An Ejecta Kinematics Study of Kepler's Supernova Remnant with High-Resolution $Chandra$ HETG Spectroscopy

We report our measurements of the bulk radial velocity from a sample of small, metal-rich ejecta knots in Kepler's Supernova Remnant (SNR). We measure the Doppler shift of the He-like Si K$\alpha$ line center energy in the spectra of these knots based on our $Chandra$ High-Energy Transmission Grating Spectrometer (HETGS) observation to estimate their radial velocities. We estimate high radial velocities of up to $\sim$ 8,000 km s$^{-1}$ for some of these ejecta knots. We also measure proper motions for our sample based on the archival $Chandra$ Advanced CCD Imaging Spectrometer (ACIS) data taken in 2000, 2006, and 2014. Our measured radial velocities and proper motions indicate that some of these ejecta knots are almost freely-expanding after $\sim$ 400 years since the explosion. The fastest moving knots show proper motions up to $\sim$ 0.2 arcseconds per year. Assuming that these high velocity ejecta knots are traveling ahead of the forward shock of the SNR, we estimate the distance to Kepler's SNR $d$ $\sim$ 4.4 to 7.5 kpc. We find that the ejecta knots in our sample have an average space velocity of $v_{s} \sim$ 4,600 km s$^{-1}$ (at a distance of 6 kpc). We note that 8 out of the 15 ejecta knots from our sample show a statistically significant (at the 90$\%$ confidence level) redshifted spectrum, compared to only two with a blueshifted spectrum. This may suggest an asymmetry in the ejecta distribution in Kepler's SNR along the line of sight, however a larger sample size is required to confirm this result.