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Dispersion measures (DM) of fast radio bursts (FRBs) probe the density of electrons in the intergalactic medium (IGM) along their lines-of-sight, including the average density versus distance to the source and its variations in direction. While previous study focused on low-redshift, FRBs are potentially detectable out to high redshift, where their DMs can, in principle, probe the epoch of reionization (EOR) and its patchiness. We present the first predictions from large-scale, radiation-hydrodynamical simulation of fully-coupled galaxy formation and reionization, using Cosmic Dawn (``CoDa")~II to model the density and ionization fields of the universe down to redshifts through the end of the EOR at $z_{re}\approx6.1$. Combining this with an N-body simulation CoDa~II--Dark Matter of the fully-ionized epoch from the EOR to the present, we calculate the mean and standard deviation of FRB DMs as functions of their source redshift. The mean and standard deviation of DM increase with redshift, reaching a plateau by $z(x_{HII}\lesssim0.25)\gtrsim8$, i.e. well above $z_{re}$. The mean-DM asymptote $\mathcal{DM}_{max} \approx 5900~\mathrm{pc\, cm^{-3}}$ reflects the end of the EOR and its duration. The standard deviation there is $\sigma_{DM, max}\approx497 ~\mathrm{pc\, cm^{-3}}$, reflecting inhomogeneities of both patchy reionization and density. Inhomogeneities in ionization during the EOR contribute $\mathcal{O}(1$ per cent) of this value of $\sigma_{DM,max}$ from FRBs at redshifts $z\gtrsim 8$. Current estimates of FRB rates suggest this may be detectable within a few years of observation., Comment: 14 pages, 10 figures, 2 tables, 2 appendices

We present the results of our multi-wavelength (X-ray to radio) follow-up campaign of the Einstein Probe transient EP240408a. The initial 10 s trigger displayed bright soft X-ray (0.5-4 keV) radiation with peak luminosity $L_\textrm{X} \gtrsim 10^{49}$ ($10^{50}$) erg s$^{-1}$ for an assumed redshift z>0.5 (2.0). The Neil Gehrels Swift Observatory and Neutron star Interior Composition ExploreR discovered a fading X-ray counterpart lasting for $\sim$5 d (observer frame), which showed a long-lived (~4 d) plateau-like emission ($t^{-0.5}$) before a sharp powerlaw decline ($t^{-7}$). The plateau emission was in excess of $L_\textrm{X} \gtrsim 10^{46}$ ($10^{47}$) erg s$^{-1}$ at z>0.5 (2.0). Deep optical and radio observations resulted in non-detections of the transient. Our observations with Gemini South revealed a faint potential host galaxy ($r \approx 24$ AB mag) near the edge of the X-ray localization. The faint candidate host, and lack of other potential hosts ($r \gtrsim 26$ AB mag; $J \gtrsim 23$ AB mag), implies a higher redshift origin (z>0.5), which produces extreme X-ray properties that are inconsistent with many known extragalactic transient classes. In particular, the lack of a bright gamma-ray counterpart, with the isotropic-equivalent energy ($10 - 10,000$ keV) constrained by GECam and Konus-Wind to $E_{\gamma,\textrm{iso}} \lesssim 4\times10^{51}$ ($6\times10^{52}$) erg at z>0.5 (2.0), conflicts with known gamma-ray bursts (GRBs) of similar X-ray luminosities. We therefore favor a jetted tidal disruption event (TDE) as the progenitor of EP240408a at z>1.0, possibly caused by the disruption of a white dwarf by an intermediate mass black hole. The alternative is that EP240408a may represent a new, previously unknown class of transient., Comment: Submitted; 33 pages; 9 figures

We propose a model that can describe the entire range of FRBs, from non-repeating to highly prolific repeaters. Coherent radio waves in these bursts are produced in the polar cap region of a magnetar, where magnetic field lines are open. The angle between the rotation and magnetic axes, relative to the angular size of the polar cap region, partially determines the repetition rate and polarization properties of FRBs. We discuss how many of the properties of repeating FRBs - such as their lack of periodicity, energetics, small PA swing, spectro-temporal correlation and inferred low source density are explained by this model. The systematic PA swing and the periodic modulation of long duration bursts from non-repeaters are also natural outcomes. We derive a lower limit of about 400 on the Lorentz factor of FRB sources using this model for bursts with a linear polarization degree greater than 95%., Comment: Submitted

We study the observable spectral and temporal properties of kilonova remnants analytically, and showcase quantitative differences with respect to supernova remnants. We provide detection prospects of kilonova remnants in the context of ongoing radio surveys. We find that there is a good chance to expect 10s of such objects in future surveys with a flux threshold of $\sim 0.1$ mJy. Kilonova remnants from a postulated population of long lived supramassive neutron star remnants of neutron star mergers are even more likely to be detected as they are extremely bright and peak earlier. For ongoing survey with threshold of $\sim$ mJy, we expect to find 10-100s of such objects if they are a significant fraction of total kilonova population. Considering that there are no promising such kilonovae candidates in current surveys, we constrain the fraction of such extreme kilonova to be no more than 30 percent of the overall kilonovae rate, depending on the details of ejecta mass and external density distribution., Comment: Comments welcome

We propose different estimators to probe the epoch of reionization (EoR) intergalactic medium (IGM) using the dispersion measure (${\rm DM}$) of the FRBs. We consider three different reionization histories which we can distinguish with a total of $\lesssim 1000$ ${\rm DM}$ measurements during EoR if their redshifts are known. We note that the redshift derivatives of ${\rm DM}$ are also directly sensitive to the reionization history. The major point of this work is exploring the variance in the ${\rm DM}$ measurements and the information encoded in them. We find that the all-sky average $\overline{{\rm DM}}(z)$ gets biased from the LoS fluctuations in the ${\rm DM}$ measurements introduced by the ionization of IGM during EoR. We find that the ratio $\sigma_{\rm DM}/\overline{{\rm DM}}$ depends directly on the ionization bubble sizes as well as the reionization history. On the other hand, we also find that angular variance (coined as $structure$ $function$) of ${\rm DM}$ encodes the information about the duration of reionization and the typical bubble sizes as well. We establish the usefulness of variances in ${\rm DM}$ using toy models of reionization and later verify it with the realistic reionization simulations., Comment: 18 pages, 16 figures, Comments are welcome

We constrain the redshift dependence of (rest frame) host galaxy dispersion measures of localized FRBs by assuming it to vary as a simple power law ($\propto (1+z)^{\alpha}$). We simultaneously fit $\alpha$ as well as the host dispersion measure to the data of FRBs with known redshifts. We find that $\alpha\approx 0$ is preferred over higher values of $\alpha$ with either a positive or negative sign. Such constraints have implications for our understanding of galaxy formation and can be used to inform galaxy and large scale simulations., Comment: Comments welcome

We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result is an $\widetilde{\mathcal{O}}(n^2)$-time algorithm for $k=6$ and $k=7$. The proof relies heavily on a new family of graphs that we introduce, called pattern-trees. Every such tree corresponds to an integer linear combination of permutations in $\mathbb{S}_k$, and is associated with linear extensions of partially ordered sets. We design an evaluation algorithm for these combinations, and apply it to a family of linearly-independent trees. For $k=8$, we show a barrier: the subspace spanned by trees in the previous family has dimension exactly $|\mathbb{S}_8| - 1$, one less than required. Our second result is an $\widetilde{\mathcal{O}}(n^{7/4})$-time algorithm for $k=5$. This algorithm extends the framework of pattern-trees by speeding-up their evaluation in certain cases. A key component of the proof is the introduction of pair-rectangle-trees, a data structure for dominance counting.

