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Abstract:

Abstract Supermassive black hole (SMBH) masses can be measured using molecular gas kinematics. Here we present high angular resolution (0.12 arcsec or ≈11 pc) Atacama Large Millimeter/submillimeter Array observations of the 12CO(2–1) line emission of the early-type galaxy NGC 1387. The observations reveal a face-on, regularly-rotating central molecular gas disc with a diameter of ≈18 arcsec (≈1.7 kpc) and a central depression slightly larger than the SMBH sphere of influence. We forward model the CO data cube in a Bayesian framework with the Kinematic Molecular Simulation code, and use Hubble Space Telescope data to constrain the stellar gravitational potential contribution to the molecular gas kinematics. We infer a SMBH mass of $1.10^{+1.71}_{-0.95}[\textrm{stat},3\sigma ]^{+2.45}_{-1.09}[\textrm{sys}]\times 10^8$ M⊙ and a F160W-filter stellar mass-to-light ratio of $0.90^{+0.44}_{-0.35}[\textrm{stat}, 3\sigma ]^{+0.46}_{-0.36}[\textrm{sys}]$ M⊙/L⊙, F160W. This SMBH mass is consistent with the SMBH mass – stellar velocity dispersion relation.

Abstract:

Abstract Axisymmetric Jeans modelling is widely used to infer galaxy mass profiles from integral-field kinematics, but existing implementations maintain tractability by adopting highly restricted anisotropy prescriptions. I present a new spectral method that solves the axisymmetric Jeans equations as a two-dimensional boundary-value problem. Remarkably, this breaks the traditional trade-off between model flexibility and computational cost, accommodating completely general anisotropy distributions β(r, θ) while executing significantly faster than standard restrictive techniques. The method relies on three key choices: (i) solving for the intrinsic dispersion $\overline{v_r^2}$ rather than the rapidly varying pressure $\nu \overline{v_r^2}$ to improve numerical conditioning; (ii) working in logarithmic radius to efficiently resolve the large dynamic range of galaxies, uniquely matching scale-free (power-law) regimes; and (iii) imposing a Robin outer boundary condition that enforces the correct asymptotic decay on a finite computational domain. Orbit integrations in realistic galaxy potentials motivate spherical alignment of the velocity ellipsoid as a physically plausible default, though the framework easily adapts to other alignments. Validated against exact analytic benchmarks—including new analytic Jeans solutions derived herein—the solver recovers intrinsic second moments with high accuracy, showing radially uniform residuals for power-law tests. In practice, it delivers orders-of-magnitude speed-ups over high-accuracy quadrature schemes and is naturally suited to massive GPU parallelization. Released in the public JamPy package, this enables the routine application of highly general Jeans models to large surveys and the extensive parameter-space exploration required for rigorous uncertainty quantification.

Abstract:

We present a new stellar-dynamical measurement of the supermassive black hole (SMBH) mass in the nearby spiral galaxy NGC 4258 (M106), a critical benchmark for extragalactic mass measurements. We use archival James Webb Space Telescope (JWST) Near-Infrared Spectrograph (NIRSpec) integral field unit data (G235H/F170LP grating) to extract high-resolution two-dimensional stellar kinematics from the CO bandhead absorption features within the central 3″ × 3″. We extract the stellar kinematics after correcting for instrumental artifacts and separating the stellar light from the nonthermal active galactic nucleus (AGN) continuum. We employ Jeans anisotropic models to fit the observed kinematics, exploring a grid of 12 models to systematically test the impact of different assumptions for the point-spread function, stellar mass-to-light ratio profile, and orbital anisotropy. All 12 models provide broadly acceptable fits, albeit with minor differences. The ensemble median and 68% (1σ) bootstrap confidence interval of our 12 models yield a black hole mass of MBH=(4.08−0.33+0.19)×107 M⊙. This paper showcases the utility of using the full model ensemble to robustly account for systematic uncertainties, rather than relying on formal errors from a single preferred model, as has been common practice. Our result is just 5% larger than, and consistent with, the benchmark SMBH mass derived from water-maser dynamics, validating the use of NIRSpec stellar kinematics for robust SMBH mass determination. Our analysis demonstrates JWST’s ability to resolve the SMBH’s sphere of influence and deliver precise dynamical masses, even in the presence of significant AGN continuum emission.