Improving the model of emission from spinning dust: Effects of grain wobbling and transient spin-up

Observations continue to support the interpretation of the anomalous microwave foreground as electric dipole radiation from spinning dust grains as proposed by Draine & Lazarian. In this paper, we present a refinement of the original model by improving the treatment of a number of physical effects. First, we consider a disk-like grain rotating with angular velocity at an arbitrary angle with respect to the grain symmetry axis (i.e., grain wobbling) and derive the rotational damping and excitation coefficients arising from infrared emission, plasma-grain interactions, and electric dipole emission. The angular velocity distribution and the electric dipole emission spectrum for disk-like grains is calculated using the Langevin equation, for cases both with and without fast internal relaxation. Our results show that for fast internal relaxation, the peak emissivity of spinning dust, compared to earlier studies, increases by a factor of ∼ 2 for the warm neutral medium (WNM), the warm ionized medium (WIM), the cold neutral medium (CNM), and the photodissociation region, and by a factor ∼ 4 for reflection nebulae. The frequency at the emission peak also increases by factors ∼ 1.4 to ∼ 2 for these media. Without internal relaxation, the increase of emissivity is comparable, but the emission spectrum is more extended to higher frequency. The increased emission results from the non-sphericity of grain shape and from the anisotropy in damping and excitation along directions parallel and perpendicular to the grain symmetry axis. Second, we provide a detailed numerical study including transient spin-up of grains by single-ion collisions. The range of grain size in which single-ion collisions are important is identified. The impulses broaden the emission spectrum and increase the peak emissivity for the CNM, WNM, and WIM, although the increases are not as large as those due to the grain wobbling. In addition, we present an improved treatment of rotational excitation and damping by infrared emission.