Fast radio bursts (FRBs) are micro-to-millisecond duration radio transients that originate mostly from extragalactic distances. The emission mechanism responsible for these high luminosity, short duration transients remains debated. The models are broadly grouped into two classes: physical processes that occur within close proximity to a central engine; and central engines that release energy which moves to large radial distances and subsequently interacts with surrounding media producing radio waves. The expected emission region sizes are notably different between these two types of models. FRB emission size constraints can therefore be used to distinguish between these competing models and inform on the physics responsible. Here we present the measurement of two mutually coherent scintillation scales in the frequency spectrum of FRB 20221022A: one originating from a scattering screen located within the Milky Way, and the second originating from a scattering screen located within its host galaxy or local environment. We use the scattering media as an astrophysical lens to constrain the size of the lateral emission region, $R_{\star\mathrm{obs}} \lesssim 3\times10^{4}$ km. We find that this is inconsistent with the expected emission sizes for the large radial distance models, and is more naturally explained with an emission process that operates within or just beyond the magnetosphere of a central compact object. Recently, FRB 20221022A was found to exhibit an S-shaped polarisation angle swing, supporting a magnetospheric emission process. The scintillation results presented in this work independently support this conclusion, while highlighting scintillation as a useful tool in our understanding of FRB emission physics and progenitors., Comment: Submitted, comments welcome

The observed behavior of a short gamma-ray burst (sGRB) afterglow lightcurve can reveal the angular structure of the relativistic jet and constrain the observer's viewing angle $\theta_\textrm{obs}$. Regardless of viewing angle, the afterglow emission is produced by the interaction between the relativistic jet and its surrounding environment. However, the observed deceleration time of the jet, and, therefore, the time of the afterglow peak, depends on the observer's viewing angle. A larger viewing angle leads to a later peak of the afterglow and a lower flux at peak. We use the the earliest X-ray afterglow detections of 58 cosmological sGRBs detected with the Neil Gehrels Swift Observatory X-ray Telescope to set an upper limit on the ratio of the viewing angle $\theta_\textrm{obs}$ to the jet's half-opening angle $\theta_\textrm{c}$. We adopt a power-law angular jet structure in both energy $E(\theta)\propto\theta^{-a}$ and Lorentz factor $\Gamma(\theta)\propto\theta^{-b}$ beyond the core. For this structured jet scenario we find that either sGRBs are viewed within $\theta_\textrm{obs}/\theta_\textrm{c}<1$ or the initial Lorentz factor of material in their jet's core is extremely high ($\Gamma_0>500$). If we consider a tophat jet structure, we constrain 90% of our sample to be viewed within $\theta_\textrm{obs}/\theta_\textrm{c}<1.06$ and 1.15 for our canonical and conservative afterglow scenarios. For a subset of events with measurements of the jet break, under the assumption that they on-axis we can constrain $\Gamma_0\theta_\textrm{c}\gtrsim 30$. This confirmation that cosmological sGRBs are viewed either on-axis or very close to their jet's core has significant implications for the nature of the prompt gamma-ray production mechanism and for the rate of future sGRB detections coincident with gravitational waves (GWs), implying that they are extremely rare., Comment: Accepted in MNRAS; minor revisions

Gamma-ray bursts (GRBs) are powered by ultra-relativistic jets. The launching sites of these jets are surrounded by dense media, which the jets must cross before they can accelerate and release the high energy emission. Interaction with the medium leads to the formation of a mildly relativistic sheath around the jet resulting in an angular structures in the jet's asymptotic Lorentz factor and energy per solid angle, which modifies the afterglow emission. We build a semi-analytical tool to analyze the afterglow light curve and polarization signatures of jets observed from a wide range of viewing angles, and focus on ones with slowly declining energy profiles known as shallow jets. We find overall lower polarization compared to the classical top-hat jet model. We provide an analytical expression for the peak polarization degree as a function of the energy profile power-law index, magnetic field configuration and viewing angle, and show that it occurs near the light curve break time for all viewers. When applying our tool to GRB 221009A, suspected to originate from a shallow jet, we find that the suggested jet structures for this event agree with the upper limits placed on the afterglow polarization in the optical and X-ray bands. We also find that at early times the polarization levels may be significantly higher, allowing for a potential distinction between different jet structure models and possibly constraining the magnetization in both forward and reverse shocks at that stage., Comment: 16 pages, 11 figures

A graph is called Rank-Ramsey if (i) Its clique number is small, and (ii) The adjacency matrix of its complement has small rank. We initiate a systematic study of such graphs. Our main motivation is that their constructions, as well as proofs of their non-existence, are intimately related to the famous log-rank conjecture from the field of communication complexity. These investigations also open interesting new avenues in Ramsey theory. We construct two families of Rank-Ramsey graphs exhibiting polynomial separation between order and complement rank. Graphs in the first family have bounded clique number (as low as $41$). These are subgraphs of certain strong products, whose building blocks are derived from triangle-free strongly-regular graphs. Graphs in the second family are obtained by applying Boolean functions to Erd\H{o}s-R\'enyi graphs. Their clique number is logarithmic, but their complement rank is far smaller than in the first family, about $\mathcal{O}(n^{2/3})$. A key component of this construction is our matrix-theoretic view of lifts. We also consider lower bounds on the Rank-Ramsey numbers, and determine them in the range where the complement rank is $5$ or less. We consider connections between said numbers and other graph parameters, and find that the two best known explicit constructions of triangle-free Ramsey graphs turn out to be far from Rank-Ramsey.

