Influence of Alfven waves on the Thermal Instability in the Interstellar Medium

The effect of Alfv\'en waves on the thermal instability of the Interstellar Medium (ISM) is investigated both analytically and numerically. A stability analysis of a finite amplitude circularly polarized Alfv\'en wave propagating parallel to an ambient magnetic field in a thermally unstable gas at thermal equilibrium is performed, leading to a dispersion relation which depends on 3 parameters, namely the square ratio of the sonic and Alfv\'en velocities ($\beta$), the wave amplitude and the ratio between the wave temporal period and the cooling time. Depending on the values of these 3 parameters, the Alfv\'en waves can stabilize the large-scale perturbations, destabilize those whose wavelength is a few times the Alfv\'en wavelength $\lambda_{AW}$ or leave the growth rate of the short scales unchanged. In order to investigate the non-linear regime, two different numerical experiments are performed in a slab geometry. (TBC)