arXiv subjects

H. Baumgardt

Publications and source records attributed to H. Baumgardt.

At least 55 records · Page 3Linked to original sources

arXiv2009

How well do STARLAB and NBODY4 compare? I: Simple models

N-body simulations are widely used to simulate the dynamical evolution of a variety of systems, among them star clusters. Much of our understanding of their evolution rests on the results of such direct N-body simulations. They provide insight in the structural evolution of star clusters, as well as into the occurrence of stellar exotica. Although the major pure N-body codes STARLAB/KIRA and NBODY4 are widely used for a range of applications, there is no thorough comparison study yet. Here we thoroughly compare basic quantities as derived from simulations performed either with STARLAB/KIRA or NBODY4. We construct a large number of star cluster models for various stellar mass function settings (but without stellar/binary evolution, primordial binaries, external tidal fields etc), evolve them in parallel with STARLAB/KIRA and NBODY4, analyse them in a consistent way and compare the averaged results quantitatively. For this quantitative comparison we develop a bootstrap algorithm for functional dependencies. We find an overall excellent agreement between the codes, both for the clusters' structural and energy parameters as well as for the properties of the dynamically created binaries. However, we identify small differences, like in the energy conservation before core collapse and the energies of escaping stars, which deserve further studies. Our results reassure the comparability and the possibility to combine results from these two major N-body codes, at least for the purely dynamical models (i.e. without stellar/binary evolution) we performed. (abridged)

astro-ph.IM↗

arXiv2008

Dynamical mixing of two stellar populations in globular clusters

Stars in globular clusters (GCs) exhibit a peculiar chemical pattern with strong abundance variations in light elements along with a constant abundance in heavy elements. These abundance anomalies can be explained by a primordial pollution due to a first generation of fast rotating massive stars which released slow winds into the ISM from which a second generation of chemically anomalous stars can be formed. In particular the observed ratio of anomalous and standard stars in clusters can be used to constrain the dynamical evolution of GCs as around 95% of the standard stars need to be lost by the clusters. We show that both residual gas expulsion during the cluster formation and long term evolution are needed to achieve this ratio.

astro-ph↗

arXiv2008

The ages of Galactic globular clusters in the context of self-enrichment

A significant fraction of stars in globular clusters (about 70%-85%) exhibit peculiar chemical patterns with strong abundance variations in light elements along with constant abundances in heavy elements. These abundance anomalies can be created in the H-burning core of a first generation of fast rotating massive stars and the corresponding elements are convoyed to the stellar surface thanks to rotational induced mixing. If the rotation of the stars is fast enough this matter is ejected at low velocity through a mechanical wind at the equator. It then pollutes the ISM from which a second generation of chemically anomalous stars can be formed. The proportion of anomalous to normal star observed today depends on at least two quantities : (1) the number of polluter stars; (2) the dynamical history of the cluster which may lose during its lifetime first and second generation stars in different proportions. Here we estimate these proportions based on dynamical models for globular clusters. When internal dynamical evolution and dissolution due to tidal forces are accounted for, starting from an initial fraction of anomalous stars of 10% produces a present day fraction of about 25%, still too small with respect to the observed 70-85%. In case gas expulsion by supernovae is accounted for, much higher fraction is expected to be produced. In this paper we also address the question of the evolution of the second generation stars that are He-rich, and deduce consequences for the age determination of globular clusters.

astro-ph↗

arXiv2008

The evolution of two stellar populations in globular clusters I. The dynamical mixing timescale

We investigate the long-term dynamical evolution of two distinct stellar populations of low-mass stars in globular clusters in order to study whether the energy equipartition process can explain the high number of stars harbouring abundance anomalies seen in globular clusters. We analyse N-body models by artificially dividing the low-mass stars (m<0.9 Msun) into two populations: a small number of stars (second generation) consistent with an invariant IMF and with low specific energies initially concentrated towards the cluster-centre mimic stars with abundance anomalies. These stars form from the slow winds of fast-rotating massive stars. The main part of low-mass (first generation) stars has the pristine composition of the cluster. We study in detail how the two populations evolve under the influence of two-body elaxation and the tidal forces due to the host galaxy.Stars with low specific energy initially concentrated toward the cluster centre need about two relaxation times to achieve a complete homogenisation throughout the cluster. For realistic globular clusters, the number ratio between the two populations increases only by a factor 2.5 due to the preferential evaporation of the population of outlying first generation stars. We also find that the loss of information on the stellar orbital angular momentum occurs on the same timescale as spatial homogenisation.

astro-ph↗

arXiv2008

High M/L ratios of UCDs: a variation of the IMF?