We explore the joint detection prospects of short gamma-ray bursts (sGRBs) and their gravitational wave (GW) counterparts by the current and upcoming high-energy GRB and GW facilities from binary neutron star (BNS) mergers. We consider two GW detector networks: (1) A four-detector network comprising LIGO Hanford, Livingston, Virgo, and Kagra, (IGWN4) and (2) a future five-detector network including the same four detectors and LIGO India (IGWN5). For the sGRB detection, we consider existing satellites Fermi and Swift and the proposed all-sky satellite Daksha. Most of the events for the joint detection will be off-axis, hence, we consider a broad range of sGRB jet models predicting the off-axis emission. Also, to test the effect of the assumed sGRB luminosity function, we consider two different functions for one of the emission models. We find that for the different jet models, the joint sGRB and GW detection rates for Fermi and Swift with IGWN4 (IGWN5) lie within 0.07-0.62$\mathrm{\ yr^{-1}}$ (0.8-4.0$\mathrm{\ yr^{-1}}$) and 0.02-0.14$\mathrm{\ yr^{-1}}$ (0.15-1.0$\mathrm{\ yr^{-1}}$), respectively, when the BNS merger rate is taken to be 320$\mathrm{\ Gpc^{-3}~yr^{-1}}$. With Daksha, the rates increase to 0.2-1.3$\mathrm{\ yr^{-1}}$ (1.3-8.3$\mathrm{\ yr^{-1}}$), which is 2-9 times higher than the existing satellites. We show that such a mission with higher sensitivity will be ideal for detecting a higher number of fainter events observed off-axis or at a larger distance. Thus, Daksha will boost the joint detections of sGRB and GW, especially for the off-axis events. Finally, we find that our detection rates with optimal SNRs are conservative, and noise in GW detectors can increase the rates further., Comment: 9 pages, 6 figures, 2 tables; accepted for publication in MNRAS. The definitive version will be available on the journal page

The duration of orbital decay induced by gravitational waves (GWs) is often the bottleneck of the evolutionary phases going from star formation to a merger. We show here that kicks imparted to the newly born compact object during the second collapse generically result in a GW merger time distribution behaving like $dN/d\log t \propto t^{2/7}$ at short durations, leading to ultrafast mergers. Namely, a nonnegligible fraction of neutron star binaries, formed in this way, will merge on a time scale as short as 10 Myr, and a small fraction will merge even on a time scale less than 10 kyr. The results can be applied to different types of compact binaries. We discuss here the implications for binary neutron star mergers. These include unique short gamma-ray bursts (GRBs), eccentric and misaligned mergers, $r$-process enrichment in the very early Universe and in highly star-forming regions, and possible radio precursors. Interestingly, we conclude that among the few hundred short GRBs detected so far, a few must have formed via this ultrafast channel., Comment: 19 pages, 8 figures. Accepted for publication in ApJ

Emission in many astrophysical transients originates from a shocked fluid. A central engine typically produces an outflow with varying speeds, leading to internal collisions within the outflow at finite distances from the source. Each such collision produces a pair of forward and reverse shocks with the two shocked regions separated by a contact discontinuity (CD). As a useful approximation, we consider the head-on collision between two cold and uniform shells (a slower leading shell and a faster trailing shell) of finite radial width, and study the dynamics of shock propagation in planar geometry. We find significant differences between the forward and reverse shocks, in terms of their strength, internal energy production efficiency, and the time it takes for the shocks to sweep through the respective shells. We consider the subsequent propagation of rarefaction waves in the shocked regions and explore the cases where these waves can catch up with the shock fronts and thereby limit the internal energy dissipation. We demonstrate the importance of energy transfer from the trailing to leading shell through $pdV$ work across the CD. We outline the parameter space regions relevant for models of different transients,e.g., Gamma-ray burst (GRB) internal shock model, fast radio burst (FRB) blastwave model, Giant flare due to magnetars, and superluminous supernovae (SLSN) ejecta. We find that the reverse shock likely dominates the internal energy production for many astrophysical transients., Comment: Accepted for publication in MNRAS

The tidal disruption event AT2018hyz was a regular optically detected one with no special prompt features. However, it suddenly displayed a fast-rising radio flare almost three years after the disruption. The flare is most naturally interpreted as arising from an off-axis relativistic jet. We didn't see the jet at early times as its emission was relativistically beamed away from us. However, we could see the radiation once the jet has slowed down due to interaction with the surrounding matter. Analysis of the radio data enabled estimates of the jet's kinetic energy and opening angle, as well as the conditions (size and magnetic field) within the radio-emitting region. We show here that such a jet satisfies the Hillas condition for the acceleration of UHECRs to the highest energies. We also show that the rate and total power of this event are consistent with the observed luminosity density of UHECRs. These results strongly support earlier suggestions that TDEs are the sources of UHECRs., Comment: Accepted for publication in JCAP. The revised version includes a rebuttle to Cendes et al., 2023 arXiv:2308.13595 and additional references to earlier work on the relation between UHECRs and TDEs

Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but the complex nature of the relevant astrophysical flows often requires higher dimensional studies. Here we study the two-dimensional problem of the reflection of a planer shock off of a wall for a general incidence angle and a cold unshocked medium. We use primarily relativistic hydrodynamic numerical simulations, and elaborately compare the results to an analytic treatment. The simulations are performed both in the rest frame S of the unshocked fluid, where the dimensionless proper speed of the singly shocked fluid is $u_1=\Gamma_1\beta_1$ and the shock incidence angle is $\alpha_1$, and in the rest frame S$^\prime$ of the point P of intersection of the incident shock and the wall for regular reflection (RR). Good agreement is obtained between the simulations in these two frames and with the analytic solution. The establishment of a steady flow in frame S$^\prime$ is explored, along with the transition between the strong and weak shock RR solutions. The transition line between RR and Mach reflection (MR) is studied numerically in the $u_1$-$\alpha_1$ plane and found to coincide with the analytic detachment/sonic line. The flow properties along the sonic line are investigated in detail focusing on how they vary between the Newtonian and relativistic limits., Comment: Submitted to MNRAS

Kilonovae are optical transients following the merger of neutron star binaries, which are powered by the r-process heating of merger ejecta. However, if a merger remnant is a long-living supramassive neutron star supported by its uniform rotation, it will inject energy into the ejecta through spindown power. The energy injection can boost the peak luminosity of a kilonova by many orders of magnitudes, thus significantly increasing the detectable volume. Therefore, even if such events are only a small fraction of the kilonovae population, they could dominate the detection rates. However, after many years of optical sky surveys, no such event has been confirmed. In this work, we build a boosted kilonova model with rich physical details, including the description of the evolution and stability of a proto neutron star, and the energy absorption through X-ray photoionization. We simulate the observation prospects and find the only way to match the absence of detection is to limit the energy injection by the newly born magnetar to only a small fraction of the neutron star rotational energy, thus they should collapse soon after the merger. Our result indicates that most supramassive neutron stars resulting from binary neutron star mergers are short lived and they must be rare in the universe., Comment: 16 pages, 9 figures. Submitted to MNRAS

The Tidal Disruption Event (TDE) AT 2018hyz exhibited a delayed radio flare almost three years after the stellar disruption. Here we report new radio observations of the TDE AT 2018hyz with the AMI-LA and ATCA spanning from a month to more than four years after the optical discovery and 200 days since the last reported radio observation. We detected no radio detection from 30-220 days after the optical discovery in our observations at 15.5 GHz down to a $3\sigma$ level of < 0.14 mJy. The fast-rising, delayed, radio flare is observed in our radio data set and continues to rise almost ~1580 days after the optical discovery. We find that the delayed radio emission, first detected $972$ days after optical discovery, evolves as $t^{4.2 \pm 0.9}$, at 15.5 GHz. Here, we present an off-axis jet model that can explain the full set of radio observations. In the context of this model, we require a powerful narrow jet with an isotropic equivalent kinetic energy $E_{\rm k,iso} \sim 10^{55}$ erg, an opening angle of $ \rm \sim 7^{\circ}$, and a relatively large viewing angle of $ \rm \sim 42^{\circ}$, launched at the time of the stellar disruption. Within our framework, we find that the minimal collimated energy possible for an off-axis jet from AT 2018hyz is $E_k \geq 3 \times 10^{52}$ erg. Finally, we provide predictions based on our model for the light curve turnover time, and for the proper motion of the radio emitting source., Comment: 8 pages, 6 figures, submitted to MNRAS

