  To investigate impact vaporization for planetary atmosphere formation, we
have studied the thermodynamic state generated by the shock wave due to a
high-velocity impact, called the shock field. We have carried out iSALE
simulations for high-velocity vertical impacts using ANEOS for an
equation-of-state (EoS) model. To understand the shock fields obtained from
simulations, we have investigated the contribution of the thermal and cold
terms in the EoS model on the Hugoniot curves. Although the thermal and cold
terms are important for the pressure, the internal energy is mainly determined
by the thermal term. We thus assume a simple EoS determined by the thermal term
and then analytically derive the shock internal-energy field, which reproduces
the results of simulations well. Using the analytical solution of internal
energy and the Hugoniot curve, we have derived the shock pressure field
analytically as well. The analytical solutions for internal energy and pressure
are valid even for impact velocities as low as the sound speed. The solution is
good for the vertical direction or within the angles of about 60 degrees. We
have applied the solution to impact vaporization for the formation of planetary
atmospheres. This gives good estimation of reformation of the planetary
atmospheres of Earth sized planet.