Various studies have established that the dynamical M/L ratios of ultra-compact dwarf galaxies (UCDs) tend to be at the limit or beyond the range explicable by standard stellar populations with canonical IMF. We discuss how IMF variations may account for these high M/L ratios and how observational approaches may in the future allow to discriminate between those possibilities. We also briefly discuss the possibility of dark matter in UCDs.

astro-ph↗

arXiv2008

Lifetimes of tidally limited star clusters with different radii

We study the escape rate, dN/dt, from clusters with different radii in a tidal field using analytical predictions and direct N-body simulations. We find that dN/dt depends on the ratio R=r_h/r_j, where r_h is the half-mass radius and r_j the radius of the zero-velocity surface. For R>0.05, the "tidal regime", there is almost no dependence of dN/dt on R. To first order this is because the fraction of escapers per relaxation time, t_rh, scales approximately as R^1.5, which cancels out the r_h^1.5 term in t_rh. For R<0.05, the "isolated regime", dN/dt scales as R^-1.5. Clusters that start with their initial R, Ri, in the tidal regime dissolve completely in this regime and their t_dis is insensitive to the initial r_h. We predicts that clusters that start with Ri<0.05 always expand to the tidal regime before final dissolution. Their t_dis has a shallower dependence on Ri than what would be expected when t_dis is a constant times t_rh. For realistic values of Ri, the lifetime varies by less than a factor of 1.5 due to changes in Ri. This implies that the "survival" diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime t_dis scales as N^0.65/w, with w the angular frequency of the cluster in the host galaxy. [ABRIDGED]

astro-ph↗

arXiv2008

The shape of the initial cluster mass function: what it tells us about the local star formation efficiency

We explore how the expulsion of gas from star-cluster forming cloud-cores due to supernova explosions affects the shape of the initial cluster mass function, that is, the mass function of star clusters when effects of gas expulsion are over. We demonstrate that if the radii of cluster-forming gas cores are roughly constant over the core mass range, as supported by observations, then more massive cores undergo slower gas expulsion. Therefore, for a given star formation efficiency, more massive cores retain a larger fraction of stars after gas expulsion. The initial cluster mass function may thus differ from the core mass function substantially, with the final shape depending on the star formation efficiency. A mass-independent star formation efficiency of about 20 per cent turns a power-law core mass function into a bell-shaped initial cluster mass function, while mass-independent efficiencies of order 40 per cent preserve the shape of the core mass function.

astro-ph↗

arXiv2008

A new method to create initially mass segregated star clusters in virial equilibrium

Mass segregation stands as one of the most robust features of the dynamical evolution of self-gravitating star clusters. In this paper we formulate parametrised models of mass segregated star clusters in virial equilibrium. To this purpose we introduce mean inter-particle potentials for statistically described unsegregated systems and suggest a single-parameter generalisation of its form which gives a mass-segregated state. We describe an algorithm for construction of appropriate star cluster models. Their stability over several crossing-times is verified by following the evolution by means of direct N-body integration.

astro-ph↗

arXiv2007

The influence of residual gas expulsion on the evolution of the Galactic globular cluster system and the origin of the Population II halo

We present new results on the evolution of the mass function of the globular cluster system of the Milky Way, taking the effect of residual gas expulsion into account. We assume that gas embedded star clusters start with a power-law mass function with slope β=2. The dissolution of the clusters is then studied under the combined influence of residual gas expulsion driven by energy feedback from massive stars, stellar mass-loss, two-body relaxation and an external tidal field. The influence of residual gas expulsion is studied by applying results from a large grid of N-body simulations computed by Baumgardt & Kroupa (2007). In our model, star clusters with masses less than 10^5 M_sun lose their residual gas on timescales much shorter than their crossing time and residual gas expulsion is the main dissolution mechanism for star clusters, destroying about 95% of all clusters within a few 10s of Myr. We find that in this case the final mass function of globular clusters is established mainly by the gas expulsion and therefore nearly independent of the strength of the external tidal field, and that a power-law mass function for the gas embedded star clusters is turned into a present-day log-normal one. Another consequence of residual gas expulsion and the associated strong infant mortality of star clusters is that the Galactic halo stars come from dissolved star clusters. Since field halo stars would come mainly from low-mass, short-lived clusters, our model provides an explanation for the observed abundance variations of light elements among globular cluster stars and the absence of such variations among the halo field stars.

astro-ph↗

arXiv2007

UCDs - more massive than allowed?

