A more accurate numerical scheme for diffusive shock acceleration

We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. We compare the results for the slope of the momentum distribution with those obtained from a perturbation analysis valid for finite but small shock width. These calculations show that this scheme, although computationally more expensive, provides a significantly better performance than the Cauchy-Euler type schemes that were proposed earlier in the case where steep gradients in the cosmic ray diffusivity occur. For constant diffusivity the proposed scheme gives similar results as the Cauchy-Euler scheme.Comment: 9 pages, 2 figures. Published in MNRA

Cosmic ray acceleration in young supernova remnants

We investigate the appearance of magnetic field amplification resulting from a cosmic ray escape current in the context of supernova remnant shock waves. The current is inversely proportional to the maximum energy of cosmic rays, and is a strong function of the shock velocity. Depending on the evolution of the shock wave, which is drastically different for different circumstellar environments, the maximum energy of cosmic rays as required to generate enough current to trigger the non-resonant hybrid instability that confines the cosmic rays follows a different evolution and reaches different values. We find that the best candidates to accelerate cosmic rays to ~few PeV energies are young remnants in a dense environment, such as a red supergiant wind, as may be applicable to Cassiopeia A. We also find that for a typical background magnetic field strength of 5 microG the instability is quenched in about 1000 years, making SN1006 just at the border of candidates for cosmic ray acceleration to high energies.Comment: 14 pages, 8 figures. Accepted for publication in MNRA

Confining the high-energy cosmic rays

Diffusive shock acceleration is the prime candidate for efficient acceleration of cosmic rays. Galactic cosmic rays are believed to originate predominantly from this process in supernova remnant shock waves. Confinement of the cosmic rays in the shock region is key in making the mechanism effective. It has been known that on small scales (smaller than the typical gyroradius) high-amplitude non-resonant instabilities arise due to cosmic ray streaming ahead of the shock. For the efficiency of scattering of the highest energy cosmic rays it is of interest to determine the type of instabilities that act on longer length scales, i.e. larger than the cosmic ray gyroradius. We will present the results of our analysis of an instability that acts in this regime and will discuss its driving mechanism and typical growth times.Comment: 4 pages, 1 figure. Proceedings for the conference on Cosmic Rays and the Interstellar Medium (CRISM) in June 2011, Montpellier, France. To appear in MSA

Magnetic field amplification by cosmic rays in supernova remnants

Magnetic field amplification is needed to accelerate cosmic cays to PeV energies in supernova remants. Escaping cosmic rays trigger a return current in the plasma that drives a non-resonant hybrid instability. We run simulations in which we represent the escaping cosmic rays with the plasma return current, keeping the maximum cosmic ray energy fixed, and evaluate its effects on the upstream medium. In addition to magnetic field amplification, density perturbations arise that, when passing through the shock, further increase amplification levels downstream. As the growth rate of the instability is most rapid for the smaller scales, the resolution is a limiting factor in the amplification that can be reached with these simulations.Comment: 4 pages, 2 figures, to appear in the proceedings of the conference "370 years of Astronomy in Utrecht", eds. G. Pugliese, A. de Koter and M. Wijbur

From cosmic ray source to the Galactic pool

The Galactic cosmic ray spectrum is a remarkably straight power law. Our current understanding is that the dominant sources that accelerate cosmic rays up to the knee ($3 \times 10^{15}$ eV) or perhaps even the ankle ($3 \times 10^{18}$ eV), are young Galactic supernova remnants. In theory, however, there are various reasons why the spectrum may be different for different sources, and may not even be a power law if nonlinear shock acceleration applies during the most efficient stages of acceleration. We show how the spectrum at the accelerator translates to the spectrum that make up the escaping cosmic rays that replenish the Galactic pool of cosmic rays. We assume that cosmic ray confinement, and thus escape, is linked to the level of magnetic field amplification, and that the magnetic field is amplified by streaming cosmic rays according to the non-resonant hybrid or resonant instability. When a fixed fraction of the energy is transferred to cosmic rays, it turns out that a source spectrum that is flatter than $E^{-2}$ will result in a $E^{-2}$ escape spectrum, whereas a steeper source spectrum will result in an escape spectrum with equal steepening. This alleviates some of the concern that may arise from expected flat or concave cosmic ray spectra associated with nonlinear shock modification.Comment: 5 pages, 1 figure. Accepted for publication in MNRA

