively. The error bars of laboratory experiments are the standard deviation of three samples. The upper curve is from SU17 . The inverse triangle is the FEM simulation result for the a = R cylinder (without shrinkage due to sintering). Two sets of laboratory experiment results are shown in Figure 6 ; the difference between these sets is the force range used to determine the spring constant. Figure 7 displays the applied force as a function of displacement as measured in the laboratory experiment. This relationship was not linear, particularly for small forces; thus, the spring constant is dependent on the range of the applied force. In contrast, the FEM simulation was based on a linear response. The spring constant at the commencement of the compression was small compared to that at a large compressive force. There are two possible causes for this nonlinear behavior. First, the misalignment of the two end planes led to a nonlinear behavior because the force required to enable deformation until perfect fitting to the autograph was small compared to the force required after the perfect fitting. Second, if there is a bump on the end surface, the compression force changes at the commencement of compression. Figure 7. An example of a laboratory experiment result. At the beginning, the force increases nonlinearly, and then increases almost linearly after reaching 20 N. The neck shape was adopted from the second curve from the bottom in Figure 2 . The spring constant was determined using the data in the linear region of the force-displacement curve. For comparison, two ranges of the compression force were used; 40–90 and 90–95 N. Although there was a considerable scatter in the data, the results from the laboratory experiments were consistent with the numerical simulation results. The maximum radius in Figure 6 is 2.375 mm, corresponding to the original radius of the sphere prior to sintering. However, this radius was not realized by sintering, because the volume of the sphere decreased as a result of sintering. The maximum radius () following sintering was . The solid curve in Figure 6 is the model in SU17 . In contrast to the experimental and numerical results, the spring constant of the model increased as the neck radius decreased. In this model, the deformable region was restricted to the neck between the spheres, and the length of the neck decreased with the neck radius. As a result, the


mergers might be detectable for longer (e.g. through stellar streams, bright cores) than gas-poor galaxies. CO surveys of protocluster and identically selected field galaxies would allow one to compare the gas mass fractions of these two populations. Protocluster galaxies might be expected to have higher gas fractions due to efficient supply of pristine intergalactic gas through filamentary accretion, but this is a picture yet to be empirically tested. Lyα blobs are generally found in high- z protoclusters and indicate the presence of large volumes of cold gas around forming galaxies. Fakhouri Ma ( 2009 ) examined the role of environment on the halo merger rate in N -body simulations, using the friend-of-friends group finder (Davis et al. 1985 ) within the millennium simulation (Springel, Matteo Hernquist 2005 ) to trace the merger histories of dark matter sub-haloes out to z = 2. A key finding was a correlation between environment and merger rate, such that sub-haloes in the densest environments underwent merger rates 2–2.5 times higher than those in the lowest density regions. With the caveat that galaxies are biased tracers of the matter field, it is reasonable to assume that there will be a similar trend for the galaxies themselves. It is interesting that the level of enhancement of the merger rate found by Fakhouri Ma ( 2009 ) in the simulations is broadly in agreement with the enhancement we find for SSA22. Our analysis traces the rest-frame ultraviolet emission which is very sensitive to dust obscuration; for example, extended/clumpy star-forming regions could be hidden and the merger fraction understated, or a clumpy dust distribution could lead to very high extinction to certain stellar populations, giving the stellar emission overall a clumpy morphology, that could possibly be misinterpreted as a merger. We do not expect the use of rest-frame UV observations to lead to a significant bias in our interpretation unless there is a significant difference between the obscuration properties of galaxies in the protocluster and the field, since we have applied an identical analysis to both. Nevertheless, we are now obtaining near-infrared HST -WFC3 observations that will allow us to repeat our analysis based on the morphology of the rest-frame optical flux. Similarly, we have ALMA follow-up observations of LBGs along the ‘merger sequence’ in SSA22 that will allow us to directly detect the thermal emission from cold dust responsible for extinction in the ultraviolet/optical light. Our result is marginal mainly due to small number statistics, which dominate the size of the uncertainties on our merger fractions. This arises from the lack of a complete LBG catalogue covering the whole SSA22 field and sparse HST coverage of SSA22. It would be useful to extend our analysis to additional protoclusters and fields at a similar redshift to overcome the potential issues of small number statistics and cosmic variance, but high- z protoclusters are


