Nuclear Star Cluster Research Articles

Gas dynamics of the central few parsec region of NGC 1068 fuelled by the evolving nuclear star cluster

High resolution observations with the NIR adaptive optics integral field spectrograph SINFONI at the VLT proved the existence of massive and young nuclear star clusters in the centres of a sample of Seyfert galaxies. With the help of three-dimensional high resolution hydrodynamical simulations with the Pluto code, we follow the evolution of such clusters, focusing on stellar mass loss. This leads to clumpy or filamentary inflow of gas on large scales (tens of parsec), whereas a turbulent and very dense disc builds up on the parsec scale. In order to capture the relevant physics in the inner region, we treat this disc separately by viscously evolving the radial surface density distribution. This enables us to link the tens of parsec scale region (accessible via SINFONI observations) to the (sub-)parsec scale region (observable with the MIDI instrument and via water maser emission). In this work, we concentrate on the effects of a parametrised turbulent viscosity to generate angular momentum and mass transfer in the disc and additionally take star formation into account. Input parameters are constrained by observations of the nearby Seyfert 2 galaxy NGC 1068. At the current age of its nuclear starburst of 250 Myr, our simulations yield disc sizes of the order of 0.8 to 0.9 pc, gas masses of 1.0e6 solar masses and mass transfer rates of 0.025 solar masses per year through the inner rim of the disc. This shows that our large scale torus model is able to approximately account for the disc size as inferred from interferometric observations in the mid-infrared and compares well to the extent and mass of a rotating disc structure as inferred from water maser observations. Several other observational constraints are discussed as well.

Peering through the veil: near-infrared photometry and extinction for the Galactic nuclear star cluster

Context. The nuclear star cluster of the Galaxy is an important template for understanding its extragalactic counterparts, which can currently not be resolved into individual stars. Important drawbacks of observations of the Galactic center are, however, the presence of strong and spatially highly variable interstellar extinction and extreme crowding of the sources, which makes the use of adaptive optics techniques necessary. Both points pose serious obstacles to precise photometry that is needed for analyzing the stellar population.Aims. The aims of this work are to provide accurate photometry in multiple near-infrared broadband filters, to determine the power-law index of the extinction-law toward the central parsec of the Galaxy, to provide measurements of the absolute extinction toward the Galactic center, and finally to measure the spatial variability of extinction on arcsecond scales.Methods. We use observations of the central parsec of the Milky Way that were obtained with the near-infrared camera and adaptive optics system NAOS/CONICA at the ESO VLT unit telescope 4. The photometric method takes into account anisoplanatic effects and limits the corresponding systematic uncertainties to ≲ 2%. Absolute values for the extinction in the H , , and L' -bands as well as of the power-law indices of the H to and to L' extinction-laws are measured based on the well-known properties of red clump stars. Extinction maps are derived based on and colors.Results. We present -band photometry for ~7700 stars, and additionally photometry for stars detected in the H and/or L' -bands. From a number of recently published values we compute a mean distance of the Galactic center of kpc, which has an uncertainty of just . Based on this and on the RC method, we derive absolute mean extinction values toward the central parsec of the Galaxy of mag, mag, and mag. We estimate values of the power-law indices of the extinction-law of and . A -band extinction map for the Galactic center is computed based on this extinction law and on stellar colors. Both its statistical and systematic uncertainties are estimated to be 10%. Extinction in this map derived from stellar color excesses is found to vary on arcsecond scales, with a mean value of mag. Mean extinction values in a circular region with 0.5'' radius centered on Sagittarius A* are , , and .

ORIGIN OF THE GALACTIC CENTER S-STARS: GRAVITATIONAL TORQUES FROM LIN-SHU-TYPE SPIRAL DENSITY WAVES

The supermassive ~4 × 106 M ☉ black hole at the Galactic center is surrounded by a parsec-scale star disk, with several thousands of dynamically relaxed, evolved, late-type CO absorption line stars and a small ~100 population of luminous O and Wolf-Rayet stars which move in approximately circular Keplerian orbits. These bluish in color massive O and Wolf-Rayet stars are very young with an estimated age of 6 ± 2 Myr. Another small group of roughly 20 young (<10 Myr) blue B stars with the orbital periods as short as 15 years (S-stars) follow eccentric, randomly oriented orbits well inside the disk stars. A model is proposed to explain the S-stars. Accordingly, the stars formed originally in the parsec-scale disk through Jeans' gravitational fragmentation of gas. The newly formed S-stars then migrated inward to the Galactic center via the torques exerted by Lin-Shu-type spiral density waves on the stars at an inner Lindblad resonance. The model explains both the number of observed S-stars orbiting the Galactic black hole within the nuclear (<0.05 pc) star cluster and the key property of the S-star orbits, namely, their high eccentricities.

