X-MRIs: 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 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.