SNe roughly match the required luminosity and timescale, but we would not expect their progenitors to explode two years later as SNe Ia (Bildsten et al. 2007 ). The fast-declining light curves of SNe Ibn also indicate that very little 56 Ni is produced in the explosion (Foley et al. 2007 ; Pastorello et al. 2008a ), which may challenge white dwarf explosion models. One way of avoiding these issues is to allow PS1-12sk and SN 2006jc to come from different types of stars. SNe Ibn would then be a mixed class, with some low- and some high-mass progenitors. This could potentially explain some of the spectral diversity we see among SNe Ibn (Hosseinzadeh et al. 2017b ). The five spectra that we have of PS1-12sk look almost identical to spectra of SN 2006jc, 12 12 SN 2006jc was discovered after peak, so the phases of these spectra are not well constrained. but perhaps any explosion into helium-rich CSM would look the same. This situation would be analogous to the discovery that some events initially classified as SNe IIn are actually the explosions of white dwarfs with hydrogen-rich CSM (now called SNe Ia-CSM; Dilday et al. 2012 ; Silverman et al. 2013 ). In fact, this may be the reason that events classified as SNe IIn are less correlated with star formation than other classes of core-collapse SNe (Anderson et al. 2012 ; Habergham et al. 2014 ), despite some having luminous progenitor detections. 5. Summary and Conclusions We have presented a very deep limit on the star formation rate at the site of the SN Ibn PS1-12sk, nominally ruling out a massive star origin. We present three alternative proposals for how this SN could have occurred in such a unique environment. 1. The progenitor of PS1-12sk was a massive star ejected or tidally stripped from a nearby ultra-compact dwarf galaxy. 2. The progenitor of PS1-12sk was a rare massive star in a region with a very low star formation rate. 3. The progenitor of PS1-12sk was a low-mass star. Our result only deepens the mystery surrounding PS1-12sk, in that none of these possibilities is fully satisfactory in explaining the origins of SNe Ibn. Given that there is not much more data to collect on this particular event, the resolution will likely come from a statistical study of SN Ibn host galaxies. Although this is currently the only SN Ibn discovered in a non-star-forming environment, we still suffer from a small sample size of only tens of events. Current and future large-scale surveys will be much better suited to find these rare, fast-evolving transients, allowing us to better understand the statistical properties of their host environments. Appendix A Extinction Sanders et al. ( 2013 , p. 4) claimed that “the SED of [PS1-12sk] is not consistent with significant reddening given reasonable assumptions about the photospheric temperature” and neglect extinction throughout their analysis. However, as an additional check, we calculate an upper limit on the host galaxy extinction based on the nondetection of


find (their Table 1, with ). On the other hand, Hoang et al. ( 2018 ) find much higher merger fractions of up to for their nominal GC model, which are higher than the merger fractions of Petrovich Antonini ( 2017 ) and our merger fraction by 2 orders of magnitude. This large difference can be ascribed to different initial conditions. About half of the binaries in Hoang et al. ( 2018 ) merge due the gravitational wave emission only (i.e., even in the absence of the torque of the MBH). Moreover, Hoang et al. ( 2018 ) considered binaries much closer to the MBH ( to (∼10 −2 )) for which the octupole-order terms are important, in contrast to our simulations. The merger rate predicted by Hoang et al. ( 2018 ) is ∼1–, which is one (two) order(s) of magnitude larger than our GC rate estimate without VRR assuming a top-heavy (canonical) IMF. This can be ascribed to the following. 1. The merger fraction adopted by Hoang et al. ( 2018 ) is , which is 0.15/0.005 = 30 times larger than our adopted fraction. 2. The “conversion” factor from the merger fraction to the rate adopted by Hoang et al. ( 2018 ) is . We assumed a “conversion” factor of and for the canonical and top-heavy IMFs, respectively. These two points combined explain the different merger rates. In calculating their rates, Hoang et al. ( 2018 ) assumed that there exists a steady-state population of BH–BH binaries in the central 0.1 pc, with a number of corresponding to a merger rate of . This requires replenishment of the BH–BH binaries on a timescale of 100 Myr, which would be consistent with in situ star formation in a disk of massive O/B stars close to the MBH (e.g., Bartko et al. 2009 ). In our rate calculation, we assumed a global influx of compact objects, which is more appropriate in our