Radiation-mediated Shocks Research Articles

Observational Characteristics of Radiation-mediated Shocks in Photospheric Gamma-Ray Burst Emission

Emission from the photosphere in gamma-ray burst jets can be substantially affected by subphotospheric energy dissipation, which is typically caused by radiation-mediated shocks. We study the observational characteristics of such emission, in particular the spectral signatures. Relevant shock initial conditions are estimated using a simple internal collision framework, which then serve as inputs for a radiation-mediated shock model that generates synthetic photospheric spectra. Within this framework, we find that if the free fireball acceleration starts at r 0 ∼ 1010 cm, in agreement with hydrodynamical simulations, then the typical spectrum consists of a broad, soft power-law segment with a cutoff at high energies and a hardening in X-rays. The synthetic spectra are generally well fitted with a standard cutoff power-law (CPL) function, as the hardening in X-rays is commonly outside the observable energy range of current detectors. The CPL-fits yield values for the low-energy index, α, and the peak energy, E peak, that are centered around ∼ −0.8 and ∼220 keV, respectively, similar to typical observed values. We also identify a nonnegligible parameter region for what we call optically shallow shocks: shocks that do not accumulate enough scatterings to reach a steady-state spectrum before decoupling and thereby produce more complex spectra. These occur for optical depths , where u u = γ u β u is the dimensionless specific momentum of the upstream as measured in the shock rest frame.

Magnetically driven coupling in relativistic radiation-mediated shocks

ABSTRACT The radiation drag in photon-rich environments of cosmic explosions can seed kinetic instabilities by inducing velocity spreads between relativistically streaming plasma components. Such microturbulence is likely imprinted on the breakout signals of radiation-mediated shocks. However, large-scale, transverse magnetic fields in the deceleration region of the shock transition can suppress the dominant kinetic instabilities by preventing the development of velocity separations between electron–positron pairs and a heavy ion species. We use a 1D five-fluid radiative transfer code to generate self-consistent profiles of the radiation drag force and plasma composition in the deceleration region. For increasing magnetization, our models predict rapidly growing pair multiplicities and a substantial radiative drag developing self-similarly throughout the deceleration region. We extract the critical magnetization parameter σc, determining the limiting magnetic field strength at which a three-species plasma can develop kinetic instabilities before reaching the isotropized downstream. For a relativistic, single ion plasma drifting with γu = 10 in the upstream of a relativistic radiation-mediated shock, we find the threshold σc ≈ 10−7 for the onset of microturbulence. Suppression of plasma instabilities in the case of multi-ion composition would likely require much higher values of σc. Identifying high-energy signatures of microturbulence in shock breakout signals and combining them with the magnetization limits provided in this work will allow a deeper understanding of the magnetic environment of cosmic explosions like supernovae, gamma-ray bursts, and neutron star binary mergers.

The role of plasma instabilities in relativistic radiation-mediated shocks: stability analysis and particle-in-cell simulations

ABSTRACT Relativistic radiation-mediated shocks are likely formed in prodigious cosmic explosions. The structure and emission of such shocks are regulated by copious production of electron–positron pairs inside the shock-transition layer. It has been pointed out recently that substantial abundance of positrons inside the shock leads to a velocity separation of the different plasma constituents, which is expected to induce a rapid growth of plasma instabilities. In this paper, we study the hierarchy of plasma microinstabilities growing in an electron-ion plasma loaded with pairs and subject to a radiation force. Linear stability analysis indicates that such a system is unstable to the growth of various plasma modes which ultimately become dominated by a current filamentation instability driven by the relative drift between the ions and the pairs. These results are validated by particle-in-cell simulations that further probe the non-linear regime of the instabilities, and the pair-ion coupling in the microturbulent electromagnetic field. Based on this analysis, we derive a reduced-transport equation for the particles via pitch-angle scattering in the microturbulence and demonstrate that it can couple the different species and lead to non-adiabatic compression via a Joule-like heating. The heating of the pairs and, conceivably, the formation of non-thermal distributions, arising from the microturbulence, can affect the observed shock-breakout signal in ways unaccounted for by current single-fluid models.

An Efficient Method for Fitting Radiation-mediated Shocks to Gamma-Ray Burst Data: The Kompaneets RMS Approximation

Abstract Shocks that occur below a gamma-ray burst (GRB) jet photosphere are mediated by radiation. Such radiation-mediated shocks (RMSs) could be responsible for shaping the prompt GRB emission. Although well studied theoretically, RMS models have not yet been fitted to data owing to the computational cost of simulating RMSs from first principles. Here we bridge the gap between theory and observations by developing an approximate method capable of accurately reproducing radiation spectra from mildly relativistic (in the shock frame) or slower RMSs, called the Kompaneets RMS approximation (KRA). The approximation is based on the similarities between thermal Comptonization of radiation and the bulk Comptonization that occurs inside an RMS. We validate the method by comparing simulated KRA radiation spectra to first-principle radiation hydrodynamics simulations, finding excellent agreement both inside the RMS and in the RMS downstream. The KRA is then applied to a shock scenario inside a GRB jet, allowing for fast and efficient fitting to GRB data. We illustrate the capabilities of the developed method by performing a fit to a nonthermal spectrum in GRB 150314A. The fit allows us to uncover the physical properties of the RMS responsible for the prompt emission, such as the shock speed and the upstream plasma temperature.