Dynamical mass estimates of ultra-compact dwarfs galaxies and massive globular clusters in the Fornax and Virgo clusters and around the giant elliptical Cen A have revealed some surprising results: 1) above about 10^6 M_sun the mass-to-light (M/L) ratio increases with the objects' mass; 2) some UCDs/massive GCs show high M/L values (4 to 6) that are not compatible with standard stellar population models; and 3) in the luminosity-velocity dispersion diagram, UCDs deviate from the well defined relation of `normal' GCs, being more in line with the Faber-Jackson relation of early-type galaxies. In this contribution, we present the observational evidences for high mass-to-light ratios of UCDs and discuss possible explanations for them.

astro-ph↗

arXiv2006

Dynamical masses of ultra-compact dwarf galaxies in Fornax

Aims. We determine masses and mass-to-light ratios of five ultra-compact dwarf galaxies and one dwarf elliptical nucleus in the Fornax cluster from high resolution spectroscopy. Methods. Velocity dispersions were derived from selected wavelength regions using a direct-fitting method. To estimate the masses of the UCDs a new modelling program has been developed that allows a choice of different representations of the surface brightness profile (i.e. Nuker, Sersic or King laws) and corrects the observed velocity dispersions for observational parameters (i.e. seeing, slit size). Results. The observed velocity dispersions range between 22 and 30 km/s. The resulting masses are between 1.8 and 9.5x10^7M_sun. These, as well as the central and global projected velocity dispersions, were derived from the generalized King model which turned out to give the most stable results. The masses of two UCDs, that are best fitted by a two-component profile, were derived from a combined King+Sersic model. The mass-to-light ratios of the Fornax UCDs range between 3 and 5 (M/L_V)_sun. Within 1-2 half-mass radii dark matter is not dominating UCDs. Conclusions. We show that the mass-to-light ratios of UCDs in Fornax are consistent with those expected for pure stellar populations. Thus UCDs seem to be the result of cluster formation processes within galaxies rather than being compact dark matter dominated substructures themselves. Whether UCDs gained their mass in super-star cluster complexes of mergers or in nuclear star cluster formation processes remains an open question. It appears, however, clear that star clusters more massive than about 5\times10^6M_sun exhibit a more complex formation history than the less massive `ordinary' globular clusters.

astro-ph↗

arXiv2006

Neutron Stars and Black Holes in Star Clusters

This article was co-authored by all invited speakers at the Joint Discussion on `Neutron Stars and Black Holes in Star Clusters,' which took place during the IAU General Assembly in Prague, Czech Republic, on August 17 and 18, 2006. Each section presents a short summary of recent developments in a key area of research, incorporating the main ideas expressed during the corresponding panel discussion at the meeting. Our meeting, which had close to 300 registered participants, was broadly aimed at the large community of astronomers around the world working on the formation and evolution of compact objects and interacting binary systems in dense star clusters, such as globular clusters and galactic nuclei. Great advances have occurred in this field during the past few years, including the introduction of fundamentally new theoretical paradigms for the formation and evolution of compact objects in binaries as well as countless new discoveries by astronomers that have challenged many accepted models. Some of the highlights include: a nearly complete census of all the millisecond pulsars in 47 Tuc; first detections of many new radio pulsars in other clusters, particularly Terzan 5; detailed studies of X-ray binary populations and their luminosity functions in many galaxies and extragalactic globular clusters; increasing evidence for intermediate-mass black holes in clusters and greatly improved theoretical understanding of their possible formation processes.

astro-ph↗

arXiv2006

Star cluster disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N-body simulations of cluster-GMC encounters and excellent agreement is found. The fractional mass loss from the cluster is 0.25 times the fractional energy gain. This is because 75% of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We derive an expression for the cluster disruption time (t_dis) based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. The disruption time depends on the cluster mass (M_c) and half-mass radius (r_h) as t_dis=2.0 S (M_c/10^4 M_sun)(3.75 pc/r_h)^3 Gyr, with S=1 for the solar neighbourhood and inversely proportional to the GMC density. The observed shallow relation between cluster radius and mass gives t_dis a power-law dependence on the mass with index 0.7, similar to that found from observations and from simulations of clusters dissolving in tidal fields (0.62). The constant of 2.0 Gyr is about a factor of 3.5 shorter than found from earlier simulations of clusters dissolving under the combined effect of galactic tidal field and stellar evolution. It is somewhat higher than the observationally determined value of 1.3 Gyr. It suggests, however, that the combined effect of tidal field and encounters with GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC encounters can also explain the (very) short disruption time that was observed for star clusters in the central region of M51, since there rho_n is an order of magnitude higher than in the solar neighbourhood.

