Dynamical Modeling of Velocity Profiles: The Dark Halo Around the Elliptical Galaxy NGC2434

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Abstract
We describe a powerful technique to model and interpret the stellar line-of-sight velocity profiles of galaxies. Following Schwarzschild's modeling approach, a representative library of orbits is calculated in a given potential; then the non-negative superposition of these orbits is determined to fit best a given set of observational constraints. Our implementation incorporates several new features: (i) we calculate velocity profiles and represent them by a Gauss-Hermite series. This allows us to constrain the orbital anisotropy in the fit. (ii) we take into account the error on each observational constraint to obtain an objective chi2 measure for the quality-of-fit. Only projected, observable quantities are included in the fit, and aperture binning and seeing convolution of the data are properly taken into account. This scheme is valid for any geometry, but here we focus on spherical geometry and the issue of dark halos around elliptical galaxies. We model radially extended velocity profiles of the E0 galaxy NGC 2434, and find that constant M/L models are clearly ruled out, regardless of the orbital anisotropy. To study how much dark matter is needed, we considered a sequence of cosmologically motivated `star+halo' potentials, which are specified by the stellar 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 to the 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 roughly half of the mass within an effective radius appears to be dark.

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