X-ray Constraints on the Intrinsic Shape of the Lenticular Galaxy NGC 1332

We have analyzed ROSAT PSPC X-ray data of the optically elongated S0 galaxy NGC 1332 with the purposes of constraining the intrinsic shape of its underlying mass and presenting a detailed investigation of the uncertainties resulting from the assumptions underlying this type of analysis. The X-ray isophotes are elongated with ellipticity $0.10 - 0.27$ (90% confidence) for semi-major axes $75\arcsec -90\arcsec$ and have orientations consistent with the optical isophotes (ellipticity $\sim 0.43$). The spectrum is poorly constrained by the PSPC data and cannot rule out sizeable radial temperature gradients or an emission component due to discrete sources equal in magnitude to the hot gas. Using (and clarifying) the "geometric test" for dark matter, we determined that the hypothesis that mass-traces-light is not consistent with the X-ray data at 68% confidence and marginally consistent at 90% confidence independent of the gas temperature profile. Detailed modeling gives constraints on the ellipticity of the underlying mass of \epsilon_{mass} = 0.47 - 0.72 (0.31 - 0.83) at 68% (90%) confidence for isothermal and polytropic models. The total mass of the isothermal models within a=43.6$ kpc (D = 20h^{-1}_{80} Mpc) is M_{tot} = (0.38 - 1.7) \times 10^{12}M_{\sun} (90% confidence) corresponding to total blue mass-to-light ratio \Upsilon_B = (31.9 - 143) \Upsilon_{\sun}. Similar results are obtained when the dark matter is fit directly using the known distributions of the stars and gas. When possible rotation of the gas and emission from discrete sources are included flattened mass distributions are still required, although the constraints on $\epsilon_{mass}$, but not the total mass, are substantially weakened.