Radio-Optical Galaxy Shape and Shear Correlations in the COSMOS Field
  using 3 GHz VLA Observations
  We present a weak lensing analysis of the 3 GHz VLA radio survey of the
COSMOS field, which we correlate with overlapping HST-ACS optical observations
using both intrinsic galaxy shape and cosmic shear correlation statistics.
After cross-matching sources between the two catalogues, we measure the
correlations of galaxy position angles and find a Pearson correlation
coefficient of $0.14 \pm 0.03$. This is a marked improvement from previous
studies which found very weak, or non-existent correlations, and gives insight
into the emission processes of radio and optical galaxies. We also extract
power spectra of averaged galaxy ellipticities (the primary observable for
cosmic shear) from the two catalogues, and produce optical-optical,
radio-optical and radio-radio spectra. The optical-optical auto-power spectrum
was measured to a detection significance of 9.80$\sigma$ and is consistent with
previous observations of the same field. For radio spectra (which we do not
calibrate, given the unknown nature of their systematics), although we do not
detect significant radio-optical (1.50$\sigma$) or radio-radio (1.45$\sigma$)
$E$-mode power spectra, we do find the $E$-mode spectra to be more consistent
with the shear signal expected from previous studies than with a null signal,
and vice versa for $B$-mode and $EB$ cross-correlation spectra. Our results
give promise that future radio weak lensing surveys with larger source number
densities over larger areas will have the capability to measure significant
weak lensing signals.
