Roche Accretion of stars close to massive black holes

TL;DR

This paper investigates Roche accretion in EMRI systems with stars orbiting massive black holes, providing new relativistic formulas for inspiral, Roche lobe volume, and mass transfer, with implications for gravitational wave detection and X-ray variability.

Contribution

It introduces new relativistic fitting and interpolation formulae for inspiral time, Roche lobe volume, and mass transfer dynamics in EMRI systems, advancing understanding of stellar accretion near black holes.

Findings

New relativistic formulas for inspiral time and radiation-reaction torque.

Relativistic interpolation formulae for Roche lobe volume.

Predicted observable luminosity modulation due to mass transfer.

Abstract

In this paper we consider Roche accretion in an Extreme Mass-Ratio Inspiral (EMRI) binary system formed by a star orbiting a massive black hole. The ultimate goal is to detect the mass and spin of the black hole and provide a test of general relativity in the strong-field regime from the resultant quasi-periodic signals. Before accretion starts, the stellar orbit is presumed to be circular and equatorial, and shrinks due to gravitational radiation. New fitting formulae are presented for the inspiral time and the radiation-reaction torque in the relativistic regime. If the inspiralling star fills its Roche lobe outside the Innermost Stable Circular Orbit (ISCO) of the hole, gas will flow through the inner Lagrange point (L1) to the hole. We give new relativistic interpolation formulae for the volume enclosed by the Roche lobe. If this mass-transfer happens on a time scale faster than the thermal time scale but slower than the dynamical time scale, the star will evolve adiabatically, and, in most cases, will recede from the hole while filling its Roche lobe. We calculate how the stellar orbital period and mass-transfer rate will change through the "Roche evolution" for various types of stars in the relativistic regime. We envisage that the mass stream eventually hits the accretion disc, where it forms a hot spot orbiting the hole and may ultimately modulate the luminosity with the stellar orbital frequency. The observability of such a modulation is discussed along with a possible interpretation of an intermittent 1 hour period in the X-ray emission of RE J1034+396.