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Holger Baumgardt

Publications and source records attributed to Holger Baumgardt.

At least 127 records · Page 7Linked to original sources

On the number of young stellar discs in the Galactic Centre

Observations of the Galactic Centre show evidence of disc-like structures of very young stars orbiting the central super-massive black hole within a distance of a few 0.1 pc. While it is widely accepted that about half of the stars form a relatively flat disc rotating clockwise on the sky, there is a substantial ongoing debate on whether there is a second, counter-clockwise disc of stars. By means of N-body simulations using our bhint code, we show that two highly inclined stellar discs with the observed properties cannot be recognised as two flat circular discs after 5 Myr of mutual interaction. Instead, our calculations predict a significant warping of the two discs, which we show to be apparent among the structures observed in the Galactic Centre. While the high eccentricities of the observed counter-clockwise orbits suggest an eccentric origin of this system, we show the eccentricity distribution in the inner part of the more massive clockwise disc to be perfectly consistent with an initially circular disc in which stellar eccentricities increase due to both non-resonant and resonant relaxation. We conclude that the relevant question to ask is therefore not whether there are two discs of young stars, but whether there were two such discs to begin with.

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High mass-to-light ratios of UCDs - Evidence for dark matter ?

Ultra-compact dwarf galaxies (UCDs) are stellar systems with masses of around 10^7 to 10^8 Msun and half mass radii of 10-100 pc. They have some properties in common with massive globular clusters, however dynamical mass estimates have shown that UCDs have mass-to-light ratios which are on average about twice as large than those of globular clusters at comparable metallicity, and tend to be larger than what one would expect for old stellar systems with standard mass functions. One possible explanation for elevated high mass-to-light ratios in UCDs is the existence of a substantial amount of dark matter, which could have ended up in UCDs if they are the remnant nuclei of tidally stripped dwarf galaxies. Tidal stripping of dwarf galaxies has also been suggested has the origin of several massive globular clusters like Omega Cen, in which case globular clusters could have also formed with substantial amounts of dark matter. In this paper, we present collisional N-body simulations which study the co-evolution of a system composed out of stars and dark matter. We find that the dark matter gets removed from the central regions of such systems due to dynamical friction and mass segregation of stars. The friction timescale is significantly shorter than a Hubble time for typical globular clusters, while most UCDs have friction times much longer than a Hubble time. Therefore, a significant dark matter fraction remains within the half-mass radius of present-day UCDs, making dark matter a viable explanation for the elevated M/L ratios of UCDs. If at least some globular clusters formed in a way similar to UCDs, we predict a substantial amount of dark matter in their outer parts.

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Origin of the S Stars in the Galactic Center

Over the last 15 years, around a hundred very young stars have been observed in the central parsec of our Galaxy. While the presence of young stars forming one or two stellar disks at approx. 0.1 pc from the supermassive black hole (SMBH) can be understood through star formation in accretion disks, the origin of the S stars observed a factor of 10 closer to the SMBH has remained a major puzzle. Here we show the S stars to be a natural consequence of dynamical interaction of two stellar disks at larger radii. Due to precession and Kozai interaction, individual stars achieve extremely high eccentricities at random orientation. Stellar binaries on such eccentric orbits are disrupted due to close passages near the SMBH, leaving behind a single S star on a much tighter orbit. The remaining star may be ejected from the vicinity of the SMBH, thus simultaneously providing an explanation for the observed hypervelocity stars in the Milky Way halo.

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The Nature of UCDs: Internal Dynamics from an Expanded Sample and Homogeneous Database

We have obtained high-resolution spectra of 23 ultra-compact dwarf galaxies (UCDs) in the Fornax cluster with -10.4>M_V>-13.5 mag (10^6 2*10^6 M_*) have M/L ratios twice as large as GCs (M < 2*10^6 M_*). We show that stellar population models tend to under-predict dynamical M/L ratios of UCDs and over-predict those of GCs. Considering the scaling relations of stellar spheroids, UCDs align well along the 'Fundamental Manifold', constituting the small-scale end of the galaxy sequence. The alignment for UCDs is especially clear for r_e >~ 7 pc, which corresponds to dynamical relaxation times that exceed a Hubble time. In contrast, GCs exhibit a broader scatter and do not appear to align along the manifold. We argue that UCDs are the smallest dynamically un-relaxed stellar systems, with M > 2*10^6 M_* and 7<r_e<100 pc. Future studies should aim at explaining the elevated M/L ratios of UCDs and the environmental dependence of their properties.

