We derive the pre-shock density and scale length along the line of sight for the collisionless shock from a deep HST image that resolves the H \alpha filament in SN1006 and updated model calculations .
The very deep ACS high-resolution image of the Balmer line filament in the northwest ( NW ) quadrant shows that 0.25 \leq~ { } n _ { 0 } ~ { } \leq 0.4 cm ^ { -3 } and that the scale along the line of sight is about 2 \times 10 ^ { 18 } ~ { } cm , while bright features within the filament correspond to ripples with radii of curvature less than 1/10 that size .
The derived densities are within the broad range of earlier density estimates , and they agree well with the ionization time scale derived from the Chandra X-ray spectrum of a region just behind the optical filament .
This provides a test for widely used models of the X-ray emission from SNR shocks .
The scale and amplitude of the ripples are consistent with expectations for a shock propagating though interstellar gas with \sim 20 % density fluctuations on parsec scales as expected from studies of interstellar turbulence .
One bulge in the filament corresponds to a knot of ejecta overtaking the blast wave , however .
The interaction results from the rapid deceleration of the blast wave as it encounters an interstellar cloud .