Extremely large mass-ratio inspirals

The detection of the gravitational waves emitted in the capture process of a compact object by a massive black hole (MBH) is known as an extreme-mass ratio inspiral (EMRI), it represents a unique probe of gravity in the strong regime, and it is one of the main targets of the Laser Interferometer Space Antenna (LISA). The possibility of observing a compact-object EMRI at the Galactic Center (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 ∼10⁸ cycles before merger, and hence stays on band for millions of years. About 2 ×10⁶ yrs before merger they have a signal-to-noise ratio (SNR) at the GC of 10. Later, 1 0⁴ yrs before merger, the SNR is of several thousands, and 1 0³ yrs before the merger a few 1 0⁴. Based on these values, this kind of EMRIs is also detectable at neighbor 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 (LSO). We estimate that at any given moment, and using a conservative approach, there are of the order of ≳20 sources in band. From these, ≳5 are circular and are located at higher frequencies, and about ≳15 are highly eccentric and are at lower frequencies. Because of 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 ∼10⁸ , i.e., 3 orders of magnitude larger than stellar-mass black hole EMRIs. Since backreaction depends on q , the orbit more closely follows 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.