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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 ($L_K$) and half-light radii ($R_e$) 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 $L_K$, suggesting that low-mass and high-mass slow rotators have different formation histories. The curvatures in the $R_e-L_K$ and $\sigma-L_K$ relations cancel, leading to a relation between dynamical mass and luminosity that is well described by a single power-law: $R_e\sigma^2 \propto {L_K}^b$ with $b \approx 1.2$. This is consistent with the tilt of the fundamental plane observed in lower mass elliptical galaxies., Comment: 17 pages, 7 figures, accepted for publication in MNRAS

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 integral field spectroscopy (IFS) from the Gemini Multi-Object Spectrograph (GMOS) with wide-field data from the Mitchell Spectrograph at McDonald Observatory to extract and model stellar kinematics of NGC 2693 from the central $\sim 150$ pc out to $\sim2.5$ effective radii. Observations from Hubble Space Telescope (HST) 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 6-D galaxy model parameter space to determine NGC 2693's SMBH mass ($M_\text{BH}$), stellar mass-to-light ratio, dark matter content, and intrinsic shape. We find $M_\text{BH} = \left(1.7\pm 0.4\right)\times 10^{9}\ M_\odot$ and a triaxial intrinsic shape with axis ratios $p=b/a=0.902 \pm 0.009$ and $q=c/a=0.721^{+0.011}_{-0.010}$, triaxiality parameter $T = 0.39 \pm 0.04$. In comparison, the best-fit orbit model in the axisymmetric limit and (cylindrical) Jeans anisotropic model of NGC 2693 prefer $M_\text{BH} = \left(2.4\pm 0.6\right)\times 10^{9}\ M_\odot$ and $M_\text{BH} = \left(2.9\pm 0.3\right)\times 10^{9}\ M_\odot$, respectively. Neither model can account for the non-axisymmetric stellar velocity features present in the IFS data., Comment: 18 pages, 9 figures, 2 tables, accepted to ApJ 2022/02/24

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. (2008) 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 $p=b/a=0.933^{+0.014}_{-0.015}$ and $q=c/a=0.779\pm0.012$ for the intrinsic axis ratios and $T=0.33\pm0.06$ 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., Comment: 19 pages, 8 figures, accepted to ApJ. In press

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 ($M_\mathrm{BH}$) 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 $M_\mathrm{BH}$ in orbit modeling of the massive elliptical galaxy NGC 1453 reported in Liepold et al. 2020. In addition, we verify the efficacy of our updated code on a mock galaxy dataset. 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., Comment: 19 pages, 7 figures. Accepted for publication in ApJ

We present a new stellar dynamical mass measurement ($M_\mathrm{BH}$) 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 ($S/N \sim 130$) spectra from the Gemini-North GMOS integral-field spectrograph (IFS). Combining with wide-field IFS kinematics out to $\sim 3$ 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 $M_\mathrm{BH} =(2.9 \pm 0.4) 10^9 M_\odot$; the mass models without a central black hole are excluded at the $8.7\sigma$ level. The NGC 1453 black hole lies within the intrinsic scatter of the SMBH and galaxy scaling relations, unlike three other galaxies hosting $\gtrsim 10^{10} M_\odot$ 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 $M_\mathrm{BH}$ 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., Comment: Accepted for publication in The Astrophysical Journal. 22 pages, 12 figures; References updated

We measure the stellar populations as a function of radius for 90 early-type galaxies (ETGs) in the MASSIVE survey, a volume-limited integral-field spectroscopic (IFS) galaxy survey targeting all northern-sky ETGs with absolute K-band magnitude M_K < -25.3 mag, or stellar mass M* 4x10^11 M_sun, within 108 Mpc. We are able to measure reliable stellar population parameters for individual galaxies out to 10-20 kpc (1-3 R_e) depending on the galaxy. Focusing on ~R_e (~10 kpc), we find significant correlations between the abundance ratios, sigma, and M* at large radius, but we also find that the abundance ratios saturate in the highest-mass bin. We see a strong correlation between the kurtosis of the line of sight velocity distribution (h4) and the stellar population parameters beyond R_e. Galaxies with higher radial anisotropy appear to be older, with metal-poorer stars and enhanced [alpha/Fe]. We suggest that the higher radial anisotropy may derive from more accretion of small satellites. Finally, we see some evidence for correlations between environmental metrics (measured locally and on >5 Mpc scales) and the stellar populations, as expected if satellites are quenched earlier in denser environments., Comment: 17 pages, 7 figures, Appendix not included here due to size constraints. Posted after responding to referee's comments

A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental states. The non-predictive model complexity has been shown to lower-bound the thermodynamic dissipation. Here we explore these statistical and physical quantities at steady state in simple models. We show that under quasi-static driving this model complexity saturates the dissipation. Beyond the quasi-static limit, we demonstrate a lower bound on the ratio of this model complexity to total dissipation, that is realized in the limit of weak driving., Comment: 10 pages, 6 figures