Structure and Instability of the Ionization Fronts around Moving Black Holes

Abstract

In this paper we focus on understanding the physical processes that lead to stable or unstable ionization fronts (I-fronts) observed in simulations of moving black holes (BHs). The front instability may trigger bursts of gas accretion, rendering the BH significantly more luminous than at steady-state. We perform a series of idealized three dimensional radiation hydrodynamics simulations resolving the I-fronts around BHs of mass $M_\mathrm{BH}$ and velocity $v_\infty$ accreting from a medium of density $n_\mathrm{H}$. The I-front, with radius $R_\mathrm{I}$, transitions from D-type to R-type as the BH velocity becomes larger than a critical value $v_\mathrm{R}\sim 40\,\mathrm{km/s}$. The D-type front is preceded by a bow-shock of thickness $\Delta R_\mathrm{I}$ that decreases as $v_\infty$ approaches $v_\mathrm{R}$. We find that both D-type and R-type fronts can be unstable given the following two conditions: i) for D-type fronts the shell thickness must be $\Delta R_\mathrm{I}/R_\mathrm{I}<0.05$ (i.e., $v_\infty \gtrsim 20\,\mathrm{km/s}$.), while no similar restriction holds for R-type fronts; ii) the temperature jump across the I-front must be $T_\mathrm{II}/T_\mathrm{I}>3$. This second condition is satisfied if $T_\mathrm{I}<5000\,\mathrm{K}$ or if $n_\mathrm{H}\,M_\mathrm{BH} \gtrsim 10^6\,M_\odot\,\mathrm{cm^{-3}}$. Due to X-ray pre-heating typically $T_\mathrm{I} \sim 10^4\,\mathrm{K}$, unless the D-type shell is optically thick to X-rays, which also happens when $n_\mathrm{H}\,M_\mathrm{BH}$ is greater than a metallicity-dependent critical value. We thus conclude that I-fronts around BHs are unstable only for relatively massive BHs moving trough very dense molecular clouds. We briefly discuss the observational consequences of the X-ray luminosity bursts likely associated with this instability.