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Evidence for the majority of the supermassive black holes in the local Universe has been obtained dynamically from stellar motions with the Schwarzschild orbit superposition method. However, there have been only a handful of studies using simulated data to examine the ability of this method to reliably recover known input black hole massesM_BHand other galaxy parameters. Here, we conduct a comprehensive assessment of the reliability of the triaxial Schwarzschild method atsimultaneouslydeterminingM_BH, stellar mass-to-light ratioM*/L, dark matter mass, and three intrinsic triaxial shape parameters of simulated galaxies. For each of 25 rounds of mock observations using simulated stellar kinematics and theTriOScode, we derive best-fitting parameters and confidence intervals after a full search in the 6D parameter space with our likelihood-based model inference scheme. The two key mass parameters,M_BHandM*/L, are recovered within the 68% confidence interval, and other parameters are recovered between the 68% and 95% confidence intervals. The spatially varying velocity anisotropy of the stellar orbits is also well recovered. We explore whether the goodness-of-fit measure used for galaxy model selection in our pipeline is biased by variable complexity across the 6D parameter space. In our tests, adding a penalty term to the likelihood measure either makes little difference, or worsens the recovery in some cases.

We present wide-field, deep K-band photometry of 98 luminous early-type galaxies (ETGs) from the MASSIVE survey based on observations taken with the WIRCam instrument on the Canada–France–Hawaii Telescope. Using these images, we extract accurate total K-band luminosities (LK) and half-light radii (Re) for this sample of galaxies. We use these new values to explore the size–luminosity and Faber–Jackson relations for massive ETGs. Within this volume-limited sample, we find clear evidence for curvature in both relations, indicating that the most luminous galaxies tend to have larger sizes and smaller velocity dispersions than expected from a simple power-law fit to less luminous galaxies. Our measured relations are qualitatively consistent with the most massive elliptical galaxies forming largely through dissipationless mergers. When the sample is separated into fast and slow rotators, we find the slow rotators to exhibit similar changes in slope with increasing LK, suggesting that low-mass and high-mass slow rotators have different formation histories. The curvatures in the Re–LK and σ–LK relations cancel, leading to a relation between dynamical mass and luminosity that is well described by a single power law: Reσ2 ∝ LKb with b ≈ 1.2. This is consistent with the tilt of the fundamental plane observed in lower mass elliptical galaxies.

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⁻¹rotational 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 ofp= 0.845 for the middle-to-long principal axes andq= 0.722 for the short-to-long principal axes, and determine the black hole mass to be$({5.37}_{-0.25}^{+0.37}\pm 0.22)\times {10}^9{M}_{\odot }$, where the second error indicates the systematic uncertainty associated with the distance to M87.