Chaos and loss: reevaluating the loss-cone formalism in the context of chaotic diving orbits in flattened potentials

Abstract

The region close to a massive black hole is one of the few truly spherical geometries in galactic dynamics. Stellar structures, which dominate from pc to kpc scales, are generally at least flattened (axisymmetric) if not more irregular and time evolving. Here we show that orbits that pass between these diverse geometries are commonly chaotic, especially those which dive - visiting their minimum possible periapse. We show that these chaotic diving orbits are common across a wide range of potentials, and can lead to large variation in angular momentum orbit to orbit. We characterise the transition from regular to chaotic orbits with a notional critical angular momentum, $j_d$. We then model the flux of orbits into the loss cone including the effects of these diving orbits combined with evolution through two-body scattering. Systems which cross into the chaotic region are quickly advected away, and thus there is a large net flux across the boundary. We formulate the problem as a probability density, rather than a number density, allowing us to find a true equilibrium state. We find that the rate of disruptions when including diving orbits is boosted by a multiplicative factor of $1+\ln(j_d/j_t)$, where $j_t$ is the angular momentum corresponding to a disruption. This boost can increase disruption rates by an order of magnitude compared to the classical loss cone formalism.