Chemical Enhancements in Shock-Accelerated Particles: Ab initio Simulations

We study the thermalization, injection, and acceleration of ions with different mass/charge ratios, $A/Z$, in nonrelativistic collisionless shocks via hybrid (kinetic ions–fluid electrons) simulations. In general, ions thermalize to a postshock temperature proportional to $A$. When diffusive shock acceleration is efficient, ions develop a nonthermal tail whose extent scales with $Z$ and whose normalization is enhanced as $(A/Z{)}^2$ so that incompletely ionized heavy ions are preferentially accelerated. We discuss how these findings can explain observed heavy-ion enhancements in Galactic cosmic rays.

Figure 1

Normalized postshock spectra for ion species with mass $A$ and charge $Z$ as in the legend, for a quasiparallel ($\vartheta =20°$) shock with $M=10$. The thermal peaks correspond to the Maxwellian distributions (color-matching dotted lines) expected if the temperature scaled with $A$; the nonthermal tails have a maximum extent $\propto E/Z$ and a normalization enhanced as a function of $A/Z$.

Figure 2

Preferential acceleration of ions with large $A/Z$ at quasiparallel shocks with different Mach numbers. For $M\gtrsim 10$, the fraction of injected ions ${\eta }_i$ is linear in $A/Z$ (top panel), and the ion enhancement [Eq. (2)] scales as $K_{ip}\propto (A/Z{)}^2$ (bottom panel). For $M=5$, the self-generated magnetic turbulence is weaker and ion enhancements $K_{ip}\propto A/Z$ only.

Figure 3

Chemical enhancements in GCRs [Eq. (3)] compared to the ones obtained for a quasiparallel shock with $M=20$, assuming that species are singly ionized. The dashed line corresponds to the scaling $\propto (A/Z{)}^2$ in Fig. 2.

Figure 4

$x-p_x$ phase space at $t=\{200,700\}{\omega }_c^{-1}$ (left to right) for our benchmark case; top to bottom panels correspond to species with $A/Z=\{1,4,8\}$, respectively. Ions with larger $A/Z$ isotropize further downstream of the shock marked with dashed lines. At $t=200{\omega }_c^{-1}$, energetic protons are already diffusing, ions with $A/Z=4$ have just started being injected, and ions with $A/Z=8$ are still anisotropic and not injected. At $t=700{\omega }_c^{-1}$, instead, all species exhibit typical DSA spectra.