A maximum stellar surface density in dense stellar systems

Abstract We compile observations of the surface mass density profiles of dense stellar systems, including globular clusters in the Milky Way and nearby galaxies, massive star clusters in nearby starbursts, nuclear star clusters in dwarf spheroidals and late-type discs, ultra-compact dwarfs, and galaxy spheroids spanning the range from low-mass ‘cusp’ bulges and ellipticals to massive ‘core’ ellipticals. We show that in all cases the maximum stellar surface density attained in the central regions of these systems is similar, Σmax ∼ 1011 M⊙ kpc−2 (∼20 g cm−2), despite the fact that the systems span ∼7 orders of magnitude in total stellar mass M* and ∼5 in effective radius Re, and have a wide range in effective surface density M*/R2e. The surface density limit is reached on a wide variety of physical scales in different systems and is thus not a limit on three-dimensional stellar density. Given the very different formation mechanisms involved in these different classes of objects, we argue that a single piece of physics likely determines Σmax. The radiation fields and winds produced by massive stars can have a significant influence on the formation of both star clusters and galaxies, while neither supernovae nor black hole accretion is important in star cluster formation. We thus conclude that feedback from massive stars likely accounts for the observed Σmax, plausibly because star formation reaches an Eddington-like flux that regulates the growth of these diverse systems. This suggests that current models of galaxy formation, which focus on feedback from supernovae and active galactic nuclei, are missing a crucial ingredient.

Hydrodynamic Studies of Turbulent AGN Tori

Recently, the MID-infrared Interferometric instrument (MIDI) at the VLTI has shown that dust tori in the two nearby Seyfert galaxies NGC 1068 and the Circinus galaxy are geometrically thick and can be well described by a thin, warm central disk, surrounded by a colder and fluffy torus component. By carrying out hydrodynamical simulations with the help of the TRAMP code (Klahr et al. 1999), we follow the evolution of a young nuclear star cluster in terms of discrete mass-loss and energy injection from stellar processes. This naturally leads to a filamentary large scale torus component, where cold gas is able to flow radially inwards. The filaments join into a dense and very turbulent disk structure. In a post-processing step, we calculate spectral energy distributions and images with the 3D radiative transfer code MC3D Wolf (2003) and compare them to observations. Turbulence in the dense disk component is investigated in a separate project.

AN EXTREMELY TOP-HEAVY INITIAL MASS FUNCTION IN THE GALACTIC CENTER STELLAR DISKS

We present new observations of the nuclear star cluster in the central parsec of the Galaxy with the adaptive optics assisted, integral field spectrograph SINFONI on the ESO/VLT. Our work allows the spectroscopic detection of early- and late-type stars to mK ⩾ 16, more than 2 mag deeper than our previous data sets. Our observations result in a total sample of 177 bona fide early-type stars. We find that most of these Wolf Rayet (WR), O-, and B-stars reside in two strongly warped disks between 08 and 12'' from Sgr A*, as well as a central compact concentration (the S-star cluster) centered on Sgr A*. The later type B-stars (mK>15) in the radial interval between 08 and 12'' seem to be in a more isotropic distribution outside the disks. The observed dearth of late-type stars in the central few arcseconds is puzzling, even when allowing for stellar collisions. The stellar mass function of the disk stars is extremely top heavy with a best-fit power law of dN/dm ∝ m−0.45± 0.3. WR/O-stars were formed in situ in a single star formation event ∼6 Myr ago, this mass function probably reflects the initial mass function (IMF). The mass functions of the S-stars inside 08 and of the early-type stars at distances beyond 12'' are compatible with a standard Salpeter/Kroupa IMF (best-fit power law of dN/dm ∝ m−2.15± 0.3).