Internal shocks are a leading candidate for the dissipation mechanism that powers the prompt $\gamma$-ray emission in gamma-ray bursts (GRBs). In this scenario a compact central source produces an ultra-relativistic outflow with varying speeds, causing faster parts or shells to collide with slower ones. Each collision produces a pair of shocks -- a forward shock (FS) propagating into the slower leading shell and a reverse shock (RS) propagating into the faster trailing shell. The RS's lab-frame speed is always smaller, while the RS is typically stronger than the FS, leading to different conditions in the two shocked regions that both contribute to the observed emission. We show that optically-thin synchrotron emission from both (weaker FS + stronger RS) can naturally explain key features of prompt GRB emission such as the pulse shapes, time-evolution of the $\nu{}F_\nu$ peak flux and photon-energy, and the spectrum. Particularly, it can account for two features commonly observed in GRB spectra: (i) a sub-dominant low-energy spectral component (often interpreted as ``photospheric''-like), or (ii) a doubly-broken power-law spectrum with the low-energy spectral slope approaching the slow cooling limit. Both features can be obtained while maintaining high overall radiative efficiency without any fine-tuning of the physical conditions., Comment: Published in MNRAS Letters

Most FRB models can be divided into two groups based on the distance of the radio emission region from the central engine. The first group of models, the so-called `nearby' or magnetospheric models, invoke FRB emission at distances of 10$^9$ cm or less from the central engine, while the second `far-away' models involve emission from distances of 10$^{11}$ cm or greater. The lateral size for the emission region for the former class of models ($\lesssim$ 10$^7$ cm) is much smaller than the second class of models ($\gtrsim 10^9$ cm). We propose that an interstellar scattering screen in the host galaxy is well-suited to differentiate between the two classes of models, particularly based on the level of modulations in the observed intensity with frequency, in the regime of strong diffractive scintillation. This is because the diffractive length scale for the host galaxy's ISM scattering screen is expected to lie between the transverse emission-region sizes for the `nearby' and the `far-away' class of models. Determining the strength of flux modulation caused by scintillation (scintillation modulation index) across the scintillation bandwidth ($\sim 1/2\pi\delta t_s$) would provide a strong constraint on the FRB radiation mechanism when the scatter broadening ($\delta t_s$) is shown to be from the FRB host galaxy. The scaling of the scintillation bandwidth as $\sim \nu^{4.4}$ may make it easier to determine the modulation index at $\gtrsim$ 1 GHz., Comment: Paper accepted for publication in MNRAS

A permutation $\pi \in \mathbb{S}_n$ is $k$-balanced if every permutation of order $k$ occurs in $\pi$ equally often, through order-isomorphism. In this paper, we explicitly construct $k$-balanced permutations for $k \le 3$, and every $n$ that satisfies the necessary divisibility conditions. In contrast, we prove that for $k \ge 4$, no such permutations exist. In fact, we show that in the case $k \ge 4$, every $n$-element permutation is at least $\Omega_n(n^{k-1})$ far from being $k$-balanced. This lower bound is matched for $k=4$, by a construction based on the Erd\H{o}s-Szekeres permutation.

The \textit{Swift} Deep Galactic Plane Survey is a \textit{Swift} Key Project consisting of 380 tiled pointings covering 40 deg$^{2}$ of the Galactic Plane between longitude $10$\,$<$\,$|l|$\,$<$\,$30$ deg and latitude $|b|$\,$<$\,$0.5$ deg. Each pointing has a $5$ ks exposure, yielding a total of 1.9 Ms spread across the entire survey footprint. Phase-I observations were carried out between March 2017 and May 2021. The Survey is complete to depth $L_X$\,$>$\,$10^{34}$ erg s$^{-1}$ to the edge of the Galaxy. The main Survey goal is to produce a rich sample of new X-ray sources and transients, while also covering a broad discovery space. Here, we introduce the Survey strategy and present a catalog of sources detected during Phase-I observations. In total, we identify 928 X-ray sources, of which 348 are unique to our X-ray catalog. We report on the characteristics of sources in our catalog and highlight sources newly classified and published by the DGPS team., Comment: Accepted in ApJS. This is the final version

GRB030329 displays one clear and, possibly, multiple less intense fast-rising ($\Delta t / t \sim 0.3$) jumps in its optical afterglow light curve. The decay rate of the optical light curve remains the same before and after the photon flux jumps. This may be the signature of energy injection into the forward and reverse shocked material at the front of the jet. In this study, we model the Gamma-Ray Burst (GRB) ejecta as a series of shells of material. We follow the dynamical evolution of the ejecta as it interacts with itself (i.e., internal shocks) and with the circumburst medium (i.e., external forward and reverse shocks), and we calculate the emission from each shock event assuming synchrotron emission. We confirm the viability of the model proposed by \citet{2003Natur.426..138G} in which the jumps in the optical afterglow light curve of GRB030329 are produced via refreshed shocks. The refreshed shocks may be the signatures of the collisions between earlier ejected material with an average Lorentz factor $\bar{\Gamma}\gtrsim 100$ and later ejected material with $\bar{\Gamma} \sim 10$ once the early material has decelerated due to interaction with the circumburst medium. We show that even if the late material is ejected with a spread of Lorentz factors, internal shocks naturally produce a narrow distribution of Lorentz factors ($\Delta\Gamma/\Gamma\lesssim0.1$), which is a necessary condition to produce the observed quick rise times of the jumps. These results imply a phase of internal shocks at some point in the dynamical evolution of the ejecta, which requires a low magnetization in the outflow., Comment: 11 pages, 6 figures

One of the intriguing puzzles concerning Swift J1644+57, the first jetted tidal disruption event (TDE) discovered, is the constant increase in its jet energy, as implied by radio observations. During the first two hundred days the jet energy has increased by an order of magnitude. We suggest that the jet was viewed slightly off-axis. In this case, the apparent energy increase arises due to the slowing down of the jet and the corresponding broadening of its beaming cone. Using equipartition analysis, we infer an increasing jet energy as a larger region of the jet is observed. A simple off-axis model accounts nicely for the multi-wavelength radio observations, resolving this long-standing puzzle. The model allows us to self-consistently evolve the synchrotron signature from an off-axis jet as a function of time. It also allows us to estimate, for the first time, the beaming angle of the jet, $\theta_0 \approx 21^{\circ}$. Considering existing limits on the black hole mass, $\lesssim 10^{7}M_{\odot}$, this angle implies that the prompt phase beaming corrected luminosity of Swift J1644+57, $\sim 10^{47}$ergs/sec, was super Eddington. We also present a closure relation between the spectral and temporal flux for off-axis jets, which can be used to test whether a given radio transient is off-axis or not., Comment: 10 pages, 8 figures. Published in MNRAS

