DARK MATTER

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DARK MATTER Ken Freeman RSAA, ANU
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Dark Matter in Galaxies
We believe that galaxies formed through a
hierarchy of merging. The merging elements were
a mixture of baryonic and dark matter.
The dark matter settled into a partially
virialized spheroidal halo while the baryons (in
disk galaxies) settled into a rotating disk and
bulge
What can we learn about the properties of
dark halos ? Do the properties of dark halos
predicted by simulations correspond to what is
inferred from observational studies ?
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Start with disk galaxies These are the simplest
galaxies for studying the properties of the
dark halos - they are flat systems, supported
against gravity by their rotation
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NGC 2997 - a typical spiral galaxy
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NGC 4414 - another spiral galaxy
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NGC 4622 yet another spiral note how different
the spiral structure can be from galaxy to galaxy
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NGC 891 A spiral galaxy seen edge-on
Note the small central bulge
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Rotation of spirals Mostly dont rotate rigidly
- wide variety of rotation curve morphology
depending on their light distribution. Here are a
couple of extremes - the one on the left is
typical for lower luminosity disks, while the
one on the right is more typical of the brighter
disks like the Milky Way
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What keeps the disk in equilibrium ? (always ask
this question for any stellar system) ? Most of
the kinetic energy is in the rotation in the
radial direction, gravity provides the radial
acceleration needed for the circular motion of
the stars and gas in the vertical direction,
gravity is balanced by the vertical pressure
gradient associated with the random vertical
motions of the disk stars.
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The radial equilibrium of disks
For the gas in a disk galaxies, the radial
potential gradient provides the acceleration for
the circular motion.
where M(R) is the mass enclosed within radius R.
The shape of V(R) can be anything from solid body
to V constant (flat). For larger spirals like
our Galaxy, V(R) is usually flat, so the enclosed
mass M(R) ??R
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M(R) ??R is not what we would expect for a
gravitating system of stars - we would expect
the Keplerian
Is this evidence for a dark halo ? Not
necessarily - it depends on how far the rotation
curve extends.
Most spirals have a light distribution that is
roughly exponential
I(R) Io exp (-R / h) (for a large
galaxy like the Milky Way, the scale length h 4
kpc)
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Optical rotation curves, measured from the
spectra of ionized gas, typically extend to R
3 h
Now assume that the surface density distribution
of stars in our disk galaxy follows the optical
surface brightness distribution.
Can this surface density distribution, with its
gravitational potential ?(R) explain the observed
rotation curve V(R) ?
The answer to this question is yes and no
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Yes, for optical rotation curves extending out to
about 3 disk scale lengths In the next slide,
the points are the observations and the curve is
the expected rotation curve Despite the very
different shapes of the two rotation curves, the
light distribution can explain the
observed optical rotation curves out to about 3
scale lengths
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Two very different rotation curves. The points
are the rotation data and the curves are as
expected if mass follows light. The only
scaling is through the adopted M/L ratio
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No for galaxies with 21 cm HI rotation curves
that extend far out, to R gtgt 3 h.
eg maximum disk decomposition for NGC 3198
M/LB 3.8 for disk
observed
Begeman 1987
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For NGC 3198 the HI rotation curve extends out to
11 h. (for some galaxies the rotation data go to
more than 20 h) The expected V(R) from stars and
gas falls well below the observed rotation curve
in the outer region of the galaxy. This is seen
for almost all spirals with rotation curves
that extend out to many scale lengths. We
conclude that the luminous matter dominates the
radial protential gradient ?????R for R lt 3h
but beyond this radius the dark halo becomes
progressively more important.
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Typically, out to the radius where the HI data
ends, the ratio of dark to luminous mass is 3 to
5 values up to about 10 are found in a few
examples.
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For the decomposition of NGC 3198, the stellar
M/L ratio was taken to be as large as possible
without leading to a hollow dark halo - this is a
maximum disk (minimum halo) decomposition.
Many galaxies have been analysed in this way -
the decomposition often works out as for NGC
3198, with comparable peak circular velocity
contributions from disk and dark halo
This is believed to be at least partly to the
adiabatic compression of the dark halo by the
baryons as they condense to form the disk.