Simulations of momentum feedback by black hole winds

The observed super-massive black hole (SMBH) mass -- galaxy velocity dispersion ($M_{\rm bh} - \sigma$) correlation may be established when winds/outflows from the SMBH drive gas out of the potential wells of classical bulges. Here we present numerical simulations of this process in a static isothermal potential. Simple spherically symmetric models of SMBH feedback at the Eddington luminosity can successfully explain the $M_{\rm bh} - \sigma$ and nuclear cluster mass $M_{\rm NC}-\sigma$ correlations, as well as why larger bulges host SMBHs while smaller ones host nuclear star clusters. However these models do not specify how SMBHs feed on infalling gas whilst simultaneously producing feedback that drives gas out of the galaxy. More complex models with rotation and/or anisotropic feedback allow SMBHs to feed via a disc or regions not exposed to SMBH winds, but in these more realistic cases it is not clear why a robust $M_{\rm bh} - \sigma$ relation should be established. In fact, some of the model predictions contradict observations. For example, an isotropic SMBH wind impacting on a disc (rather than a shell) of aspect ratio $H/R \ll 1$ requires the SMBH mass to be larger by a factor $\sim R/H$, which is opposite to what is observed. We conclude that understanding how a SMBH feeds is as important a piece of the puzzle as understanding how its feedback affects its host galaxy. Finally, we note that in aspherical cases the SMBH outflows induce differential motions in the bulge. This may pump turbulence that is known to hinder star formation in star forming regions. SMBH feedback thus may not only drive gas out of the bulge but also reduce the fraction of gas turned into stars.

LOCAL LYMAN BREAK GALAXY ANALOGS: THE IMPACT OF MASSIVE STAR-FORMING CLUMPS ON THE INTERSTELLAR MEDIUM AND THE GLOBAL STRUCTURE OF YOUNG, FORMING GALAXIES

We present HST UV/optical imaging, Spitzer mid-IR photometry, and optical spectroscopy of a sample of 30 low-redshift (z=0.1-0.3) galaxies chosen from SDSS/GALEX to be accurate local analogs of the high-z Lyman Break Galaxies. The Lyman Break Analogs (LBAs) are similar in mass, metallicity, dust, SFR, size and gas velocity dispersion, thus enabling a detailed investigation of processes that are important at high-z. The optical emission line properties of LBAs are also similar to those of LBGs, indicating comparable conditions in their ISM. In the UV, LBAs are characterized by complexes of massive star-forming "clumps", while in the optical they most often show evidence for (post-)mergers/interactions. In 6 cases, we find an extremely massive (>10^9 Msun) compact (R~100 pc) dominant central object (DCO). The DCOs are preferentially found in LBAs with the highest mid-IR luminosities and correspondingly high SFRs (15-100 Msun/yr). We show that the massive SF clumps (including the DCOs) have masses much larger than the nuclear super star clusters seen in normal late type galaxies. However, the DCOs have masses, sizes, and densities similar to the excess-light/central-cusps seen in typical elliptical galaxies with masses similar to the LBA galaxies. We suggest that the DCOs form in present-day examples of the dissipative mergers at high redshift that are believed to have produced the central-cusps in local ellipticals. More generally, the properties of the LBAs are consistent with the idea that instabilities in a gas-rich disk lead to very massive star-forming clumps that eventually coalesce to form a spheroid. We speculate that the DCOs are too young at present to be growing a supermassive black hole because they are still in a supernova-dominated outflow phase.

