We investigate the theoretical and observational implications of the acceleration of protons and heavier nuclei in supernova remnants (SNRs). By adopting a semi-analytical technique, we study the non-linear interplay among particle acceleration, magnetic field generation and shock dynamics, outlining a self-consistent scenario for the origin of the spectrum of Galactic cosmic rays as produced in this class of sources. Moreover, the inferred chemical abundances suggest nuclei heavier than Hydrogen to be relevant not only in the shock dynamics but also in the calculation of the gamma-ray emission from SNRs due to the decay of neutral pions produced in nuclear interactions.
For more than 70 years scientists have been regarding supernova remnants (SNRs) as the most plausible sources for Galactic cosmic rays (GCRs), but only in recent times the theoretical comprehension of the ongoing processes have made important steps forward (see also P. Blasi's contribution in this volume). Once a model for CR propagation in the Milky Way is assumed, it is possible to infer from observations at Earth the spectra of single chemical species expected at the sources. In this work we investigate a scenario in which Galactic SNRs are responsible for the acceleration of protons and heavier nuclei (hereafter HN), trying to disentangle the solid, physical ingredients and the phenomenological recipes which have to be included in order to account for many observational constraints. In particular we show that, according to this SNR paradigm for the origin of GCRs, HN may play a fundamental role in the shock dynamics and also contribute in a non-negligible way to the γ-ray emission from SNRs.
We consider here a semi-analytical approach to the problem of non-linear diffusive acceleration of particles at shocks (NLDSA) following the basic implementation put forward in Ref. 1-3, also including the effects of the magnetic field amplification on the shock dynamics 4 and the pressure of the most abundant CR species. 5 The evolution of a remnant in a homogeneous circumstellar medium is followed in a quasi-stationary way as in Ref. 6 and coupled with the acceleration of particles at the forward shock as in Refs. 5,7. For the details of the computational apparatus, the reader may refer to the papers above. Here, we only would like to highlight how such a semi-analytical approach to NLDSA is typically much faster than, and as much rigorous as, other fully numerical or Monte Carlo methods for non-relativistic shocks, 8 and therefore it is very useful for including multi-specie CRs or, in general, for studying problems with a wide range of environmental parameters.
In our calculations protons are injected into the acceleration process from the thermal bath through a “thermal-leakage” mechanism, 9 which is sensitive to the shock dynamics and tends to suppress the number of injected particles when the the acceleration becomes more and more efficient. The amounts of injected HN are tuned by hand relatively to protons to reproduce the abundances measured at Earth. This recipe, while including a reasonable feedback which self-regulates the efficiency of the injection, has to be regarded as a necessary phenomenological description since, unfortunately, the HN injection at SNR shocks is still poorly understood for two main reasons. First, injection strongly depends on the charge/mass ratio and it is very difficult to follow the degree of ionization of heavy atoms during their acceleration; second, refractory elements (Mg, Si, Fe,…) are thought to be injected as a result of sputtering of accelerating dust grains. 10,11 The latter phenomenon, though very hard to deal with quantitatively, is however expected to produce largely suprathermal (but still non-relativistic) ions able to cross the shock from downstream to upstream because of their large gyroradii. For the same reason, partially ionized heavy atoms are expected to be preferentially injected, in agreement with the relative abundances measured in GCRs. 10,11 Nevertheless, since our abundances are tuned on the relativistic region of the GCR spectrum, we can bypass the problem above and make safe predictions about the role of HN in the shock dynamics and in the SNR γ-ray emission.
At any given time the shock dynamics is regulated by the non-linear interplay between particle acceleration, occurring via first-order Fermi mechanism, and magnetic field amplification, which we model as due to resonant streaming instability excited by all the accelerated particles. 12 On one hand, the pressure in CRs diffusing around the shock leads to the formation of a precursor which slows down the incoming fluid and tends to make the shock weaker while, on the other hand, the pressure in the shape of self-generated magnetic turbulence may become comparable to, or even larger than, the gas pressure upstream, preventing an excessive modification of the velocity profile. This magnetic feedback 13 has proved itself to be a very common mechanism able to account, at the same time, for both the level of magnetization and the hydrodynamics inferred by multi-wavelength studies of young SNRs. 4 In addition, when the velocity of the scattering centres, which we assume to be transverse Alfvén waves as predicted by the quasi-linear theory of resonant streaming instability, becomes a non-negligible fraction of the fluid velocity, the compression ratios actually felt by the fluid and by the accelerated particles are no longer the same. A physically motivated account for the relative velocity between the fluid and the waves leads to conclude that the more efficient the magnetic field amplification (t
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