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The Main Sequence of Star Clusters

A novel way of looking at the evolution of star clusters is presented. With a dynamical temperature, given by the mean kinetic energy of the cluster stars, and a dynamical luminosity, which is defined as the kinetic energy of the stars leaving the cluster in analogy to the energy of photons emitted by a star, the dissolution of star clusters is studied using a new dynamical temperature-luminosity diagram for star clusters. The investigation contains a parameter-space study of open clusters of up to N = 32768 single-mass stars with different initial density distributions, half-mass radii, tidal conditions and binary fractions. The clusters show a strong correlation between dynamical temperature and dynamical luminosity and most of the investigated cluster families share a common sequence in such a dynamical temperature-luminosity diagram. Deviations from this sequence are analyzed and discussed. After core collapse, the position of a cluster within this diagram can be defined by three parameters: the mass, the tidal conditions and the binary fraction. Due to core collapse all initial conditions are lost and the remaining stars adjust to the given tidal conditions. Binaries as internal energy sources influence this adjustment. A further finding concerns the Lagrange radii of star clusters: Throughout the investigated parameter space nearly all clusters show a constant half-mass radius for the time after core collapse until dissolution. Furthermore, the ratio of half-mass radius to tidal radius evolves onto a common sequence which only depends on the mass left in the cluster.

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Evidence for primordial mass segregation in globular clusters

We have studied the dissolution of initially mass segregated and unsegregated star clusters due to two-body relaxation in external tidal fields, using Aarseth's collisional N-body code NBODY4 on GRAPE6 special-purpose computers. When extrapolating results of initially not mass segregated models to globular clusters, we obtain a correlation between the time until destruction and the slope of the mass function, in the sense that globular clusters which are closer to dissolution are more strongly depleted in low-mass stars. This correlation fits observed mass functions of most globular clusters. The mass functions of several globular clusters are however more strongly depleted in low-mass stars than suggested by these models. Such strongly depleted mass functions can be explained if globular clusters started initially mass segregated. Primordial mass segregation also explains the correlation between the slope of the stellar mass function and the cluster concentration which was recently discovered by De Marchi et al. (2007). In this case, it is possible that all globular clusters started with a mass function similar to that seen in young open clusters in the present-day universe, at least for stars below m=0.8 Msun. This argues for a near universality of the mass function for different star formation environments and metallicities in the range -2 < [Fe/H] < 0. We finally describe a novel algorithm which can initialise stationary mass segregated clusters with arbitrary density profile and amount of mass segregation.

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The influence of initial mass segregation on the runaway merging of stars

We have investigated the effect of initial mass segregation on the runaway merging of stars. The evolution of multi-mass, dense star clusters was followed by means of direct N-body simulations of up to 131.072 stars. All clusters started from King models with dimensionless central potentials of 3.0 <= W_0 <= 9.0. Initial mass segregation was realized by varying the minimum mass of a certain fraction of stars whose either (1) distances were closest to the cluster center or (2) total energies were lowest. The second case is more favorable to promote the runaway merging of stars by creating a high-mass core of massive, low-energy stars. Initial mass segregation could decrease the central relaxation time and thus help the formation of a high-mass core. However, we found that initial mass segregation does not help the runaway stellar merger to happen if the overall mass density profile is kept constant. This is due to the fact that the collision rate of stars is not increased due to initial mass segregation. Our simulations show that initial mass segregation is not sufficient to allow runaway merging of stars to occur in clusters with central densities typical for star clusters in the Milky Way.

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Tracing intermediate-mass black holes in the Galactic Centre

We have developed a new method for post-Newtonian, high-precision integration of stellar systems containing a super-massive black hole (SMBH), splitting the forces on a particle between a dominant central force and perturbations. We used this method to perform fully collisional N-body simulations of inspiralling intermediate-mass black holes (IMBHs) in the centre of the Milky Way. We considered stellar cusps of different power-law indices and analysed the effects of IMBHs of different masses, all starting from circular orbits at an initial distance of 0.1 pc. Our simulations show how IMBHs deplete the central cusp of stars, leaving behind a flatter cusp with slope consistent with what has recently been observed. If an additional IMBH spirals into such a flat cusp, it can take 50 Myr or longer to merge with the central SMBH, thus allowing for direct observation in the near future. The final merger of the two black holes involves gravitational wave radiation which may be observable with planned gravitational wave detectors. Furthermore, our simulations reveal detailed properties of the hypervelocity stars (HVSs) created, and how generations of HVSs can be used to trace IMBHs in the Galactic Centre. We find that significant rotation of HVSs (which would be evidence for an IMBH) can only be expected among very fast stars (v > 1000 km/s). Also, the probability of creating a hypervelocity binary star is found to be very small.

