Discovery of a star sensitive to the spin of Sgr A*

Technical Summary: Discovery of a Star Sensitive to the Spin of Sgr A*

Problem and Context
The supermassive black hole (MBH) Sgr A* at the center of the Milky Way is the closest massive black hole, offering a unique laboratory for testing general relativity. While the orbits of stars like S2 have successfully measured the central mass to sub-percent precision and confirmed relativistic effects of order $\beta^2 = (v/c)^2$ (gravitational redshift, transverse Doppler effect, and Schwarzschild precession), measuring the black hole's spin remains a significant challenge. Spin-induced effects (Lense-Thirring precession) appear at order $\beta^3$ and fall off as $r^{-3}$, making them difficult to detect for stars with large pericenter distances. Current instrumentation requires prohibitively long time series to detect spin effects using known stars like S2. The paper addresses the need for a test particle with a sufficiently small pericenter distance ($r_p$) to make the spin of Sgr A* measurable within a decade.

Methodology
The study utilizes near-infrared interferometric data from the GRAVITY instrument on the European Southern Observatory's Very Large Telescope (VLT).

• Observations: Regular observations of the central arcsecond around Sgr A* were conducted between 2017 and 2025, totaling approximately 80–100 hours per year.
• Data Analysis: The team employed two primary analysis methods:
  1. Model Fitting: Fitting models of known sources to retrieve positions and fluxes.
  2. Image Reconstruction: Using the GRAVITY-RESOLVE (GR) code to Fourier-invert complex visibilities into images. This method, combined with classical algorithms like CLEAN, allows for the identification of faint, previously unknown sources.
• Orbit Determination: Astrometric positions of the newly discovered star, S301, were measured relative to Sgr A*. A preliminary Keplerian orbit was fitted using $\chi^2$ minimization, incorporating $\beta^2$ relativistic effects (Rømer delay and Schwarzschild precession) consistent with the model used for S2. Due to the lack of radial velocity data, two degenerate solutions for the orbit's 3D orientation exist, though the orbital elements ($a$, $e$, $P$) remain consistent.
• Spin Sensitivity Forecast: The authors performed mock data analyses combining current astrometry with simulated future observations (up to 2035) to forecast the detectability of the Lense-Thirring precession. They also modeled Newtonian perturbations from a cluster of stellar-mass black holes to assess their impact on spin measurements.

Key Results

• Discovery of S301: The team discovered a faint main-sequence star, S301, with a K-band magnitude of $m_K = 19.3 \pm 0.3$.
• Orbital Parameters: S301 follows an 8.7-year orbit, setting a new record for the shortest known orbital period around Sgr A*. The orbit is highly eccentric ($e \approx 0.983$), resulting in a pericenter distance of $r_p \approx 136\text{--}142 R_S$ (Schwarzschild radii). This is approximately ten times closer to the event horizon than S2's pericenter.
• Relativistic Velocity: At pericenter, S301 reaches velocities of $\approx 25,000$ km/s ($\approx 8.5\%$ of the speed of light).
• Stellar Characterization: Based on its brightness and evolutionary tracks, S301 is identified as an F1.5 main-sequence star with a mass $\lesssim 1.5 M_\odot$ and radius $\sim 1.4\text{--}1.6 R_\odot$. This classification implies the star is small enough to avoid tidal disruption at its current pericenter.
• Spin Sensitivity: The small pericenter distance makes S301 sensitive to the spin of Sgr A*. For a maximally rotating black hole ($\chi=1$), the Lense-Thirring precession contributes $\approx 0.11^\circ$ per revolution (depending on spin orientation). The authors estimate that with current and planned instrumentation (including GRAVITY+ and future ELT spectroscopy), a direct measurement of the spin parameter $\chi$ with an uncertainty $< 0.2$ is feasible within a decade.
• Origin: The extreme eccentricity and short period suggest S301 is the captured component of a compact binary system disrupted by the MBH via the Hills mechanism. The progenitor binary likely had a semi-major axis of $\sim 0.1$ AU.

Significance and Claims
The paper claims that S301 constitutes the first and currently only practical way to measure the spin of Sgr A* using stellar dynamics. Unlike other known S-stars, which are insensitive to frame-dragging on observable timescales due to larger pericenter distances, S301's orbit allows for the detection of $\beta^3$ effects within a reasonable timeframe.

The authors state that while the current dataset is consistent with General Relativity at the 1PN level, the long-term monitoring of S301 offers a path to:

1. Directly constrain the spin parameter of Sgr A*.
2. Tighten constraints on deviations from General Relativity (e.g., strong-field PPN parameters).
3. Eventually test the Kerr no-hair theorem by constraining the quadrupole moment of the black hole.

The paper modestly notes that while Newtonian perturbations from a stellar cusp exist, the distinct temporal and spatial signatures of the Lense-Thirring effect (concentrated near pericenter) compared to stellar perturbations (dominant near apocenter) offer a promising avenue to disentangle these effects. The discovery also provides a self-consistent picture of the Hills mechanism populating the innermost S-star cluster.