Long duration gamma-ray bursts (GRBs) are powerful cosmic explosions, signaling the death of massive stars. Among them, GRB 221009A is by far the brightest burst ever observed. Due to its enormous energy ($E_\textrm{iso}\!\approx$10$^{55}$ erg) and proximity ($z\!\approx$0.15), GRB 221009A is an exceptionally rare event that pushes the limits of our theories. We present multi-wavelength observations covering the first three months of its afterglow evolution. The X-ray brightness decays as a power-law with slope $\approx\!t^{-1.66}$, which is not consistent with standard predictions for jetted emission. We attribute this behavior to a shallow energy profile of the relativistic jet. A similar trend is observed in other energetic GRBs, suggesting that the most extreme explosions may be powered by structured jets launched by a common central engine., Comment: Submitted version. 53 pages, 9 figures, 6 tables

We present the science case for the proposed Daksha high energy transients mission. Daksha will comprise of two satellites covering the entire sky from 1~keV to $>1$~MeV. The primary objectives of the mission are to discover and characterize electromagnetic counterparts to gravitational wave source; and to study Gamma Ray Bursts (GRBs). Daksha is a versatile all-sky monitor that can address a wide variety of science cases. With its broadband spectral response, high sensitivity, and continuous all-sky coverage, it will discover fainter and rarer sources than any other existing or proposed mission. Daksha can make key strides in GRB research with polarization studies, prompt soft spectroscopy, and fine time-resolved spectral studies. Daksha will provide continuous monitoring of X-ray pulsars. It will detect magnetar outbursts and high energy counterparts to Fast Radio Bursts. Using Earth occultation to measure source fluxes, the two satellites together will obtain daily flux measurements of bright hard X-ray sources including active galactic nuclei, X-ray binaries, and slow transients like Novae. Correlation studies between the two satellites can be used to probe primordial black holes through lensing. Daksha will have a set of detectors continuously pointing towards the Sun, providing excellent hard X-ray monitoring data. Closer to home, the high sensitivity and time resolution of Daksha can be leveraged for the characterization of Terrestrial Gamma-ray Flashes., Comment: 19 pages, 7 figures. Accepted in Experimental Astronomy. More details about the mission at https://www.dakshasat.in/

We show that the 216.8$\pm$0.1 ms periodicity reported for the fast radio burst (FRB) 20191221A is very constraining for burst models. The high accuracy of burst periodicity (better than one part in 10$^3$), and the 2\% duty cycle (ratio of burst-duration and inter-burst interval), suggest a pulsar-like rotating beam model for the observed activity; the radio waves are produced along open field lines within $\sim 10^7$ cm of the neutron star surface, and the beam periodically sweeps across the observer as the star spins. According to this picture, FRB 20191221A is a factor $\sim 10^{12}$ scaled up version of galactic pulsars with one major difference: whereas pulsars convert rotational kinetic energy to EM waves, the outbursts of 20191221A require conversion of magnetic energy to radiation., Comment: 7 pages, 3 figures. Accepted for publication in MNRAS

Studies of gamma-ray bursts (GRBs) and their multi-wavelength afterglows have led to insights in electron acceleration and emission properties from relativistic, high-energy astrophysical sources. Broadband modeling across the electromagnetic spectrum has been the primary means of investigating the physics behind these sources, although independent diagnostic tools have been developed to inform and corroborate assumptions made in particle acceleration simulations and broadband studies. We present a methodology to constrain three physical parameters related to electron acceleration in GRB blast waves: the fraction of shock energy in electrons, $\epsilon_e$; the fraction of electrons that gets accelerated into a power-law distribution of energies, $\xi_e$; and the minimum Lorentz factor of the accelerated electrons, $\gamma_m$. These parameters are constrained by observations of the peaks in radio afterglow light curves and spectral energy distributions. From a sample of 49 radio afterglows, we are able to find narrow distributions for these parameters, hinting at possible universality of the blast wave microphysics, although observational bias could play a role in this. Using radio peaks and considerations related to the prompt gamma-ray emission efficiency, we constrain the allowed parameter ranges for both $\epsilon_e$ and $\xi_e$ to within about one order of magnitude, $0.01\lesssim\epsilon_e\lesssim0.2$ and $0.1\lesssim\xi_e\lesssim1$. Such stringent constraints are inaccessible for $\xi_e$ from broadband studies due to model degeneracies., Comment: 10 pages, 6 figures, 2 tables; accepted for publication in MNRAS

Two recent discoveries, namely PSR J0901-4046 and GLEAM-X J162759.5-523504.3 (hereafter GLEAM-X J1627), have corroborated an extant population of radio-loud periodic sources with long periods (76 s and 1091 s respectively) whose emission can hardly be explained by rotation losses. We argue that GLEAM-X J1627 is a highly-magnetized object consistent with a magnetar (an ultra long period magnetar - ULPM), and demonstrate it is unlikely to be either a magnetically or a rotationally-powered white dwarf. By studying these sources together with previously detected objects, we find there are at least a handful of promising candidates for Galactic ULPMs. The detections of these objects imply a substantial number, $N \gtrsim 13000$ and $N \gtrsim 500$ for PSR J0901--4046 like and GLEAM-X J1627 like objects, respectively, within our Galaxy. These source densities, as well as cooling age limits from non-detection of thermal X-rays, Galactic offsets, timing stability and dipole spindown limits, all imply the ULPM candidates are substantially older than confirmed Galactic magnetars and that their formation channel is a common one. Their existence implies widespread survival of magnetar-like fields for several Myr, distinct from the inferred behaviour in confirmed Galactic magnetars. ULPMs may also constitute a second class of FRB progenitors which could naturally exhibit very long periodic activity windows. Finally, we show that existing radio campaigns are biased against detecting objects like these and discuss strategies for future radio and X-ray surveys to identify more such objects. We estimate that ${\cal O}(100)$ more such objects should be detected with SKA-MID and DSA-2000., Comment: 22 pages, 10 figures. Published in MNRAS

