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Lyskova, Natalya (2014): Mass determination of elliptical galaxies. Dissertation, LMU München: Fakultät für Physik



The work presented here focuses on the investigation and further development of simple mass estimators for early-type galaxies which are suitable for large optical galaxy surveys with poor and/or noisy data. We consider simple and robust methods that provide an anisotropy-independent estimate of the galaxy mass relying on the stellar surface brightness and projected velocity dispersion profiles. Under reasonable assumptions a fundamental mass-anisotropy degeneracy can be circumvented without invoking any additional observational data, although at a special (characteristic) radius only, i.e these approaches do not recover the radial mass distribution. Reliable simple mass estimates at a single radius could be used (i) to cross-calibrate other mass determination methods; (ii) to estimate a non-thermal contribution to the total gas pressure when compared with the X-ray mass estimate at the same radius; (iii) to evaluate a dark matter fraction when compared with the luminous mass estimate; (iv) to derive the slope of the mass profile when combined with the mass estimate from strong lensing; (v) or as a virial mass proxy. Two simple mass estimators have been suggested recently - the local (Churazov et al. 2010) and the global (Wolf et al. 2010) methods - which evaluate mass at a particular radius and are claimed to be weakly dependent on the anisotropy of stellar orbits. One approach (Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and evaluates the mass at a deprojected half-light radius, i.e. relies on the global properties of a galaxy. In contrast, the Churazov et al. technique uses local properties: logarithmic slopes of the surface brightness and velocity dispersion profiles, and recovers the mass at a radius where the surface brightness declines as R^{-2} (see also Richstone and Tremaine 1984, Gerhard 1993). To test the robustness and accuracy of the methods I applied them to analytic models and to simulated galaxies from a sample of cosmological zoom-simulations which are similar in properties to nearby early-type galaxies. Both local and global simple mass estimates are found to be in good agreement with the true mass at the corresponding characteristic radius. Particularly, for slowly rotating simulated galaxies the local method gives an almost unbiased mass-estimate (when averaged over the sample) with a modest RMS-scatter of 12% (Chapter 2). When applied to massive simulated galaxies with a roughly flat velocity dispersion profile, the global approach on average also provides the almost unbiased mass-estimate, although the RMS-scatter is slightly larger (14-20 %) than for the local estimator (Chapter 4). A noticeable scatter in the determination of the characteristic radius is also expected since the half-light radius depends on the radial range used for the analysis and applied methodology. Next I tested the simple mass estimators on a sample of real early-type galaxies which had previously been analyzed in detail using state-of-the-art dynamical modeling. For this set of galaxies the simple mass estimates are in remarkable agreement with the results of the Schwarzschild modeling despite the fact that some of the considered galaxies are flattened and mildly rotating. When averaged over the sample the simple local method overestimates the best-fit mass from dynamical modeling by 10% with the RMS-scatter 13% between different galaxies. The bias is comparable to measurement uncertainties. Moreover, it is mainly driven by a single galaxy which has been found to be the most compact one in the sample. When this galaxy is excluded from the sample, the bias and the RMS-scatter are both reduced to 6%. The global estimator for the same sample gives the mean deviation 4% with the slightly larger RMS-scatter of 15% (Chapter 4). Given the encouraging results of the tests I apply the local mass estimation method to a sample of five X-ray bright early-type galaxies observed with the 6-m telescope BTA in Russia. Using publicly available Chandra data I derived the X-ray mass profile assuming spherical symmetry and hydrostatic equilibrium of hot gas. A comparison between the X-ray and optical mass estimates allowed me to put constraints on the non-thermal contribution (sample averaged value is 4%) to the total gas pressure arising from, for instance, microturbulent gas motions. Once the X-ray derived circular speed is corrected for the non-thermal contribution, the mismatch between the X-ray circular speed V_c^X and the optical circular velocity for isotropic stellar orbits V_c^{iso} provides a clue to the orbital structure of the galaxy. E.g., at small radii V_c^X > V_c^{iso} would suggest more circular orbits, while at larger radii this would correspond to more radial orbits. For two galaxies in our sample there is a clear indication that at radii larger than the half-light radius stellar orbits become predominantly radial. Finally, the difference between the optical mass-estimate at the characteristic radius and the stellar contribution to the total mass permitted the derivation of a dark-matter fraction. A typical dark matter fraction for our sample of early-type galaxies is 50% for Salpeter IMF and 70% for Kroupa IMF at the radius which is close to the half-light radius (Chapter 3).