Using two Chandra observations we have derived estimates of the dust distribution and distance to the eclipsing high mass X-ray binary (HMXB) Cen X-3 using the energy-resolved dust-scattered X-ray halo. By comparing the observed X-ray halos in 200 eV bands from 2-5 keV to the halo profiles predicted by the Weingartner & Draine interstellar grain model, we find that the vast majority (about 70%) of the dust along the line of sight to the system is located within about 300 pc of the Sun, although the halo measurements are insensitive to dust very close to the source. One of the Chandra observations occurred during an egress from eclipse as the pulsar emerged from behind the mass-donating primary. By comparing model halo light curves during this transition to the halo measurements, a source distance of 5.7 +/- 1.5 kpc (68% confidence level) is estimated, although we find this result depends on the distribution of dust on very small scales. Nevertheless, this value is marginally inconsistent with the commonly accepted distance to Cen X-3 of 8 kpc. We also find that the energy scaling of the scattering optical depth predicted by the Weingartner & Draine interstellar grain model does not accurately represent the results determined by X-ray halo studies of Cen X-3. Relative to the model, there appears to be less scattering at low energies or more scattering at high energies in Cen X-3.
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