Context. The environment of Sagittarius A* (Sgr A*), the central black hole of the Milky Way, is the only place in the Universe where we can currently study the interaction between a nuclear star cluster and a massive black hole and infer the properties of a nuclear cluster from observations of individual stars. Aims. This work aims to explore the star formation history of the nuclear cluster and the structure of the innermost stellar cusp around Sgr A*. Methods. We combined and analysed multi epoch high quality AO observations. For the region close to Sgr A* we apply the speckle holography technique to the AO data and obtain images that are ≥50% complete down to K_s ≈ 19 within a projected radius of 5″ around Sgr A*. We used H-band images to derive extinction maps. Results. We provide K_s photometry for roughly 39 000 stars and H-band photometry for ∼11 000 stars within a field of about 40″ × 40″, centred on Sgr A*. In addition, we provide K_s photometry of ∼3000 stars in a very deep central field of 10″ × 10″, centred on Sgr A*. We find that the K_s luminosity function (KLF) is rather homogeneous within the studied field and does not show any significant changes as a function of distance from the central black hole on scales of a few 0.1 pc. By fitting theoretical luminosity functions to the KLF, we derive the star formation history of the nuclear star cluster. We find that about 80% of the original star formation took place 10 Gyr ago or longer, followed by a largely quiescent phase that lasted for more than 5 Gyr. We clearly detect the presence of intermediate-age stars of about 3 Gyr in age. This event makes up about 15% of the originally formed stellar mass of the cluster. A few percent of the stellar mass formed in the past few 100 Myr. Our results appear to be inconsistent with a quasi-continuous star formation history. The mean metallicity of the stars is consistent with being slightly super solar. The stellar density increases exponentially towards Sgr A* at all magnitudes between K_s = 15−19. We also show that the precise properties of the stellar cusp around Sgr A* are hard to determine because the star formation history suggests that the star counts can be significantly contaminated, at all magnitudes, by stars that are too young to be dynamically relaxed. We find that the probability of observing any young (non-millisecond) pulsar in a tight orbit around Sgr A* and beamed towards Earth is very low. We argue that typical globular clusters, such as they are observed in and around the Milky Way today, have probably not contributed to the nuclear cluster’s mass in any significant way. The nuclear cluster may have formed following major merger events in the early history of the Milky Way.

The S-star cluster in the Galactic center allows us to study the physics close to a supermassive black hole, including distinctive dynamical tests of general relativity. Our best estimates for the mass of and the distance to Sgr A* using the three stars with the shortest period (S2, S38, and S55/S0-102) and Newtonian models are M _BH = (4.15 ± 0.13 ± 0.57) × 10⁶ M _⊙ and R ₀ = 8.19 ± 0.11 ± 0.34 kpc. Additionally, we aim at a new and practical method to investigate the relativistic orbits of stars in the gravitational field near Sgr A*. We use a first-order post-Newtonian approximation to calculate the stellar orbits with a broad range of periapse distance r _p . We present a method that employs the changes in orbital elements derived from elliptical fits to different sections of the orbit. These changes are correlated with the relativistic parameter defined as ϒ ≡ r _s /r _p (with r _s being the Schwarzschild radius) and can be used to derive ϒ from observational data. For S2 we find a value of ϒ = 0.00088 ± 0.00080, which is consistent, within the uncertainty, with the expected value of ϒ = 0.00065 derived from M _BH and the orbit of S2. We argue that the derived quantity is unlikely to be dominated by perturbing influences such as noise on the derived stellar positions, field rotation, and drifts in black hole mass.

Context. The Milky Way nuclear star cluster (MWNSC) is a crucial laboratory for studying the galactic nuclei of other galaxies, but its properties have not been determined unambiguously until now. Aims. We aim to study the size and spatial structure of the MWNSC. Methods. This study uses data and methods that address potential shortcomings of previous studies on the topic. We use 0.2″ angular resolution K_s data to create a stellar density map in the central 86.4 pc × 21 pc at the Galactic center. We include data from selected adaptive-optics-assisted images obtained for the inner parsecs. In addition, we use Spitzer/IRAC mid-infrared (MIR) images. We model the Galactic bulge and the nuclear stellar disk in order to subtract them from the MWNSC. Finally, we fit a Sérsic model to the MWNSC and investigate its symmetry. Results. Our results are consistent with previous work. The MWNSC is flattened with an axis ratio of q = 0.71 ± 0.10, an effective radius of R_e = (5.1 ± 1.0) pc, and a Sérsic index of n = 2.2 ± 0.7. Its major axis may be tilted out of the Galactic plane by up to −10°. The distribution of the giants brighter than the Red Clump (RC) is found to be significantly flatter than the distribution of the faint stars. We investigate the 3D structure of the central stellar cusp using our results on the MWNSC structure on large scales to constrain the deprojection of the measured stellar surface number density, obtaining a value of the 3D inner power law of γ = 1.38 ± 0.06_sys ± 0.01_stat. Conclusions. The MWNSC shares its main properties with other extragalactic NSCs found in spiral galaxies. The differences in the structure between bright giants and RC stars might be related to the existence of not completely mixed populations of different ages. This may hint at recent growth of the MWNSC through star formation or cluster accretion.

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