  We investigate the influence of impacts of large planetesimals and small
planetary embryos on the early Martian surface on the hydrodynamic escape of an
early steam atmosphere that is exposed to the high soft X-ray and EUV flux of
the young Sun. Impact statistics in terms of number, masses, velocities, and
angles of asteroid impacts onto the early Mars are determined via n-body
integrations. Based on these statistics, smoothed particle hydrodynamics (SPH)
simulations result in estimates of energy transfer into the planetary surface
material and according surface heating. For the estimation of the atmospheric
escape rates we applied a soft X-ray and EUV absorption model and a 1-D upper
atmosphere hydrodynamic model to a magma ocean-related catastrophically
outgassed steam atmosphere with surface pressure values of 52 bar H2O and 11
bar CO2. The estimated impact rates and energy deposition onto an early Martian
surface can account for substantial heating. The energy influx and conversion
rate into internal energy is most likely sufficient to keep a shallow magma
ocean liquid for an extended period of time. Higher surface temperatures keep
the outgassed steam atmosphere longer in vapor form and therefore enhance its
escape to space within about 0.6 Myr after its formation.
