Annual Report 2011 Max Planck Institute for Astronomy

58 III. Selected Research Areas
they are collision-less much less sensitive to perturbations.
The kinematics of stars are now routinely measured:
along the line of sight via the Doppler shifts in absorption
features in spectra, and in the sky-plane via the
proper motion of stars that are close enough.
Stars, however, are not cold tracers as they generally
move on orbits that are neither circular nor confined to
a single plane. This means that in order to recover the
mass distribution we need to know their velocity dispersion
in addition to their mean velocity, i.e., their random
motion as well as their ordered motion. Whereas
the ordered motion is always around the short or long
axis, the random motion can be different in all three directions,
which is also referred to as velocity anisotropy.
Ordered motion around the intermediate axis is unstable,
but in a triaxial system a mix of ordered motion
around short and long axis is possible. Moreover, we
need to know the ordered and random motion throughout
the galaxy to recover the intrinsic 3D mass distribution.
Unfortunately, except for the Milky Way (see below
“Dynamics in the Solar Neighborhood”), we observe
every galaxy in projection, and except for the nearest
stellar systems (see below “Lighting up the dark in the
Local Group”), we only have access to the line-of-sight
stellar kinematics. This means the recovery of the mass
distribution is not only degenerate with the 3D shape
but also with the velocity anisotropy. The mass-shape
degeneracy can be reduced, or even be broken, by constraints
on the symmetry and/or viewing direction of
the galaxy. For example, the case that the stellar rotation
and photometry are aligned is consistent with oblate axisymmetry,
and moreover, if we can infer the inclination
from the presence of a dust disk, the 3D oblate shape
is well constrained. The mass-anisotropy degeneracy
can be reduced by observing moments of the line-ofsight
velocity distribution (LOSVD) beyond the mean
velocity V and velocity dispersion σ like the skewness
and kurtosis. In practice, we use the higher-order moments
of a Gauss-Hermite distribution (h 3 , h 4 , …) because
they are less sensitive to the difficult-to-measure
wings of the LOSVD.
It is evident that to reliably infer the total mass distribution,
one needs high-quality imaging and kinematics
fitted with sophisticated dynamical models. We are
in particular using integral-field spectrographs – delivering
spectra in two dimensions across galaxies – to
obtain maps of stellar and gas kinematics, as shown in
the Figures III.3.1 and III.3.2. At the same time, we are
developing dynamical modeling tools that allow us to
infer both the 3D mass distribution as well as the internal
dynamical structure of galaxies. In what follows,
we give a brief description of the results obtained so far
on external galaxies, the Milky Way, and supermassive
black holes in the centers of galaxies.
Dark matter in nearby galaxies
One can infer the fraction of dark matter in nearby galaxies
by comparing the total mass-to-light ratio (M/L) DYN ,
derived through detailed dynamical modeling of the galaxy
under study, to the total baryonic mass-to-light ratio
(M/L) BAR , as derived from the properties of the stellar
populations and gas in it.
To construct a dynamical model of a galaxy, we start
by expanding its surface brightness image into a sum
of two-dimensional Gaussians. In this way, seeing effects
are easily taking into account and the de-projection
for a given viewing direction – the inclination in the
case of axisymmetry – is analytical. Another advantage
is that, after multiplying each luminous Gaussian with
a mass-to-light ratio, the resulting intrinsic mass density
yields the gravitational potential after a straightforward
single numerical integral. Whereas the contribution of
a dark matter halo to the gravitational potential can be
achieved by including additional Gaussians, the (preliminary)
results shown in Fig. III.3.2 are under the assumption
that mass follows light. In this case, each luminous
Gaussian is multiplied with the same mass-to-light ratio
(M/L) DYN – still allowing for a constant dark matter fraction
– to arrive at the total gravitational potential. Even
though a central black hole is not resolved here (but see
below “Super-massive black holes”), we do add a central
round Gaussian with mass predicted from the (cor)
relation between black-hole mass and host galaxy velocity
dispersion.
Next, we use a solution of the Jeans equations in
axisymmetric geometry to turn the multi-Gaussian luminosity
density and total gravitational potential into a
prediction for the line-of-sight second velocity moment
V RMS
V 2 σ 2 . As shown in the top panel of Fig.
III.3.2 for the galaxy NGC 488, combining the observed
line-of-sight mean velocity V obs and velocity dispersion
σ obs yields the observed second velocity moment V RMS, obs
which can be compared with the predicted V RMS, mod to
infer the best-fit model parameters: inclination, velocity
anisotropy in the meridional plane, and total massto-light
ratio.
The bottom panel of Fig. III.3.2 shows the total massto-light
ratio (M/L) DYN for a range of galaxy types from
spheroid-dominated ellipticals (red) through disk-dominated
spirals (purple), based on fitting stellar kinematic
maps obtained with either the sauroN (triangles) or
PPAK (circles) integral-field unit – the latter as part of
the califa survey (Calar Alto Legacy Integral Field
Area survey: http://www.caha.es/CALIFA/) to obtain
integral-field spectroscopic data of 600 nearby galaxies.
The horizontal axis shows the mass-to-light ratio of the
stars (M/L) POP , based on fitting stellar population models
to multi-band photometry of each galaxy, assuming a
Chabrier initial mass function (IMF). The notable scat-