The Effect of Pair Cascades on the High-Energy Spectral Cutoff in Gamma-Ray Bursts

The highly luminous and variable prompt emission in Gamma-Ray Bursts (GRBs) arises in an ultra-relativistic outflow. The exact underlying radiative mechanism shaping its non-thermal spectrum is still uncertain, making it hard to determine the outflow's bulk Lorentz factor $\Gamma$. GRBs with spectral cutoff due to pair production ($\gamma\gamma\to e^+e^-$) at energies $E_c\gtrsim10\;$MeV are extremely useful for inferring $\Gamma$. We find that when the emission region has a high enough compactness, then as it becomes optically thick to scattering, Compton downscattering by non-relativistic $e^\pm$-pairs can shift the spectral cutoff energy well below the self-annihilation threshold, $E_{\rm sa}=\Gamma m_ec^2/(1+z)$. We treat this effect numerically and show that $\Gamma$ obtained assuming $E_c=E_{\rm sa}$ can under-predict its true value by as much as an order of magnitude.Comment: 5 pages, 3 figures, Accepted for publication in MNRAS Letter

Hot Electromagnetic Outflows. III. Displaced Fireball in a Strong Magnetic Field

The evolution of a dilute electron-positron fireball is calculated in the regime of strong magnetization and very high compactness (l ~10^3-10^8). Heating is applied at a low effective temperature (< 25 keV), and the fireball is allowed to expand, so that the formation of a black-body spectral distribution is inhibited by pair annihilation. The diffusion equation for Compton scattering is coupled to a single-temperature pair gas and an exact (trans-relativistic) cyclo-synchrotron photon source. We find that the photon spectrum develops a quasi-thermal peak, with a power-law slope below it that is characteristic of gamma-ray bursts. The formation of a thermal high-frequency spectrum is checked using the full kinetic equations at l ~ 10^3. These results have several implications for the central engine of GRBs, and the mechanism of energy transport. 1. Baryon rest mass carries less than ~ 10^{-5} of the energy flux at jet breakout inside ~ 10^{12} cm from the engine, with most carried by the magnetic field. 2. This degree of baryon purity points to the presence of an event horizon in the engine, and neutrons play a negligible role in the prompt emission mechanism. 3. X-ray flashes are emitted by outflows carrying enough baryons that the photosphere is pair-depleted, which we show results in faster thermalization. 4. The relation between observed peak frequency and burst luminosity is bounded below by the observed Amati et al. relation if jet Lorentz factor ~ 1/(opening angle) at breakout. 5. Stellar models are used to demonstrate an inconsistency between the highest observed GRB energies, and a hydrodynamic nozzle: magnetic collimation is required. 6. The magnetized pair gas is dilute enough that high-frequency Alfven waves may become charge starved. Finally, we suggest that limitations on magnetic reconnection from plasma collisionality have been overestimated.Comment: 29 pages, 34 figures, submitted to the Ap

Pulse Structure of Hot Electromagnetic Outflows with Embedded Baryons

Gamma-ray bursts (GRBs) show a dramatic pulse structure that requires bulk relativistic motion, but whose physical origin has remained murky. We focus on a hot, magnetized jet that is emitted by a black hole and interacts with a confining medium. Strongly relativistic expansion of the magnetic field, as limited by a corrugation instability, may commence only after it forms a thin shell. Then the observed $T_{90}$ burst duration is dominated by the curvature delay, and null periods arise from angular inhomogeneities, not the duty cycle of the engine. We associate the $O(1)$ s timescale observed in the pulse width distribution of long GRBs with the collapse of the central 2.5-3$M_\odot$ of a massive stellar core. A fraction of the baryons are shown to be embedded in the magnetized outflow by the hyper-Eddington radiation flux; they strongly disturb the magnetic field after the compactness drops below $\sim 4\times 10^3(Y_e/0.5)^{-1}$. The high-energy photons so created have a compressed pulse structure. Delayed breakout of magnetic field from heavier baryon shells is also a promising approach to X-ray flares. In the second part of the paper, we calculate the imprint of an expanding, scattering photosphere on pulse evolution. Two models for generating the high-energy spectral tail are contrasted: i) pair breakdown due to reheating of an optically thin pair plasma embedded in a thermal radiation field; and ii) continuous heating extending from large to small scattering depth. The second model is strongly inconsistent with the observed hard-to-soft evolution in GRB pulses. The first shows some quantitative differences if the emission is purely spherical, but we show that finite shell width, mild departures from spherical curvature, and latitudinal Lorentz factor gradients have interesting effects.Comment: Submitted to the ApJ, 21 pages, 22 figure

