We perform particleincell simulations to elucidate the microphysics of relativistic weakly magnetized shocks loaded with electronpositron pairs. Various external magnetizations
Identifying the accelerators of Galactic cosmic ray (CR) protons with energies up to a few PeV (10^{15}eV) remains a theoretical and observational challenge. Supernova remnants (SNRs) represent strong candidates because they provide sufficient energetics to reproduce the CR flux observed at Earth. However, it remains unclear whether they can accelerate particles to PeV energies, particularly after the very early stages of their evolution. This uncertainty has prompted searches for other source classes and necessitates comprehensive theoretical modeling of the maximum proton energy,
Presented as a thesis to the Department of Astronomy and Astrophysics, The University of Chicago, in partial fulfillment of the requirements for a Ph.D. degree.
more » « less NSFPAR ID:
 10473089
 Publisher / Repository:
 DOI PREFIX: 10.3847
 Date Published:
 Journal Name:
 The Astrophysical Journal
 Volume:
 958
 Issue:
 1
 ISSN:
 0004637X
 Format(s):
 Medium: X Size: Article No. 3
 Size(s):
 ["Article No. 3"]
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract σ ≲ 10^{−4}and pairloading factorsZ _{±}≲ 10 are studied, whereZ _{±}is the number of loaded electrons and positrons per ion. We find the following: (1) The shock becomes mediated by the ion Larmor gyration in the mean field whenσ exceeds a critical valueσ _{L}that decreases withZ _{±}. Atσ ≲σ _{L}the shock is mediated by particle scattering in the selfgenerated microturbulent fields, the strength and scale of which decrease withZ _{±}, leading to lowerσ _{L}. (2) The energy fraction carried by the postshock pairs is robustly in the range between 20% and 50% of the upstream ion energy. The mean energy per postshock electron scales as . (3) Pair loading suppresses nonthermal ion acceleration at magnetizations as low as ${\overline{E}}_{\mathrm{e}}\propto {\left({Z}_{\pm}+1\right)}^{1}$σ ≈ 5 × 10^{−6}. The ions then become essentially thermal with mean energy , while electrons form a nonthermal tail, extending from ${\overline{E}}_{\mathrm{i}}$ to $E\sim {\left({Z}_{\pm}+1\right)}^{1}{\overline{E}}_{\mathrm{i}}$ . When ${\overline{E}}_{\mathrm{i}}$σ = 0, particle acceleration is enhanced by the formation of intense magnetic cavities that populate the precursor during the late stages of shock evolution. Here, the maximum energy of the nonthermal ions and electrons keeps growing over the duration of the simulation. Alongside the simulations, we develop theoretical estimates consistent with the numerical results. Our findings have important implications for models of early gammaray burst afterglows. 
Abstract We measure the thermal electron energization in 1D and 2D particleincell simulations of quasiperpendicular, lowbeta (
β _{p}= 0.25) collisionless ion–electron shocks with mass ratiom _{i}/m _{e}= 200, fast Mach number –4, and upstream magnetic field angle ${\mathcal{M}}_{\mathrm{ms}}=1$θ _{Bn}= 55°–85° from the shock normal . It is known that shock electron heating is described by an ambipolar, $\stackrel{\u02c6}{\mathit{n}}$ parallel electric potential jump, ΔB ϕ _{∥}, that scales roughly linearly with the electron temperature jump. Our simulations have –0.2 in units of the preshock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure $\mathrm{\Delta}{\varphi}_{\parallel}/(0.5{m}_{\mathrm{i}}{{u}_{\mathrm{sh}}}^{2})\sim 0.1$ϕ _{∥}, including the use of de Hoffmann–Teller frame fields, agree to tensofpercent accuracy. Neglecting offdiagonal electron pressure tensor terms can lead to a systematic underestimate ofϕ _{∥}in our lowβ _{p}shocks. We further focus on twoθ _{Bn}= 65° shocks: a ( ${\mathcal{M}}_{\mathrm{s}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}4$ ) case with a long, 30 ${\mathcal{M}}_{\mathrm{A}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}1.8$d _{i}precursor of whistler waves along , and a $\stackrel{\u02c6}{\mathit{n}}$ ( ${\mathcal{M}}_{\mathrm{s}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}7$ ) case with a shorter, 5 ${\mathcal{M}}_{\mathrm{A}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}3.2$d _{i}precursor of whistlers oblique to both and $\stackrel{\u02c6}{\mathit{n}}$ ;B d _{i}is the ion skin depth. Within the precursors,ϕ _{∥}has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the , ${\mathcal{M}}_{\mathrm{s}}\phantom{\rule{0.25em}{0ex}}=\phantom{\rule{0.25em}{0ex}}4$θ _{Bn}= 65° case,ϕ _{∥}shows a weak dependence on the electron plasmatocyclotron frequency ratioω _{pe}/Ω_{ce}, andϕ _{∥}decreases by a factor of 2 asm _{i}/m _{e}is raised to the true proton–electron value of 1836. 
