Modelling the high mass accretion rate spectra of GX 339-4: Black hole spin from reflection?

We extract all the XMM-Newton EPIC pn burst mode spectra of GX 339-4, together with simultaneous/contemporaneous RXTE data. These include three disc dominated and two soft intermediate spectra, and the combination of broad bandpass/moderate spectral resolution gives some of the best data on these bright soft states in black hole binaries. The disc dominated spectra span a factor three in luminosity, and all show that the disc emission is broader than the simplest multicolour disc model. This is consistent with the expected relativistic smearing and changing colour temperature correction produced by atomic features in the newest disc models. However, these models do not match the data at the 5 per cent level as the predicted atomic features are not present in the data, perhaps indicating that irradiation is important even when the high energy tail is weak. Whatever the reason, this means that the data have smaller errors than the best physical disc models, forcing use of more phenomenological models for the disc emission. We use these for the soft intermediate state data, where previous analysis using a simple disc continuum found an extremely broad residual, identified as the red wing of the iron line from reflection around a highly spinning black hole. However, the iron line energy is close to where the disc and tail have equal fluxes, so using a broader disc continuum changes the residual iron line profile dramatically. With a broader disc continuum model, the inferred line is formed outside of 30 ${rm{R_g}}$, so cannot constrain black hole spin. We caution that a robust determination of black hole spin from the iron line profile is very difficult where the disc makes a significant contribution at the iron line energy i.e. in most bright black hole states.