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1. TriOS Schwarzschild Orbit Modeling: Robustness of Parameter Inference for Masses and Shapes of Triaxial Galaxies with Supermassive Black Holes

   https://doi.org/10.3847/1538-4357/ad3935  

   Pilawa, Jacob; Liepold, Emily R.; Ma, Chung-Pei (May 2024, The Astrophysical Journal)

   Abstract 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. 

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2. A 22 Billion M⊙ Black Hole in Holmberg 15A with Keck KCWI Spectroscopy and Triaxial Orbit Modeling

   https://doi.org/10.3847/1538-4357/ada4b0  

   Liepold, Emily R; Ma, Chung-Pei; Walsh, Jonelle L (February 2025, The Astrophysical Journal)

   Holmberg 15A (H15A), the brightest cluster galaxy of A85, has an exceptionally low central surface brightness even among local massive elliptical galaxies with distinct stellar cores, making it exceedingly challenging to obtain high-quality spectroscopy to detect a supermassive black hole (SMBH) at its center. Aided by the superb sensitivity and efficiency of KCWI at the Keck II Telescope, we have obtained spatially resolved stellar kinematics over a ∼100″ x 100″ contiguous field of H15A for this purpose. The velocity field exhibits a low-amplitude (∼20 km/s) rotation along a kinematic axis that is prominently misaligned from the photometric major axis, a strong indicator that H15A is triaxially shaped with unequal lengths for the three principal axes. Using 2500 observed kinematic constraints, we perform extensive calculations of stellar orbits with the triaxial Schwarzschild code, TriOS, and search over ~40,000 galaxy models to simultaneously determine the mass and intrinsic 3D shape parameters of H15A. We determine a ratio of p = 0.89 for the middle-to-long principal axes and q = 0.65 for the short-to-long principal axes. Our best estimate of the SMBH mass, M_BH = (2.16_{−0.18}^{+0.23})x10^{10} M⊙, makes H15A — along with NGC 4889 — the galaxy hosting the most massive SMBHs known in the local Universe. Both SMBHs lie significantly above the mean M_BH–σ scaling relation. Repeating the orbit modeling with the axisymmetrized version of TriOS produces worse fits to the KCWI kinematics and increases M_BH to (2.55 ± 0.20)x10^{10} M⊙, which is still significantly below the M_BH = (4.0 ± 0.8)x10^{10} M⊙ reported in a prior axisymmetric study of H15A. 

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3. The MASSIVE Survey. XVII. A Triaxial Orbit-based Determination of the Black Hole Mass and Intrinsic Shape of Elliptical Galaxy NGC 2693

   https://doi.org/10.3847/1538-4357/ac58fd  

   Pilawa, Jacob D.; Liepold, Emily R.; Delgado Andrade, Silvana C.; Walsh, Jonelle L.; Ma, Chung-Pei; Quenneville, Matthew E.; Greene, Jenny E.; Blakeslee, John P. (April 2022, The Astrophysical Journal)

   Abstract 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 $M_{\mathrm{BH}}=\left(1.7\pm 0.4\right)\times {10}^9{M}_{\odot }$and a triaxial intrinsic shape with axis ratiosp=b/a= 0.902 ± 0.009 and $q=c/a={0.721}_{-0.010}^{+0.011}$, triaxiality parameterT= 0.39 ± 0.04. In comparison, the best-fit orbit model in the axisymmetric limit and (cylindrical) Jeans anisotropic model of NGC 2693 prefer $M_{\mathrm{BH}}=\left(2.4\pm 0.6\right)\times {10}^9{M}_{\odot }$and $M_{\mathrm{BH}}=\left(2.9\pm 0.3\right)\times {10}^9{M}_{\odot }$, respectively. Neither model can account for the non-axisymmetric stellar velocity features present in the IFS data. 

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4. Keck Integral-field Spectroscopy of M87 Reveals an Intrinsically Triaxial Galaxy and a Revised Black Hole Mass

   https://doi.org/10.3847/2041-8213/acbbcf  

   Liepold, Emily R.; Ma, Chung-Pei; Walsh, Jonelle L. (March 2023, The Astrophysical Journal Letters)

   Abstract 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. 

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5. Separatrix divergence of stellar streams in galactic potentials

   https://doi.org/10.1093/mnras/staa3687  

   Yavetz, Tomer D; Johnston, Kathryn V; Pearson, Sarah; Price-Whelan, Adrian M; Weinberg, Martin D (December 2020, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT Flattened axisymmetric galactic potentials are known to host minor orbit families surrounding orbits with commensurable frequencies. The behaviour of orbits that belong to these orbit families is fundamentally different than that of typical orbits with non-commensurable frequencies. We investigate the evolution of stellar streams on orbits near the boundaries between orbit families (separatrices) in a flattened axisymmetric potential. We demonstrate that the separatrix divides these streams into two groups of stars that belong to two different orbit families, and that as a result, these streams diffuse more rapidly than streams that evolve elsewhere in the potential. We utilize Hamiltonian perturbation theory to estimate both the time-scale of this effect and the likelihood of a stream evolving close enough to a separatrix to be affected by it. We analyse two prior reports of stream-fanning in simulations with triaxial potentials, and conclude that at least one of them is caused by separatrix divergence. These results lay the foundation for a method of mapping the orbit families of galactic potentials using the morphology of stellar streams. Comparing these predictions with the currently known distribution of streams in the Milky Way presents a new way of constraining the shape of our Galaxy’s potential and distribution of dark matter. 

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