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.