X-ray photons scattered by the interstellar medium , carry the information of dust distribution , dust grain model , scattering cross section , and the distance of the source and so on ; they also take longer time than the unscattered photons to reach the observer .
Using a cross-correlation method , we study the light curves of the X-ray dust scattering halo of Cyg X-1 , observed with the Chandra X-ray Observatory .
Significant time lags are found between the light curves of the point source and its halo .
This time lag increases with the angular distance from Cyg X-1 , implying a dust concentration at a distance along the line of sight of 2.0 kpc \times ( 0.876 \pm 0.002 ) from the Earth .
By fitting the observed light curves of the halo at different radii with simulated light curves , we obtain a width of \mathit { \Delta L } = 33 _ { -13 } ^ { +18 } pc of this dust concentration .
The origin of this dust concentration is still not clearly known .
The advantage of our method is that we need no assumption of scattering cross section , dust grain model , or dust distribution along the line of sight .
Combining the derived dust distribution from the cross-correlation study with the surface brightness distribution of the halo , we conclude that the two commonly accepted models of dust grain size distribution need to be modified significantly .