ASTR3002

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ASTR3002 GALAXY DYNAMICS
K.C. Freeman, RSAA
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Introduction Galaxies are collections of stars,
gas, dust and dark matter Masses are between
about 106 and 1012 solar masses. The Milky Way is
near the upper end of the mass range. Two main
kinds of galaxies disk galaxies and elliptical
galaxies
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NGC 2997 - a typical disk-like spiral galaxy
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NGC 891 A spiral galaxy seen edge-on
Note the small central bulge and the dust in
the equatorial plane
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UGC 7321 - a very flat disk galaxy seen edge-on -
no bulge
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Disk galaxies
Flat rotating disk-like systems, often with
spiral structure
Surface brightness distribution I(R) Io exp(-R
/ h) Io is the central surface brightness,
typically around 140 pc-2 h is the scale
length 4 kpc for a large galaxy like the MW
1.5 kpc for a smaller
galaxy like the LMC Ratio of stars/gas varies -
for the MW stars 95, gas 5 of the visible
matter.
Dark/visible mass ratio is about 10-20
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NGC 1300
NGC 1365
A couple of strongly barred disk galaxies About
2/3 of disk galaxies show some kind of central
bar - believed to come from instability of a
rotating disk of stars
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The nearby spiral galaxy M83 in blue light (L)
and at 2.2? (R)
The blue image shows young star-forming regions
and is affected by dust obscuration. The NIR
image shows mainly the old stars and is
unaffected by dust. Note how clearly the central
bar can be seen in the NIR image
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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.
Where do the bars come from ? Believed to come
from barlike (m2) instabilities of
rotationally supported disks. See this happen in
numerical simulations
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Believed to be much like NGC 891, with weak
bar like M83. Rotational velocity 220 km/s
Our Galaxy
Schematic picture of our Galaxy, showing bulge,
thin disk, thick disk, stellar halo and dark halo
Our Galaxy at 2.4?
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Elliptical Galaxies
Spheroidal systems with intrinsic axial ratios
from about 1 to 0.5
Surface brightness distribution log I (R) ? - R
1/4
Content visible component is almost entirely
stars (except for some of the largest ellipticals
which contain some hot X-ray emitting gas).
The dark/visible mass ratio is 5-10
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M87 the dominant elliptical galaxy in the Virgo
cluster note the globular clusters in its outer
regions
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Leo I - a dwarf elliptical in the Local Group
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What keeps elliptical galaxies in equilibrium
? mainly a balance between gravity and the
pressure gradient associated with the random
velocities (ie orbital motions) of the stars The
less massive ellipticals (M lt 1011 ) are
flattened by rotation The more massive
ellipticals (M gt 1011 ) are
flattened by their anisotropic velocity dispersion
Some of the faintest ellipticals like Leo I
have very large dark/luminous mass fractions, up
to about 501
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Disk galaxies interact tidally and merge.
Merging stimulates star formation and disrupts
the galaxies. This is NGC 4038/ 9 - note the
long tidal arms . The end product of single
or multiple mergers is usually an elliptical
galaxy.
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MOVIE
Start by showing a numerical simulation of
galaxy formation.
The simulation summarizes our current view of how
a disk galaxy like the Milky Way came together
from dark matter and baryons, through the merging
of smaller objects in the cosmological hierarchy.
much dynamical and chemical evolution halo
formation starts at high z dissipative
formation of the disk
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Simulation of galaxy formation
cool gas warm gas hot gas
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Movie synopsis
z 13 star formation begins - drives gas out
of the protogalactic mini-halos. Surviving
stars will become part of the stellar halo -
the oldest stars in the Galaxy z 3 galaxy
is partly assembled - surrounded by hot gas
which is cooling out to form the disk z 2
large lumps are falling in - now have a well
defined rotating disk galaxy.
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Another kind of stellar system The globular
cluster 47 Tuc
dense very old object - part of the MW
150 of these clusters in the MW
its mass 106 M_sun
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Course Objectives
To study the properties and dynamics of
galaxies Most galaxies are made up mostly of
stars, so the dynamical theory is mostly stellar
dynamics
Following this basic descriptive introduction, I
will go straight to the lectures on the
theoretical dynamics. This will give you
maximum opportunity to complete the
assignments. There will also be some more
advanced descriptive material on the properties
of galaxies. These properties may make
more sense once you have some dynamical
background. You will be asked to read the
handouts on this material yourself.
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Lecture times and places Monday
Physics seminar room 1100-1200 Tuesday
Physics seminar room 1300-1400 Thursday
Physics seminar room 1100-1200
I will mostly be available after lectures outside
the lecture room for informal questions.
In the period, Sept 27 to Oct 8, Helmut Jerjen
will give the lectures
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Assessment
There will be two problem sheet assignments on
which you will be assessed. They are the only
form of assessment. I use these problems as part
of the teaching process, as well as
for assessment, so please do them. They require
some time and effort. I encourage you to discuss
the problems with others, but the work you
submit should be your own. It is very obvious if
people collaborate in the submitted work, and it
will cost both (all) parties some marks.
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Assignments are due October 12 and October 26.
I will hand out paper copies of the assignment
problems The assignment problem sheets will also
be on the web http//www.mso.anu.edu.au/kcf/A3002
after the first few lectures
RSAA honours graduate students are expected to
do these assignments on schedule as part of the
course requirement.
I will do a tutorial on each assignment
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You can find the lecture notes at http//www.mso.a
nu.edu.au/kcf/A3002 (separate .ppt or .pdf files
for each section of the course)

