The Sedov (1959) similarity solution for the dynamical evolution of
SNRs predicts an expansion rate of n=0.4. As is well known, this
model assumes that the ejecta are dynamically insignificant, so its
applicability to Tycho's SNR, where the ejecta are clearly dominant,
is questionable. Models where the SN ejecta are important have been
developed by Chevalier (1982) in which the ejecta and the ambient
medium are assumed to be in the form of power-law density profiles.
For parameters appropriate to Tycho (i.e., a uniform interstellar
medium and a steep power law, 
, for the exploded
white dwarf envelope), these similarity solutions predict a rate of
n=0.57. Neither of these models accounts for differential
expansion. Hamilton, Sarazin, & Szymkowiak (1986) proposed a model
for Tycho wherein the blast wave was expanding as n=0.70 and the
ejecta (specifically the contact discontinuity) were expanding more
slowly: n=0.60. The azimuthally-averaged X-ray results presented
here are rather consistent with this latter model.
The expansion shows significant azimuthal variation as well. The two small X-ray bright knots in the southeast are particularly interesting, since earlier work (Vancura, Gorenstein, & Hughes 1995) has revealed that these features are almost surely highly enriched knots of SN ejecta with very different abundance distributions. The northern one is apparently rich in Si and S, while the southern one is Fe rich. These knots are moving considerably more rapidly than the rest of the remnant (as shown clearly in Fig. 1), and, in addition, the current expansion rate is consistent with their time-averaged expansion rate, implying that these clumps of ejecta have not been decelerated.
I propose that these are fragments or ``bullets'' of ejecta formed in
the SN explosion, which is believed to be Type Ia. For an assumed
distance to Tycho of 2.5 kpc, the transverse velocity of these knots
is approximately 8300 km s 
. The clump masses are of order
(for the Si+S knot) and 
(for the Fe
knot) and the kinetic energies are 
ergs s and
ergs s , respectively, again for purely
transverse motion. These ejecta fragments in Tycho are similar in
many respects to the recently discovered ejecta fragments beyond the
apparent boundary of the Vela SN blast wave (Aschenbach, Egger, &
Trümper 1995). Although the current velocities of the Vela ejecta
bullets are small (390-650 km s ), their angular distance from
the estimated site of the SN explosion require large mean transverse
velocities: 4000-5000 km s as well as significant
deceleration. The initial kinetic energy of the Vela knots is in the
range (0.3-5) 
ergs s , however, their masses,
0.01-0.5 
, are quite a bit larger than the knots in
Tycho.
In summary it appears likely that the rapidly moving, chemically enriched features seen in Tycho's SNR are ejecta fragments being observed at an early stage of evolution before much interaction with the ambient medium has occurred. Since their expansion rate is greater than the rest of the remnant, at some time in the future they will clearly precede the blast wave. Their differing chemical composition require widely different origination sites in the exploded star: the Fe-rich knot must have originated from near the center where explosive Si-burning led to only Fe-group nuclei and the Si+S-rich knot must have come from further out where the flame temperature dropped and explosive O-burning predominated. Whether instabilities of this type prove to be intrinsic to the nature of flame front propagation in Type Ia SNe or arise from Rayleigh-Taylor and other instabilities operating on the expanding ejecta at later times remains to be studied. In any event the results presented here make clear that Type Ia SN explosions are considerably more inhomogeneous than previously thought.