Peculiar Transverse Velocities of Galaxies from Quasar Microlensing.
  Tentative Estimate of the Peculiar Velocity Dispersion at $z\sim 0.5$
  We propose to use the flux variability of lensed quasar images induced by
gravitational microlensing to measure the transverse peculiar velocity of lens
galaxies over a wide range of redshift. Microlensing variability is caused by
the motions of the observer, the lens galaxy (including the motion of the stars
within the galaxy), and the source; hence, its frequency is directly related to
the galaxy's transverse peculiar velocity. The idea is to count time-event
rates (e.g., peak or caustic crossing rates) in the observed microlensing light
curves of lensed quasars that can be compared with model predictions for
different values of the transverse peculiar velocity. To compensate for the
large time-scale of microlensing variability we propose to count and model the
number of events in an ensemble of gravitational lenses. We develop the
methodology to achieve this goal and apply it to an ensemble of 17 lensed
quasar systems. In spite of the shortcomings of the available data, we have
obtained tentative estimates of the peculiar velocity dispersion of lens
galaxies at $z\sim 0.5$, $\sigma_{\rm
pec}(0.53\pm0.18)\simeq(638\pm213)\sqrt{\langle m \rangle/0.3 M_\odot} \, \rm
km\, s^{-1}$. Scaling at zero redshift we derive, $\sigma_{\rm
pec}(0)\simeq(491\pm164) \sqrt{\langle m \rangle/0.3 M_\odot} \, \rm km\,
s^{-1}$, consistent with peculiar motions of nearby galaxies and with recent
$N$-body nonlinear reconstructions of the Local Universe based on $\Lambda$CDM.
We analyze the different sources of uncertainty of the method and find that for
the present ensemble of 17 lensed systems the error is dominated by Poissonian
noise, but that for larger ensembles the impact of the uncertainty on the
average stellar mass may be significant.