THE INCIDENCE OF ACTIVE GALACTIC NUCLEI IN PURE DISK GALAXIES: THESPITZERVIEW

Using the Spitzer telescope, we have conducted a high-resolution spectroscopic study of 18 bulgeless (Hubble type of Sd or Sdm) galaxies that show no definitive signatures of nuclear activity in their optical spectra. This is the first systematic mid-infrared (MIR) search for weak or hidden active galactic nuclei (AGNs) in a statistically significant sample of bulgeless (Sd/Sdm) disk galaxies. Based on the detection of the high-ionization [Ne v] 14.3 μm line, we report the discovery of an AGN in 1 out of the 18 galaxies in the sample. This galaxy, NGC 4178, is a nearby edge-on Sd galaxy, which likely hosts a prominent nuclear star cluster (NSC). The bolometric luminosity of the AGN inferred from the [Ne v] line luminosity is ∼8 × 1041 ergs s−1. This is almost 2 orders of magnitude greater than the luminosity of the AGN in NGC 4395, the best studied AGN in a bulgeless disk galaxy. Assuming that the AGN in NGC 4178 is radiating below the Eddington limit, the lower mass limit for the black hole is ∼6 × 103 M☉. The fact that none of the other galaxies in the sample shows any evidence for an AGN demonstrates that while the AGN detection rate based on MIR diagnostics is high (30%–40%) in optically quiescent galaxies with pseudobulges or weak classical bulges (Hubble type Sbc and Sc), it drops drastically in Sd/Sdm galaxies. Our observations, therefore, confirm that AGNs in completely bulgeless disk galaxies are not hidden in the optical but truly are rare. Of the three Sd galaxies with AGNs known so far, all have prominent NSCs, suggesting that in the absence of a well-defined bulge, the galaxy must possess an NSC in order to host an AGN. On the other hand, while the presence of an NSC appears to be a requirement for hosting an AGN in bulgeless galaxies, neither the properties of the NSC nor those of the host galaxy appear exceptional in late-type AGN host galaxies. The recipe for forming and growing a central black hole in a bulgeless galaxy therefore remains unknown.

HIGH ANGULAR RESOLUTION INTEGRAL-FIELD SPECTROSCOPY OF THE GALAXY'S NUCLEAR CLUSTER: A MISSING STELLAR CUSP?

We report on the structure of the nuclear star cluster in the innermost 0.16 pc of the Galaxy as measured by the number density profile of late-type giants. Using laser guide star adaptive optics in conjunction with the integral field spectrograph, OSIRIS, at the Keck II telescope, we are able to differentiate between the older, late-type ($\sim$ 1 Gyr) stars, which are presumed to be dynamically relaxed, and the unrelaxed young ($\sim$ 6 Myr) population. This distinction is crucial for testing models of stellar cusp formation in the vicinity of a black hole, as the models assume that the cusp stars are in dynamical equilibrium in the black hole potential. Based on the late-type stars alone, the surface stellar number density profile, $\Sigma(R) \propto R^{-\Gamma}$, is flat, with $\Gamma = -0.27\pm0.19$. Monte Carlo simulations of the possible de-projected volume density profile, n(r) $\propto r^{-\gamma}$, show that $\gamma$ is less than 1.0 at the 99.73 % confidence level. These results are consistent with the nuclear star cluster having no cusp, with a core profile that is significantly flatter than predicted by most cusp formation theories, and even allows for the presence of a central hole in the stellar distribution. Of the possible dynamical interactions that can lead to the depletion of the red giants observable in this survey -- stellar collisions, mass segregation from stellar remnants, or a recent merger event -- mass segregation is the only one that can be ruled out as the dominant depletion mechanism. The lack of a stellar cusp around a supermassive black hole would have important implications for black hole growth models and inferences on the presence of a black hole based upon stellar distributions.

Stellar clusters in the nuclear regions of AGN with the Advanced Camera for Surveys

We explore the role of star clusters in the nuclear regions of galaxies through their connection with active galactic nuclei (AGN). Nuclear star clusters (NCs) are conspicuous in the centers of most nearby galaxies, all along the Hubble sequence. These clusters are probably the faint-end distribution of the central supermassive black holes (SMBHs) in massive bulges. On the other hand, star formation is known to be ongoing in the majority of Seyfert nuclei and in many low-luminosity active galactic nuclei (LLAGN). We study two samples of AGN galaxies (75 Seyferts and 26 LLAGN) in the near-ultraviolet with the Hubble Space Telescope’s Advanced Camera for Surveys. We aim to better understand the connection between the growing of the SMBH and the build-up of the bulge, and we also intend to make statistical progress and determine the properties of the population of NCs coexisting with growing SMBHs.

