Influence of the hydrodynamic drag from an accretion torus on extreme mass-ratio inspirals

Abstract

We have studied extreme mass-ratio inspirals (EMRIs) in spacetimes containing a rotating black hole and a non-self-gravitating torus with a constant distribution of specific angular momentum. We have found that the dissipative effect of the hydrodynamic drag exerted by the torus on the satellite is much smaller than the corresponding one due to radiation reaction, for systems such as those generically expected in active galactic nuclei and at distances from the central supermassive black hole (SMBH) which can be probed with the Laser Interferometer Space Antenna (LISA). However, given the uncertainty on the parameters of these systems, namely, on the masses of the SMBH and of the torus, as well as on its size, there exist configurations in which the effect of the hydrodynamic drag on the orbital evolution can be comparable to the radiation reaction one in phases of the inspiral which are detectable by the Laser Interferometer Space Antenna. This is the case, for instance, for a 10 6 M SMBH surrounded by a corotating torus of comparable mass and with radius of 10 3 -10 4 gravitational radii, or for a 10 5 M SMBH surrounded by a corotating 10 4 M torus with radius of 10 5 gravitational radii. Should these conditions be met in astrophysical systems, EMRI-gravitational waves could provide a characteristic signature of the presence of the torus. In fact, while radiation reaction always increases the inclination of the orbit with respect to the equatorial plane (i.e., orbits evolve towards the equatorial retrograde configuration), the hydrodynamic drag from a torus corotating with the SMBH always decreases it (i.e., orbits evolve towards the equatorial prograde configuration). However, even when initially dominating over radiation reaction, the influence of the hydrodynamic drag decays very rapidly as the satellite moves into the very strong-field region of the SMBH (i.e., p & 5M), thus allowing one to use pure-Kerr templates for the last part of the inspiral. Although our results have been obtained for a specific class of tori, we argue that they will be qualitatively valid also for more generic distributions of the specific angular momentum.

Forced motion near black holes

“…It is gratifying that this simple model produces this expected feature qualitatively. The same paper [25] found that the eccentricity would increase in parts of the parameter space and decrease in other parts. For Newtonian orbits, the osculating element equations predict that the eccentricity will remain constant under the action of a simple drag force of this type (see Appendix C).…”

“…If observed, this would provide a robust observational signature for an orbit that was evolving under the influence of drag. A decrease in orbital inclination due to hydrodynamic drag was also seen in [25], in which a more sophisticated model for the drag force was employed. It is gratifying that this simple model produces this expected feature qualitatively.…”

Fundamental physics with LISA

“…So far, studies of the accuracy of this test [6,7] have focused on the ability of LISA to discriminate between the Kerr solution and other metric solutions of Einstein's field equations, for example metrics containing massive accretion disks [8,9] as well as central black holes. In such situations the basic field equations are unchanged, and one simply has to determine if the observed radiation came from an orbit in one metric or another.…”

“…If they are not in phase then the propagation speeds of the two forms of radiation must be different. Assuming a timing accuracy of ±1 min for a system that is at a distance of 100 pc, LISA could test the relative speeds to parts in 10 9 . Much more accurate would be a bound within a model of a 'massive graviton', where dispersion of gravitational waves distorts the observed signal from an inspiralling pair of supermassive black holes [4].…”

Effect of massive perturbers on extreme mass-ratio inspiral waveforms

“…[2,[11][12][13][14] for a study of differences caused by an accretion disk around the SMBH). Here we point out an effect that has not been considered in this context: the acceleration of the EMRI system by a nearby (distance of roughly a few tenths of a parsec or less) secondary SMBH.…”