Non-thermal Gamma-ray Emission from Delayed Pair Breakdown in a Magnetized and Photon-rich Outflow

We consider delayed, volumetric heating in a magnetized outflow that has broken out of a confining medium and expanded to a high Lorentz factor ($\Gamma \sim 10^2-10^3$) and low optical depth to scattering ($\tau_{\rm T} \sim 10^{-3}-10^{-2}$). The energy flux at breakout is dominated by the magnetic field, with a modest contribution from quasi-thermal gamma rays whose spectrum was calculated in Paper I. We focus on the case of extreme baryon depletion in the magnetized material, but allow for a separate baryonic component that is entrained from a confining medium. Dissipation is driven by relativistic motion between these two components, which develops once the photon compactness drops below $4\times 10^3(Y_e/0.5)^{-1}$. We first calculate the acceleration of the magnetized component following breakout, showing that embedded MHD turbulence provides significant inertia, the neglect of which leads to unrealistically high estimates of flow Lorentz factor. After re-heating begins, the pair and photon distributions are evolved self-consistently using a one-zone kinetic code that incorporates an exact treatment of Compton scattering, pair production and annihilation, and Coulomb scattering. Heating leads to a surge in pair creation, and the scattering depth saturates at $\tau_{\rm T} \sim$ 1-4. The plasma maintains a very low ratio of particle to magnetic pressure, and can support strong anisotropy in the charged particle distribution, with cooling dominated by Compton scattering. High-energy power-law spectra with photon indices in the range observed in GRBs ($-3 < \beta < -3/2$) are obtained by varying the ratio of heat input to the seed energy in quasi-thermal photons. We contrast our results with those for continuous heating across an expanding photosphere, and show that the latter model produces soft-hard evolution that is inconsistent with observations of GRBs.Comment: Submitted to the ApJ, 27 pages, 19 figure

Magnetic Reconnection Instabilities in Soft-Gamma Repeaters

We examine an external trigger mechanism that gives rise to the intense soft gamma-ray repeater (SGR) giant flares. Out of the three giant flares, two showcased the existence of a precursor, which we show to have had initiated the main flare. We develop a reconnection model based on the hypothesis that shearing motion of the footpoints causes the materialization of a Sweet-Parker current layer in the magnetosphere. The thinning of this macroscopic layer due to the development of an embedded super-hot turbulent current layer switches on the impulsive Hall reconnection, which powers the giant flare. We show that the thinning time is on the order of the pre-flare quiescent time.Comment: 4 pages, 2 figures, submission for the Proceedings of the Thirteenth Marcel Grossman Meeting on General Relativity edited by Kjell Rosquist, Robert T Jantzen, Remo Ruffini World Scientific, Singapore, 201

Statistical ages and the cooling rate of X-ray dim isolated neutron stars

The cooling theory of neutron stars is corroborated by its comparison with observations of thermally emitting isolated neutron stars and accreting neutron stars in binary systems. An important ingredient for such an analysis is the age of the object, which, typically, is obtained from the spin-down history. This age is highly uncertain if the object's magnetic field varies appreciably over time. Other age estimators, such as supernova remnant ages and kinematic ages, only apply to few handful of neutron stars. We conduct a population synthesis study of the nearby isolated thermal emitters and obtain their ages statistically from the observed luminosity function of these objects. We argue that a more sensitive blind scan of the galactic disk with the upcoming space telescopes can help to constrain the ages to higher accuracy.Comment: 9 pages, 2 figures, 2 tables. Figures and tables updated. Added discussion on errors. Accepted for publication in MNRA

