X-MRIs: Extremely Large Mass-Ratio Inspirals

Abstract

The detection of the gravitational waves emitted in the capture process of a compact object by a massive black hole is known as an extreme-mass ratio inspiral (EMRI) and represents a unique probe of gravity in the strong regime and is one of the main targets of LISA. The possibility of observing a compact-object EMRI at the Galactic Centre (GC) when LISA is taking data is very low. However, the capture of a brown dwarf, an X-MRI, is more frequent because these objects are much more abundant and can plunge without being tidally disrupted. An X-MRI covers some $\sim 10^8$ cycles before merger, and hence stay on band for millions of years. About $2\times 10^6$ yrs before merger they have a signal-to-noise ratio (SNR) at the GC of 10. Later, $10^4$ yrs before merger, the SNR is of several thousands, and $10^3$ yrs before the merger a few $10^4$. Based on these values, this kind of EMRIs are also detectable at neighbour MBHs, albeit with fainter SNRs. We calculate the event rate of X-MRIs at the GC taking into account the asymmetry of pro- and retrograde orbits on the location of the last stable orbit. We estimate that at any given moment, and using a conservative approach, there are of the order of $\gtrsim 20$ sources in band. From these, $\gtrsim 5$ are circular and are located at higher frequencies, and about $\gtrsim 15$ are highly eccentric and are at lower frequencies. Due to their proximity, X-MRIs represent a unique probe of gravity in the strong regime. The mass ratio for a X-MRI at the GC is $q\sim 10^8$, i.e., three orders of magnitude larger than stellar-mass black hole EMRIs. Since backreaction depends on $q$, the orbit follows closer a standard geodesic, which means that approximations work better in the calculation of the orbit. X-MRIs can be sufficiently loud so as to track the systematic growth of their SNR, which can be high enough to bury that of MBH binaries.

arXiv commentAccepted and matches the publication at PRD (which did not allow to have the dedicatory to Tal on the first page and the acronym on the title, both kept here). Abstract abridged. See related paper by Gourgoulhon et al. 2019, arXiv:1903.02049

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