  In 2004, SGR 1806-20 underwent a period of intense and long-lasting burst
activity that included the giant flare of 27 December 2004 -- the most intense
extra-solar transient event ever detected at Earth. During this active episode,
we routinely monitored the source with Rossi X-ray Timing Explorer and
occasionally with Chandra. During the course of these observations, we
identified two relatively bright bursts observed with Konus-Wind in hard X-rays
that were followed by extended X-ray tails or afterglows lasting hundreds to
thousands of seconds. Here, we present detailed spectral and temporal analysis
of these events observed about 6 and 1.5 months prior to the 27 December 2004
Giant Flare. We find that both X-ray tails are consistent with a cooling
blackbody of constant radius. These spectral results are qualitatively similar
to those of the burst afterglows recorded from SGR 1900+14 and recently from
SGR 1550-5418. However, the latter two sources exhibit significant increase in
their pulsed X-ray intensity following the burst, while we did not detect any
significant changes in the RMS pulsed amplitude during the SGR 1806-20 events.
Moreover, we find that the fraction of energy partitioned to the burst (prompt
energy release) and the tail (afterglow) differs by an order of magnitude
between SGR 1900+14 and SGR 1806-20. We suggest that such differences can be
attributed to differences in the crustal heating mechanism of these neutron
stars combined with the geometry of the emitting areas.
