Structure and Instability of the Ionization Fronts around Moving Black Holes

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 $M_{\mathrm{B}\mathrm{H}}$ and velocity $v_{\mathrm{\infty }}$ 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{k}\mathrm{m}\mathrm{/}\mathrm{s}$$\mathrm{.}TheD-typefrontisprecededbyabow-shockofthickness$\Delta R_$\mathrm{I}$$thatdecreasesas$v_\infty$approaches$v_$\mathrm{R}$$. We find that both D-type and R-type fronts can be unstable given the following two conditions: i) for D-type fronts the shell thickness must be $\Delta R_$\mathrm{I}$/R_$\mathrm{I}$<0.05$(i\mathrm{.}e\mathrm{.},$v_\infty \gtrsim 20,$\mathrm{k}\mathrm{m}\mathrm{/}\mathrm{s}$$.), while no similar restriction holds for R-type fronts; ii) the temperature jump across the I-front must be $T_{\mathrm{I}\mathrm{I}}\mathrm{/}{T}_{\mathrm{I}}>3$. This second condition is satisfied if $T_{\mathrm{I}}<5000\mathrm{K}$ or if $n_{\mathrm{H}}{M}_{\mathrm{B}\mathrm{H}}\gtrsim {10}^6{M}_{\odot }\mathrm{c}{\mathrm{m}}^{-3}$. 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 $n_{\mathrm{H}}{M}_{\mathrm{B}\mathrm{H}}$ 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.