Lessons from the short GRB \,170817A - the First Gravitational Wave Detection of a Binary Neutron Star Merger

The first, long awaited, detection of a gravitational wave (GW) signal from the merger of a binary neutron-star (NS-NS) system was finally achieved (GW$\,$170817), and was also accompanied by an electromagnetic counterpart -- the short-duration GRB 170817A. It occurred in the nearby ($D\approx40\;$Mpc) elliptical galaxy NGC$\,$4993, and showed optical, IR and UV emission from half a day up to weeks after the event, as well as late time X-ray (at $\geq 8.9\;$days) and radio (at $\geq 16.4\;$days) emission. There was a delay of $\Delta t \approx 1.74\;$s between the GW merger chirp signal and the prompt-GRB emission onset, and an upper limit of $\theta_{\rm obs}<28^\circ$ was set on the viewing angle w.r.t the jet's symmetry axis from the GW signal. In this letter we examine some of the implications of these groundbreaking observations. The delay $\Delta t$ sets an upper limit on the prompt-GRB emission radius, $R_\gamma\lesssim 2c\Delta t/(\theta_{\rm obs}-\theta_0)^2$, for a jet with sharp edges at an angle $\theta_0<\theta_{\rm obs}$. GRB 170817A's relatively low isotropic equivalent $\gamma$-ray energy-output may suggest a viewing angle slightly outside the jet's sharp edge, $\theta_{\rm{}obs}-\theta_0\sim(0.05-0.1)(\Gamma/100)^{-1}$, but its peak $\nu{}F_\nu$ photon energy and afterglow emission suggest instead that the jet does not have sharp edges and the prompt emission was dominated by less energetic material along our line of sight, at $\theta_{\rm{}obs}\gtrsim 2\theta_0$. Finally, we consider the type of remnant that is produced by the NS-NS merger and find that a relatively long-lived ($>2\;$s) massive NS is strongly disfavored, while a hyper-massive NS of lifetime $\sim1\;$s appears to be somewhat favored over the direct formation of a black hole.Comment: 5 pages, 3 figures, minor changes; accepted to ApJ

2D Relativistic MHD Simulations of the Kruskal-Schwarzschild Instability in a Relativistic Striped Wind

We study the linear and non-linear development of the Kruskal-Schwarzchild Instability in a relativisitically expanding striped wind. This instability is the generalization of Rayleigh-Taylor instability in the presence of a magnetic field. It has been suggested to produce a self-sustained acceleration mechanism in strongly magnetized outflows found in active galactic nuclei, gamma-ray bursts, and micro-quasars. The instability leads to magnetic reconnection, but in contrast with steady-state Sweet-Parker reconnection, the dissipation rate is not limited by the current layer's small aspect ratio. We performed two-dimensional (2D) relativistic magneto-hydrodynamic (RMHD) simulations featuring two cold and highly magnetized ($1\leq\sigma\leq10^{3}$) plasma layers with an anti-parallel magnetic field separated by a thin layer of relativistically hot plasma with a local effective gravity induced by the outflow's acceleration. Our simulations show how the heavier relativistically hot plasma in the reconnecting layer drips out and allows oppositely oriented magnetic field lines to reconnect. The instability's growth rate in the linear regime matches the predictions of linear stability analysis. We find turbulence rather than an ordered bulk flow near the reconnection region, with turbulent velocities up to $\sim0.1$c, largely independent of model parameters. However, the magnetic energy dissipation rate is found to be much slower, corresponding to an effective ordered bulk velocity inflow into the reconnection region $v_{\rm in}=\beta_{\rm in}c$, of $10^{-3}\lesssim\beta_{\rm in}\lesssim 5\times10^{-3}$. This occurs due to the slow evacuation of hot plasma from the current layer, largely because of the Kelvin-Helmholtz instability experienced by the dripping plasma. 3D RMHD simulations are needed to further investigate the non-linear regime.Comment: 12 pages, 12 figures, Accepted for Publication in MNRA

When Did the Remnant of GW170817 Collapse to a Black Hole?

