156 research outputs found
N-body modeling of globular clusters: Masses, mass-to-light ratios and intermediate-mass black holes
We have determined the masses and mass-to-light ratios of 50 Galactic
globular clusters by comparing their velocity dispersion and surface brightness
profiles against a large grid of 900 N-body simulations of star clusters of
varying initial concentration, size and central black hole mass fraction. Our
models follow the evolution of the clusters under the combined effects of
stellar evolution and two-body relaxation allowing us to take the effects of
mass segregation and energy equipartition between stars self-consistently into
account. For a subset of 16 well observed clusters we also derive their
kinematic distances. We find an average mass-to-light ratio of Galactic
globular clusters of , which agrees very well with the
expected M/L ratio if the initial mass function of the clusters was a standard
Kroupa or Chabrier mass function. We do not find evidence for a decrease of the
average mass-to-light ratio with metallicity. The surface brightness and
velocity dispersion profiles of most globular clusters are incompatible with
the presence of intermediate-mass black holes (IMBHs) with more than a few
thousand in them. The only clear exception is Cen, where the
velocity dispersion profile provides strong evidence for the presence of a
40,000 IMBH in the centre of the cluster.Comment: 31 pages, 21 figures, accepted for publication in MNRA
The Global Mass Functions of 35 Galactic globular clusters: II. Clues on the Initial Mass Function and Black Hole Retention Fraction
In this paper we compare the mass function slopes of Galactic globular
clusters recently determined by Sollima & Baumgardt (2017) with a set of
dedicated N-body simulations of star clusters containing between 65,000 to
200,000 stars. We study clusters starting with a range of initial mass
functions (IMFs), black hole retention fractions and orbital parameters in the
parent galaxy. We find that the present-day mass functions of globular clusters
agree well with those expected for star clusters starting with Kroupa or
Chabrier IMFs, and are incompatible with clusters starting with single
power-law mass functions for the low-mass stars. The amount of mass segregation
seen in the globular clusters studied by Sollima & Baumgardt (2017) can be
fully explained by two-body relaxation driven mass segregation from initially
unsegregated star clusters. Based on the present-day global mass functions, we
expect that a typical globular cluster in our sample has lost about 75% of its
mass since formation, while the most evolved clusters have already lost more
than 90% of their initial mass and should dissolve within the next 1 to 2 Gyr.
Most clusters studied by Sollima & Baumgardt also show a large difference
between their central and global MF slopes, implying that the majority of
Galactic globular clusters is either near or already past core collapse. The
strong mass segregation seen in most clusters also implies that only a small
fraction of all black holes formed in globular clusters still reside in them.Comment: 8 pages, 6 figures, MNRAS, 472, 74
Testing Photometric Diagnostics for the Dynamical State and Possible IMBH presence in Globular Clusters
Surface photometry is a necessary tool to establish the dynamical state of
stars clusters. We produce realistic HST-like images from N-body models of star
clusters with and without central intermediate-mass black holes (IMBHs) in
order to measure their surface brightness profiles. The models contain ~600,000
individual stars, black holes of various masses between 0% to 2% of the total
mass, and are evolved for a Hubble time. We measure surface brightness and star
count profiles for every constructed image in order to test the effect of
intermediate mass black holes on the central logarithmic slope, the core
radius, and the half-light radius. We use these quantities to test diagnostic
tools for the presence of central black holes using photometry. We find that
the the only models that show central shallow cusps with logarithmic slopes
between -0.1 and -0.4 are those containing central black holes. Thus, the
central logarithmic slope seems to be a good way to choose clusters suspect of
containing intermediate-mass black holes. Clusters with steep central cusps can
definitely be ruled out to host an IMBH. The measured r_c/r_h ratio has similar
values for clusters that have not undergone core-collapse, and those containing
a central black hole. We notice that observed Galactic globular clusters have a
larger span of values for central slope and r_c/r_h than our modeled clusters,
and suggest possible reasons that could account for this and contribute to
improve future models.Comment: Accepted for publication in Ap
Dynamical Constraints on the Origin of Multiple Stellar Populations in Globular Clusters
We have carried out a large grid of N-body simulations in order to
investigate if mass-loss as a result of primordial gas expulsion can be
responsible for the large fraction of second generation stars in globular
clusters (GCs) with multiple stellar populations (MSPs). Our clusters start
with two stellar populations in which of all stars are second generation
stars. We simulate clusters with different initial masses, different ratios of
the half-mass radius of first to second generation stars, different primordial
gas fractions and Galactic tidal fields with varying strength. We then let our
clusters undergo primordial gas-loss and obtain their final properties such as
mass, half-mass radius and the fraction of second generation stars. Using our
N-body grid we then perform a Monte Carlo analysis to constrain the initial
masses, radii and required gas expulsion time-scales of GCs with MSPs. Our
results can explain the present-day properties of GCs only if (1) a substantial
amount of gas was present in the clusters after the formation of second
generation stars and (2) gas expulsion time-scales were extremely short
( yr). Such short gas expulsion time-scales are in agreement
with recent predictions that dark remnants have ejected the primordial gas from
globular clusters, and pose a potential problem for the AGB scenario. In
addition, our results predict a strong anti-correlation between the number
ratio of second-generation stars in GCs and the present-day mass of GCs. So
far, the observational data show only a significantly weaker anti-correlation,
if any at all.Comment: 14 pages, 6 figures, 3 tables, typos corrected. Accepted for
publication in MNRA
Catch me if you can: is there a runaway-mass black hole in the Orion Nebula Cluster?
