Mass determination of elliptical galaxies

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).