Cosmic Ray Spectra in Supernova Remnants – I. Loss-Free Self-Similar Solution. (arXiv:1901.01284v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Malkov_M/0/1/0/all/0/1">Mikhail Malkov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Aharonian_F/0/1/0/all/0/1">Felix Aharonian</a>
The direct measurements of cosmic rays (CRs), after correction for the
propagation effects in the interstellar medium, indicate that their source
spectra should be significantly steeper than the canonical $E^{-2}$ spectrum
predicted by the standard Diffusive Shock Acceleration (DSA) mechanism. The DSA
has long been held responsible for the production of galactic CRs in supernova
remnant (SNR) shocks. The $gamma$-ray “probes” of the acceleration spectra of
CRs on-the-spot, inside of the SNRs, lead to the same conclusion. We show that
the steep acceleration spectrum can be attributed to the combination of (i)
spherical expansion, (ii) tilting of the magnetic field along the shock surface
and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient
only on two “polar caps” of a spherical shock where the local magnetic field is
within $simeq45^{circ}$ to its normal. The shock-produced spectrum observed
edge-on steepens with the particle energy because the number of freshly
accelerated particles with lower energies continually adds up to a growing
acceleration region. We demonstrate the steepening effect by obtaining an exact
self-similar solution for the particle acceleration at expanding shock surface
with an arbitrary energy dependence of particle diffusivity $kappa$. We show
that its increase toward higher energy leads to the spectrum steepening. We
contrast our results with the “standard” DSA predictions under comparable
acceleration conditions.
The direct measurements of cosmic rays (CRs), after correction for the
propagation effects in the interstellar medium, indicate that their source
spectra should be significantly steeper than the canonical $E^{-2}$ spectrum
predicted by the standard Diffusive Shock Acceleration (DSA) mechanism. The DSA
has long been held responsible for the production of galactic CRs in supernova
remnant (SNR) shocks. The $gamma$-ray “probes” of the acceleration spectra of
CRs on-the-spot, inside of the SNRs, lead to the same conclusion. We show that
the steep acceleration spectrum can be attributed to the combination of (i)
spherical expansion, (ii) tilting of the magnetic field along the shock surface
and (iii) shock deceleration. Because of (i) and (ii), the DSA is efficient
only on two “polar caps” of a spherical shock where the local magnetic field is
within $simeq45^{circ}$ to its normal. The shock-produced spectrum observed
edge-on steepens with the particle energy because the number of freshly
accelerated particles with lower energies continually adds up to a growing
acceleration region. We demonstrate the steepening effect by obtaining an exact
self-similar solution for the particle acceleration at expanding shock surface
with an arbitrary energy dependence of particle diffusivity $kappa$. We show
that its increase toward higher energy leads to the spectrum steepening. We
contrast our results with the “standard” DSA predictions under comparable
acceleration conditions.
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