Competitive feedback in galaxy formation

Abstract It is now well established that many galaxies have nuclear star clusters (NCs) whose total masses correlate with the velocity dispersion σ of the galaxy spheroid in a very similar way to the well-known supermassive black hole (SMBH) M−σ relation. Previous theoretical work suggested that both correlations can be explained by a momentum feedback argument. Observations further show that most known NCs have masses ≲108 M⊙, while SMBHs frequently have measured masses ≳108 M⊙, which remained unexplained in earlier treatments. We suggest here that this changeover reflects a competition between the SMBH and nuclear clusters in the feedback they produce. When one of the massive objects reaches its limiting M−σ value, it drives the gas away and hence cuts off its own mass and also the mass of the ‘competitor’. The latter is then underweight with respect to the expected M−σ mass. More specifically, we find that the bulge dynamical time-scale is a steeply rising function of velocity dispersion, and that the NC–SMBH changeover occurs where the dynamical time is about equal to the Salpeter time. We propose that SMBHs, growing on the Salpeter time-scale, are unable to reach their M−σ mass quickly enough in small bulges. The central regions of these bulges are swamped with gas which fragments into stars, creating the nuclear clusters. The latter then limit their own growth by the feedback they produce, settling on their (offset) M−σ relation. The SMBH in such bulges should be underweight as their growth is curtailed before they reach the M−σ mass. In large bulges, on the other hand, the SMBH catches up quickly enough to settle on its M−σ relation. Nuclear star clusters may also exist in such bulges but they should be underweight with respect to their M−σ sequence.

On the nature of the near-UV extended light in Seyfert galaxies

We study the nature of the extended near-UV emission in the inner kiloparsec of a sample of 15 Seyfert (Sy) galaxies which have both near-UV (F330W) and narrow-band [O iii] high-resolution Hubble images. For the majority of the objects, we find a very similar morphology in both bands. From the [O iii] images, we construct synthetic images of the nebular continuum plus the emission-line contribution expected through the F330W filter, which can be subtracted from the F330W images. We find that the emission of the ionized gas dominates the near-UV extended emission in half of the objects. A further broad-band photometric study, in the bands F330W (U), F547M (V) and F160W (H), shows that the remaining emission is dominated by the underlying galactic bulge contribution. We also find a blue component whose nature is not clear in four out of 15 objects. This component may be attributed to scattered light from the active galactic nuclei, to a young stellar population in unresolved star clusters, or to early disrupted clusters. Star-forming regions and/or bright off nuclear star clusters are observed in 4/15 galaxies of the sample.

Nuclear star clusters

AbstractThe centers of most galaxies in the local Universe are occupied by compact, barely resolved sources. Based on their structural properties, position in the Fundamental Plane, and integrated spectra, these sources clearly have a stellar origin. They are therefore called ‘nuclear star clusters’ (NCs) or ‘stellar nuclei’. NCs are found in galaxies of all Hubble types, suggesting that their formation is intricately linked to galaxy evolution. Here, I review some recent studies of NCs, describe ideas for their formation and subsequent growth, and touch on their possible evolutionary connection with both supermassive black holes and globular clusters.

Obscuring and Feeding Supermassive Black Holes with Evolving Nuclear Star Clusters

AbstractRecently, high-resolution observations made with the help of the near-infrared adaptive optics integral field spectrograph SINFONI at the VLT proved the existence of massive and young nuclear star clusters in the centers of a sample of Seyfert galaxies. With the help of high-resolution hydrodynamical simulations with the pluto code, we follow the evolution of such clusters, especially focusing on mass and energy feedback from young stars. This leads to a filamentary inflow of gas on large scales (tens of parsecs), whereas a turbulent and very dense disk builds up on the parsec scale. Here we concentrate on the long-term evolution of the nuclear disk in NGC 1068 with the help of an effective viscous disk model, using the mass input from the large-scale simulations and accounting for star formation in the disk. This two-stage modeling enables us to connect the tens-of-parsecs scale region (observable with SINFONI) with the parsec-scale environment (MIDI observations). At the current age of the nuclear star cluster, our simulations predict disk sizes of the order 0.8 to 0.9 pc, gas masses of order 106M⊙, and mass transfer rates through the inner boundary of order 0.025 M⊙yr−1, in good agreement with values derived from observations.

