  Accreting black holes show characteristic 'reflection' features in their
X-ray spectra, including the iron K$\alpha$ fluorescence line, which result
from X-rays radiated by a compact central corona being reprocessed in the
accretion disc atmosphere. The observed line profile is distorted by
relativistic effects, providing a diagnostic for disc geometry. Nearly all
previous X-ray reflection spectroscopy studies have made the simplifying
assumption that the disc ionization state is independent of radius in order to
calculate the restframe reflection spectrum. However, this is unlikely to be
the case in reality, since the irradiating flux should drop off steeply with
radius. Here we analyse a Nuclear Spectroscopic Telescope ARray observation of
GRS 1915+105 that exhibits strong reflection features. We find that using a
self-consistently calculated radial ionization profile returns a better fit
than assuming constant ionization. Our results are consistent with the inner
disc being radiation pressure dominated, as is expected from the high inferred
accretion rate for this observation. We also find that the assumed ionization
profile impacts on the best fitting disc inner radius. This implies that the
black hole spin values previously inferred for active galactic nuclei and X-ray
binaries by equating the disc inner radius with the innermost stable circular
orbit may be changed significantly by the inclusion of a self-consistent
ionization profile.
