Extreme hydrodynamic atmospheric loss near the critical thermal escape regime

By considering martian-like planetary embryos inside the habitable zone of solar-like stars we study the behaviour of the hydrodynamic atmospheric escape of hydrogen for small values of the Jeans escape parameter beta < 3, near the base of the thermosphere, that is defined as a ratio of the gravitational and thermal energy. Our study is based on a 1D hydrodynamic upper atmosphere model that calculates the volume heating rate in a hydrogen-dominated thermosphere due to the absorption of the stellar soft X-ray and extreme ultraviolet (XUV) flux. In case of a monatomic gas, we find that when the beta value near the mesopause/homopause level exceeds a critical value of similar to 2.5, there exists a steady hydrodynamic solution with a smooth transition from subsonic to supersonic flow. For a fixed XUV flux, the escape rate of the upper atmosphere is an increasing function of the temperature at the lower boundary. Our model results indicate a crucial enhancement of the atmospheric escape rate, when the Jeans escape parameter beta decreases to this critical value. When beta becomes <= 2.5, there is no stationary hydrodynamic transition from subsonic to supersonic flow. This is the case of a fast non-stationary atmospheric expansion that results in extreme thermal atmospheric escape rates.