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The influence of gas expulsion and initial mass-segregation on the stellar mass-function of globular star clusters

Recently de Marchi, Paresce & Pulone (2007) studied a sample of twenty globular clusters and found that all clusters with high concentrations have steep stellar mass-functions while clusters with low concentration have comparatively shallow mass-functions. No globular clusters were found with a flat mass-function and high concentration. This seems curious since more concentrated star clusters are believed to be dynamically more evolved and should have lost more low-mass stars via evaporation, which would result in a shallower mass-function in the low-mass part. We show that this effect can be explained by residual-gas expulsion from initially mass-segregated star clusters, and is enhanced further through unresolved binaries. If gas expulsion is the correct mechanism to produce the observed trend, then observation of these parameters would allow to constrain cluster starting conditions such as star formation efficiency and the time-scale of gas expulsion.

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Star cluster life-times: dependence on mass, radius and environment

The dissolution time (t_dis) of clusters in a tidal field does not scale with the ``classical'' expression for the relaxation time. First, the scaling with N, and hence cluster mass, is shallower due to the finite escape time of stars. Secondly, the cluster half-mass radius is of little importance. This is due to a balance between the relative tidal field strength and internal relaxation, which have an opposite effect on t_dis, but of similar magnitude. When external perturbations, such as encounters with giant molecular clouds (GMC) are important, t_dis for an individual cluster depends strongly on radius. The mean dissolution time for a population of clusters, however, scales in the same way with mass as for the tidal field, due to the weak dependence of radius on mass. The environmental parameters that determine t_dis are the tidal field strength and the density of molecular gas. We compare the empirically derived t_dis of clusters in six galaxies to theoretical predictions and argue that encounters with GMCs are the dominant destruction mechanism. Finally, we discuss a number of pitfalls in the derivations of t_dis from observations, such as incompleteness, with the cluster system of the SMC as particular example.

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N-body simulations of star clusters

Two aspects of our recent N-body studies of star clusters are presented: (1) What impact does mass segregation and selective mass loss have on integrated photometry? (2) How well compare results from N-body simulations using NBODY4 and STARLAB/KIRA?

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On the efficiency of field star capture by star clusters

An exciting recent finding regarding scaling relations among globular clusters is the so-called 'blue tilt': clusters of the blue sub-population follow a trend of redder colour with increasing luminosity. In this paper we evaluate to which extent field star capture over a Hubble time may explain the 'blue tilt'. We perform collisional N-body simulations to quantify the amount of field star capture occuring over a Hubble time to star clusters with 10^3 to 10^6 stars. In the simulations we follow the orbits of field stars passing through a star cluster and calculate the energy change that the field stars experience due to gravitational interaction with cluster stars during one passage through the cluster. The capture condition is that their total energy after the passage is smaller than the gravitational potential at the cluster's tidal radius. By folding this with the fly-by rates of field stars with an assumed space density as in the solar neighbourhood and a range of velocity dispersions, we derive estimates on the mass fraction of captured field stars as a function of environment. We find that integrated over a Hubble time, the ratio between captured field stars and total number of clusters stars is very low (<~ 10^(-4)), even for the smallest considered field star velocity dispersion sigma=15 km/s. This holds for star clusters in the mass range of both open clusters and globular clusters. We furthermore show that tidal friction has a negligible effect on the energy distribution of field stars after interaction with the cluster. We conclude that field star capture is not a probable mechanism for creating the colour-magnitude trend of metal-poor globular clusters.

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A comprehensive set of simulations studying the influence of gas expulsion on star cluster evolution

We have carried out a large set of N-body simulations studying the effect of residual-gas expulsion on the survival rate and final properties of star clusters. We have varied the star formation efficiency, gas expulsion timescale and strength of the external tidal field, obtaining a three-dimensional grid of models which can be used to predict the evolution of individual star clusters or whole star cluster systems by interpolating between our runs. The complete data of these simulations is made available on the Internet. Our simulations show that cluster sizes, bound mass fraction and velocity profile are strongly influenced by the details of the gas expulsion. Although star clusters can survive star formation efficiencies as low as 10% if the tidal field is weak and the gas is removed only slowly, our simulations indicate that most star clusters are destroyed or suffer dramatic loss of stars during the gas removal phase. Surviving clusters have typically expanded by a factor 3 or 4 due to gas removal, implying that star clusters formed more concentrated than as we see them today. Maximum expansion factors seen in our runs are around 10. If gas is removed on timescales smaller than the initial crossing time, star clusters acquire strongly radially anisotropic velocity dispersions outside their half-mass radii. Observed velocity profiles of star clusters can therefore be used as a constraint on the physics of cluster formation.

