X-ray photons coming from an X-ray point source not only arrive at the detector directly, but also can be strongly forward-scattered by the interstellar dust along the line of sight (LOS), leading to a detectable diffuse halo around the X-ray point s
ource. The geometry of small angle X-ray scattering is straightforward, namely, the scattered photons travel longer paths and thus arrive later than the unscattered ones; thus the delay time of X-ray scattered halo photons can reveal information of the distances of the interstellar dust and the point source. Here we present a study of the X-ray scattered around IGR J17544-2619, which is one of the so-called supergiant fast X-ray transients. IGR J17544-2619 underwent a striking outburst when observed with Chandra on 2004 July 3, providing a near delta-function lightcurve. We find that the X-ray scattered halo around IGR J17544-2619 is produced by two interstellar dust clouds along the LOS. The one which is closer to the observer gives the X-ray scattered at larger observational angles; whereas the farther one, which is in the vicinity of the point source, explains the halo with a smaller angular size. By comparing the observational angle of the scattered halo photons with that predicted by different dust grain models, we are able to determine the normalized dust distance. With the delay times of the scattered halo photons, we can determine the point source distance, given a dust grain model. Alternatively we can discriminate between the dust grain models, given the point source distance.
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 ric
hest 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.
X-ray photons scattered by the interstellar medium carry information about dust distribution, dust grain model, scattering cross section, and the distance of the source; they also take longer time than 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 textit{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 (LOS) 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 LOS. 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.