Abstract While it is well known that cosmic rays (CRs) can gain energy from turbulence via secondorder Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time
becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gasCR fluid with diffusive CR transport show clear imprints of CRinduced damping, saturating at ${t}_{\mathrm{damp}}\sim \rho {v}^{2}/{\stackrel{\u0307}{E}}_{\mathrm{CR}}\propto {E}_{\mathrm{CR}}^{1}$ , where ${\stackrel{\u0307}{E}}_{\mathrm{CR}}\sim \tilde{\u03f5}$ is the turbulent energy input rate. In that case, almost all of the energy in largescale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering smallscale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of $\tilde{\u03f5}$E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp largescale motions, with kinetic energy reduced by up to 1 order of magnitude in realisticE _{CR}∼E _{g}scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such largescale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., . $\tilde{\u03f5}\gg \rho {v}^{3}/L$ 
Abstract We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,
r _{p}, is well within the tidal radius of the black hole,r _{t}, i.e., whenβ ≡r _{t}/r _{p}≫ 1. We find that shocks form forβ ≳ 3, but they are weak (with Mach numbers ∼1) for allβ , and that they reach the center of the star prior to the time of maximum adiabatic compression forβ ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβ than the previously predicted and ${\rho}_{\mathrm{max}}\propto {\beta}^{3}$ scalings. Below ${T}_{\mathrm{max}}\propto {\beta}^{2}$β ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the freefalling gas, while aboveβ ≃ 10, we find that shocks prematurely halt the compression and yield the scalings and ${\rho}_{\mathrm{max}}\propto {\beta}^{1.62}$ . We find excellent agreement between our results and highresolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus nonpolytropic stars, and general relativistic effects, which become important when the pericenter of the star nears the direct capture radius, at ${T}_{\mathrm{max}}\propto {\beta}^{1.12}$β ∼ 12.5 (2.7) for a solarlike star disrupted by a 10^{6}M _{⊙}(10^{7}M _{⊙}) supermassive black hole. 
Abstract A steadystate, semianalytical model of energetic particle acceleration in radiojet shear flows due to cosmicray viscosity obtained by Webb et al. is generalized to take into account more general cosmicray boundary spectra. This involves solving a mixed Dirichlet–Von Neumann boundary value problem at the edge of the jet. The energetic particle distribution function
f _{0}(r ,p ) at cylindrical radiusr from the jet axis (assumed to lie along thez axis) is given by convolving the particle momentum spectrum with the Green’s function ${f}_{0}(\infty ,p\prime )$ , which describes the monoenergetic spectrum solution in which $G(r,p;p\prime )$ as ${f}_{0}\to \delta (pp\prime )$r → ∞ . Previous work by Webb et al. studied only the Green’s function solution for . In this paper, we explore for the first time, solutions for more general and realistic forms for $G(r,p;p\prime )$ . The flow velocity ${f}_{0}(\infty ,p\prime )$ =u u (r ) _{z}is along the axis of the jet (thee z axis). is independent ofu z , andu (r ) is a monotonic decreasing function ofr . The scattering time in the shear flow region 0 < $\tau {(r,p)={\tau}_{0}(p/{p}_{0})}^{\alpha}$r <r _{2}, and , where $\tau {(r,p)={\tau}_{0}(p/{p}_{0})}^{\alpha}{(r/{r}_{2})}^{s}$s > 0 in the regionr >r _{2}is outside the jet. Other original aspects of the analysis are (i) the use of cosmic ray flow lines in (r ,p ) space to clarify the particle spatial transport and momentum changes and (ii) the determination of the probability distribution that particles observed at ( ${\psi}_{p}(r,p;p\prime )$r ,p ) originated fromr → ∞ with momentum . The acceleration of ultrahighenergy cosmic rays in active galactic nuclei jet sources is discussed. Leaky box models for electron acceleration are described. $p\prime $