The structure of relativistic radiation mediated shocks (RRMS) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors $\Gamma_u$ in the range $6\le\Gamma_u\le30$, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor $ \Gamma $ drops from $ \Gamma_u $ to $ \sim 1 $, is characterized by high plasma temperatures $ T\sim \Gamma m_ec^2 $ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\times\, m_ec^2$ and $\sim \Gamma^2 m_ec^2$, respectively.Photon scattering is dominated by e$^\pm$ pairs, with pair to proton density ratio reaching $\approx10^2\Gamma_u$. The width of the deceleration region, in terms of Thomson optical depths for upstream going photons, is large, $\Delta\tau\sim\Gamma_u^2$ ($\Delta\tau\sim1$ neglecting the contribution of pairs) due to Klein Nishina suppression of the scattering cross section. A high energy photon component, narrowly beamed in the downstream direction, with a nearly flat power-law like spectrum, $\nu I_\nu\propto\nu^0$, and an energy cutoff at $ \sim \Gamma_u^2 m_ec^2 $ carries a fair fraction of the energy flux at the end of the deceleration region. An approximate analytic model of RRMS, reproducing the main features of the numerical results, is provided.
Deep Dive into Relativistic Radiation Mediated Shocks.
The structure of relativistic radiation mediated shocks (RRMS) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors $\Gamma_u$ in the range $6\le\Gamma_u\le30$, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor $ \Gamma $ drops from $ \Gamma_u $ to $ \sim 1 $, is characterized by high plasma temperatures $ T\sim \Gamma m_ec^2 $ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\times\, m_ec^2$ and $\sim \Gamma^2
1. INTRODUCTION Radiation mediated shocks (RMSs) are shocks in which the downstream (DS) energy density is dominated by radiation rather than by particle thermal energy, and in which the fast upstream (US) plasma approaching the shock is decelerated by scattering of photons, generated in the DS and propagating into the US, by the fast US electrons. RMS are expected to occur in a variety of astrophysical flows. The shock waves propagating through, and expelling, the envelopes of massive stars undergoing core collapse supernova explosions, are non relativistic (NR) RMS (Weaver 1976). Relativistic RMS (RRMS) may play an important role in, e.g., gamma-ray bursts, transrelativistic suprenovae, and pulsar accretion flows.
[1] Gamma Ray Bursts (GRBs). Within the framework of the collapsar model of GRBs (e.g. Woosley 1993), a highly relativistic jet driven by the collapsed core of a massive star penetrates through the stellar envelope. The shock that decelerates the jet is expected to be a highly relativistic RMS (Mészáros & Waxman 2001;Aloy et al. 2000).
[2] Trans Relativistic SNe. Several recent SN events, that were identified in very early stages of the explosion, have been shown to deposit a significant fraction, ∼ 1%, of the explosion energy in mildly relativistic, γβ 1, ejecta (Soderberg et al. 2006, and references therein). The existence of mildly relativistic ejecta components suggests that a mildly relativistic RMS shock traversed the outer envelope of the progenitor.
[3] Pulsar accretion flows. Accretion onto the polar cap of a pulsar is expected to produce a mildly relativistic RMS which is approximately stationary in the neutron star frame (Burnard et al. 1991;Becker 1988, and references therein).
NR RMS were studied in detail in (Weaver 1976), describing photon propagation using the diffusion approximation and 1 Physics Faculty, Weizmann Institute, Rehovot 76100, Israel;
ranny.budnik@weizmann.ac.il; boaz.katz@weizmann.ac.il; eli.waxman@weizmann.ac.il describing the radiation field using two parameters, photon effective temperature and density. These approximations hold for slow shocks, v/c < 0.2, for which relativistic effects are negligible and the Thomson optical depth of the shock deceleration region is large, ∼ c/v (ensuring that the radiation field is nearly isotropic and that the photons are in Compton equilibrium). The NR approximations do not hold for faster shocks. For such shocks, relativistic effects (such as pair production and relativistic corrections to the cross sections of radiative processes) are important, and the radiation field becomes highly anisotropic.
A simplified solution for the structure of RRMS, neglecting pair production, photon production and relativistic corrections, was derived by Levinson & Bromberg (2008). This solution may be applicable only in cases where the US plasma holds a significant photon density, which keeps the plasma at low temperatures throughout the shock, much lower than those obtained in a self-consistent solution where the photon density vanishes at US infinity. In a preceding paper (Katz et al. 2010) we derived a simple approximate analytic model for the structure of radiation mediated shocks. This model accurately reproduces the numerical results of Weaver (1976) for v/c 0.2, and provides an approximate description of the shock structure at larger velocities, v/c → 1. We confirmed that at shock velocities v/c 0.1 the shock transition region is far from thermal equilibrium, with electrons and photons (and positrons) in Compton (pair) equilibrium at temperatures T s significantly exceeding the far downstream temperature. We have found that T s 10 keV is reached at shock velocities v/c ≈ 0.2, and that at higher velocities, v/c 0.6, the plasma is dominated in the transition region by e ± pairs and 60 keV T s 200 keV. We have suggested that the spectrum of radiation emitted during the breaking out of supernova shocks from the stellar envelopes of Blue Super Giants and Wolf-Rayet stars, which reach v/c > 0.1 for reasonable stellar parameters, may include a hard compo-nent with photon energies reaching tens or even hundreds of keV. This may account for the X-ray outburst associated with SN2008D (Soderberg et al. 2008), and possibly for other SNassociated outbursts with spectra not extending beyond few 100 keV [e.g. XRF060218/SN2006aj (Campana et al. 2006)].
In this paper we derive exact numerical solutions for the steady state structure of RRMS, propagating into a cold upstream plasma of protons and electrons, for shock Lorentz factors ≤ 30 and upstream proper densities ≪ 10 25 cm -3 . The solutions are obtained using a novel iteration method for selfconsistently solving the energy, momentum and particle conservation equations along with the equation of radiation transport. We assume that the electrons, positrons and protons may be described as a fluid, that the (plasma rest frame) energy distribution of positrons and electrons is thermal, and that t
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
