Dust grains scatter X-ray light through small angles , producing a diffuse ‘ halo ’ image around bright X-ray point sources situated behind a large amount of interstellar material .
We present analytic solutions to the integral for the dust scattering intensity , which allow for a Bayesian analysis of the scattering halo around Cygnus X-3 .
Fitting the halo surface brightness profile yields the dust grain size and spatial distribution .
We assume a power law distribution of grain sizes ( n \propto a ^ { - p } ) and fit for p , the grain radius cut-off a _ { max } , and dust mass column .
A model where dust is distributed uniformly along the line of sight to Cyg X-3 fits the halo profile well , with p = 3.6 and a _ { max } = 0.18 \mu { m } .
We also attempt a model consisting of dust screens , representative of a foreground spiral arm and star forming complex Cyg OB2 .
This requires a minimum of two dust screens : the closest containing 80 % of the total dust mass , and the furthest being within 1 kpc of Cyg X-3 .
The best two-screen fit parameters yield p = 4.8 and a _ { max } = 0.3 \mu { m } .
Regardless of which model was used , we found \tau _ { sca } \sim 0.8 E _ { keV } ^ { -2 } .
X-ray spectroscopy yields a total ISM column N _ { H } \approx 7 \times 10 ^ { 22 } cm ^ { -2 } , which is higher than previous estimates .
We combine this information with the dust mass column to calculate a dust-to-gas mass ratio .
The uniform ( two-screen ) fit yields a ratio that is a fraction of ( on the order of ) that typically assumed for the Milky Way .
By comparing halo profiles in different energy bins , we find hints that large dust grains may be contributing to the absorption of E < 2.5 keV X-rays from Cyg X-3 .