UC Berkeley

Supermassive black holes lie at the centers of all elliptical galaxies and are thought to play fundamental roles in guiding the evolution of their host galaxies. A number of well-established empirical scaling relations are known between the mass of the black hole to various galaxy properties, such as the stellar velocity dispersion, the break radius of the light profile, and the bulge mass of the galaxy. The behavior of these relations at their upper end is less well-established as only a handful of black holes above one billion solar masses have been been detected and measured. Galaxies harboring these black holes are now known to frequently have kinematic features which indicate that the galaxies have triaxial intrinsic shapes, while the modelling that has produced these few black hole mass measurements has nearly always assumed axisymmetry. The assumed symmetry of a galaxy has potentially significant impact on the resulting inferred black hole mass. This dissertation follows the development of a code for triaxial Schwarzschild orbit modelling and application of that technique to measure the intrinsic three-dimensional triaxial shape of massive elliptical galaxies simultaneously with the masses of their central supermassive black holes and other parameters which describe their mass distributions.

We begin by exploring simpler axisymmetric Schwarzschild models. We found that our adopted Schwarzschild modelling code (TriOS) was frequently ill-behaved when running triaxial models with nearly axisymmetric shapes. To ensure that the code was robust once moving further from axisymmetry, we first focused on refining these axisymmetric models, including making changes to the code to allow for properly axisymmetric models, along the way developing further understanding of the conditions required for proper axisymmetry and then applying the updated code to the massive elliptical galaxy NGC1453, a fast-rotating galaxy in the MASSIVE sample. With the updated code and procedures, we detected a black hole in NGC1453 which was consistent with models using axisymmetric Jeans modelling and consistent with the M-sigma relation.

We then turn to triaxiality. As with the axisymmetric case, we found that a number of procedures within the TriOS code and prior prescriptions for usage of the code lead to erroneous models. Quite significantly, one of the symmetries associated with triaxiality was mis-applied and the mass distributions were mis-constrained in the original code, leading to potential biases in the inferred parameters. We found a triplet of parameters which intuitively specify a particular deprojection of the light profile and allows for efficient searches over the space of allowed intrinsic shapes. We again apply our refinements to NGC1453, finding consistent mass parameters with the axisymmetric case, but now with a constraint on the intrinsic shape which strongly rejects axisymmetry.

We finally focus on the massive elliptical galaxies M87, Holmberg 15A, and IC1101, performing observations on them over five years to build comprehensive maps of the stellar kinematics for each galaxy extending from the central region within the black hole's sphere of influence to deep within the dark matter halo. For Holmberg 15A and IC1101, the stellar kinematic maps extend to beyond 50 kpc from the center of the galaxy. Both M87 and Holmberg 15A's velocity fields exhibit prominent kinematic misalignments, a tell-tale indication of triaxiality. We use the TriOS code to perform triaxial Schwarzschild orbit modelling on all three galaxies, adding a new measurement of the black hole mass to the long history of measurements of M87's black hole and measuring the three-dimensional triaxial shape of its stellar halo for the first time, as well as significantly refining the mass measurement of Holmberg 15A* and making the most detailed measurements of the stellar kinematics of IC1101 to date.