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Expansion measurement of Supernova Remnant RX J1713.7-3946

Supernova remnant (SNR) RX J1713.7-3946 is well known for its bright TeV gamma-ray emission with shell-like morphology. To constrain the hydrodynamical evolution, we have performed six times observations of the northwestern (NW) shell with the Chandra X-ray Observatory from 2005 to 2011, and measured the proper motion by using these data and the first epoch observation taken in 2000. The blast-wave shock speed at the NW shell is measured to be $(3900\pm 300) (d/{\rm kpc})\ {\rm km}\ {\rm s}^{-1}$ with an estimated distance of $d = 1$ kpc, and the proper motions of other structures within the NW shell are significantly less than that. Assuming that the measured blast-wave shock speed is the representative of the remnant's outer shock wave as a whole, we have confronted our measurements as well as a recent detection of thermal X-ray lines, with the analytic solution of the hydrodynamical properties of SNRs. Our hydrodynamical analysis indicates that the age of the remnant is 1580-2100 years, supporting the association with SN393. A model with SN kinetic energy of $E = 10^{51}\, \rm erg$, the ejecta mass of $M_{\rm ej} = 3\, M_{\odot}$, and the ambient density at the current blast wave location of $n_2 = 0.015\, {\rm cm}^{-3}$, provides reasonable explanation for our measurements and previous findings at the X-ray and gamma-ray wavelengths. We find that the transition to the Sedov-Taylor (ST) phase is incomplete for any reasonable set of parameters, implying that the current maximum energy of accelerated protons in RX J1713.7-3946 would not correspond to the maximum attainable energy for this remnant.