Quantifying the coexistence of massive black holes and dense nuclear star clusters

In large spheroidal stellar systems, such as elliptical galaxies, one invariably finds a 10^6-10^9 M_Sun supermassive black hole at their centre. In contrast, within dwarf elliptical galaxies one predominantly observes a 10^5-10^7 M_Sun nuclear star cluster. To date, few galaxies have been found with both type of nuclei coexisting and even less have had the masses determined for both central components. Here we identify one dozen galaxies housing nuclear star clusters and supermassive black holes whose masses have been measured. This doubles the known number of such hermaphrodite nuclei - which are expected to be fruitful sources of gravitational radiation. Over the host spheroid (stellar) mass range from 10^8 to 10^11 M_Sun, we find that a galaxy's nucleus-to-spheroid (baryon) mass ratio is not a constant value but decreases from a few percent to ~0.3 percent such that log[(M_BH+M_NC)/M_sph] = -(0.39+/-0.07)log[M_sph/10^10 M_Sun] -(2.18+/-0.07). Once dry merging has commenced by M_sph ~ 10^11 M_Sun and the nuclear star clusters have disappeared, this ratio is expected to become a constant value. As a byproduct of our investigation, we have found that the projected flux from resolved nuclear star clusters can be well approximated with Sersic functions having a range of indices from ~0.5 to ~3, the latter index describing the Milky Way's nuclear star cluster.

Recurrent gas accretion by massive star clusters, multiple stellar populations and mass thresholds for spheroidal stellar systems

We explore the gravitational influence of pressure-supported stellar systems on the internal density distribution of a gaseous environment. We conclude that compact massive star clusters with masses ≳106 M⊙ act as cloud condensation nuclei and are able to accrete gas recurrently from a warm interstellar medium which may cause further star formation events and account for multiple stellar populations in the most massive globular and nuclear star clusters. The same analytical arguments can be used to decide whether an arbitrary spherical stellar system is able to keep warm or hot interstellar material or not. These mass thresholds coincide with transition masses between pressure supported galaxies of different morphological types.

EVOLUTION OF NUCLEAR STAR CLUSTERS

Two-body relaxation times of nuclear star clusters are short enough that gravitational encounters should substantially affect their structure in 10 Gyr or less. In nuclear star clusters without massive black holes, dynamical evolution is a competition between core collapse, which causes densities to increase, and heat input from the surrounding galaxy, which causes densities to decrease. The maximum extent of a nucleus that can resist expansion is derived numerically for a wide range of initial conditions; observed nuclei are shown to be compact enough to resist expansion, although there may have been an earlier generation of low-density nuclei that were dissolved. An evolutionary model for NGC 205 is presented which suggests that the nucleus of this galaxy has already undergone core collapse. Adding a massive black hole to a nucleus inhibits core collapse, and nuclear star clusters with black holes always expand, due primarily to heat input from the galaxy and secondarily to heating from stellar disruptions. The expansion rate is smaller for larger black holes due to the smaller temperature difference between galaxy and nucleus when the black hole is large. The rate of stellar tidal disruptions and its variation with time are computed for a variety of initial models. The disruption rate generally decreases with time due to the evolving nuclear density, particularly in the faintest galaxies, assuming that scaling relations derived for luminous galaxies can be extended to low luminosities.

Globular cluster systems in nearby dwarf galaxies - II. Nuclear star clusters and their relation to massive Galactic globular clusters

(Abridged) Using luminosities and structural parameters of globular clusters (GCs) in the nuclear regions (nGCs) of low-mass dwarf galaxies from HST/ACS imaging we derive the present-day escape velocities (v_esc) of stellar ejecta to reach the cluster tidal radius and compare them with those of Galactic GCs with extended (hot) horizontal branches (EHBs-GCs). For EHB-GCs, we find a correlation between the present-day v_esc and their metallicity as well as (V-I)_0 colour. The similar v_esc, (V-I)_0 distribution of nGCs and EHB-GCs implies that nGCs could also have complex stellar populations. The v_esc-[Fe/H] relation could reflect the known relation of increasing stellar wind velocity with metallicity, which in turn could explain why more metal-poor clusters typically show more peculiarities in their stellar population than more metal-rich clusters of the same mass do. Thus the cluster v_esc can be used as parameter to describe the degree of self-enrichment. The nGCs populate the same Mv vs. rh region as EHB-GCs, although they do not reach the sizes of the largest EHB-GCs like wCen and NGC 2419. We argue that during accretion the rh of an nGC could increase due to significant mass loss in the cluster vicinity and the resulting drop in the external potential in the core once the dwarf galaxy dissolves. Our results support the scenario in which Galactic EHB-GCs have originated in the centres of pre-Galactic building blocks or dwarf galaxies that were later accreted by the Milky Way.

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.