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  1. ABSTRACT

    Cosmic rays (CRs) are thought to escape their sources streaming along the local magnetic field lines. We show that this phenomenon generally leads to the excitation of both resonant and non-resonant streaming instabilities. The self-generated magnetic fluctuations induce particle diffusion in extended regions around the source, so that CRs build up a large pressure gradient. By means of two-dimensional (2D) and three-dimensional (3D) hybrid particle-in-cell simulations, we show that such a pressure gradient excavates a cavity around the source and leads to the formation of a cosmic ray dominated bubble, inside which diffusivity is strongly suppressed. Based on the trends extracted from self-consistent simulations, we estimate that, in the absence of severe damping of the self-generated magnetic fields, the bubble should keep expanding until pressure balance with the surrounding medium is reached, corresponding to a radius of ∼10–50 pc. The implications of the formation of these regions of low diffusivity for sources of Galactic CRs are discussed. Special care is devoted to estimating the self-generated diffusion coefficient and the grammage that CRs might accumulate in the bubbles before moving into the interstellar medium. Based on the results of 3D simulations, general considerations on the morphology of the γ-ray and synchrotronmore »emission from these extended regions also are outlined.

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  2. Abstract The origin of cosmic rays is a pivotal open issue of high-energy astrophysics. Supernova remnants are strong candidates to be the Galactic factory of cosmic rays, their blast waves being powerful particle accelerators. However, supernova remnants can power the observed flux of cosmic rays only if they transfer a significant fraction of their kinetic energy to the accelerated particles, but conclusive evidence for such efficient acceleration is still lacking. In this scenario, the shock energy channeled to cosmic rays should induce a higher post-shock density than that predicted by standard shock conditions. Here we show this effect, and probe its dependence on the orientation of the ambient magnetic field, by analyzing deep X-ray observations of the Galactic remnant of SN 1006. By comparing our results with state-of-the-art models, we conclude that SN 1006 is an efficient source of cosmic rays and obtain an observational support for the quasi-parallel acceleration mechanism.
    Free, publicly-accessible full text available December 1, 2023
  3. Abstract Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While the standard prediction for strong shocks is that the spectrum of accelerated particles is universal, f ( p ) ∝ p −4 , numerous phenomena affect this simple conclusion. In general, the nonlinear dynamical reaction of accelerated particles leads to a concave spectrum, steeper than p −4 at momenta below a few tens of GeV c −1 and harder than the standard prediction at high energies. However, the nonlinear effects become important in the presence of magnetic field amplification, which in turn leads to higher values of the maximum momentum p max . It was recently discovered that the self-generated perturbations that enhance particle scattering, when advected downstream, move in the same direction as the background plasma, so that the effective compression factor at the shock decreases and the spectrum becomes steeper. We investigate the implications of the excitation of the non-resonant streaming instability on these spectral deformations, the dependence of the spectral steepening on the shock velocity, and the role played by the injection momentum.
    Free, publicly-accessible full text available May 1, 2023
  4. Abstract Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than E −2 , the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of nonlinear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than E −2 and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs (∝ E −2.2 ) and the very steep spectra of young radio supernovae (∝ E −3 ).
  5. Context. The spectrum of cosmic ray protons and electrons released by supernova remnants throughout their evolution is poorly known because of the difficulty in accounting for particle escape and confinement downstream of a shock front, where both adiabatic and radiative losses are present. Since electrons lose energy mainly through synchrotron losses, it is natural to ask whether the spectrum released into the interstellar medium may be different from that of their hadronic counterpart. Independent studies of cosmic ray transport through the Galaxy require that the source spectrum of electrons and protons be very different. Therefore, the above question acquires a phenomenological relevance. Aims. Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from the upstream region and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons, where in addition to adiabatic losses we take the radiative losses suffered behind the shock into account. These electrons are dominated by synchrotron losses in the magnetic field, which most likely is self-generated by cosmic rays accelerated at the shock. Methods. We use standard temporal evolution relationsmore »for supernova shocks expanding in different types of interstellar media together with an analytic description of particle acceleration and magnetic field amplification to determine the density and spectrum of cosmic ray particles. Their evolution in time is derived by numerically solving the equation describing advection with adiabatic and radiative losses for electrons and protons. The flux from particles continuously escaping the supernova remnants is also accounted for. Results. The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to nonresonant and resonant streaming instability and their saturation. The resulting field is compared with the available set of observational results concerning the dependence of the magnetic field strength upon shock velocity. We find that when the field is the result of the growth of the cosmic-ray-driven nonresonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different; however, such a difference becomes appreciable only at energies ≳100−1000 GeV, while observations of the electron spectrum require such a difference to be present at energies as low as ∼10 GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of supernova remnant evolution (shock velocity ≪1000 km s −1 ); this may not be due to streaming instability but rather hydrodynamical processes. We comment on the feasibility of such conditions and speculate on the possibility that the difference in spectral shape between electrons and protons may reflect either some unknown acceleration effect or additional energy losses in cocoons around the sources.« less