• 1. Introduction
• 2. Stellar orbits
• 3. Potential theory
• 4. Collisionless Boltzmann Equation
• 5. Jeans theorem, the Galaxy
• 6. The self-consistency problem. Galaxy mergers
• Also some material to read about disk galaxies,
  elliptical
• galaxies and dark matter

Feel free to contact me about the problems or any
other aspect of the course phone 50264
email kcf_at_mso.anu.edu.au
(preferred)
jerjen_at_mso.anu.edu.au (Sept 27-October 8)
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References Binney Tremaine Galactic Dynamics
(1987). The dynamical lectures are partly based
on this book, which is still the best book on the
subject. It covers more ground than we can cover
in these lectures. New edition imminent. Binney
Merrifield Galactic Astronomy (1998). This is
a more descriptive book and well worth reading
for background. Sparke Gallagher Galaxies in
the Universe (2007). Ditto - good book, with some
theory
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13.7 Gyr
GOT TO HERE
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• Two important timescales
• The dynamical time (rotation period, crossing
  time
• ???????????G?? ???? where ? is a mean density.
  Typically
• 2 x 108 yr for galaxies

2) The relaxation time. In a galaxy, each star
moves in the potential field ? of all the other
stars. Its equation of motion is
where is
Poissons equation The density ?(r) is the sum of
106 to 1012 ??-functions. As the star orbits,
it feels the smooth potential of distant stars
and the fluctuating potential of the nearby stars
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Question do these fluctuations have a
significant effect on the stars orbit ?
This is a classical problem - to evaluate the
relaxation time TR - ie the time for encounters
to affect significantly the orbit of a typical
star
Say v is the typical random stellar velocity in
the system m
mass n
number density of
stars Then TR v3 / 8? G2 m2 n ln (v3 TR /
2Gm) (see BT 187-190) TR / Tdyn 0.1 N /
ln N where N is the total number of stars in
the system
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In galactic situations, TR is usually gtgt age eg
in the solar neighborhood, m 1
n 0.1 pc-3
v
20 km s -1 so TR 5.10 12 yr gtgt age of
the universe In the center of a large spiral
where n 10 4 pc -3 and v 200 km s -1, TR
5.10 11 yr (However, in the centers of globular
clusters, the relaxation time TR ranges from
about 107 to 5.109 yr, so encounters have
a slow but important effect on their dynamical
evolution)
Conclusion in galaxies, stellar encounters are
negligible they are collisionless stellar
systems. ? is the potential of the
smoothed-out mass distribution. ( In spirals,
encounters between disk stars and giant molecular
clouds do have some dynamical effect.)
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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 - this is not understood
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NGC 4594 - a disk galaxy with a large bulge