Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $tilde B/langle Brangle sim 1$ is present on top of the mean field gradient, the diffusion b
ecomes asymmetric. As an example, we consider the vertical transport of cosmic rays in our Galaxy propagating away from a point-like source. We solve this diffusion problem analytically using a one-dimensional Markov chain analysis. We obtained that the cosmic ray density markedly differs from the standard diffusion prediction and has a sizable effect on their distribution throughout the galaxy. The equation for the continuous limit is also derived, which shows limitations of the convection-diffusion equation.
Merging binaries of compact relativistic objects (neutron stars and black holes) are thought to be progenitors of short gamma-ray bursts and sources of gravitational waves, hence their study is of great importance for astrophysics. Because of the str
ong magnetic field of one or both binary members and high orbital frequencies, these binaries are strong sources of energy in the form of Poynting flux (e.g., magnetic-field-dominated outflows, relativistic leptonic winds, electromagnetic and plasma waves). The steady injection of energy by the binary forms a bubble (or a cavity) filled with matter with the relativistic equation of state, which pushes on the surrounding plasma and can drive a shock wave in it. Unlike the Sedov-von Neumann-Taylor blast wave solution for a point-like explosion, the shock wave here is continuously driven by the ever-increasing pressure inside the bubble. We calculate from the first principles the dynamics and evolution of the bubble and the shock surrounding it and predict that such systems can be observed as radio sources a few hours before and after the merger. At much later times, the shock is expected to settle onto the Sedov-von Neumann-Taylor solution, thus resembling an explosion.
Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amount of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, which dynamics is markedly
different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, $L(t)$. In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling $Lpropto (t/t_s)^p$ law (with $p$ and $t_s$ being constants) and the finite activity time case, $Lpropto (1-t/t_s)^{-p}$. The latter with $p>0$ describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions.
Relativistic shocks are usually thought to occur in violent astrophysical explosions. These collisionless shocks are mediated by a plasma kinetic streaming instability, often loosely referred to as the Weibel instability, which generates strong magne
tic fields from scratch very efficiently. In this review paper we discuss the shock micro-physics and present a recent model of pre-conditioning of an initially unmagnetized upstream region via the cosmic-ray-driven Weibel-type instability.
Weibel instability turns out to be the a ubiquitous phenomenon in High-Energy Density environments, ranging from astrophysical sources, e.g., gamma-ray bursts, to laboratory experiments involving laser-produced plasmas. Relativistic particles (electr
ons) radiate in the Weibel-produced magnetic fields in the Jitter regime. Conventionally, in this regime, the particle deflections are considered to be smaller than the relativistic beaming angle of 1/$gamma$ ($gamma$ being the Lorentz factor of an emitting particle) and the particle distribution is assumed to be isotropic. This is a relatively idealized situation as far as lab experiments are concerned. We relax the assumption of the isotropy of radiating particle distribution and present the extension of the jitter theory amenable for comparisons with experimental data.
Radiation from GRBs in the prompt phase, flares and an afterglow is thought to be produced by accelerated electrons in magnetic fields. Such emission may be produced at collisionless shocks of baryonic outflows or at reconnection sites (at least for
the prompt and flares) of the magnetically dominated (Poynting flux driven) outflows, where no shocks presumably form at all. An astonishing recent discovery is that during reconnection strong small-scale magnetic fields are produced via the Weibel instability, very much like they are produced at relativistic shocks. The relevant physics has been successfully and extensively studied with the PIC simulations in 2D and, to some extent, in 3D for the past few years. We discuss how these simulations predict the existence of MeV-range synchrotron/jitter emission in some GRBs, which can be observed with Fermi. Recent results on modeling of the spectral variability and spectral correlations of the GRB prompt emission in the Weibel-jitter paradigm applicable to both baryonic and magnetic-dominated outflows is reviewed with the emphasis on observational predictions.
Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region. If the ambient fields are negligible compared to the shock and cosmic ray energetics, a stronger magnetic field can be generated in the sh
ock upstream via the streaming (Weibel-type) instability. Here we develop a self-similar model of the foreshock region and calculate its structure, e.g., the magnetic field strength, its coherence scale, etc., as a function of the distance from the shock. Our model indicates that the entire foreshock region of thickness $sim R/(2Gamma_{rm sh}^2)$, being comparable to the shock radius in the late afterglow phase when $Gamma_{rm sh}sim1$, can be populated with large-scale and rather strong magnetic fields (of sub-gauss strengths with the coherence length of order $10^{17} {rm cm}$) compared to the typical interstellar medium magnetic fields. The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock. Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band, depending on time and shock parameters. We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock.
We address the question of whether numerical particle-in-cell (PIC) simulations and laboratory laser-plasma experiments can (or will be able to, in the near future) model realistic gamma-ray burst (GRB) shocks. For this, we compare the radiative cool
ing time, t_cool, of relativistic electrons in the shock magnetic fields to the microscopic dynamical time of collisionless relativistic shocks -- the inverse plasma frequency of protons, omega_pp^{-1}. We obtain that for t_cool*omega_pp^{-1}lesssim ~few hundred, the electrons cool efficiently at or near the shock jump and are capable of emitiing away a large fraction of the shock energy. Such shocks are well-resolved in existing PIC simulations; therefore, the microscopic structure can be studied in detail. Since most of the emission in such shocks would be coming from the vicinity of the shock, the spectral power of the emitted radiation can be directly obtained from finite-length simulations and compared with observational data. Such radiative shocks correspond to the internal baryon-dominated GRB shocks for the conventional range of ejecta parameters. Fermi acceleration of electrons in such shocks is limited by electron cooling, hence the emitted spectrum should be lacking a non-thermal tail, whereas its peak likely falls in the multi-MeV range. Incidentally, the conditions in internal shocks are almost identical to those in laser-produced plasmas; thus, such GRB-like plasmas can be created and studied in laboratory experiments using the presently available Petawatt-scale laser facilities. An analysis of the external shocks shows that only the highly relativistic shocks, corresponding to the extremely early afterglow phase, can have efficient electron cooling in the shock transition. We emphasize the importance of radiative PIC simulations for further studies.
