We report on the evolution of the X-ray energy spectrum for the black hole candidate (BHC) X-ray transient XTE J1550-564 during the decay of the 2000 outburst. The Rossi X-Ray Timing Explorer (RXTE) and Chandra observations span nearly 5 orders of magnitude in luminosity. The RXTE spectra are dominated by a power-law component, and a comparatively weak soft component was also detected for the first two observations. The source made a transition to the canonical hard state near a luminosity of 9 × 1036 ergs s-1 over several observations, as evidenced by a drop in the flux of the soft component in the RXTE energy band and a hardening of the power-law component to a photon index near 1.6. The power law did not exhibit this behavior for the previous XTE J1550-564 outburst. For some observations, we detect a high-energy cutoff and find that the cutoff is more significant and at lower energy during the transition than in the hard state. The cutoff in the hard state is at higher energy than has been seen for most previous accreting BHCs. The Chandra spectrum provides evidence for spectral evolution after the hard-state transition. It is well, but not uniquely, described by a power law with a photon index of 2.30 (90% confidence) and interstellar absorption. Advection-dominated accretion flow models predict gradual spectral softening as the luminosity drops, but our observations do not allow us to determine whether the spectral evolution is gradual or sudden. The lowest luminosity we measure for XTE J1550-564 with Chandra is 5 × 1032 ergs s-1 (0.5-7 keV, for a distance of 4 kpc). Although this is probably not the true quiescent luminosity, it represents a useful upper limit on this quantity.
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