We present a new stellar dynamical mass measurement (M BH ) of the supermassive black hole (SMBH) in NGC 1453, a fast-rotating massive elliptical galaxy in the MASSIVE survey. We measure stellar kinematics in 135 spatial bins in the central 1.5 kpc by 2 kpc region of the galaxy using high signal-to-noise (S/N ∼ 130) spectra from the Gemini-North GMOS integral-field spectrograph (IFS). Combining with wide-field IFS kinematics out to ∼ 3 effective radii and stellar light distributions from Hubble Space Telescope (HST ) WFC3 images, we perform Schwarzschild orbit-based mass modeling in the axisymmetric limit to constrain the mass components in NGC 1453. The best-fit black hole mass is M BH = (2.9 ± 0.4) × 10 9 M ; the mass models without a central black hole are excluded at the 8.7σ level. The NGC 1453 black hole lies within the intrinsic scatter of the SMBH and galaxy scaling relations, unlike three other galaxies hosting 10 10 M SMBHs in the MASSIVE sample. The high-S/N GMOS spectra enable us to determine 8 moments of the Gauss-Hermite expansion of the line-of-sight velocity distributions (LOSVDs), which are used as constraints in the orbit modeling. The stellar orbits in the mass models are further constrained to produce negligible h 9 through h 12 to minimize spurious behavior in the LOSVDs. We show that truncating the series at h 4 , as was often done in prior work, leads to a much weaker constraint on the inferred M BH for NGC 1453. Furthermore, we discuss precautions and modifications that are needed to achieve axisymmetry in triaxial orbit codes that use the Schwarzschild method to sample the start space of stellar orbits in triaxial gravitational potentials.

Most stellar-dynamical determinations of the masses of nearby supermassive black holes (SMBHs) have been obtained with the orbit superposition technique under the assumption of axisymmetry. However, few galaxies—in particular massive early-type galaxies—obey exact axisymmetry. Here we present a revised orbit superposition code and a new approach for dynamically determining the intrinsic shapes and mass parameters of triaxial galaxies based on spatially resolved stellar kinematic data. The triaxial TriOS code described here corrects an error in the original van den Bosch et al. code that gives rise to incorrect projections for most orbits in triaxial models and can significantly impact parameter search results. The revised code also contains significant improvements in orbit sampling, mass constraints, and run time. Furthermore, we introduce two new parameter-searching strategies—a new set of triaxial shape parameters and a novel grid-free sampling technique—that together lead to a remarkable gain in efficiency in locating the best-fit model. We apply the updated code and search method to NGC 1453, a fast-rotating massive elliptical galaxy. A full 6D parameter search finds p = b / a = 0.933 − 0.015 + 0.014 and q = c/a = 0.779 ± 0.012 for the intrinsic axis ratios and T = 0.33 ± 0.06 for the triaxiality parameter. Despite the deviations from axisymmetry, the best-fit SMBH mass, stellar mass-to-light ratio, and dark matter enclosed mass for NGC 1453 are consistent with the axisymmetric results. More comparisons between axisymmetric and triaxial modeling are needed before drawing general conclusions.

We present a detailed analysis of the behavior of the triaxial Schwarzschild orbit superposition method near the axisymmetric limit. Orbit superposition modeling is the primary method used to determine dynamical masses of supermassive black holes (M BH) in nearby galaxies; however, prior studies have reported conflicting results when comparing the outcome from axisymmetric orbit codes with that from a triaxial orbit code in the axisymmetric limit. We show that in order to achieve (oblate) axisymmetry in a triaxial code, care needs to be taken to axisymmetrize the short-axis tube orbits and to exclude both the long-axis tube and box orbits from the orbit library. Using up to 12 Gauss–Hermite moments of the line-of-sight velocity distributions as constraints, we demonstrate the effects of orbit types on the best-fit M BH in orbit modeling of the massive elliptical galaxy NGC 1453 reported in Liepold et al. In addition, we verify the efficacy of our updated code on a mock galaxy data set. We identify a subset of slowly precessing quasi-planar orbits for which the typical integration times can be insufficient to fully capture the equilibrium orbital behavior in both axisymmetric and triaxial systems with central black holes. Further investigation is needed for a more reliable treatment of these orbits.

We present a stellar dynamical mass measurement of a newly detected supermassive black hole (SMBH) at the center of the fast-rotating, massive elliptical galaxy NGC 2693 as part of the MASSIVE survey. We combine high signal-to-noise ratio integral field spectroscopy (IFS) from the Gemini Multi-Object Spectrograph with wide-field data from the Mitchell Spectrograph at McDonald Observatory to extract and model stellar kinematics of NGC 2693 from the central ∼150 pc out to ∼2.5 effective radii. Observations from Hubble Space Telescope WFC3 are used to determine the stellar light distribution. We perform fully triaxial Schwarzschild orbit modeling using the latest TriOS code and a Bayesian search in 6D galaxy model parameter space to determine NGC 2693's SMBH mass (M BH), stellar mass-to-light ratio, dark matter content, and intrinsic shape. We find M BH = 1.7 ± 0.4 × 10 9 M ⊙ and a triaxial intrinsic shape with axis ratios p = b/a = 0.902 ± 0.009 and q = c / a = 0.721 − 0.010 + 0.011 , triaxiality parameter T = 0.39 ± 0.04. In comparison, the best-fit orbit model in the axisymmetric limit and (cylindrical) Jeans anisotropic model of NGC 2693 prefer M BH = 2.4 ± 0.6 × 10 9 M ⊙ and M BH = 2.9 ± 0.3 × 10 9 M ⊙ , respectively. Neither model can account for the non-axisymmetric stellar velocity features present in the IFS data.

The three-dimensional intrinsic shape of a galaxy and the mass of the central supermassive black hole provide key insight into the galaxy’s growth history over cosmic time. Standard assumptions of a spherical or axisymmetric shape can be simplistic and can bias the black hole mass inferred from the motions of stars within a galaxy. Here, we present spatially resolved stellar kinematics of M87 over a two-dimensional 250″ × 300″ contiguous field covering a radial range of 50 pc–12 kpc from integral-field spectroscopic observations at the Keck II Telescope. From about 5 kpc and outward, we detect a prominent 25 km s−1 rotational pattern, in which the kinematic axis (connecting the maximal receding and approaching velocities) is 40° misaligned with the photometric major axis of M87. The rotational amplitude and misalignment angle both decrease in the inner 5 kpc. Such misaligned and twisted velocity fields are a hallmark of triaxiality, indicating that M87 is not an axisymmetrically shaped galaxy. Triaxial Schwarzschild orbit modeling with more than 4000 observational constraints enabled us to determine simultaneously the shape and mass parameters. The models incorporate a radially declining profile for the stellar mass-to-light ratio suggested by stellar population studies. We find that M87 is strongly triaxial, with ratios of p = 0.845 for the middle-to-long principal axes and q = 0.722 for the short-to-long principal axes, and determine the black hole mass to be ( 5.37 − 0.25 + 0.37 ± 0.22 ) × 10 9 M ⊙ , where the second error indicates the systematic uncertainty associated with the distance to M87.