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We present analysis and spectral fits of the RXTE data from the May/June 1999outburst of Aql X-1. These data include observations in the rising portion ofthe hard state, in the soft state, and in the falling portion of the hardstate. We show that the data can be fit by a purely thermal Comptonizationmodel for all the observations, but that more complicated models cannot beruled out. Up to 60% of the corona's power in the soft state may be injectedinto non-thermal electrons. The soft state data show approximately constantoptical depth and coronal temperatures over a range of $\sim10$ in luminosity,while they show evidence for a reduction of seed photon temperature withreduced luminosity and indicate that the characteristic size of the seed photonemitting region is roughly constant throughout the soft state. The hard statebefore the soft state shows a higher luminosity, higher optical depth, andlower electron temperature than the hard state after the soft state. We find areduction of the hard (30-60 keV) X-ray flux during a type I burst and showthat it requires a total corona energy reservoir of less than $\sim 10^{38}$ergs.Comment: 10 pages, 7 figues, accepted to A+

Spectral fits to the 1999 Aql X-1 outburst data