Exciting modes due to the aberration of gravitational waves:
  Measurability for extreme-mass-ratio inspirals
  Gravitational waves from a source moving relative to us can suffer from
special-relativistic effects such as aberration. The required velocities for
these to be significant are on the order of $1000\,\textrm{km s}^{-1}$. This
value corresponds to the velocity dispersion that one finds in clusters of
galaxies. Hence, we expect a large number of gravitational-wave sources to have
such effects imprinted in their signals. In particular, the signal from a
moving source will have its higher modes excited, i.e., $(3,3)$ and beyond. We
derive expressions describing this effect, and study its measurability for the
specific case of a circular, non-spinning extreme-mass-ratio inspiral. We find
that the excitation of higher modes by a peculiar velocity of
$1000\,\textrm{km\,s}^{-1}$ is detectable for such inspirals with
signal-to-noise ratios of $\gtrsim20$. Using a Fisher matrix analysis, we show
that the velocity of the source can be measured to a precision of just a few
percent for a signal-to-noise ratio of 100. If the motion of the source is
ignored parameter estimates could be biased, e.g., the estimated masses of the
components through a Doppler shift. Conversely, by including this effect in
waveform models, we could measure the velocity dispersion of clusters of
galaxies at distances inaccessible to light.
