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 Cygnus 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 kpc or 1.82 kpc, the inferred distance for Cyg X-3 is $3.4^{+0.2}_{-0.2}$ kpc 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 Cygnus 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.