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X-ray photons scattered by the interstellar medium carry information aboutdust distribution, dust grain model, scattering cross section, and the distanceof the source; they also take longer time than unscattered photons to reach theobserver. Using a cross-correlation method, we study the light curves of theX-ray dust scattering halo of Cyg X-1, observed with the \textit{Chandra X-rayObservatory}. Significant time lags are found between the light curves of thepoint source and its halo. This time lag increases with the angular distancefrom Cyg X-1, implying a dust concentration at a distance along the line ofsight (LOS) of 2.0 kpc $\times$ (0.876 $\pm$ 0.002) from the Earth. By fittingthe observed light curves of the halo at different radii with simulated lightcurves, we obtain a width of $\mathit{\Delta L}=33_{-13}^{+18}$ pc of this dustconcentration. The origin of this dust concentration is still not clearlyknown. The advantage of our method is that we need no assumption of scatteringcross section, dust grain model, or dust distribution along the LOS. Combiningthe derived dust distribution from the cross-correlation study with the surfacebrightness distribution of the halo, we conclude that the two commonly acceptedmodels of dust grain size distribution need to be modified significantly.

A Study of the X-Ray Dust Scattering Halo of Cyg X-1 with a Cross-Correlation Method