ith radiative transfer modelling. Finally, we present in Section \[conclusions\] our conlusions.

Models
======

Current models of spinning dust [@DL98; @Ali2009; @Ysard2010a; @Hoang2010; @Silsbee2011] take into account a number of processes for the rotational excitation and damping of the grains: the emission of IR photons, the collisions with neutral and ionised gas particles (, , and ), the plasma drag ( and ), the photoelectric effect, and the formation of H$_2$ molecules at the surface of the grains. The publically available SpDust[^1] code [@Ali2009; @Silsbee2011] includes the most recent developments regarding the gas-grain interactions and the grain dynamics (rotation around non-principal axis of inertia). The results of SpDust agree well with other models that include a more detailed treatment of the IR emission or of the gas-grain interactions [@Ysard2010a; @Hoang2010]. SpDust is fast and well-suited for coupling to other codes, especially radiative transfer codes. In the following, we use SpDust to model the spinning dust emission.

In order to estimate dust emission from the mid-IR to the microwave range in a consistent way, we coupled SpDust with the dust emission model described by @Compiegne2011, DustEM[^2]. DustEM is based on the formalism of @Desert1990 and includes three dust types: interstellar PAHs, amourphous carbonaceous grains, and amourphous silicates. We used the dust populations defined by @Compiegne2011 for the diffuse, high galactic latitude interstellar medium (DHGL). For PAHs we assumed a log-normal size distribution with centroid $a_0=0.64$ nm and width $\sigma=0.4$, with a dust-to-gas mass ratio $M_{PAH}/M_H=7.8\times 10^{-4}$.

In current models, the smallest grains (PAHs) carry the spinning dust emission that is sensitive to the gas density and the radiation field intensity[^3], $G_0$, but also to the ionisation state (abundance of the $\ion{H}{ii}$ and $\ion{C}{ii}$ ions, noted $x_H$ and $x_C$ respectively). Radiative transfer calculations are performed with the CRT[^4] tool [@J