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The inferred stellar M/L ratios are usually
consistent with those expected from synthetic
stellar populations, at least for the brighter
galaxies like the Milky Way
Nevertheless, some people still do not believe
that this maximum disk, minimum halo approach is
correct. One reason is that the estimated
surface density of the galactic disk near the
sun is only about 50 solar masses pc -2 which
may be too low to be consistent with a maximum
disk
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The maximum disk question is important for us
here, because inferences about the properties of
dark halos from rotation curves depend so much on
the correctness of the maximum disk
interpretation. eg if the maximum disk
decompositions are correct, then the dark halos
have approximately uniform density cores which
are much larger than the scale length of the disk
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halo
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In contrast, the halos that form in cosmological
simulations have steeply cusped inner halos with
????r -1 or even steeper near the center
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Optical rotation curves favor the maximum disk
interpretation. In the inner regions of the
disks of larger spirals, the rotation curves are
well fit by assuming that mass follows
light. eg Buchhorn (1991) analysed 552 galaxies
with optical V(R) and I-band surface photometry,
and a wide range of rotation curve morphology.
He was able to match the rotation curves well
for 97 of his sample, with realistic M/L ratios
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The implication is that either the stellar
disk dominates the gravitational field in the
inner parts of the disk (R lt 3h) or the
potential gradient of the halo faithfully mimics
the potential gradient of the disk in almost
every spiral.
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Other support for the maximum disk
Athanassoula et al (1987) used spiral structure
dynamics to give a dynamical constraint on the
stellar M/L ratio of the disk. From the number of
spiral arms observed in their sample, they argue
that most of the disks are indeed close to
maximum.
Recently Bell de Jong (2001) and Perez (2002)
compared the M/L ratio from synthetic stellar
populations with those derived from maximum disk
rotation curves. The agreement is good, when a
stellar mass function like that derived for the
solar neighborhood is used.
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NGC 1300 a barred galaxy
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Debattista Sellwood (1998) showed that a dense
halo (ie sub-maximal disk) rapidly slows down the
rotation rate of the bars of barred galaxies. In
a low density halo (maximum disk), the bar
rotation stays high. Evidence from bar flows
in barred galaxies (Weiner et al 2001 Perez
Fux 2002) indicates that bars do rotate
rapidly,with corotation just beyond the end of
the bar.
I conclude that the maximum disk picture is
probably correct, at least for galaxies of normal
surface brightness
( we will discuss low surface brightness galaxies
soon)
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How to model the dark halo
Our goal is to estimate typical parameters for
dark halos (density, scale length, velocity
dispersion, shape) to compare with halo
properties from simulations
Since about 1985, observers have used model dark
halos with constant density cores to interpret
rotation curves
Commonly used models include the non-singular
isothermal sphere, which has a well defined core
radius and central density, and has ????r -2 at
large radius, so V(r) constant as often
observed.
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A simple analytic form is the pseudo-isothermal
sphere ?????????????????????????????o 1 (r /
rc ) 2 -1 which again has a well defined core
radius and central density, and has ?? r - 2 at
large radius. Using this model for the dark
halo of large galaxies like the Milky Way, we
find that ?o 0.01 solar masses pc -3 and rc
10 kpc (for comparison, the stellar density of
ourGalaxy near the sun is about 0.01 solar
masses pc -3 )
We will see later that the values of ?o and rc
depend strongly on the luminosity of the galaxy.
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NGC 6822
V
Why were these models used ? I think it was
because rotation curves of spirals do appear
to have an inner solid-body component which
indicates a core of roughly constant
density hot stellar systems like globular
clusters were successfully modelled by King
models, which are modified isothermal spheres
with cores
R
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On the other hand .... CDM simulations
consistently produce halos that are cusped at
the center. This has been known since the
1980s, and has been popularized by Navarro et
al 1996 with the NFW density distribution which
represents the CDM halos ????????????????????????
???????(r / rs ) - 1 1 (r/rs) - 2
These are cusped at the center, with ???????r - 1