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X-Ray Measured Dynamics of Tycho's Supernova Remnant

We present X-ray proper-motion measurements of the forward shock and reverse-shocked ejecta in Tycho's supernova remnant, based on three sets of archival Chandra data taken in 2000, 2003, and 2007. We find that the proper motion of the edge of the remnant (i.e., the forward shock and protruding ejecta knots) varies from 0".20 yr^{-1} (expansion index m=0.33, where R = t^m) to 0".40 yr^{-1} (m=0.65) with azimuthal angle in 2000-2007 measurements, and 0".14 yr^{-1} (m=0.26) to 0".40 yr^{-1} (m=0.65) in 2003-2007 measurements. The azimuthal variation of the proper motion and the average expansion index of ~0.5 are consistent with those derived from radio observations. We also find proper motion and expansion index of the reverse-shocked ejecta to be 0".21-0".31 yr^{-1} and 0.43-0.64, respectively. From a comparison of the measured m-value with Type Ia supernova evolutionary models, we find a pre-shock ambient density around the remnant of <~0.2 cm^{-3}.