situation given that we considered a binary population at larger distances from the MBH. VanLandingham et al. ( 2016 ) were the first to consider the combined effects of VRR and LK evolution by means of hybrid N -body methods. Due to computational limitations, the MBH masses were limited to up to . VanLandingham et al. ( 2016 ) found high merger fractions in their simulations. This is consistent with our results, in the sense that we find that the enhancement due to VRR is most significant for low MBH masses. More quantitatively, VanLandingham et al. ( 2016 ) found a merger fraction of in their simulation with (10k stars). This is very similar to our merger fraction of for the case and γ = 2 (adding the semisecular and non-semisecular fractions). This apparent agreement may be fortuitous, however, given that we did not consider a number of potentially important effects (see Section 6.1 ). In particular, DF is an important process in the simulations of VanLandingham et al. ( 2016 ); prior to their merger, most merging binaries sink inwards to the MBH. DF could therefore be important for bringing a binary from a regime with , where LK–VRR coupling is unimportant, to a region in which , where LK–VRR


the test set, where the training set builds the model, and the testing set evaluates the model's performance. In principle, the predictor performs better with a larger fraction of training data. On the other hand, the performance statistic will have greater variance if there is less testing data (Kohavi 1995 ). To strike a balance, we have tried changing the ratios of our training and testing sets from 50:50 to 90:10, and we verify that the XGBoost performs the best in both AUROCC and f1-score with a 70:30 split. To avoid over-fitting, we adopt an early stopping in XGBoost after five training iterations that do not yield any improvements. To control the balance of positive and negative weights, we set the scale _ pos _ weight = 28.7, which is given by the ratio between the number of negative and positive instances (4705/164; see Section 2.3 ). 3.3. Feature Selection Feature selection is an important process in machine learning that strongly influences the performance of the model. Feature selection is a procedure of selecting a subset of relevant features for model construction. In general, proper feature selection can increase the efficiency by reducing the training duration, enhancing generalization by reducing over-fitting, and improving the prediction performance (see Chen Guestrin 2016 ; An et al. 2019 ). A trained XGBoost model will automatically calculate feature importance and provide the feature importance scores. In this work, we first trained the XGBoost model based on the training data set and selected features by sorting feature importance scores calculated from the trained model. We then iteratively trained the model based on the selected subset of features until the point of best performance. We verified that both f1-score and AUROCC increase with the number of selected features until we use up all 79 features. Therefore, we did not reduce the number of feature vectors in this work. Considering the limitations of our computational resources, we repeated this procedure 10 times by using a different combination of training and test data sets in each iteration and estimated the average feature importance score from these 10 realizations. The top five important features in our sample are: K , ([3.6]−[4.5]), ( K − [4.5]), ([3.6]–[5.8]), and ( H − K ), which are similar to those photometric wave bands used by Chen et al. ( 2016 ; Optical-Infrared Triple Color: ( z − K ), ( K − [3.6]), and ([3.6]–[4.5])) and An et al. ( 2019 ; ( z − K ), ( J − K ), ( K − [3.6]), and ([3.6]–[4.5])). The top five important features in our sample can be associated to fundamental physical properties. The K -band flux roughly maps to the stellar mass, while the SMGs appear to be red and occupy a relatively well-defined region in near-infrared color–color space (see also Chen et al. 2016 ; An et al. 2019 ). 3.4. Tuning the Hyper-parameters The hyper-parameters are a set of parameters that define the machine-learning algorithm as a mathematical formula. The


site at a coronal location at or above the looptop. Having said that, we note that some spectral evolution of the electrons injected at the looptop along with the pitch-angle distribution can still affect the exact delay values, while the field inclination is taken into account within our 3D model. We checked that an SHS evolution of the injected nonthermal electron spectrum, where the spectral index varies by a few percent, while the electrons are beamed along the magnetic field can reduce the TOF distance by a factor of two as needed. However, such a model does not contain any population of nonthermal electrons reflected back to the coronal portion of the flaring loop(s) needed to account for the microwave emission. From this, we conclude that an electron beam with a modest angular scatter, rather than an ideal field-aligned beam, is responsible for the observed deviation