We describe how gravitational lensing of fast radio bursts (FRBs) is affected by a plasma screen in the vicinity of the lens or somewhere between the source and the observer. Wave passage through a turbulent medium affects gravitational image magnification, lensing probability (particularly for strong magnification events), and the time delay between images. The magnification is suppressed because of the broadening of the angular size of the source due to scattering by the plasma. The time delay between images is modified as the result of different dispersion measure (DM) along photon trajectories for different images. Each of the image lightcurve is also broadened due to wave scattering so that the images could have distinct temporal profiles. The first two effects are most severe for stellar and sub-stellar mass lens, and the last one (scatter broadening) for lenses and plasma screens at cosmological distances from the source/observer. This could limit the use of FRBs to measure their cosmic abundance. On the other hand, when the time delay between images is large, such that the lightcurve of a transient source has two or more well separated peaks, the different DMs along the wave paths of different images can probe density fluctuations in the IGM on scales $\lesssim 10^{-6}$ rad and explore the patchy reionization history of the universe using lensed FRBs at high redshifts. Different rotation measure (RM) along two image paths can convert linearly polarized radiation from a source to partial circular polarization., Comment: 11 pages, 5 figures

We consider the extremal family of graphs of order $2^n$ in which no two vertices have identical neighbourhoods, yet the adjacency matrix has rank only $n$ over the field of two elements. A previous result from algebraic geometry shows that such graphs exist for all even $n$ and do not exist for odd $n$. In this paper we provide a new combinatorial proof for this result, offering greater insight to the structure of graphs with these properties. We introduce a new graph product closely related to the Kronecker product, followed by a construction for such graphs for any even $n$. Moreover, we show that this is an infinite family of strongly-regular quasi-random graphs whose signed adjacency matrices are symmetric Hadamard matrices. Conversely, we provide a combinatorial proof that for all odd $n$, no twin-free graphs of minimal $\mathbb{F}_2$-rank exist, and that the next best-possible rank $(n+1)$ is attainable, which is tight., Comment: Added comparison to the results of Godsil and Royle. We thank Sam Adriaensen for bringing them to our attention

A significant fraction (30\%) of well-localized short gamma-ray bursts (sGRBs) lack a coincident host galaxy. This leads to two main scenarios: \textit{i}) that the progenitor system merged outside of the visible light of its host, or \textit{ii}) that the sGRB resided within a faint and distant galaxy that was not detected by follow-up observations. Discriminating between these scenarios has important implications for constraining the formation channels of neutron star mergers, the rate and environments of gravitational wave sources, and the production of heavy elements in the Universe. In this work, we present the results of our observing campaign targeted at 31 sGRBs that lack a putative host galaxy. Our study effectively doubles the sample of well-studied sGRB host galaxies, now totaling 72 events of which $28\%$ lack a coincident host to deep limits ($r$\,$\gtrsim$\,$26$ or $F110W$\,$\gtrsim$\,$27$ AB mag), and represents the largest homogeneously selected catalog of sGRB offsets to date. We find that 70\% of sub-arcsecond localized sGRBs occur within 10 kpc of their host's nucleus, with a median projected physical offset of $5.6$ kpc. Using this larger population, we discover an apparent redshift evolution in their locations: bursts at low-$z$ occur at $2\times$ larger offsets compared to those at $z$\,$>$\,$0.5$. This evolution could be due to a physical evolution of the host galaxies themselves or a bias against faint high-$z$ galaxies. Furthermore, we discover a sample of hostless sGRBs at $z$\,$\gtrsim$\,$1$ that are indicative of a larger high-$z$ population, constraining the redshift distribution and disfavoring log-normal delay time models., Comment: Accepted by MNRAS

The ultra-relativistic outflows powering gamma-ray bursts (GRBs) acquire angular structure through their interaction with external material. They are often characterized by a compact, nearly uniform narrow core (with half-opening angle $\theta_{c,\{\epsilon,\Gamma\}}$) surrounded by material with energy per unit solid angle ($\epsilon=\epsilon_c\Theta_{\epsilon}^{-a}$, where $\Theta_{\{\epsilon,\Gamma\}}=[1+\theta^2/\theta_{c,\{\epsilon,\Gamma\}}^2]^{1/2}$) and initial specific kinetic energy ($\Gamma_0-1=[\Gamma_c-1]\Theta_\Gamma^{-b}$) declining as power laws. Multi-wavelength afterglow lightcurves of off-axis jets (with viewing angle $\theta_{\rm obs} > \theta_c$) offer robust ways to constrain $a$, $b$ and the external density radial profile ($\rho\propto R^{-k}$), even while other burst parameters may remain highly degenerate. We extend our previous work on such afterglows to include more realistic angular structure profiles derived from three-dimensional hydrodynamic simulations of both long and short GRBs (addressing also jets with shallow angular energy profiles, whose emission exhibits unique evolution). We present afterglow lightcurves based on our parameterized power-law jet angular profiles for different viewing angles $\theta_{\rm obs}$ and $k=\{0,1,2\}$. We identify a unique evolutionary power-law phase of the characteristic synchrotron frequencies ($\nu_m$ and $\nu_c$) that manifests when the lightcurve is dominated by emission sensitive to the angular structure of the outflow. We calculate the criterion for obtaining single or double peaked light-curves in the general case when $\theta_{c,\Gamma}\neq\theta_{c,\epsilon}$. We emphasize how the shape of the lightcurve and the temporal evolution of $\nu_m$ and $\nu_c$ can be used to constrain the outflow structure and potentially distinguish between magnetic and hydrodynamic jets., Comment: 15 pages, 13 figures. Accepted for publication in MNRAS

We obtain complete characterizations of the Unique Bipartite Perfect Matching function, and of its Boolean dual, using multilinear polynomials over the reals. Building on previous results, we show that, surprisingly, the dual description is sparse and has low $\ell_1$-norm -- only exponential in $\Theta(n \log n)$, and this result extends even to other families of matching-related functions. Our approach relies on the M\"obius numbers in the matching-covered lattice, and a key ingredient in our proof is M\"obius' inversion formula. These polynomial representations yield complexity-theoretic results. For instance, we show that unique bipartite matching is evasive for classical decision trees, and nearly evasive even for generalized query models. We also obtain a tight $\Theta(n \log n)$ bound on the log-rank of the associated two-party communication task.

Fast radio bursts (FRBs) are brief, intense flashes of radio waves from unidentified extragalactic sources. Polarized FRBs originate in highly magnetized environments. We report observations of the repeating FRB 20190520B spanning seventeen months , which show its amount of Faraday rotation is highly variable and twice changes its sign. The FRB also depolarizes below radio frequencies around 1 to 3 GHz. We interpret these properties as due to change in the parallel component of the integrated magnetic field along the line-of-sight, including reversals. This could result from propagation through a turbulent, magnetized screen of plasma located between $10^{-5}$ to 100 parsecs of the FRB source. This is consistent with the bursts passing through the stellar wind of a binary companion of the FRB source., Comment: arXiv:2203.08151 has been merged into this

In this work we consider the eruption of a tenuous relativistic hydrodynamic jet from a dense baryonic envelope. As the jet moves out and away, it carries along and continues to accelerate a layer of baryonic material which we refer to as the plug. We solve the relativistic equations of motion for the trajectory of the plug, and verify it using a relativistic hydrodynamic simulation. We show that under these conditions, the plug breaks up at a radius larger by a factor of a few from the radius of the envelope, due to the onset of the Rayleigh Taylor instability. After breakup the jet continues to accelerate to higher Lorentz factors while the plug fragments maintain a moderate Lorentz factor. The presence of slower moving ejecta can explain late time features of GRBs such as X ray flares without recourse to a long lived engine.

