Temperature spectra of interstellar dust grains heated by cosmic-rays I: translucent clouds

Heating of whole interstellar dust grains by cosmic-ray (CR) particles affects the gas-grain chemistry in molecular clouds by promoting molecule desorption, diffusion, and chemical reactions on grain surfaces. The frequency of such heating $f_T$, s$^{-1}$, determines how often a certain temperature $T_{\rm CR}$, K, is reached for grains hit by CR particles. This study aims to provide astrochemists with comprehensive and updated dataset on the CR-induced whole-grain heating. We present calculations of $f_T$ and $T_{\rm CR}$ spectra for bare olivine grains with radius $a$ of 0.05; 0.1; 0.2 $\mu$m, and such grains covered with ice mantles of thickness 0.1$a$ and 0.3$a$. Grain shape and structure effects are considered, as well as 30 CR elemental constituents with an updated energy spectrum corresponding to a translucent cloud with $A_V=2$ mag. Energy deposition by CRs in grain material was calculated with the SRIM program. We report full $T_{\rm CR}$ spectra for all nine grain types and consider initial grain temperatures of 10 K and 20 K. We also provide frequencies for a range of minimum $T_{\rm CR}$ values. The calculated dataset can be simply and flexibly implemented in astrochemical models. The results show that, in the case of translucent clouds, the currently adopted rate for heating of whole grains to temperatures in excess of 70 K is underestimated by approximately two orders of magnitude in astrochemical numerical simulations. Additionally, grains are heated by CRs to modest temperatures (20--30 K) with intervals of a few years, which reduces the possibility of ice chemical explosions.