As a result of the fitting procedure, we obtain a normalization factor for
each spatial bin, NF, defined as:
where D is the distance of the source, V is the volume of the emitting
plasma element whose section perpendicular to the line of sight is A,
and whose extension along the line of sight is l, and is the
subtended solid angle (in steradians). It is important to stress that
NF does not depend on distance, unless the source fills less than the
instrumental beam (as in the case of a point source, for example); this
has the important consequence that a reliable estimate of SNR density
can be derived from the X-ray observation, as we shall see below.
Since the bins are spatially independent (i.e. their size is less than
the width of the PSPC Point Spread Function), we can treat the
emitting plasma in each pixel as an independent source. In
our case, , and an estimate of l is required
to compute the density; this estimate can be obtained if we assume that the
remnant is approximately spherical, as Aschenbach (1993) suggests, and
if we further assume that the emission originates from a thin () shell (the spherical shell model). In
this case, l is a cord section,whose length is know analytically.
The spherical shell model is suited for middle-aged SNR's expanding in
a homogeneous medium, but it could run into problems if there are many
clouds. Nevertheless, depends weakly on l
(), and possible deviations from the ideal case are not
so important.
Following the above hypothesis, we have computed the post-shock density in the T3 bins (table 3) and the pressure. The latter was computed considering the plasma as a perfect gas, with equation of state . We estimate an error of 25% on the density and not more than 50% on the pressure. Assuming a compression factor of 4, we derive, from post-shock density values reported in Table 3, a pre-shock density of 0.03-0.05 in the T3 bins.