I have been studying the central regions of galaxies in order to
understanding their evolutionary history. The fist step involves
measuring the mass of any central black hole. Together with the Nuker Team ,
we have found that nearly all galaxies contain a central supermassive
black hole. Furthermore, the mass of the black hole strongly
correlates with various galaxy properties. I have been working on a Black Hole Webpage that
describes the data and results. In order to measure the mass of the
black hole, we use a sophisticated orbit-based model to represent the
galaxy. These models provide one of the most general solutions for how
stars can orbit in a galaxy. This modeling code allows us to not
only measure the central black hole accurately, but also to determine
how the stars orbit throughout the galaxy. Both of these relate to how
the galaxy formed and evolved.
With the velocity measurements from the FP, I have been developing new techniques which can determine the mass density profile non-parametrically. The technique takes estimates of the velocity dispersion and the surface brightness profile and, after inversion through the Abel integrals, uses the Jeans equation, assuming isotropy, to provide a non-parametric estimate of the mass density and mass-to-light (M/L) ratio as a function of radius. Applying this technique to many clusters, we have found increases in the M/L in the central and the outer regions. The central increase is explained through mass segregation and, for the first time, we are able to directly estimate the heavy remnant population. The increase in the outer parts can be explained with having a population of low mass stars at those radii. The advantage of using the non-parametric techniques is that we are now able to put strong constraints on models, either N-body or Fokker-Plank, and we can directly estimate the present-day mass function. The mass functions for all of the clusters studied show a significant number of objects with a mass around 0.7~M$_\odot$. If we assume these are primarily white dwarfs, we can use their numbers to place constraints on the initial mass function.
From the two-dimensional FP data, I am able to measure a velocity map, pixel-by-pixel, using the integrated light of the cluster, providing an accurate measure of any rotation. For most of clusters, there is a clear indication of rotation in the inner 0.5 parsecs. We also have a measure of the rotation at 3 parsecs, and the amplitude of the rotation is generally the same. Although not dynamically significant, the flat rotation curve has not been seen in standard models and N-body codes, since solid body rotation is expected. For M15, we have measured a significant increase in the rotation amplitude at small radii. This increase is not expected from evolutionary models and may be the result of a central mass concentration. A $1000\Msun$ black hole is consistent with both the rotation and velocity dispersion profiles.
I analyzed velocity measurements from clusters of galaxies to determine both the significance of cD galaxy velocity offsets and the existence of bound populations around cD galaxies. Using robust statistical techniques we showed that a much smaller percentage of cD galaxies exhibited significant velocity offsets or bound populations than had previously been reported. This difference was due to the more robust statistical analysis and we encouraged a better understanding in the astronomical community of current statistical techniques.
To study positional data from galaxy clusters, I implemented an adaptive kernel technique (Silverman, B.W. 1986, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London) for density estimation, which allowed us to better determine the significance of substructure. In addition, we used clustering algorithms, incorporating both velocity and positional data, to provide an estimate of sub-clumps within a cluster. When applied to Abell 400, these techniques showed that the cluster is best modeled as two groups which are presently merging. This result has an important effect on estimates of the velocity dispersion of the cluster since the dispersion was significantly higher when using all the velocities from the whole system as compared to calculating the dispersions separately for the two groups. The inferred M/L was a factor of four lower if the subclumps were considered separately. We have looked at other galaxy clusters and, after applying the adaptive kernel to determine the membership of particular sub-groups, we have calculated robust velocity dispersions and locations in order to better understand the present-day kinematical states of the clusters. We found that if substructure is present, but ignored, the derived velocity dispersion may be overestimated by a factor of two.