The dark mass signature in the orbit of S2

Abstract

Context. The Schwarzschild precession of star S2, which orbits the massive black hole at the centre of the Milky Way, has recently been detected with the result of ∼12 arcmin per orbit. The same study also improved the 1σ upper bound on a possibly present dark continuous extended mass distribution (e.g. faint stars, stellar remnants, stellar mass black holes, or dark matter) within the orbit of S2 to ∼4000 M⊙. The secular (i.e. net) effect of an extended mass onto a stellar orbit is known as mass precession, and it runs counter to the Schwarzschild precession. Aims. We explore a strategy for how the Schwarzschild and mass precessions can be separated from each other despite their secular interference, by pinpointing their signatures within a single orbit. From these insights, we then seek to assess the prospects for improving the dark mass constraints in the coming years. Methods. We analysed the dependence of the osculating orbital elements and of the observables on true anomaly, and we compared these functions for models with and without extended mass. We then translated the maximum astrometric impacts within one orbit to detection thresholds given hypothetical data of different accuracies. These theoretical investigations were then supported and complemented by an extensive mock-data fitting analysis. Results. We have four main results. 1. While the mass precession almost exclusively impacts the orbit in the apocentre half, the Schwarzschild precession almost exclusively impacts it in the pericentre half, allowing for a clear separation of the effects. 2. Data that are limited to the pericentre half are not sensitive to a dark mass, while data limited to the apocentre half are, but only to a limited extent. 3. A full orbit of data is required to substantially constrain a dark mass. 4. For a full orbit of astrometric and spectroscopic data, the astrometric component in the pericentre halff plays the stronger role in constraining the dark mass than the astrometric data in the apocentre half. Furthermore, we determine the 1σ dark mass detection thresholds given different datasets on one full orbit. In particular, with a full orbit of data of 50 microarcsec (VLTI/GRAVITY) and 10 km s−1 (VLT/SINFONI) precision, the 1σ bound would improve to ∼1000 M⊙, for example. Conclusions. The current upper dark mass bound of ∼4000 M⊙ has mainly been obtained from a combination of GRAVITY and VLT/NACO astrometric data, as well as from SINFONI spectroscopic data, where the GRAVITY data were limited to the pericentre half. From our results 3 and 4, we know that all components were thereby crucial, but also that the GRAVITY data were dominant in the astrometric components in constraining the dark mass. From results 1 and 2, we deduce that a future population of the apocentre half with GRAVITY data points will substantially further improve the dark mass sensitivity of the dataset, and we note that at the time of publication, we already entered this regime. In the context of the larger picture, our analysis demonstrates how precession effects that interfere on secular timescales can clearly be distinguished from each other based on their distinct astrometric signatures within a single orbit. The extension of our analysis to the Lense-Thirring precession should thus be of value in order to assess future spin detection prospects for the galactic centre massive black hole.

Mass distribution in the Galactic Center based on interferometric astrometry of multiple stellar orbits

“…In the following, we fix f SP = 1 at its GR value and allow now for an extended mass component parameterized by f Pl . We find f Pl = (2.7 ± 3.5) × 10 −3 from a single S2 fit and f Pl = (−3.8 ± 2.4) × 10 −3 for the four-star fit, in accordance with the findings of Heißel et al (2022). The latter 1σ error is consistent, albeit three to four times smaller than that of L12, page 4 of 17 Fig.…”

“…3 right). This comparison illustrates that the Schwarzschild precession dominates the entire orbit and that there is no detectable retrograde (Newtonian) precession due to an extended mass component (see Heißel et al 2022).…”

“…Since the higher resolution GRAVITY astrometry became available, S2 has completely dominated our knowledge about the central potential. Another reason is that it is only for S2 that we have data at or near pericenter, which are the most sensitive component of the data to the mass distribution, as the explicit analysis in Gillessen et al (2017) and Heißel et al (2022) shows.…”

“…The impact of an extended mass is naturally largest near apocenter of an orbit (e.g. Heißel et al 2022). Figure C.2 shows the result of adding various amounts of extended mass on top of the best-fit residuals with a point mass only.…”

Constraining ultralight bosonic dark matter with Keck observations of S2's orbit and kinematics

“…1. Clearly, the upper limits from S2 with 23 years data are stronger than the result obtained by Keck [91] and GRAVITY [33].…”