Active galactic nuclei at z ~ 1.5: III. Accretion discs and black hole
  spin
  This is the third paper in a series describing the spectroscopic properties
of a sample of 39 AGN at $z \sim 1.5$, selected to cover a large range in black
hole mass ($M_{BH}$) and Eddington ratio ($L/L_{Edd}$). In this paper, we
continue the analysis of the VLT/X-shooter observations of our sample with the
addition of 9 new sources. We use an improved Bayesian procedure, which takes
into account intrinsic reddening, and improved $M_{BH}$ estimates, to fit thin
accretion disc (AD) models to the observed spectra and constrain the spin
parameter ($a_*$) of the central black holes. We can fit 37 out of 39 AGN with
the thin AD model, and for those with satisfactory fits, we obtain constraints
on the spin parameter of the BHs, with the constraints becoming generally less
well defined with decreasing BH mass. Our spin parameter estimates range from
$\sim$$-$0.6 to maximum spin for our sample, and our results are consistent
with the "spin-up" scenario of BH spin evolution. We also discuss how the
results of our analysis vary with the inclusion of non-simultaneous GALEX
photometry in our thin AD fitting. Simultaneous spectra covering the rest-frame
optical through far-UV are necessary to definitively test the thin AD theory
and obtain the best constraints on the spin parameter.
