A self-consistent model of shock-heated plasma in non-equilibrium states for direct parameter constraints from X-ray observations

X-ray observations of shock-heated plasmas, such as those found in supernova remnants, often exhibit features of temperature and ionization non-equilibrium. For accurate interpretation of these observations, proper calculations of the equilibration processes are essential. Here, we present a self-consistent model of thermal X-ray emission from shock-heated plasmas that accounts for both temperature and ionization non-equilibrium conditions. For a given pair of shock velocity and initial electron-to-ion temperature ratio, the temporal evolution of the temperature and ionization state of each element was calculated by simultaneously solving the relaxation processes of temperature and ionization. The resulting thermal X-ray spectrum was synthesized by combining our model with the AtomDB spectral code. Comparison between our model and the \texttt{nei} model, a constant-temperature non-equilibrium ionization model available in the XSPEC software package, reveals a 30\% underestimation of the ionization timescale in the \texttt{nei} model. We implemented our model in XSPEC to directly constrain the shock wave properties, such as the shock velocity and collisionless electron heating efficiency, from the thermal X-ray emission from postshock plasmas. We applied this model to archival Chandra data of the supernova remnant N132D, providing a constraint on the shock velocity of $\sim 800~\mathrm{km\,s^{-1}}$, in agreement with previous optical studies.