  We present a combined analysis of the Chandra and Swift observations of the
2015 X-ray echo of V404 Cygni. Using stacking analysis, we identify eight
separate rings in the echo. We reconstruct the soft X-ray lightcurve of the
June 2015 outburst using the high-resolution Chandra images and
cross-correlations of the radial intensity profiles, indicating that about 70%
of the outburst fluence occurred during the bright flare at the end of the
outburst on MJD 57199.8.By deconvolving the intensity profiles with the
reconstructed outburst lightcurve, we show that the rings correspond to eight
separate dust concentrations with precise distance determinations. We further
show that the column density of the clouds varies significantly across the
field of view, with the centroid of most of the clouds shifted toward the
Galactic plane, relative to the position of V404 Cyg, invalidating the
assumption of uniform cloud column typically made in attempts to constrain dust
properties from light echoes. We present a new XSPEC spectral dust scattering
model that calculates the differential dust scattering cross section for a
range of commonly used dust distributions and compositions and use it to
jointly fit the entire set of Swift echo data. We find that a standard
Mathis-Rumpl-Nordsieck model provides an adequate fit to the ensemble of echo
data. The fit is improved by allowing steeper dust distributions, and models
with simple silicate and graphite grains are preferred over models with more
complex composition.