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Evolution of Collisionally Merged Massive Stars

We investigate the evolution of collisionally merged stars with mass of ~100 MSun which might be formed in dense star clusters. We assumed that massive stars with several tens Msun collide typically after ~1Myr of the formation of the cluster and performed hydrodynamical simulations of several collision events. Our simulations show that after the collisions, merged stars have extended envelopes and their radii are larger than those in the thermal equilibrium states and that their interiors are He-rich because of the stellar evolution of the progenitor stars. We also found that if the mass-ratio of merging stars is far from unity, the interior of the merger product is not well mixed and the elemental abundance is not homogeneous. We then followed the evolution of these collision products by a one dimensional stellar evolution code. After an initial contraction on the Kelvin-Helmholtz (thermal adjustment) timescale (~1000-10000 yr), the evolution of the merged stars traces that of single homogeneous stars with corresponding masses and abundances, while the initial contraction phase shows variations which depend on the mass ratio of the merged stars. We infer that, once runaway collisions have set in, subsequent collisions of the merged stars take place before mass loss by stellar winds becomes significant. Hence, stellar mass loss does not inhibit the formation of massive stars with mass of ~1000Msun.

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The core radius of a star cluster containing a massive black hole

(Simplified) We present a theoretical framework which establishes how the core radius of a star cluster varies with the mass of an assumed central black hole. Our result is that the ratio of core to half-mass radius varies as the 3/4 power of the ratio of the black hole to cluster mass, when the system is well relaxed. The theory compares favourably with a number of simulations of this problem, which extend to black hole masses of order 10% of the cluster mass. Though strictly limited as yet to clusters with stars of equal mass, our conclusion strengthens the view that clusters with large core radii are the most promising candidates in which to find a massive black hole.

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Observational templates of star cluster disruption. The stellar group NGC 1901 in front of the Large Magellanic Cloud

Observations indicate that present-day star formation in the Milky Way disk takes place in stellar ensembles or clusters rather than in isolation. Bound, long lived stellar groups are known as open clusters. They gradually lose stars and in their final evolutionary stages they are severely disrupted leaving an open cluster remnant made of a few stars. In this paper, we study in detail the stellar content and kinematics of the poorly populated star cluster NGC1901. This object appears projected against the Large Magellanic Cloud. The aim of the present work is to derive the current evolutionary status, binary fraction, age and mass of this stellar group. These are fundamental quantities to compare with those from N-body models in order to study the most general topic of star cluster evolution and dissolution.The analysis is performed using wide-field photometry in the UBVI pass-band, proper motions from the UCAC.2 catalog, and 3 epochs of high resolution spectroscopy, as well as results from extensive N-body calculations.The star group NGC1901 is found to be an ensemble of solar metallicity stars, 400+/-100 Myr old, with a core radius of 0.23 pc, a tidal radius of 1.0 pc, and located at 400+/-50 pc from the Sun. Out of 13 confirmed members, only 5 single stars have been found. Its estimated present-day binary fraction is at least 62%. The calculated heliocentric space motion of the cluster is not compatible with possible membership in the Hyades stream.Our results show that NGC1901 is a clear prototype of open cluster remnant characterized by a large value of the binary fraction and a significant depletion of low-mass stars. In the light of numerical simulations, this is compatible with NGC1901 being what remains of a larger system initially made of 500-750 stars.

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Ejection of Hyper-Velocity Stars from the Galactic Centre by Intermediate-Mass Black Holes

We have performed N-body simulations of the formation of hyper-velocity stars (HVS) in the centre of the Milky Way due to inspiralling intermediate-mass black holes (IMBHs). We considered IMBHs of different masses, all starting from circular orbits at an initial distance of 0.1 pc. We find that the IMBHs sink to the centre of the Galaxy due to dynamical friction, where they deplete the central cusp of stars. Some of these stars become HVS and are ejected with velocities sufficiently high to escape the Galaxy. Since the HVS carry with them information about their origin, in particular in the moment of ejection, the velocity distribution and the direction in which they escape the Galaxy, detecting a population of HVS will provide insight in the ejection processes and could therefore provide indirect evidence for the existence of IMBHs. Our simulations show that HVS are generated in short bursts which last only a few Myrs until the IMBH is swallowed by the supermassive black hole (SMBH). HVS are ejected almost isotropically, which makes IMBH induced ejections hard to distinguish from ejections due to encounters of stellar binaries with a SMBH. After the HVS have reached the galactic halo, their escape velocities correlate with the distance from the Galactic centre in the sense that the fastest HVS can be found furthest away from the centre. The velocity distribution of HVS generated by inspiralling IMBHs is also nearly independent of the mass of the IMBH and can be quite distinct from one generated by binary encounters. Finally, our simulations show that the presence of an IMBH in the Galactic centre changes the stellar density distribution inside r<0.02 pc into a core profile, which takes at least 100 Myrs to replenish.

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Dissolution of Globular Clusters

Globular clusters are among the oldest objects in galaxies, and understanding the details of their formation and evolution can bring valuable insight into the early history of galaxies. This review summarises the current knowledge about the dissolution of star clusters and discusses the implications of star cluster dissolution for the evolution of the mass function of star cluster systems in galaxies.

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