The main hard pulse of prompt gamma-ray emission in GRB$\,$170817A had a duration of $\sim0.5\,{\rm s}$ and its onset was delayed with respect to the gravitational-wave chirp signal by $t_{\rm del} \approx 1.74\,{\rm s}$. Detailed follow-up of the subsequent broadband kilonova emission revealed a two-component ejecta -- a lanthanide-poor ejecta with mass $M_{\rm ej,blue}\approx0.025\,M_\odot$ that powered the early but rapidly fading blue emission and a lanthanide-rich ejecta with mass $M_{\rm ej,red}\approx 0.04\,M_\odot$ that powered the longer lasting redder emission. Both the prompt gamma-ray onset delay and the existence of the blue ejecta with modest electron fraction, $0.2\lesssim Y_e\lesssim0.3$, can be explained if the collapse to a black hole was delayed by the formation of a hypermassive neutron star (HMNS). Here, we determine the survival time of the merger remnant by combining two different constraints, namely, the time needed to produce the requisite blue-ejecta mass and that necessary for the relativistic jet to bore its way out of the expanding ejecta. In this way, we determine that the remnant of GW170817 must have collapsed to a black hole after $t_{\rm coll}=0.98_{-0.26}^{+0.31}\,{\rm s}$. We also discuss how future detections and the delays between the gravitational and electromagnetic emissions can be used to constrain the properties of the merged object.Comment: 20 pages, 7 figures. Incorporated comments from the referee. Accepted for publication in Ap

Linear polarization in gamma-ray burst prompt emission

Despite being hard to measure, GRB prompt $\gamma$-ray emission polarization is a valuable probe of the dominant emission mechanism and the outflow's composition and angular structure. During the prompt emission the outflow is ultra-relativistic with Lorentz factors $\Gamma\gg1$. We describe in detail the linear polarization properties of various emission mechanisms: synchrotron radiation from different magnetic field structures (ordered: toroidal $B_{\rm tor}$ or radial $B_\parallel$, and random: normal to the radial direction $B_\perp$), Compton drag, and photospheric emission. We calculate the polarization for different GRB jet angular structures (e.g. top-hat, Gaussian, power-law) and viewing angles $\theta_{\rm obs}$. Synchrotron with $B_\perp$ can produce large polarizations, up to $25\%\lesssim\Pi\lesssim45\%$, for a top-hat jet but only for lines of sight just outside the jet's sharp edge. The same also holds for Compton drag, albeit with a slightly higher overall $\Pi$. Moreover, we demonstrate how $\Gamma$-variations during the GRB or smoother jet edges would significantly reduce $\Pi$. We construct a semi-analytic model for non-dissipative photospheric emission from structured jets. Such emission can produce up to $\Pi\lesssim15\%$ with reasonably high fluences, but this requires steep gradients in $\Gamma(\theta)$. A polarization of $50\%\lesssim\Pi\lesssim65\%$ can robustly be produced only by synchrotron emission from a transverse magnetic field ordered on angles $\gtrsim\!1/\Gamma$ around our line of sight (like a global toroidal field). Therefore, such a model would be strongly favored even by a single secure measurement within this range. We find that such a model would also be favored if $\Pi\gtrsim20\%$ is measured in most GRBs within a large enough sample, by deriving the polarization distribution for our different emission and jet models.Comment: 31 pages, 18 figures. Minor changes to the text; Accepted for publication in MNRA