Dynamical Modeling of Velocity Profiles: The Dark Halo around the Elliptical Galaxy NGC 2434

We describe a powerful technique to model and interpret the stellarline-of-sight velocity profiles of galaxies. Following Schwarzschild's modelingapproach, a representative library of orbits is calculated in a givenpotential; then the non-negative superposition of these orbits is determined tofit best a given set of observational constraints. Our implementationincorporates several new features: (i) we calculate velocity profiles andrepresent them by a Gauss-Hermite series. This allows us to constrain theorbital anisotropy in the fit. (ii) we take into account the error on eachobservational constraint to obtain an objective chi2 measure for thequality-of-fit. Only projected, observable quantities are included in the fit,and aperture binning and seeing convolution of the data are properly taken intoaccount. This scheme is valid for any geometry, but here we focus on sphericalgeometry and the issue of dark halos around elliptical galaxies. We modelradially extended velocity profiles of the E0 galaxy NGC 2434, and find thatconstant M/L models are clearly ruled out, regardless of the orbitalanisotropy. To study how much dark matter is needed, we considered a sequenceof cosmologically motivated `star+halo' potentials, which are specified by thestellar mass-to-light ratio Gamma and the characteristic halo velocity, V_200(from Navarro et al. 1996). The star+halo models provide an excellent fit tothe data, with Gamma=3.35+-0.25 (in B-band solar units) and V_200=450+-100km/s.The best-fitting potential has a circular velocity Vc that is constant (at~300km/s) to within 10% between 0.2--3 effective radii. In NGC 2434 roughlyhalf of the mass within an effective radius appears to be dark.Comment: 41 pages, Latex file with 11 PostScripts figures. Submitted to the Astrophysical Journa