Velocity Profiles Of Galaxies Research Articles

Constraints on the velocity profiles of galaxies from strong lensing statistics and semi-analytical modelling of galaxy formation

Semi-analytical models of galaxy formation can be used to predict the evolution of the number density of early-type galaxies as a function of the circular velocity at the virial radius, v_{c,vir}. Gravitational lensing probability and separation distribution on the other hand are sensitive to the velocity dispersion (or circular velocity) at about the effective radius. We adopt the singular isothermal ellipsoid (SIE) lens model to estimate the velocity dispersion at the effective radius. We use radio lenses from the Cosmic Lens All-Sky Survey and the PMN-NVSS Extragalactic Lens Survey to study how the velocity dispersions, \sigma_SIE, are related to v_{c,vir}. When we include both the lensing probability and separation distribution as our lensing constraints, we find \sigma_SIE /(200\kms) = [(1.17_{-0.26}^{+0.40}) v_{c,vir}/ (200\kms)]^{0.22^{+0.05}_{-0.04}} for 200\kms \la \sigma_SIE \la 260\kms; at \sigma_SIE = 200\kms, the ratio \sqrt{2} \sigma_SIE / v_{c,vir} is about 1.65^{+0.57}_{-0.37} (68% CL) but decreases to 0.65_{-0.12}^{+0.15} (68% CL) for \sigma_SIE = 260\kms. These results are consistent with those of Seljak (2002) obtained from galaxy-galaxy weak lensing for galaxies of around L_*. However, our results clearly suggest that the ratio must vary significantly as \sigma_SIE is varied and are marginally discrepant with the Seljak results at \sigma_SIE = 260\kms. The scaling \sigma_SIE \propto v_{c,vir}^{0.22\pm 0.05} is broadly consistent with those from galaxy occupation statistics studies and the most recent galaxy-galaxy weak lensing study. (Abridged)

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

We describe a powerful technique to model and interpret the stellar line-of-sight velocity profiles of galaxies. It is based on Schwarzschild's approach to build fully general dynamical models. A representative library of orbits is calculated in a given potential, and the non-negative superposition of these orbits is determined that best fits a given set of observational constraints. The most significant new feature of our implementation is that we calculate and fit the full velocity profile shapes, represented by a Gauss-Hermite series. This allows us to constrain the orbital anisotropy in the fit. We also use an objective χ2 measure for the quality of fit, taking into account the error on each observational constraint. Given χ2 from the observational constraints, the technique assesses the relative likelihood of different orbit combinations in a given potential, and of models with different potentials. In our implementation only projected, observable quantities are included in the fit, aperture binning and seeing convolution of the data are properly taken into account, and smoothness of the models in phase space can be enforced through regularization. This scheme is valid for any geometry. In a first application of this method, we focus here on spherical geometry; axisymmetric modeling is described in companion papers by Cretton et al. and van der Marel et al. We test the scheme on pseudo-data drawn from an isotropic Hernquist model and then apply it to the issue of dark halos around elliptical galaxies. We model radially extended stellar kinematical data for the E0 galaxy NGC 2434 obtained by Carollo et al. This galaxy was chosen because it may be nearly round, in which case the present spherical modeling is applicable. Models with constant mass-to-light ratio are clearly ruled out, regardless of the orbital anisotropy. To study the amount of dark matter needed to match the data, we considered a sequence of cosmologically motivated + potentials. These potentials are based on the CDM simulations by Navarro et al., but also account for the accumulation of baryonic matter; they are specified by the stellar mass-to-light ratio *,B and the characteristic halo velocity, V200. The star + halo models provide an excellent fit to the data, with *,B = 4.35 ± 0.35 (in B-band solar units) and V200 = 450 ± 100 km s-1. The best-fitting potential has a circular velocity Vc that is constant to within ~10% between 0.2 and 3 effective radii and is very similar to the best-fitting logarithmic potential, which has Vc = 300 ± 15 km s-1. In NGC 2434 roughly half of the mass within an effective radius is dark. In comparison, our models without a dark halo estimate a mass-to-light ratio for the stellar population that is twice as large. If NGC 2434 is a significantly flattened system seen nearly face-on, it would be considerably more difficult to limit the gravitational potential without further observational constraints.

Velocity profiles of galaxies with claimed black holes - II. f (E, Lz) models for M32

Velocity profiles of galaxies with claimed black holes - II. f (E, Lz) models for M32

Velocity profiles of galaxies with claimed black holes - III. Observations and models for M87

Velocity profiles of galaxies with claimed black holes - III. Observations and models for M87

Velocity profiles of galaxies with claimed black holes -- I. Observations of M31, M32, NGC 3115 and NGC 4594

The presence of a massive black hole has been invoked to match the observed rotation velocities and velocity dispersions at the centres of M31, M32, NGC 3115 and NGC 4594, Here we determine stellar line-of-sight velocity profiles of these galaxies, from high spatial resolution, high S/N spectra centred on the G-band, the Mg b triplet and the Ca II IR triplet. For all spectra we determine rotation velocities, V, velocity dispersions, |$\sigma$|⁠, and deviations of the velocity profiles from a Gaussian shape, as quantified by the Gauss-Hermite moments |$h_3, \ldots, h_6$|⁠. Significant deviations of the velocity profiles from a Gaussian are present in all objects. The strongest deviations are asymmetries quantified by |$h_3$| and are found primarily along the major axis. The amplitude of |$h_3$| is typically |$|h_3| \lesssim 0.15$| and is correlated with |$V/\sigma$|⁠. Its sign always indicates an excess of stars at low rotation velocities, and results in the mean stellar streaming velocity being lower than the mean of the best-fitting Gaussian, the quantity conventionally used to characterize rotation. The difference is |$\sim 10$| per cent for M31, M32 and NGC 3115, and |$\sim 20$| per cent for NGC 4594. It is thus important that models take the observed velocity profile shapes into account. We demonstrate that the observed deviations from Gaussian velocity profiles are for the most part not the result of projection and seeing convolution. We calculate the velocity profiles predicted by Tonry's model for M32, taking seeing and projection into account, but assuming the local (unprojected) velocity distributions to be Gaussian. The predicted velocity profiles are nearly Gaussian, in conflict with our data. Self-consistent dynamical models must thus be constructed to fit the observed velocity profiles. Such models should constrain the central structure quite strongly, and will hence provide improved constraints on the mass and presence of a supermassive central object.