We investigate the dynamical evolution of the Orion Nebula Cluster (ONC) by
means of direct N-body integrations. A large fraction of residual gas was
probably expelled when the ONC formed, so we assume that the ONC was much more
compact when it formed compared to its current size, in agreement with the
embedded cluster radius-mass relation from Marks & Kroupa (2012). Hence, we
assume that few-body relaxation played an important role during the initial
phase of evolution of the ONC. In particular, three body interactions among OB
stars likely led to their ejection from the cluster and, at the same time, to
the formation of a massive object via runaway physical stellar collisions. The
resulting depletion of the high mass end of the stellar mass function in the
cluster is one of the important points where our models fit the observational
data. We speculate that the runaway-mass star may have collapsed directly into
a massive black hole (Mbh > 100Msun). Such a dark object could explain the
large velocity dispersion of the four Trapezium stars observed in the ONC core.
We further show that the putative massive black hole is likely to be a member
of a binary system with appr. 70 per cent probability. In such a case, it could
be detected either due to short periods of enhanced accretion of stellar winds
from the secondary star during pericentre passages, or through a measurement of
the motion of the secondary whose velocity would exceed 10 km/s along the whole
orbit.Comment: 10 pages, 6 figures, accepted by Ap
Long-term evolution of isolated N-body sytems
We report results of N-body simulations of isolated star clusters, performed
up to the point where the clusters are nearly completely dissolved. Our main
focus is on the post-collapse evolution of these clusters. We find that after
core collapse, isolated clusters evolve along nearly a single sequence of
models whose properties are independent of the initial density profile and
particle number. Due to the slower expansion of high-N clusters, relaxation
times become almost independent of the particle number after several core
collapse times, at least for the particle range of our study. As a result, the
dissolution times of isolated clusters exhibit a surprisingly weak dependence
on N.
We find that most stars escape due to encounters between single stars inside
the half-mass radius of the cluster. Encounters with binaries take place mostly
in the cluster core and account for roughly 15% of all escapers. Encounters
between single stars at intermediate radii are also responsible for the build
up of a radial anisotropic velocity distribution in the halo. For clusters
undergoing core oscillations, escape due to binary stars is efficient only when
the cluster center is in a contracted phase. Our simulations show that it takes
about 10^5 N-body time units until the global anisotropy reaches its maximum
value. The anisotropy increases with particle number and it seems conceivable
that isolated star clusters become vulnerable to radial orbit instabilities for
large enough N. However, no indication for the onset of such instabilities was
seen in our runs.Comment: 14 pages, 20 figures, MNRAS in press, V2: Order of authors changed in
author-fiel
The distribution of stars around the Milky Way's black hole III: Comparison with simulations
The distribution of stars around a massive black hole (MBH) has been
addressed in stellar dynamics for the last four decades by a number of authors.
Because of its proximity, the centre of the Milky Way is the only observational
test case where the stellar distribution can be accurately tested. Past
observational work indicated that the brightest giants in the Galactic Centre
(GC) may show a density deficit around the central black hole, not a cusp-like
distribution, while we theoretically expect the presence of a stellar cusp. We
here present a solution to this long-standing problem. We performed
direct-summation body simulations of star clusters around massive black
holes and compared the results of our simulations with new observational data
of the GC's nuclear cluster. We find that after a Hubble time, the distribution
of bright stars as well as the diffuse light follow power-law distributions in
projection with slopes of in our simulations. This is in
excellent agreement with what is seen in star counts and in the distribution of
the diffuse stellar light extracted from adaptive-optics (AO) assisted
near-infrared observations of the GC. Our simulations also confirm that there
exists a missing giant star population within a projected radius of a few
arcsec around Sgr A*. Such a depletion of giant stars in the innermost 0.1 pc
could be explained by a previously present gaseous disc and collisions, which
means that a stellar cusp would also be present at the innermost radii, but in
the form of degenerate compact cores.Comment: Accepted for publication, few typos fixe
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