Effects of Pre-ionisation in Radiative Shocks I: Self-Consistent Models

In this paper we treat the pre-ionisation problem in shocks over the velocity range $10 < v_{\rm s} < 1500$\,km/s in a self-consistent manner. We identify four distinct classes of solution controlled by the value of the shock precursor parameter, $\Psi = {\cal Q}/v_s$, where ${\cal Q}$ is the ionization parameter of the UV photons escaping upstream. This parameter determines both the temperature and the degree of ionisation of the gas entering the shock. In increasing velocity the shock solution regimes are cold neutral precursors ($v_s \lesssim 40$\,km/s), warm neutral precursors ($40 \lesssim v_s \lesssim 75$\,km/s), warm partly-ionized precursors ($75 \lesssim v_s \lesssim 120$\,km/s), and fast shocks in which the pre-shock gas is in photoionisation equilibrium, and is fully ionized. The main effect of a magnetic field is to push these velocity ranges to higher values, and to limit the post-shock compression. In order to facilitate comparison with observations of shocks, we provide a number of convenient scaling relationships for parameters such as post-shock temperature, compression factors, cooling lengths, and H$\beta$ and X-ray luminosity.