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 accelerating the growth of supermassive BH seeds and 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 $v_\mathrm{R}\sim 30-55\,\mathrm{km/s}$. 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 $\Delta R_\mathrm{I}/R_\mathrm{I} 3$. This second condition is satisfied if $T_\mathrm{I} 10^2-10^4\,M_\odot$) moving trough very dense molecular clouds.