We develop a model to explain the flaring activity in gamma-ray burst X-ray afterglows within the framework of slightly misaligned observers to structured jets. We suggest that flares could be the manifestation of prompt dissipation within the core of the jet, appearing to a misaligned observer in the X-ray band because of less favorable Doppler boosting. These flares appear during the afterglow phase because of core--observer light travel delays. In this picture, the prompt emission recorded by this observer comes from material along their line of sight, in the lateral structure of the jet, outside the jet's core. We start by laying down the basic analytical framework to determine the flares characteristics as a function of those of the gamma-ray pulse an aligned observer would see. We show that there is viable parameter space to explain flares with typical observing times and luminosities. We then analytically explore this model, showing that it naturally produces flares with small aspect ratios, as observed. We perform fits of our model to two $Swift$/XRT flares representing two different types of morphology, to show that our model can capture both. The ejection time of the core jet material responsible of the flare is a critical parameter. While it always remains small compared to the observed time of the flare, confirming that our model does not require very late central engine activity, late ejection times are strongly favored, sometimes larger than the observed duration of the parent gamma-ray burst's prompt emission as measured by $T_{90}$., Comment: Main text 11 pages, 4 figures and 2 tables. Final version to appear in MNRAS

We introduce a toy model for the time-frequency structure of fast radio bursts (FRB), in which the observed emission is produced as a narrowly-peaked intrinsic spectral energy distribution sweeps down in frequency across the instrumental bandpass as a power-law in time. Though originally motivated by emission models which invoke a relativistic shock, the model could in principle apply to a wider range of emission scenarios. We quantify the burst's detectability using the frequency bandwidth over which most of its signal-to-noise ratio (SNR) is accumulated. We demonstrate that by varying just a single parameter of the toy model-the power-law index \beta of the frequency drift rate-one can transform a long (and hence preferentially time-resolved) burst with a narrow time-integrated spectrum into a shorter burst with a broad power-law time-integrated spectrum. We suggest that burst-to-burst diversity in the value of \beta could generate the dichotomy between burst duration and frequency-width recently found by CHIME. In shock models, the value of \beta is related to the radial density profile of external medium, which in light of the preferentially longer duration of bursts from repeating sources may point to diversity in the external environments surrounding repeating versus one-off FRB sources., Comment: 11 pages, 7 figures, to be submitted to ApJ, comments appreciated

We describe how the observed polarization properties of an astronomical object are related to its intrinsic polarization properties and the finite temporal and spectral resolutions of the observing device. Moreover, we discuss the effect that a scattering screen, with non-zero magnetic field, between the source and observer has on the observed polarization properties. We show that the polarization properties are determined by the ratio of observing bandwidth and coherence bandwidth of the scattering screen and the ratio of temporal resolution of the instrument and the variability time of screen, as long as the length over which the Faraday rotation induced by the screen changes by $\sim\pi$ is smaller than the size of the screen visible to the observer. We describe the conditions under which a source that is 100\% linearly polarized intrinsically might be observed as partially depolarized, and how the source's temporal variability can be distinguished from the temporal variability induced by the scattering screen. In general, linearly polarized waves passing through a magnetized scattering screen can develop a significant circular polarization. We apply the work to the observed polarization properties of a few fast radio bursts (FRBs), and outline potential applications to pulsars., Comment: 15 pages, 9 figures. Accepted for publication in MNRAS

A repeating source of fast radio bursts (FRBs) is recently discovered from a globular cluster of M81. Association to a globular cluster (or other old stellar systems) suggests that strongly magnetized neutron stars, which are the most likely objects responsible for FRBs, are born not only when young massive stars undergo core-collapse, but also by mergers of old white dwarfs. We find that the fractional contribution to the total FRB rate by old stellar populations is at least a few percent, and the precise fraction can be constrained by FRB searches in the directions of nearby galaxies, both star-forming and elliptical ones. Using very general arguments, we show that the activity time of the M81-FRB object is between 10^4 and 10^6 years, and more likely of order 10^5 years. The energetics of radio outbursts puts a lower limit on the magnetic field strength of 10^{13} G, and the spin period > 0.2 sec, thereby ruling out the source being a milli-second pulsar. The upper limit on the persistent X-ray luminosity (provided by Chandra), together with the high FRB luminosity and frequent repetitions, severely constrains (or rules out) the possibility that the M81-FRB is a scaled-up version of giant pulses from Galactic pulsars. Finally, the 50 ns variability time of the FRB lightcurve suggests that the emission is produced in a compact region inside the neutron star magnetosphere, as it cannot be accounted for when the emission is at distances > 10^{10} cm., Comment: MNRAS accepted after minor corrections

A binary neutron star (BNS) merger can lead to various outcomes, from indefinitely stable neutron stars, through supramassive (SMNS) or hypermassive (HMNS) neutron stars supported only temporarily against gravity, to black holes formed promptly after the merger. Up-to-date constraints on the BNS total mass and the neutron star equation of state suggest that a long-lived SMNS may form in $\sim 0.45-0.9$ of BNS mergers. A maximally rotating SMNS needs to lose $\sim 3-6\times 10^{52}$ erg of it's rotational energy before it collapses, on a fraction of the spin-down timescale. A SMNS formation imprints on the electromagnetic counterparts to the BNS merger. However, a comparison with observations reveals tensions. First, the distribution of collapse times is too wide and that of released energies too narrow (and the energy itself too large) to explain the observed distributions of internal X-ray plateaus, invoked as evidence for SMNS-powered energy injection. Secondly, the immense energy injection into the blastwave should lead to extremely bright radio transients which previous studies found to be inconsistent with deep radio observations of short gamma-ray bursts. Furthermore, we show that upcoming all-sky radio surveys will constrain the extracted energy distribution, independently of a GRB jet formation. Our results can be self-consistently understood, provided that most BNS merger remnants collapse shortly after formation (even if their masses are low enough to allow for SMNS formation). This naturally occurs if the remnant retains half or less of its initial energy by the time it enters solid body rotation., Comment: Accepted for publication in ApJ

We study the high-energy properties of GRB 181123B, a short gamma-ray burst (sGRB) at redshift $z\approx$1.75. We show that, despite its nominal short duration with $T_{90}<$2 s, this burst displays evidence of a temporally extended emission (EE) at high energies and that the same trend is observed in the majority of sGRBs at $z\gtrsim$1. We discuss the impact of instrumental selection effects on the GRB classification, stressing that the measured $T_{90}$ is not an unambiguous indicator of the burst physical origin. By examining their environment (e.g. stellar mass, star formation, offset distribution), we find that these high-$z$ sGRBs share many properties of long GRBs at a similar distance and are consistent with a short-lived progenitor system. If produced by compact binary mergers, these sGRBs with EE may be easier to localize at large distances and herald a larger population of sGRBs in the early universe., Comment: 10 pages, 7 figures, 2 tables. ApJ Letters, in press

