The preferentially magnified active nucleus in IRAS F10214+4724 - III.
  VLBI observations of the radio core
  We report 1.7 GHz Very Long Baseline Interferometry (VLBI) observations of
IRAS F10214+4724, a lensed z=2.3 obscured quasar with prodigious star
formation. We detect what we argue to be the obscured active nucleus with an
effective angular resolution of < 50 pc at z = 2.3 . The S_{1.7} = 210 micro-Jy
(9-\sigma) detection of this unresolved source is located within the HST
rest-frame ultraviolet/optical arc, however, >~100 mas northward of the arc
centre of curvature. This leads to a source plane inversion that places the
European VLBI Network detection to within milli-arcseconds of the modelled cusp
caustic, resulting in a very large magnification (\mu ~70), over an order of
magnitude larger than the CO (1-0) derived magnification of a spatially
resolved JVLA map, using the same lens model. We estimate the quasar bolometric
luminosity from a number of independent techniques and with our X-ray modelling
find evidence that the AGN may be close to Compton-thick, with an intrinsic
bolometric luminosity log(L_{bol,QSO} / L_sun) = 11.34 +- 0.27 dex. We make the
first black hole mass estimate of IRAS F10214+4724 and find log(M_{BH}/M_sun) =
8.36 +- 0.56 which suggests a low black hole accretion rate (\lambda = \dot{M}
/ \dot{M}_{Edd} ~ 3\pm^7_2 percent). We find evidence for a M_{BH}/M_{spheroid}
ratio that is 1-2 orders of magnitude larger than that of submillimetre
galaxies (SMGs) at z~2. At face value, this suggests IRAS F10214+4724 has
undergone a different evolutionary path compared to SMGs at the same epoch. A
primary result of this work is the demonstration that emission regions of
differing size and position can undergo significantly different magnification
boosts (> 1 dex) and therefore distort our view of high-redshift,
gravitationally lensed galaxies.
