Constraining VLBI-optical offsets in high redshift galaxies using strong
  gravitational lensing
  We present a multi-wavelength analysis of two highly magnified strong
gravitationally lensed galaxies, CLASS B0712+472 and CLASS B1608+656, at
redshifts $1.34$ and $1.394$, respectively, using new VLBI and archival HST
observations. We reconstruct the positions of the radio and optical emissions
with their uncertainties using Monte Carlo sampling. We find that in CLASS
B0712+472 the optical and radio emissions are co-spatial within $2\pm5$ mas
($17\pm 42$ pc at redshift of 1.34). But, in CLASS B1608+656, we reconstruct an
optical-radio offset of $25\pm16$ mas ($214\pm137$ pc at redshift of 1.394),
the smallest offset measured for an AGN at such high redshift. The spectral
features indicate that CLASS B1608+656 is a post-merger galaxy, which, in
combination with the optical-VLBI offset reported here, makes CLASS B1608+656 a
promising candidate for a high-$z$ offset-AGN. Furthermore, the milliarcsecond
angular resolution of the VLBI observations combined with the precise lens
models allow us to spatially locate the radio emission at $0.05$ mas precision
($0.4$ pc) in CLASS B0712+472, and $0.009$ mas precision ($0.08$ pc) in CLASS
B1608+656. The search for optical-radio offsets in high redshift galaxies will
be eased by the upcoming synoptic all-sky surveys, including E-ELT and SKA,
which are expected to find $\sim 10^5$ strongly lensed galaxies, opening an era
of large strong lensing samples observed at high angular resolution.