The discovery of periodicity in the arrival times of the fast radio bursts (FRBs) poses a challenge to the oft-studied magnetar scenarios. However, models that postulate that FRBs result from magnetized shocks or magnetic reconnection in a relativistic outflow are not specific to magnetar engines; instead, they require only the impulsive injection of relativistic energy into a dense magnetized medium. Motivated thus, we outline a new scenario in which FRBs are powered by short-lived relativistic outflows (``flares'') from accreting black holes or neutron stars, which propagate into the cavity of the pre-existing (``quiescent'') jet. In order to reproduce FRB luminosities and rates, we are driven to consider binaries of stellar-mass compact objects undergoing super-Eddington mass-transfer, similar to ultraluminous X-ray (ULX) sources. Indeed, the host galaxies of FRBs, and their spatial offsets within their hosts, show broad similarities with ULXs. Periodicity on timescales of days to years could be attributed to precession (e.g., Lens-Thirring) of the polar accretion funnel, along which the FRB emission is geometrically and relativistically beamed, which sweeps across the observer line of sight. Accounting for the most luminous FRBs via accretion power may require a population of binaries undergoing brief-lived phases of unstable (dynamical-timescale) mass-transfer. This will lead to secular evolution in the properties of some repeating FRBs on timescales of months to years, followed by a transient optical/IR counterpart akin to a luminous red nova, or a more luminous accretion-powered optical/X-ray transient. We encourage targeted FRB searches of known ULX sources., Comment: Accepted for publication in The Astrophysical Journal; 25 pages, 8 figures

The abundances of r-process elements of very metal-poor stars capture the history of the r-process enrichment in the early stage of star formation in a galaxy. Currently, various types of astrophysical sites including neutron star mergers, magneto-rotational supernovae, and collapsars, are suggested as the origin of r-process elements. The time delay between the star formation and the production of r-process elements is the key to distinguish these scenarios with the caveat that the diffusion of r-process elements in the interstellar medium may induce the delay in r-process enrichment because r-process events are rare. Here we study the observed Ba abundance data of very metal-poor stars as the tracer of the early enrichment history of r-process elements. We find that the gradual increase of [Ba/Mg] with [Fe/H], which is remarkably similar among the Milky Way and classical dwarfs, requires a significant time delay (100 Myr -- 1 Gyr) of r-process events from star formation rather than the diffusion-induced delay. We stress that this conclusion is robust to the assumption regarding s-process contamination in the Ba abundances because the sources with no delay would overproduce Ba at very low metallicities even without the contribution from the s-process. Therefore we conclude that sources with a delay, possibly neutron star mergers, are the origins of r-process elements., Comment: 10 pages, 6 figures, ApJ Letters in press

The environments of explosive transients link their progenitors to the underlying stellar population, providing critical clues for their origins. However, some Ca-rich supernovae (SNe) and short gamma ray burst (sGRBs) appear to be located at remote locations, far from the stellar population of their host galaxy, challenging our understanding of their origin and/or physical evolution. These findings instigated models suggesting that either large velocity kicks were imparted to their progenitors, allowing them to propagate to large distances and attain their remote locations; or that they formed in dense globular clusters residing in the halos. Here we show that instead, the large spatial-offsets of these transients are naturally explained by the observations of highly extended underlying stellar populations in (mostly early type) galaxy halos, typically missed since they can only be identified through ultra-deep/stacked images. Consequently, no large velocity kicks, nor halo globular cluster environments are required in order to explain the origin of these transients. These findings support thermonuclear explosions on white-dwarfs, for the origins of Ca-rich SNe progenitors, and no/small-natal-kicks given to sGRB progenitors. Since early-type galaxies contain older stellar populations, transient arising from older stellar populations would have larger fractions of early-type galaxy hosts, and consequently larger fractions of transients at large offsets. This is verified by our results for sGRBs and Ca-rich SNe showing different offset distributions in early vs. late-type galaxies. Furthermore, once divided between early and late type galaxies, the offsets' distributions of the different transients are consistent with each other. Finally, we point out that studies of other transients' offset distribution (e.g. Ia-SNe or FRBs) should similarly consider the host galaxy-type., Comment: Comments are welcome

We describe three different methods for exploring the hydrogen reionization epoch using fast radio bursts (FRBs) and provide arguments for the existence of FRBs at high redshift (z). The simplest way, observationally, is to determine the maximum dispersion measure (DM$_{\rm max}$) of FRBs for an ensemble that includes bursts during the reionization. The DM$_{\rm max}$ provides information regarding reionization much like the optical depth of the CMB to Thomson scattering does, and it has the potential to be more accurate than constraints from Planck, if DM$_{\rm max}$ can be measured to a precision better than 500 $\mbox{pc cm}^{-3}$. Another method is to measure redshifts of about 40 FRBs between z of 6-10 with$\sim10\%$ accuracy to obtain the average electron density in 4 different z-bins with $\sim4\%$ accuracy. These two methods don't require knowledge of the FRB luminosity function and its possible redshift evolution. Finally, we show that the reionization history is reflected in the number of FRBs per unit DM, given a fluence limited survey of FRBs that includes bursts during the reionization epoch; we show using FIRE simulations that the contributions to DM from the FRB host galaxy $\&$ CGM during the reionization era is a small fraction of the observed DM. This third method requires no redshift information but does require knowledge of the FRB luminosity function., Comment: 13 pages, 10 figures. Accepted for publication in MNRAS

The LIGO-Virgo collaboration recently reported a puzzling event, GW190814, with component masses of 23 and 2.6 solar masses. Motivated by the relatively small rate of such a coalescence and the fact that the mass of the secondary is close to the total mass of known binary neutron star (bNS) systems, we propose that GW190814 was a second-generation merger from a hierarchical triple system, i.e., the remnant from the bNS coalescence was able to merge again with the 23 Msun black hole (BH) tertiary. We show that this occurs at a sufficiently high probability provided that the semimajor axis of the outer orbit is less than a few AU at the time of bNS coalescence. It remains to be explored whether the conditions for the formation of such tight triple systems are commonly realized in the Universe, especially in low metallicity (less than 0.1 solar) environments. Our model provides a number of predictions. (1) The spin of the secondary in GW190814-like systems is 0.6 to 0.7. (2) The component mass distribution from a large sample of LIGO sources should have a narrow peak between 2.5 and ~3.5 Msun, whereas the range between ~3.5 and ~5 Msun stays empty (provided that stellar evolution does not generate such BHs in the "mass gap"). (3) About 90% (10%) of GW190814-like events have an eccentricity of e > 2x10^{-3} (> 0.1) near gravitational wave frequency of 10 mHz. (4) A significant fraction (> 10%) of bNS mergers should have signatures of a massive tertiary at a distance of a few AU in the gravitational waveform. (5) There are 10^5 undetected radio-quiet bNS systems with a massive BH tertiary in the Milky Way., Comment: MNRAS accepted