A star cluster in general is a group of stars that is gravitationally bound. Star clusters vary in size and shape and they can be distinguished in two categories: Open and Globular. Open star clusters typically contain up to a few hundred of stars and they tend to be young and irregularly shaped. In contrast globular clusters are old more compact (and subsequently more spherical) and contain up to several thousand members. Nuclear Star clusters (NSC) like globular clusters are compact conglomerations of stars located at the centers of most spiral galaxies. In addition a NSC is more luminous and more massive than a globular cluster and hosts in its center a super-massive black hole (SMBH) of several million solar masses.

The NSC of the Milky Way is of exceptional interest because of its proximity, about 8kpc (~25000 light years) from Earth. Because of high interstellar extincion that is caused by dust (only 10^-12 photons in the optical reach Earth), it is really impossible to observe the NSC with an optical telescope. Therefore we rely on observations taken in the infrared because the dust is almost transparent for larger wavelenghts. Figure 1 shows a picture of the NSC taken in the infrared (Ks band) from NACO/VLT (Very Large Telescope).

The NSC extends up to several hundred arcsecs('') (1''~ 0.13light years) from the center (Sgr A*) and its mass within 1pc (~ 3.26 light years) is 10^6 Mo with 50% uncertainty (Genzel et al. 2010). Like most of the nuclei there is strong evidence that the center of the NSC hosts a Supermassive Black Hole (SMBH) of several million solar masses. Measurements from stellar orbits show that the SMBH mass is Mbh = 4.31 +- 0.36*10^6 Mo (Gillessen et al. 2009). Due to the proximity individual stars can be resolved and therefore number counts can be derived however due to the strong interstellar extinction because of dust, the stars can only be observed in the infrared. The relaxation time (time to reach equilibrium) of the NSC within 1pc is tr~10^10yr (Alexander 2005) and the Hubble time (age of the universe) is tH~10^10 yr indicating that the NSC should be close to relaxation but not fully relaxed yet.

Chatzopoulos, S., Gerhard, O., Fritz, T. K., Wegg, C., Gillessen, S., Pfuhl, O., et al.,  2015,  MNRAS,  453,  939

The mean absolute extinction towards the central parsec of the Milky Way is A_K~3 mag, including both foreground and Galactic center dust. Here we present a measurement of dust extinction within the Galactic old nuclear star cluster (NSC), based on combining differential extinctions of NSC stars with their u_l proper motions along Galactic longitude. Extinction within the NSC preferentially affects stars at its far side, and because the NSC rotates, this causes higher extinctions for NSC stars with negative u_l, as well as an asymmetry in the u_l-histograms. We model these effects using an axisymmetric dynamical model of the NSC in combination with simple models for the dust distribution. Comparing the predicted asymmetry to data for ~7100 stars in several NSC fields, we find that dust associated with the Galactic center mini-spiral with extinction A_K~=0.15-0.8 mag explains most of the data. The largest extinction A_K~=0.8 mag is found in the region of the Western arm of the mini-spiral. Comparing with total A_K determined from stellar colors, we determine the extinction in front of the NSC. Finally, we estimate that for a typical extinction of A_K~=0.4 the statistical parallax of the NSC changes by ~0.4%.

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Chatzopoulos S., Fritz T. K., Gerhard O., Gillessen S., Wegg C., Genzel R., Pfuhl O., 2015, MNRAS, 447, 948

To model the NSC we worked with ~2500 radial velocities (velocities along the line of sight) and ~10000 proper motions (perpendicular to the line of sight ) plus stellar number counts from T. Fritz et al. (submitted). Before this work the best model in the literature for the NSC was spherical Jeans models (really simple) and therefore we decided for this project to apply 2-Integral distribution functions (DF) (in simple words, a flattened system) that possess considerable advantages over Jeans modeling but are also much more complicated to implement. A DF gives the number of stars in phase space as a function of the position and velocity. Therefore if one knows the DF of a system he knows the position and velocity of every star in this system. The best indicator for the quality of the modeling was the good prediction of the Velocity Profiles (VP) since those include all the moments of the system. The 2-I DF gave us overall very good results (Figure 2) and makes this model, the best model of the NSC in the literature. Next I describe in more detail the steps of the project.

We started by fitting a parametric oblate gamma-model (this is an axisymetric stellar system model) to the surface density (SD) as a function of the l proper motion (Galactic latitude) and b proper motion (Galactic longitude) coordinate. The shape of the SD indicates an inflection point at about 100'' from the center. After noticing this we switched to a 2-component gamma-model for the SD. The use of 2 flattened models is advantageous because it allowed for a non constant axial ratio. Having the density allows us to calculate the total potential as a sum of the 2 model potentials plus the black hole potential. The goal was to calculate the DF that corresponds to this potential. For this we used the Hunter & Qian (Hunter & Qian 1993) contour integral method. This method is a generalization of Eddington's formula (describes spherical systems) and it takes place in the complex potential plane. The method gives us the even part of the DF. To test the DF we compare its first moments with Jeans modeling. By applying axisymmetric Jeans modeling we constrained the distance R0 to the NSC, the mass of the NSC and the SMBH mass giving new estimations. The HQ method gives us only the even part of the DF which contribute only to the density. In order to add rotation an odd part is needed. Adding an odd part to the DF is equivalent with reversing the sense of rotation of some stars. This won't affect the mass of the system nor the projected dispersions. Figure 2 shows how our best model predicts the VHs of proper motions for some combinations of cells. The results are overall very good. The model is able to predict the shape of the VPs in b direction (Schodel et al. (2009) tried to fit those with a Gaussian but the result was not good) and the double peak shape in l direction.

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