This thesis studies a new method of constraining the mass distributions of elliptical galaxies and clusters of galaxies: gravitational redshift. The aim was to determine the types of astrophysical object in which gravitational redshift can be most readily detected and to attempt to observe the effect for the first time in a single object.
Longslit stellar kinematics were combined with planetary nebulae kinematics to study the mass distribution of M87. Jeans modelling showed that, although the best-fit model gave too little mass (Upsilon = 5.34+/-0.34, beta = 0.71+/-0.03, M_halo = 2.64+/-0.92 x 10^12 M_sun), by adjusting the orbital anisotropy it was possible to construct a model that was consistent with both the kinematics and existing X-ray gas measurements.
Longslit kinematics from the literature were used to attempt to determine the mass-to-light ratio of a sample of elliptical galaxies using gravitational redshift. Models were developed to calculate the expected gravitational redshift from the surface brightness profile. The best-fit mass-to-light ratios were found using this model and also obtained independently using the Jeans equation. The results were not statistically inconsistent with the expected H-band mass-to-light ratios predicted by stellar population models - the Jeans modelling gave a mean mass-to-light ratio of Upsilon_sigma = 1.67+/-0.10, while the gravitational redshift predicted Upsilon_v = 4.84+/-2.67.
Integral field spectroscopy of the centre of M60 was undertaken in an attempt to detect gravitational redshift in the centre of an individual galaxy for the first time. The velocity field was summed around the galaxy's isophotes to remove the effect of rotation. Models were constructed to predict the gravitational redshift, which were then compared to the data. It was found that the shallow slope of the light profile made it impossible to detect a gravitational redshift in this case, but that the scatter of the data points suggests that a signal of a few km/s could be detected. Consideration of the models led to a better understanding of the most suitable targets for this kind of study.
An analysis of the 2dF groups catalogue was made in order to attempt to determine the strength of the gravitational redshift in clusters of galaxies. A new method was developed for measuring the signal in clusters. As part of the analysis, the density distribution of the clusters was obtained. It was found that they followed an exponential profile, which scaled linearly with the size of the cluster. The gravitational redshift was used to attempt to constrain the mean cluster mass, but it was found that the errors were too large to rule out all but the largest masses with any certainty. Future studies would require either a much larger sample, or one which concentrates specifically on the most uniform, high mass clusters.
Gravitational redshift offers a new approach to studying the mass distributions of galaxies and clusters that requires many fewer assumptions regarding the underlying physics than many of the current methods. Unfortunately, it also suffers from a number of potential setbacks. Recent advances in instrument technology, combined with the careful selection of suitable targets should allow gravitational redshift to become a viable tool for studying the nature and distribution of dark matter
