The Possibility of Thermal Instability in Early-Type Stars Due to Alfven Waves

It was shown by dos Santos et al. the importance of Alfv\'en waves to explain the winds of Wolf-Rayet stars. We investigate here the possible importance of Alfv\'en waves in the creation of inhomogeneities in the winds of early-type stars. The observed infrared emission (at the base of the wind) of early-type stars is often larger than expected. The clumping explains this characteristic in the wind, increasing the mean density and hence the emission measure, making possible to understand the observed infrared, as well as the observed enhancement in the blue wing of the $H_\alpha$ line. In this study, we investigate the formation of these clumps a via thermal instability. The heat-loss function used, $H(T,n)$, includes physical processes such as: emission of (continuous and line) recombination radiation; resonance line emission excited by electron collisions; thermal bremsstrahlung; Compton heating and cooling; and damping of Alfv\'en waves. As a result of this heat-loss function we show the existence of two stable equilibrium regions. The stable equilibrium region at high temperature is the diffuse medium and at low temperature the clumps. Using this reasonable heat-loss function, we show that the two stable equilibrium regions can coexist over a narrow range of pressures describing the diffuse medium and the clumps.