of the loop half-length from the estimated TOF distance. Such an angular distribution is capable of reducing their “effective” speed along the magnetic field typically by a factor of 1.5–3. As we noted above, some angular spread is also required to supply a population of the upward-reflected electrons needed to interpret the microwave data. However, an isotropic angular distribution does not look likely given that it assumes a rather large pitch angle of the majority of streaming electrons and, thus, efficient trapping, which is not observed. Thus, the data favor an anisotropic beam-like distribution of the accelerated electrons with a modest opening angle of 30°–40°. The mirror ratio m = 3 in Loop II of our 3D model; thus, the electrons launched downward at the pitch-angle θ ≲ 35° will not be reflected at the footpoint and, thus, will not contribute to the trapping. The mean parallel velocity for the electrons launched at the looptop at θ = 35° is . Electrons with θ ≳ 35° will be reflected and will contribute to the brightness peaks observed at 5.7 GHz from the LF–loop. The observed delay of 70 ms between 5.7 GHz peaks and 102.2–293.5 keV emission peaks, both produced by presumably 400 keV electrons, places the 5.7 GHz source at a distance ∼5 Mm from the mirror points at the bases of loop II. Microwave emission at 17 and 34 GHz delayed by 120 ms requires an additional time for the electrons to be transported from Loop II to Loop I and, perhaps, additional time for trapping in Loop I. Thus, the time delays are naturally consistent with the identified magnetic configuration of the flare and the TPP model in which the particles are injected at the looptop of Loop II and then propagate to produce the observed variety of the HXR and microwave components. 3.2. Accelerated Electron Population In Section 2.4 we determined the HXR spectrum of subpeaks to be a single power-law with the indexes about 2.4. This spectrum is injected during a subpeak in addition to a preexisting population of nonthermal electrons responsible for a gradual (background) component of the burst.


β > 1 where L max remains irrelevant. Thus, equation ( 4 ) reduces to EE detection probability: Perley et al. ( 2009 ) caution that many non-EE short bursts are faint, and the presence of an extended emission might have gone undetected resulting in their classification as non-EE bursts. Norris et al. ( 2010 ), who did a detailed study on the sensitivity of BAT to extended emission conclude that BAT should be able to detect extended emission to intensities ∼10 −2 counts cm −2 s −1 , however it is only seen up to around ∼0.005 counts cm −2 s −1 indicating a true absence of EE in some bursts. Going by the latter, one does not necessarily have to incorporate an additional EE detection probability. However, we take a conservative stand and try to account for a possible selection bias against the detection of the faint extended emission component. The redshift-dependent EE detection probability should involve the luminosity function of extended emission, but with the limited sample it is difficult to arrive at the same. Therefore, we considered a single constant luminosity for extended emission. This approximation is simplistic, given the two orders of magnitude spread in EE luminosity (see Fig. 3 ). For the threshold of BAT, we used ε BAT = 0.005 counts cm −2 s −1 , motivated by the typical average fluxes EE is seen in BAT as mentioned by Norris et al. ( 2010 ). Thus, equation ( 4 ), in this particular case, reduces to as, P () becomes a step function, H ( L EE − 4π d L () 2 ε BAT ) which is zero if L EE 4π d L () 2 ε BAT and unity otherwise. We ran our simulations for two values of L EE around the average luminosity of the six bursts (1.5 × 10 56 counts s −1 ), L EE = 10 56 , and 2 × 10 56 counts s −1 resulting in a max of 1.8 and 2.53, respectively. The results we obtain from these are nearly identical. Figure 3. Average luminosity of the EE component, from the data presented in Norris et al. ( 2010 ). Pen symbol is GRB 090510A. The error bars on other bursts are smaller than the symbol. One of our weak-EE bursts, 080123, is not a part of the data of Norris et al. ( 2010 ). We included GRB160410 following the GCN report by Sakamoto et al. ( 2016 ). We used a det = 0.16 sq cm to convert numbers from Sakamoto et al. ( 2016 ) and calculated the average luminosity. It can be seen that L EE varies by around two orders of magnitude. For our analysis we fixed values near the mean of these bursts (dotted and dash–dotted lines). The yellow solid line is the threshold, . We also considered a P () = 1 throughout, i.e. BAT does not miss any EE component due to sensitivity issues. Throughout this paper, we have used a standard cosmological model with H 0 = 71 km s −1 Mpc −1 , Ω m = 0.3, and Ω λ = 0.7. 4 ANALYSIS AND RESULTS In this section, we describe our analysis of the redshift distribution for both EE and non-EE bursts, and compare the parameters focusing mostly on the delay time distribution function. We begin by giving a detailed account of how we set up