  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 five 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 9E36 erg/s 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^{+0.41}_{-0.48} (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 if the
spectral evolution is gradual or sudden. The lowest luminosity we measure for
XTE J1550-564 with Chandra is 5E32 erg/s (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.
