  The detection of gravitational waves from the inspiral of a neutron star or
stellar-mass black hole into an intermediate-mass black hole (IMBH) promises an
entirely new look at strong-field gravitational physics. Gravitational waves
from these intermediate-mass-ratio inspirals (IMRIs), systems with mass ratios
from ~10:1 to ~100:1, may be detectable at rates of up to a few tens per year
by Advanced LIGO/Virgo and will encode a signature of the central body's
spacetime. Direct observation of the spacetime will allow us to use the
"no-hair" theorem of general relativity to determine if the IMBH is a Kerr
black hole (or some more exotic object, e.g. a boson star). Using modified
post-Newtonian (pN) waveforms, we explore the prospects for constraining the
central body's mass-quadrupole moment in the advanced-detector era. We use the
Fisher information matrix to estimate the accuracy with which the parameters of
the central body can be measured. We find that for favorable mass and spin
combinations, the quadrupole moment of a non-Kerr central body can be measured
to within a ~15% fractional error or better using 3.5 pN order waveforms; on
the other hand, we find the accuracy decreases to ~100% fractional error using
2 pN waveforms, except for a narrow band of values of the best-fit non-Kerr
quadrupole moment.