astro-ph↗

arXiv2005

Tidal Capture of Stars by Intermediate-Mass Black Holes

Recent X-ray observations and theoretical modelling have made it plausible that some ultraluminous X-ray sources (ULX) are powered by intermediate-mass black holes (IMBHs). N-body simulations have also shown that runaway merging of stars in dense star clusters is a way to form IMBHs. In the present paper we have performed N-body simulations of young clusters such as MGG-11 of M82 in which IMBHs form through runaway merging. We took into account the effect of tidal heating of stars by the IMBH to study the tidal capture and disruption of stars by IMBHs. Our results show that the IMBHs have a high chance of capturing stars through tidal heating within a few core relaxation times and we find that 1/3 of all runs contain a ULX within the age limits of MGG-11, a result consistent with the fact that a ULX is found in this galaxy. Our results strengthen the case for some ULX being powered by intermediate-mass black holes.

astro-ph↗

arXiv2005

Using distant globular clusters as a test for gravitational theories

We propose to determine the stellar velocity dispersions of globular clusters in the outer halo of the Milky Way in order to decide whether the dynamics of the universe on large scales is governed by dark matter or modified Newtonian dynamics (MOND). We show that for a number of galactic globular clusters, both the internal and the external accelerations are significantly below the critical acceleration parameter $a_0$ of MOND. This leads to velocity dispersions in case of MOND which exceed their Newtonian counterparts by up to a factor of 3, providing a stringent test for MOND. Alternatively, in case high velocity dispersions are found, these would provide the first evidence that globular clusters are dark matter dominated.

astro-ph↗

arXiv2004

Theoretical and Observational Agreement on Mass Dependence of Cluster Life Times

Observations and N-body simulations both support a simple relation for the disruption time of a cluster as a function of its mass of the form: t_dis = t_4 * (M/10^4 Msun)^gamma. The scaling factor t_4 seems to depend strongly on the environment. Predictions and observations show that gamma ~ 0.64 +/- 0.06. Assuming that t_dis ~ M^0.64 is caused by evaporation and shocking implies a relation between the radius and the mass of a cluster of the form: r_h ~ M^0.07, which has been observed in a few galaxies. The suggested relation for the disruption time implies that the lower mass end of the cluster initial mass function will be disrupted faster than the higher mass end, which is needed to evolve a young power law shaped mass function into the log-normal mass function of old (globular) clusters.

astro-ph↗

arXiv2003

Dynamical Formation of Close Binary Systems in Globular Clusters

We know from observations that globular clusters are very efficient catalysts in forming unusual short-period binary systems or their offspring, such as low-mass X-ray binaries (LMXBs; neutron stars accreting matter from low-mass stellar companions), cataclysmic variables (CVs; white dwarfs accreting matter from stellar companions), and millisecond pulsars (MSPs; rotating neutron stars with spin periods of a few ms). Although there has been little direct evidence, the overabundance of these objects in globular clusters has been attributed by numerous authors to the high densities in the cores, which leads to an increase in the formation rate of exotic binary systems through close stellar encounters. Many such close binary systems emit X-radiation at low luminosities (L_x < 10^{34} erg/s) and are being found in large numbers through observations with the Chandra X-ray Observatory. Here we present conclusive observational evidence for a link between the number of close binaries observed in X-rays in a globular cluster and the stellar encounter rate of the cluster. We also make an estimate of the total number of LMXBs in globular clusters in our Galaxy.

astro-ph↗

arXiv2002

On the central structure of M15

We present a detailed comparison between the latest observational data on the kinematical structure of the core of M15, obtained with the Hubble STIS and WFPC2 instruments, and the results of dynamical simulations carried out using the special-purpose GRAPE-6 computer. The observations imply the presence of a significant amount of dark matter in the cluster core. In our dynamical simulations, neutron stars and/or massive white dwarfs concentrate to the center through mass segregation, resulting in a sharp increase in $M/L$ toward the center. While consistent with the presence of a central black hole, the Hubble data can also be explained by this central concentration of stellar-mass compact objects. The latter interpretation is more conservative, since such remnants result naturally from stellar evolution, although runaway merging leading to the formation of a black hole may also occur for some range of initial conditions. We conclude that no central massive object is required to explain the observational data, although we cannot conclusively exclude such an object at the level of $\sim500-1000$ solar masses. Our findings are unchanged when we reduce the assumed neutron-star retention fraction in our simulations from 100% to 0%.

astro-ph↗