Carbon ionization states and the cosmic far-UV background with HeII absorption

We constrain the spectrum of the cosmic ultraviolet background radiation by fitting the observed abundance ratios carbon ions at $z\sim 2\hbox{--}3$ with those expected from different models of the background radiation. We use the recently calculated modulation of the background radiation between 3 and 4 Ryd due to resonant line absorption by intergalactic HeII, and determine the ratios of CIII to CIV expected at these redshifts, as functions of metallicity, gas density and temperature. Our analysis of the observed ratios shows that 'delayed reionization' models, which assume a large fraction of HeII at $z\sim3$, is not favored by data. Our results suggest that HeII reionization was inhomogeneous, consistent with the predictions from recent simulations.