Annual Report 2011 Max Planck Institute for Astronomy

62 III. Selected Research Areas
q
0.9
0.86
0.82
0.9
0.86
0.82
a)
c)
–0.3
–0.2 –0.1 0
Fig. III.3.5: Posterior distribution for median projected axis ratio
(shape) versus velocity anisotropy at the end of an MCMC
run for Centauri with the points coloured according to their
likelihood (red high, blue low). a): likelihood for x proper
motions only, b) likelihood for y proper motions only, c) likelihood
for line-of-sight velocities only, d) total likelihood. The
foreground or background population) are removed via
a series of cuts before proceeding with the modeling;
this is a tricky process – make the cuts too conservative
and true members will be excised as well as the
contaminants, make the cuts too generous and contaminants
will still remain. A better approach is to include
all stars in a model, both likely members and suspected
contaminants, and allow for the presence of a contaminant
population in the likelihood calculations. As our
models have many parameters a simple grid search is
not feasible, so we turn to Markov-Chain Monte Carlo
(MCMC) methods in order to sample the large parameter
space efficiently.
One prime example that highlights what we are currently
able to achieve is the Galactic globular cluster
w Centauri. Located only 5 kpc from the Sun, it is large
and bright and has been observed many times with many
different instruments, over a long time baseline. As a result,
there are line-of-sight velocities and metal abundances
available for thousands of stars, and proper motions
measurements available for hundreds of thousands
0.1
ln L x
ln L z
b)
d)
ln L y
ln L total
0.2 –0.3
b
–0.2 –0.1 0 0.1 0.2
degeneracy between shape and anisotropy is seen in the scatter
of the points. It is clear from the first three panels that the
individual velocities do not converge on the correct answer;
however their combination (as shown in panel d) does break
the degeneracy and converges nicely.
of stars. w Centauri is an interesting object to study as
it demonstrates many qualities in common with globular
clusters, such as an apparent absence of dark matter,
and also many qualities in common with dwarf spheroidal
galaxies, such as a complex star formation history.
There is also an ongoing debate concerning the presence
(or absence) of an intermediate-mass black hole (IMBH)
at its center. High-quality data and sophisticated modeling
techniques should enable us to finally answer some
of the questions that linger over the nature of this curious
object and how it has formed and evolved. The result
of one MCMC model run for w Centauri is shown in
Fig. III.3.5 for two of our parameters: the median deprojected
axis ratio (q, a proxy for shape) and velocity anisotropy
(b). These plots demonstrate the shape-anisotropy
degeneracy that exists, and that proper motions and
line-of-sight velocities must be used together in order to
break the degeneracy.
A second object to which we are applying our modeling
tools is the prototypical core collapsed Galactic
globular cluster M 15. A longstanding debate is wheth-
Credit: Glenn van de Ven