Michele Cappellari

Abstract:

Dynamical modelling can be used to constrain the masses of central black holes, but it is challenging to model massive galaxies because of their complex kinematics. We report six new measurements of supermassive black hole masses of massive early-type galaxies from stellar kinematics, which were extracted from adaptive-optics-assisted SINFONI and MUSE observations. We combined the stellar kinematics with HST photometry to build triaxial Schwarzschild orbit-superposition models. Our Schwarzschild models can recover the complex triaxial features of the galaxies and constrain the black hole masses of all six galaxies. We found that strong triaxial kinematic features can bias the mass measurements and corrected for this effect. The derived black hole masses are $(1.14^ DYNAMITE +0.41 _ -0.63 ) _ 10^9$ M_⊙ for NGC 3706, $(1.19^ +1.34 -0.80 ) _ 10^9$ M_⊙ for NGC 3923, $(1.14^ +1.08 -0.95 ) _ 10^9$ M_⊙ for NGC 4261, $(4.68^ +2.99 -4.26 ) _ 10^8$ M_⊙ for NGC 4636, $(3.51^ +3.37 -2.57 ) _ 10^9$ M_⊙ for IC 4296, and $(2.43^ +1.53 -1.65 ) 10^9$ M_⊙ for IC 4329 at a confidence level of 3σ. We compared our measurements with published results from axisymmetric Schwarzschild modelling and with our JAM Jeans Anisotropic models and obtained mostly consistent black hole masses. Most of our black hole mass estimates can be well constrained using MUSE observations alone. All of our mass measurements agree with local black hole scaling relations.

Abstract:

Despite its proximity, the mass of the supermassive black hole (SMBH) in the spiral galaxy M81 (NGC 3031) has remained a subject of discussion, with doubts previously cast on the reliability of available dynamical measurements. We present the first robust stellar-dynamics measurement of its mass using high-resolution, two-dimensional kinematics from JWST/NIRSpec observations of the central 3″ × 3″. By tracing stellar motions in the near-infrared, our data penetrate the obscuring nuclear dust and allow for the separation of stellar light from the nonthermal AGN continuum. We modeled the kinematics using the Jeans anisotropic modelling method. Rather than relying on a standard Bayesian approach for error estimation, we constructed a suite of 24 independent models, each employing a unique combination of different physical assumptions regarding stellar mass-to-light (M/L) ratio gradients, the point-spread function, the masking of the central active galactic nucleus, and the orientation of the velocity ellipsoid. This ensemble approach allows us to robustly account for the impact of systematic uncertainties. To estimate our systematic uncertainties, we performed a bootstrap of the MBH values derived from these 24 models, thereby incorporating the variance between different physical assumptions. Our analysis yields a precise SMBH mass of MBH = (4.77 ± 0.37) × 107 M⊙ (1σ confidence, including systematic and statistical uncertainties). This result is consistent with previous determinations within their uncertainties, while providing a crucial and highly reliable anchor point for SMBH–galaxy scaling relations in spiral galaxies.

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 while executing significantly faster than standard restrictive techniques. The method relies on three key choices: (i) solving for the intrinsic dispersion rather than the rapidly varying pressure 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.