Steep Cosmic-Ray Spectra with Revised Diffusive Shock Acceleration

Diesing, Rebecca; Caprioli, Damiano

doi:10.3847/1538-4357/ac22fe

Cited by 28 publications

(30 citation statements)

References 93 publications

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“…In Figures 1 and 2 we show that, for a reasonable range of CR acceleration efficiencies and CR injection momenta, the postcursor steepening is very prominent when the shock is very fast (v sh of tens of thousands of km s −1 ) and it can lead to spectra of accelerated particles close to p −5 , while generally producing spectra slightly steeper than p −4 for historical SNRs (also see Diesing & Caprioli 2021).…”

Section: Discussionmentioning

confidence: 83%

“…Since, when spectra are very steep, non-relativistic CRs may carry a sizable fraction of the total pressure, we retain the general expression for the CR adiabatic index as This leads to a fourth-order algebraic equation for R tot . As discussed in much of the literature on nonlinear theory of DSA (e.g., Berezhko & Ellison 1999;Blasi 2002), this procedure may be tricky because it requires the knowledge of the escape flux, which in turn requires the solution of the transport equation for accelerated particles (Diesing & Caprioli 2021). However, for the cases of interest here, the spectrum becomes sufficiently steeper than p −4 that the escape flux can be neglected and the expressions derived above are good approximations to the exact ones.…”

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confidence: 99%

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Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Schwarz

Blasi

Caprioli

2022

ApJ

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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.

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Section: Discussionmentioning

confidence: 83%

mentioning

confidence: 99%

Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Schwarz

Blasi

Caprioli

2022

ApJ

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“…The DSA particle spectra depend on the scattering centers compression ratio C sc (see e.g. Bell 1978;Kang & Ryu 2018;Diesing & Caprioli 2021). In a simple test particle case, the scattering The shock crossing happened in the past.…”

Section: Adiabatic Losses/gains Mirror Instability and Aging Of Relat...mentioning

confidence: 99%

“…High magnetic field amplification and wavevector anisotropy can provide U w2 large enough to be comparable with the downstream velocity in the shock rest frame u 2 . Recent microscopic hybrid modeling of a plane shock by Diesing & Caprioli (2021) revealed a possibility of substantial spectral steepening due to the positive mean speed of the scattering centers in the downstream. Kang & Ryu (2018) also discussed a planar shock model with the negative mean velocity of the scattering centers in the downstream U w,2 < 0, which in the case of the hot cluster plasma can provide a very minor spectral flattening.…”

Section: Adiabatic Losses/gains Mirror Instability and Aging Of Relat...mentioning

confidence: 99%

Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA. II. Shock & Relic

Churazov¹,

Khabibullin²,

Bykov³

et al. 2022

Preprint

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This is the second paper in a series of studies of the Coma cluster using the SRG/eROSITA X-ray data obtained in the course of the calibration and performance verification observations. Here we focus on the region adjacent to the radio source 1253+275 (Radio Relic, RR hereafter). We show that the X-ray surface brightness steepest gradient at ∼ 79 (∼ 2.2 Mpc ≈ R 200c ) is almost co-spatial with the outer edge of RR, with an offset of about ∼ 100−150 kpc between the derived position of the shock front and the brightest part of RR. As in several other relics, the Mach number of the shock derived from the X-ray surface brightness profile (M X ≈ 1.9) appears to be lower than needed to explain the slope of the integrated radio spectrum in the DSA model (M R ≈ 3.5) if the magnetic field is uniform and the radiative losses are fast. However, the shock geometry is plausibly much more complicated than a spherical wedge centered on the cluster, given a non-trivial correlation between radio, X-ray, and SZ images. While the complicated shock geometry alone might bias M X low, we speculate on a few other processes that can affect the M X -M R relation, including a fine structure of the shock that might be modified by the presence of non-thermal filaments stretching across the shock. We also discuss the "history" of the radio galaxy NGC4789 located ahead of the relic in the context of the Coma-NGC4839 merger scenario.

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“…The exact values and mechanisms lie beyond the scope of this work. Models can be found in [53] or more recently [54]. In the following the spectral index is chosen to be α = 4.2.…”

Section: Initial Conditionsmentioning

confidence: 99%

Self-confinement of low-energy cosmic rays around supernova remnants

Jacobs,

Mertsch,

Phan

2021

Preprint

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Supernova remnants have long been considered as a promising candidate for sources of Galactic cosmic rays. However, modelling cosmic-ray transport around these sources is complicated by the fact that the overdensity of cosmic rays close to their acceleration site can lead to self-confinement, that is the generation of turbulence upon which these particles scatter. Such a highly non-linear problem can be addressed by numerically solving the coupled differential equations describing the evolution in space and time of the escaping particles and of the turbulent plasma waves. In this work, we focus essentially on the propagation of cosmic rays from supernova remnants in the warm ionized and warm neutral phases of the interstellar medium and propose an extended framework to take into account also the effect of energy loss relevant for cosmic rays of energy below 10 GeV. Interestingly, the diffusion coefficient of low-energy cosmic rays could be suppressed by up to 2 orders of magnitude for several tens of kiloyears after the escape from the shock. The cosmic-ray spectrum outside the supernova remnant flattens below 1 GeV at a sufficiently late time reminiscient of the spectral behaviour observed by Voyager. We also find the grammage accumulated around the source to be non-negligible, with important implications for precision fitting of the cosmic-ray spectra.

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Steep Cosmic-Ray Spectra with Revised Diffusive Shock Acceleration

Cited by 28 publications

References 93 publications

Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Tempestuous life beyond R500: X-ray view on the Coma cluster with SRG/eROSITA. II. Shock & Relic

Self-confinement of low-energy cosmic rays around supernova remnants

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