Determining the Distance of Cyg X-3 with its X-Ray Dust Scattering Halo

Using a cross-correlation method, we study the X-ray halo of Cyg X-3. Two components of dust distributions are needed to explain the time lags derived by the cross-correlation method. Assuming the distance as 1.7 kpc for Cyg OB2 association (a richest OB association in the local Galaxy) and another uniform dust distribution, we get a distance of 7.2^+0.3 _-0.5 kpc (68% confidence level) for Cyg X-3. When using the distance estimation of Cygnus OB2 as 1.38 or 1.82 kpc, the inferred distance for Cyg X-3 is 3.4^+0.2 _-0.2 or 9.3^+0.6 _-0.4 kpc, respectively. The distance estimation uncertainty of Cyg X-3 is mainly related to the distance of the Cyg OB2, which may be improved in the future with high-precision astrometric measurements. The advantage of this method is that the result depends weakly on the photon energy, dust grain radius, scattering cross-section, and so on.