Self-consistent equilibrium models of prominence thin threads heated by Alfvén waves propagating from the photosphere

Abstract: The fine structure of solar prominences is made by thin threads that outline the magnetic field lines. Observations show that transverse waves of Alfv\'enic nature are ubiquitous in prominence threads. These waves are driven at the photosphere and propagate to prominences suspended in the corona. Heating due to Alfv\'en wave dissipation could be a relevant mechanism in the cool and partially ionized prominence plasma. We explore the construction of 1D equilibrium models of prominence thin threads that satisfy energy balance between radiative losses, thermal conduction, and Alfv\'en wave heating. We assume the presence of a broadband driver at the photosphere that launches Alfv\'en waves towards the prominence. An iterative method is implemented, in which the energy balance equation and the Alfv\'en wave equation are consecutively solved. From the energy balance equation and considering no wave heating initially, we compute the equilibrium profiles along the thread of the temperature, density, ionisation fraction. We use the Alfv\'en wave equation to compute the wave heating rate, which is then put back in the energy balance equation to obtain new equilibrium profiles. The process is repeated until convergence to a self-consistent thread model heated by Alfv\'en waves is achieved. We have obtained equilibrium models composed of a cold and dense thread, a extremely thin PCTR, and an extended coronal region. The length of the cold thread decreases with the temperature at the prominence core and increases with the Alfv\'en wave energy flux. Equilibrium models are not possible for sufficiently large wave energy fluxes when the wave heating rate inside the cold thread becomes larger than radiative losses. The maximum value of the wave energy flux that allows an equilibrium depends on the prominence core temperature. This constrains the existence of equilibria in realistic conditions.