Interplay between physics and geometry in Balmer filaments: the case of SN 1006

The analysis of Balmer-dominated emission in supernova remnants is potentially a very powerful way to derive information on the shock structure, on the physical conditions of the ambient medium and on the cosmic-ray acceleration efficiency. However, the outcome of models developed in plane-parallel geometry is usually not easily comparable with the data, since they often come from regions with rather a complex geometry. We present here a general scheme to disentangle physical and geometrical effects in the data interpretation, which is especially powerful when the transition zone of the shock is spatially resolved and the spectral resolution is high enough to allow a detailed investigation of spatial changes of the line profile. We then apply this technique to re-analyze very high quality data of a region along the northwestern limb of the remnant of SN~1006. We show how some observed features, previously interpreted only in terms of spatial variations of physical quantities, naturally arise from geometrical effects. With these effects under control, we derive new constraints on physical quantities in the analyzed region, like the ambient density (in the range 0.03-$0.1{\,\rm cm^{-3}}$), the upstream neutral fraction (more likely in the range 0.01-0.1), the level of face-on surface brightness variations (with factors up to $\sim 3$) and the typical scale lengths related to such variations ($\ge 0.1{\,\rm pc}$, corresponding to angular scales $\ge 10{\,\rm arcsec}$).