Diffusive shock acceleration of dust grains at supernova remnants

Diffusive shock acceleration (DSA) is a prominent mechanism for energizing charged particles up to very large rigidities at astrophysical collisionless shocks. In addition to ions and electrons, it has been proposed that interstellar dust grains could also be accelerated through diffusive shock acceleration, for instance, at supernova remnants (SNRs). Considering interstellar dust grains of various size and composition, we investigate the possibility of grain acceleration at young SNR shocks (throughout the free expansion and Sedov-Taylor phases) and the maximum energies reached by the accelerated grains. We investigate the potential implications on the abundance of refractory species relative to volatile elements in the cosmic-ray composition. We rely on semi-analytical descriptions of particle acceleration at strong shocks, and on self-similar solutions for the dynamics of SNR shock waves. For simplicity, type Ia thermonuclear SNRs expanding in uniform interstellar medium are considered. We find that the acceleration of dust grains at relativistic speed is possible, up to Lorentz factor of $\sim 10^{2}$, kinetic energy $E_{\rm k}/\text{nuc}\sim 10^2$ GeV/nuc for the smaller grains of size $a\sim 5 \times 10^{-7}$ cm. We find that the subsequent sputtering of grains can produce nuclei with a rigidity sufficient to be injected in the process of diffusive shock acceleration. Such scenario can help naturally account for the overabundance of refractory elements in the Galactic cosmic-ray composition, provided that a fraction $\eta \sim 10^{-3}-10^{-2}$ of dust grains swept up by a SNR are energized through DSA.