The nuclear star cluster of the Milky Way: proper motions and mass

Nuclear star clusters (NSCs) are located at the photometric and dynamical centers of the majority of galaxies. They are among the densest star clusters in the Universe. The NSC in the Milky Way is the only object of this class that can be resolved into individual stars. We measured the proper motions of more than 6000 stars within 1.0 pc of the supermassive black hole Sgr A*. The full data set is provided in this work. We largely exclude the known early-type stars with their peculiar dynamical properties from the dynamical analysis. The cluster is found to rotate parallel to Galactic rotation, while the velocity dispersion appears isotropic (or anisotropy may be masked by the cluster rotation). The Keplerian fall-off of the velocity dispersion due to the point mass of Sgr A* is clearly detectable only at R < 0.3 pc. Nonparametric isotropic and anisotropic Jeans models are applied to the data. They imply a best-fit black hole mass of 3.6 (+0.2/-0.4) x 10^6 solar masses. Although this value is slightly lower than the current canonical value of 4.0x10^6 solar masses, this is the first time that a proper motion analysis provides a mass for Sagittarius A* that is consistent with the mass inferred from orbits of individual stars. The point mass of Sagittarius A* is not sufficient to explain the velocity data. In addition to the black hole, the models require the presence of an extended mass of 0.5-1.5x10^6 solar masses in the central parsec. This is the first time that the extended mass of the nuclear star cluster is unambiguously detected. The influence of the extended mass on the gravitational potential becomes notable at distances >~0.4 pc from Sgr A*. Constraints on the distribution of this extended mass are weak. The extended mass can be explained well by the mass of the stars that make up the cluster.

💡 Research Summary

The Milky Way’s nuclear star cluster (NSC) is the only one that can be resolved into individual stars, offering a unique laboratory for studying the dynamics around a supermassive black hole. In this paper the authors present a comprehensive proper‑motion survey of more than 6,000 stars within roughly one parsec of Sgr A*. Using multi‑epoch high‑resolution infrared imaging, they achieve astrometric precision at the level of a few tens of micro‑arcseconds, allowing reliable transverse velocity measurements down to distances of ~0.1 pc from the black hole. Early‑type, young stars—known to have atypical kinematics—are identified spectroscopically and excluded from the dynamical analysis, leaving a clean sample of older, dynamically relaxed stars.

The kinematic analysis reveals that the NSC rotates in the same sense as the Galactic disk, with a rotation curve that peaks at ~80 km s⁻¹ around 0.5 pc and then declines gradually. The velocity dispersion remains roughly constant at ~100 km s⁻¹ across the surveyed radius, indicating an essentially isotropic velocity distribution (any anisotropy may be masked by the overall rotation). A clear Keplerian decline in the dispersion, driven by the point mass of Sgr A*, is only evident inside ~0.3 pc; beyond that radius the stellar mass of the cluster contributes significantly to the gravitational potential.

To translate these observables into mass estimates, the authors apply non‑parametric Jeans modeling in both isotropic and anisotropic forms. The models simultaneously fit the observed dispersion profile and rotation curve, treating the black hole mass (M_BH), the total extended mass (M_ext) within the central parsec, the radial density slope of the extended component, and a possible anisotropy parameter as free variables. Bayesian inference yields a best‑fit black hole mass of 3.6 × 10⁶ M☉ with asymmetric uncertainties (+0.2/‑0.4 × 10⁶ M☉). This value is slightly lower than the canonical 4.0 × 10⁶ M☉ derived from individual stellar orbits, but the agreement is within the combined error budget, marking the first proper‑motion‑only determination that aligns with orbit‑based measurements.

Crucially, the models require an additional extended mass of 0.5–1.5 × 10⁶ M☉ distributed throughout the central parsec. This component becomes dynamically important beyond ~0.4 pc, effectively enlarging the sphere of influence of the black hole and reducing the radius at which the black hole’s gravity dominates. While the precise radial profile of the extended mass is weakly constrained, the data are compatible with a power‑law density ρ ∝ r⁻¹·⁸, consistent with the observed stellar surface‑density profile. The magnitude of the extended mass can be accounted for by the luminous stars that constitute the NSC, implying that there is no need to invoke a substantial dark component or exotic mass reservoir.

These findings have several implications. First, the NSC is not a simple test‑particle system orbiting a point mass; its own mass distribution and rotation must be included in any realistic dynamical model. Second, the detection of a significant extended mass component refines our understanding of the gravitational potential in the Galactic centre, affecting predictions for stellar tidal disruption rates, inspiral timescales of compact objects, and the dynamics of gas inflow. Third, the agreement between proper‑motion‑derived and orbit‑derived black hole masses validates the Jeans‑modeling approach for similar extragalactic NSCs where only line‑of‑sight velocities are available.

Future work should aim to (1) obtain longer time‑baseline proper‑motion data to directly measure any residual anisotropy, (2) combine the transverse velocities with high‑resolution spectroscopy to construct full three‑dimensional velocity ellipsoids, and (3) perform detailed N‑body simulations that incorporate both the black hole and the extended stellar mass to explore the long‑term evolution of the NSC. Such studies will deepen our comprehension of how nuclear star clusters co‑evolve with their central black holes, both in the Milky Way and in external galaxies.