Evolution of Magnetic Fields in Supernova Remnants

Supernova remnants (SNR) are now widely believed to be a source of cosmic rays (CRs) up to an energy of 1 PeV. The magnetic fields required to accelerate CRs to sufficiently high energies need to be much higher than can result from compression of the circumstellar medium (CSM) by a factor 4, as is the case in strong shocks. Non-thermal synchrotron maps of these regions indicate that indeed the magnetic field is much stronger, and for young SNRs has a dominant radial component while for old SNRs it is mainly toroidal. How these magnetic fields get enhanced, or why the field orientation is mainly radial for young remnants, is not yet fully understood. We use an adaptive mesh refinement MHD code, AMRVAC, to simulate the evolution of supernova remnants and to see if we can reproduce a mainly radial magnetic field in early stages of evolution. We follow the evolution of the SNR with three different configurations of the initial magnetic field in the CSM: an initially mainly toroidal field, a turbulent magnetic field, and a field parallel to the symmetry axis. Although for the latter two topologies a significant radial field component arises at the contact discontinuity due to the Rayleigh-Taylor instability, no radial component can be seen out to the forward shock. Ideal MHD appears not sufficient to explain observations. Possibly a higher compression ratio and additional turbulence due to dominant presence of CRs can help us to better reproduce the observations in future studies.Comment: 5 pages, 3 figures. To appear in conference proceedings of "Magnetic Fields in the Universe II" (2008), RevMexA

The relation between post-shock temperature, cosmic-ray pressure and cosmic-ray escape for non-relativistic shocks

Supernova remnants are thought to be the dominant source of Galactic cosmic rays. This requires that at least 5% of the available energy is transferred to cosmic rays, implying a high cosmic-ray pressure downstream of supernova remnant shocks. Recently, it has been shown that the downstream temperature in some remnants is low compared to the measured shock velocities, implying that additional pressure support by accelerated particles is present. Here we use a two-fluid thermodynamic approach to derive the relation between post-shock fractional cosmic-ray pressure and post-shock temperature, assuming no additional heating beyond adiabatic heating in the shock precursor and with all non-adiabatic heating occurring at the subshock. The derived relations show that a high fractional cosmic-ray pressure is only possible, if a substantial fraction of the incoming energy flux escapes from the system. Recently a shock velocity and a downstream proton temperature were measured for a shock in the supernova remnant RCW 86. We apply the two-fluid solutions to these measurements and find that the the downstream fractional cosmic-ray pressure is at least 50% with a cosmic-ray energy flux escape of at least 20%. In general, in order to have 5% of the supernova energy go into accelerating cosmic rays, on average the post-shock cosmic-ray pressure needs to be 30% for an effective cosmic-ray adiabatic index of 4/3.Comment: 9 pages, 6 color figures. This is updated with a corrected figure 5a and 5b, reflecting an ApJ erratu

Jets as diagnostics of the circumstellar medium and the explosion energetics of supernovae: the case of Cas A

We present hydrodynamical models for the Cassiopeia A (Cas A) supernova remnant and its observed jet / counter-jet system. We include the evolution of the progenitor's circumstellar medium, which is shaped by a slow red supergiant wind that is followed by a fast Wolf-Rayet (WR) wind. The main parameters of the simulations are the duration of the WR phase and the jet energy. We find that the jet is destroyed if the WR phase is sufficiently long and a massive circumstellar shell has formed. We therefore conclude that the WR phase must have been short (a few thousand yr), if present at all. Since the actual jet length of Cas A is not known we derive a lower limit for the jet energy, which is ~10^{48} erg. We discuss the implications for the progenitor of Cas A and the nature of its explosion.Comment: 9 pages, 5 figures, ApJ accepted. Version with high resolution figures available at http://www.phys.uu.nl/~schure/CasA_jet.pd

Modeling the interaction of thermonuclear supernova remnants with circumstellar structures: The case of Tycho's supernova remnant

The well-established Type Ia remnant of Tycho's supernova (SN 1572) reveals discrepant ambient medium density estimates based on either the measured dynamics or on the X-ray emission properties. This discrepancy can potentially be solved by assuming that the supernova remnant (SNR) shock initially moved through a stellar wind bubble, but is currently evolving in the uniform interstellar medium with a relatively low density. We investigate this scenario by combining hydrodynamical simulations of the wind-loss phase and the supernova remnant evolution with a coupled X-ray emission model, which includes non-equilibrium ionization. For the explosion models we use the well-known W7 deflagration model and the delayed detonation model that was previously shown to provide good fits to the X-ray emission of Tycho's SNR. Our simulations confirm that a uniform ambient density cannot simultaneously reproduce the dynamical and X-ray emission properties of Tycho. In contrast, models that considered that the remnant was evolving in a dense, but small, wind bubble reproduce reasonably well both the measured X-ray emission spectrum and the expansion parameter of Tycho's SNR. Finally, we discuss possible mass loss scenarios in the context of single- and double-degenerate models which possible could form such a small dense wind bubble.Comment: 12 pages, 7 figures, accepted for publication in MNRA

Progenitor's signatures in Type Ia supernova remnants

The remnants of Type Ia supernovae can provide important clues about their progenitor-histories. We discuss two well-observed supernova remnants (SNRs) that are believed to result from a Type Ia SN and use various tools to shed light on the possible progenitor history. We find that Kepler's SNR is consistent with a symbiotic binary progenitor consisted of a white dwarf and an AGB star. Our hydrosimulations can reproduce the observed kinematic and morphological properties. For Tycho's remnant we use the characteristics of the X-ray spectrum and the kinematics to show that the ejecta has likely interacted with dense circumstellar gas.Comment: 4 pages, 9 figures, proceedings for IAU Symposium 281, Padova, July 201