Context. The Galactic centre (GC) is of fundamental astrophysical interest, but existing near-infrared surveys fall short covering it adequately, either in terms of angular resolution, multi-wavelength coverage, or both. Here we introduce the GALACTICNUCLEUS survey, a JHKs imaging survey of the centre of the Milky Way with a 0.2″ angular resolution. Aims. The purpose of this paper is to present the observations of Field 1 of our survey, centred approximately on SgrA* with an approximate size of 7.95′ × 3.43′. We describe the observational set-up and data reduction pipeline and discuss the quality of the data. Finally, we present the analysis of the data. Methods. The data were acquired with the near-infrared camera High Acuity Wide field K-band Imager (HAWK-I) at the ESO Very Large Telescope (VLT). Short readout times in combination with the speckle holography algorithm allowed us to produce final images with a stable, Gaussian PSF (point spread function) of 0.2″ FWHM (full width at half maximum). Astrometric calibration is achieved via the VISTA Variables in the Via Lactea (VVV) survey and photometric calibration is based on the SIRIUS/Infrared Survey Facility telescope (IRSF) survey. The quality of the data is assessed by comparison between observations of the same field with different detectors of HAWK-I and at different times. Results. We reach 5σ detection limits of approximately J = 22, H = 21, and Ks = 20. The photometric uncertainties are less than 0.05 at J ≲ 20, H ≲ 17, and Ks ≲ 16. We can distinguish five stellar populations in the colour-magnitude diagrams; three of them appear to belong to foreground spiral arms, and the other two correspond to high- and low-extinction star groups at the GC. We use our data to analyse the near-infrared extinction curve and find some evidence for a possible difference between the extinction index between J − H and H − Ks. However, we conclude that it can be described very well by a power law with an index of αJHKs = 2.30 ± 0.08. We do not find any evidence that this index depends on the position along the line of sight, or on the absolute value of the extinction. We produce extinction maps that show the clumpiness of the ISM (interstellar medium) at the GC. Finally, we estimate that the majority of the stars have solar or super-solar metallicity by comparing our extinction-corrected colour-magnitude diagrams with isochrones with different metallicities and a synthetic stellar model with a constant star formation.

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Context. This is the second of three papers that search for the predicted stellar cusp around the Milky Way’s central black hole, Sagittarius A*, with new data and methods. Aims. We aim to infer the distribution of the faintest stellar population currently accessible through observations around Sagittarius A*. Methods. We used adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through optimised PSF fitting we removed the light from all detected stars above a given magnitude limit. Subsequently we analysed the remaining, diffuse light density. Systematic uncertainties were constrained by the use of data from different observing epochs and obtained with different filters. We show that it is necessary to correct for the diffuse emission from the mini-spiral, which would otherwise lead to a systematically biased light density profile. We used a Paschen α map obtained with the Hubble Space Telescope for this purpose. Results. The azimuthally averaged diffuse surface light density profile within a projected distance of R ≲ 0.5 pc from Sagittarius A* can be described consistently by a single power law with an exponent of Γ = 0.26 ± 0.02stat ± 0.05sys, similar to what has been found for the surface number density of faint stars in Paper I. Conclusions. The analysed diffuse light arises from sub-giant and main-sequence stars with Ks ≈ 19−22 with masses of 0.8−1.5 M⊙. These stars can be old enough to be dynamically relaxed. The observed power-law profile and its slope are consistent with the existence of a relaxed stellar cusp around the Milky Way’s central black hole. We find that a Nuker law provides an adequate description of the nuclear cluster’s intrinsic shape (assuming spherical symmetry). The 3D power-law slope near Sgr A* is γ = 1.13 ± 0.03model ± 0.05sys. The stellar density decreases more steeply beyond a break radius of about 3 pc, which corresponds roughly to the radius of influence of the massive black hole. At a distance of 0.01 pc from the black hole, we estimate a stellar mass density of 2.6 ± 0.3 × 107 M⊙ pc-3 and a total enclosed stellar mass of 180 ± 30  M⊙. These estimates assume a constant mass-to-light ratio and do not take stellar remnants into account. The fact that a flat projected surface density is observed for old giants at projected distances R ≲ 0.3 pc implies that some mechanism may have altered their appearance or distribution.

Context. The existence of dynamically relaxed stellar density cusp in dense clusters around massive black holes is a long-standing prediction of stellar dynamics, but it has so far escaped unambiguous observational confirmation. Aims. In this paper we aim to revisit the problem of inferring the innermost structure of the Milky Way's nuclear star cluster via star counts, to clarify whether it displays a core or a cusp around the central black hole. Methods. We used judiciously selected adaptive optics assisted high angular resolution images obtained with the NACO instrument at the ESO VLT. Through image stacking and improved PSF fitting we pushed the completeness limit about one magnitude deeper than in previous, comparable work. Crowding and extinction corrections were derived and applied to the surface density estimates. Known young, and therefore dynamically not relaxed stars, are excluded from the analysis. Contrary to previous work, we analyse the stellar density in well-defined magnitude ranges in order to be able to constrain stellar masses and ages. Results. We focus on giant stars, with observed magnitudes K = 12.5 − 16, and on stars with observed magnitudes K ≈ 18, which may have similar mean ages and masses than the former. The giants display a core-like surface density profile within a projected radius R ≤ 0.3 pc of the central black hole, in agreement with previous studies, but their 3D density distribution is not inconsistent with a shallow cusp if we take into account the extent of the entire cluster, beyond the radius of influence of the central black hole. The surface density of the fainter stars can be described well by a single power-law at R < 2 pc. The cusp-like profile of the faint stars persists even if we take into account the possible contamination of stars in this brightness range by young pre-main sequence stars. The data are inconsistent with a core-profile for the faint stars. Finally, we show that a 3D Nuker law provides a good description of the cluster structure. Conclusions. We conclude that the observed density of the faintest stars detectable with reasonable completeness at the Galactic Centre, is consistent with the existence of a stellar cusp around the Milky Way's central black hole, Sagittarius A*. This cusp is well developed inside the influence radius of Sagittarius A* and can be described by a single three-dimensional power-law with an exponent γ = 1.43 ± 0.02 ± 0.1 sys . This corroborates existing conclusions from Nbody simulations performed in a companion paper. An important caveat is that the faint stars analysed here may be contaminated significantly by dynamically unrelaxed stars that formed about 100 Myr ago. The apparent lack of giants at projected distances of R 0.3 pc (R 8") of the massive black hole may indicate that some mechanism may have altered their distribution or intrinsic luminosity. We roughly estimate the number of possibly missing giants to about 100.

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 Ks ≈ 19 within a projected radius of 5″ around Sgr A*. We used H-band images to derive extinction maps. Results. We provide Ks 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 Ks photometry of ∼3000 stars in a very deep central field of 10″ × 10″, centred on Sgr A*. We find that the Ks 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 Ks = 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.