Cosmic very small dust grains as a natural laboratory of mesoscopic physics: Modeling thermal and optical properties of graphite grains

Cosmic very small dust grains (VSGs) contain 100 to 10000 atoms, making them a mesoscopic system with specific thermal and optical characteristics due to the finite number of atoms within each grain. This paper focuses on graphite VSGs which contain free electrons. The energy level statistics devised by Kubo (1962, J. Phys. Soc. Jpn., 17, 975) are used for the first time to understand the thermal properties of free electrons in graphite VSGs. We show that the shape irregularity of the grains allows graphite VSGs to absorb or emit photons at submillimeter wavelengths or longer; otherwise, the frequency is limited to above a few THz. Additionally, we consider the decrease in Debye temperature due to the surface effect. VSGs have an extremely small volume, resulting in limited thermal energy storage, especially at low temperatures. Since a VSG is able to emit a photon with energy smaller than its internal energy, this determines the maximum frequency of the emitted photon. We develop a Monte Carlo simulation code to track the thermal history of a dust grain, considering the stochastic heating from the absorption of ambient photons and radiative cooling. This approach is applied to the interstellar environment to compute the spectral energy distributions from the interstellar graphite dust grains. The results show that graphite VSGs emit not only the mid-infrared excess emission, but also a surplus emission from submillimeter to millimeter wavelengths.