Plasma kinetic effects in relativistic radiation-mediated shocks.

Fast shocks that form in optically thick media are mediated by Compton scattering and, if relativistic, pair creation. Since the radiation force acts primarily on electrons and positrons, the question arises of how the force is mediated to the ions which are the dominant carriers of the shock energy. It has been widely thought that a small charge separation induced by the radiation force generates an electric field inside the shock that decelerates the ions. In this paper we argue that, while this is true in subrelativistic shocks which are devoid of positrons, in relativistic radiation mediated shocks (RRMS), which are dominated by newly created e^{+}e^{-} pairs, additional coupling is needed, owing to the opposite electric force acting on electrons and positrons. Specifically, we show that dissipation of the ions energy must involve collective plasma interactions. By constructing a multifluid model for RRMS that incorporates friction forces, we estimate that momentum transfer between electrons and positrons (and/or ions) via collective interactions on scales of tens to thousands of proton skin depths, depending on whether friction is effective only between e^{+}e^{-} pairs or also between pairs and ions, is sufficient to couple all particles and radiation inside the shock into a single fluid. This leaves open the question of whether in relativistic RMS particles can effectively accelerate to high energies by scattering off plasma turbulence. Such acceleration might have important consequences for relativistic shock breakout signals.

Monte Carlo simulations of relativistic radiation-mediated shocks: II. photon-starved regime

ABSTRACT Radiation-mediated shocks (RMS) play a key role in shaping the early emission observed in many transients. In most cases, e.g. shock breakout in supernovae, llGRBs, and neutron star mergers, the upstream plasma is devoid of radiation, and the photons that ultimately reach the observer are generated predominantly inside and downstream of the shock. Predicting the observed spectrum requires detailed calculations of the shock structure and thermodynamic state that account properly for the shock microphysics. We present results of self-consistent Monte Carlo simulations of photon-starved RMS, which yield the shock structure and emission for a broad range of shock velocities, from subrelativistic (βsh = 0.1) to highly relativistic (Γsh = 20). Our simulations confirm that in relativistic RMS the immediate downstream temperature is regulated by exponential pair creation, ranging from 50 keV at βsh = 0.5–200 keV at Γsh = 20. At lower velocities, the temperature becomes sensitive to the shock velocity, with kT ∼ 0.5 keV at βsh = 0.1. We also confirm that in relativistic shocks the opacity is completely dominated by newly created pairs, which has important implications for the breakout physics. We find the transition to pair dominance to occur at βsh = 0.5 roughly. In all cases examined, the spectrum below the νFν peak has been found to be substantially softer than the Planck distribution. This has important implications for the optical emission in fast and relativistic breakouts, and their detection. The applications to GRB 060218 and GRB 170817A are discussed.

Radiation-mediated Shocks in Gamma-Ray Bursts: Subshock Photon Production

Abstract Internal shocks provide a plausible heating mechanism in the jets of gamma-ray bursts (GRBs). Shocks occurring below the jet photosphere are mediated by radiation. It was previously found that radiation-mediated shocks (RMSs) inside GRB jets are inefficient photon producers, and the photons that mediate the RMS must originate from an earlier stage of the explosion. We show that this conclusion is valid only for nonmagnetized jets. RMSs that propagate in moderately magnetized plasma develop a collisionless subshock that locally heats the plasma to a relativistic temperature, and the hot electrons emit copious synchrotron photons inside the RMS. We find that this mechanism is effective for mildly relativistic shocks and may be the main source of photons observed in GRBs. We derive a simple analytical estimate for the generated photon number per proton, Z, which gives Z = 105–106, consistent with observations. The number is controlled by two main factors: (1) the abundance of electron–positron pairs created in the shock, which is self-consistently calculated, and (2) the upper limit on the brightness temperature of soft radiation set by induced Compton scattering. The photons are initially injected with low energies that are well below the observed GRB peak. The injected soft photons that survive induced downscattering and free–free absorption gain energy in the RMS via bulk Comptonization and shape its nonthermal spectrum.

Radiation-Mediated Shocks: Kinetic Processes and Transition to Collisionless Shocks

We analyze the main features of radiation-mediated shocks at arbitrary shock velocities, both non-relativistic and relativistic. We describe two mechanisms, which may lead to formation of a sharp viscous subshock within otherwise smooth velocity profile at the shock front, even if the radiation pressure in the upstream is overwhelmingly large. These mechanisms are specific to sub-relativistic and relativistic radiation-mediated shocks and set high-velocity shocks apart from their non-relativistic counterparts, which do not develop a subshock if the radiation pressure is high enough. We briefly discuss implications of this finding.

