We present analysis of the shape and radial mass distribution of the E4 galaxy NGC 3923 using archival X-ray data from the ROSAT PSPC and HRI .
The X-ray isophotes are significantly elongated with ellipticity \epsilon _ { x } = 0.15 ( 0.09 - 0.21 ) ( 90 % confidence ) for semi-major axis a \sim 10 h ^ { -1 } _ { 70 } kpc and have position angles aligned with the optical isophotes within the estimated uncertainties .
Applying the Geometric Test for dark matter , which is independent of the gas temperature profile , we find that the ellipticities of the PSPC isophotes exceed those predicted if M \propto L at a marginal significance level of 85 \% ( 80 \% ) for oblate ( prolate ) symmetry .
Detailed hydrostatic models of an isothermal gas yield ellipticities for the gravitating matter , \epsilon _ { mass } = 0.35 - 0.66 ( 90 % confidence ) , which exceed the intensity weighted ellipticity of the R -band optical light , \langle \epsilon _ { R } \rangle = 0.30 ( \epsilon _ { R } ^ { max } = 0.39 ) .

We conclude that mass density profiles with \rho \sim r ^ { -2 } are favored over steeper profiles if the gas is essentially isothermal ( which is suggested by the PSPC spectrum ) and the surface brightness in the central regions ( r \la 15 \arcsec ) is not modified substantially by a multi-phase cooling flow , magnetic fields , or discrete sources .
We argue that these effects are unlikely to be important for NGC 3923 .
( The derived \epsilon _ { mass } range is very insensitive to these issues . )
Our spatial analysis also indicates that the allowed contribution to the ROSAT emission from a population of discrete sources with \Sigma _ { x } \propto \Sigma _ { R } is significantly less than that indicated by the hard spectral component measured by ASCA .