Radiation-mediated Shocks in Gamma-Ray Bursts: Pair Creation

Abstract Relativistic sub-photospheric shocks are a possible mechanism for producing prompt gamma-ray burst (GRB) emission. Such shocks are mediated by scattering of radiation. We introduce a time-dependent, special relativistic code which dynamically couples Monte Carlo radiative transfer to the flow hydrodynamics. The code also self-consistently follows electron–positron pair production in photon–photon collisions. We use the code to simulate shocks with properties relevant to GRBs. We focus on plane-parallel solutions, which are accurate deep below the photosphere. The shock generates a power-law photon spectrum through the first-order Fermi mechanism, extending upward from the typical upstream photon energy. Strong (high Mach number) shocks produce rising νF ν spectra. We observe that in non-relativistic shocks the spectrum extends to , where v is the speed difference between the upstream and downstream. In relativistic shocks the spectrum extends to energies where its slope softens due to Klein–Nishina effects. Shocks with Lorentz factors γ > 1.5 are prolific producers of electron–positron pairs, yielding hundreds of pairs per proton. The main effect of pairs is to reduce the shock width by a factor of . Most pairs annihilate far downstream of the shock, and the radiation spectrum relaxes to a Wien distribution, reaching equilibrium with the plasma at a temperature determined by the shock jump conditions and the photon number per proton. We discuss the implications of our results for observations of radiation generated by sub-photospheric shocks.

Monte Carlo simulations of relativistic radiation-mediated shocks – I. Photon-rich regime

We explore the physics of relativistic radiation mediated shocks (RRMSs) in the regime where photon advection dominates over photon generation. For this purpose, a novel iterative method for deriving a self-consistent steady-state structure of RRMS is developed, based on a Monte-Carlo code that solves the transfer of photons subject to Compton scattering and pair production/annihilation. Systematic study is performed by imposing various upstream conditions which are characterized by the following three parameters: the photon-to-baryon inertia ratio $\xi_{u *}$, the photon-to-baryon number ratio $\tilde{n}$, and the shock Lorentz factor $\gamma_u$. We find that the properties of RRMSs vary considerably with these parameters. In particular, while a smooth decline in the velocity, accompanied by a gradual temperature increase is seen for $\xi_{u*} \gg 1$, an efficient bulk Comptonization, that leads to a heating precursor, is found for $\xi_{u*} \lesssim 1$. As a consequence, although particle acceleration is highly inefficient in these shocks, a broad non-thermal spectrum is produced in the latter case. The generation of high energy photons through bulk Comptonization leads, in certain cases, to a copious production of pairs that provide the dominant opacity for Compton scattering. We also find that for certain upstream conditions a weak subshock appears within the flow. For a choice of parameters suitable to gamma-ray bursts, the radiation spectrum within the shock is found to be compatible with that of the prompt emission, suggesting that subphotospheric shocks may give rise to the observed non-thermal features despite the absence of accelerated particles.

TeV–PeV Neutrinos from Low-Power Gamma-Ray Burst Jets inside Stars

We study high-energy neutrino production in collimated jets inside progenitors of gamma-ray bursts (GRBs) and supernovae, considering both collimation and internal shocks. We obtain simple, useful constraints, using the often overlooked point that shock acceleration of particles is ineffective at radiation-mediated shocks. Classical GRBs may be too powerful to produce high-energy neutrinos inside stars, which is consistent with IceCube nondetections. We find that ultralong GRBs avoid such constraints and detecting the TeV signal will support giant progenitors. Predictions for low-power GRB classes including low-luminosity GRBs can be consistent with the astrophysical neutrino background IceCube may detect, with a spectral steepening around PeV. The models can be tested with future GRB monitors.

OBSERVATIONAL SIGNATURES OF SUB-PHOTOSPHERIC RADIATION-MEDIATED SHOCKS IN THE PROMPT PHASE OF GAMMA-RAY BURSTS

A shock that forms below the photosphere of a gamma-ray burst (GRB) outflow is mediated by Compton scattering of radiation advected into the shock by the upstream fluid. The characteristic scale of such a shock, a few Thomson depths, is larger than any kinetic scale involved by several orders of magnitude. Hence, unlike collisionless shocks, radiation-mediated shocks cannot accelerate particles to nonthermal energies. The spectrum emitted by a shock that emerges from the photosphere of a GRB jet reflects the temperature profile downstream of the shock, with a possible contribution at the highest energies from the shock transition layer itself. We study the properties of radiation-mediated shocks that form during the prompt phase of GRBs and compute the time-integrated spectrum emitted by the shocked fluid following shock breakout. We show that the time-integrated emission from a single shock exhibits a prominent thermal peak, with the location of the peak depending on the shock velocity profile. We also point out that multiple shock emission can produce a spectrum that mimics a Band spectrum.