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ATA 2010
DYNAMICS of the MILKY WAY
Ken Freeman, ANU & UWA
Introduction
Galaxies are collections of stars, gas, dust and
dark matter
Masses are between about 106 and 1012 M.
The Milky Way is a disk galaxy and is near
the upper end of the mass range.
NGC 2997 - a typical disk-like spiral galaxy
NGC 891
A spiral galaxy
seen edge-on
Note the small
central bulge and
the dust in the
equatorial plane
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
150
pc-2
h is the scale length: 4 kpc for a large galaxy like the MW
Ratio of stars/gas varies : for the MW stars 95%, gas 5% of
the visible matter.
Dark/visible mass ratio is about 10-20
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
Rotation of spirals
Mostly don’t 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
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.
Our Galaxy
Believed to be much like
NGC 891, with weak bar
like M83. Rotational
velocity ~ 220 km/s
Schematic picture of our
Galaxy, showing bulge, thin
disk, thick disk, stellar halo and
dark halo
Our Galaxy at 2.4
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
Simulation of
galaxy formation
• cool gas
• warm gas
• hot gas
QuickTime™ and a
Microsoft Video 1 decompressor
are needed to see this picture.
Movie synopsis
• z ~ 13 : star formation begins - drives gas out of the
protogalactic dark matter 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.
You saw the evolution of the baryons. There is about 10 x
more dark matter in a dark halo, underlying what you saw:
it was built up from mergers of smaller sub-halos
Course Objectives
To study the dynamics of the Milky Way. Most of its visible mass
is in 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.
We will then return to more advanced descriptive material on
near-field cosmology: ie what we can learn about galaxy formation
from studying the detailed properties of our own Galaxy.
Lecture times
2 to 4 pm on
Monday 02, 09, 16 August 2010
ICRAR, UWA - ground floor
Assessment
30% on assignment work, 70% on examination
Assignments: one problem sheet with 5 questions: please hand in at lecture
on Fri Sep 18. 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.
There will be a brief tutorial session on the assignment in class
Examination: you will have a 2-hour examination for the 3 combined ATA modules.
For this module, you will be asked to do two questions from a choice of three.
You can find the lecture notes and assignment sheet at
http://www.mso.anu.edu.au/~kcf/ATA
Feel free to contact me about the problems or any other aspect of
the course:
office ICRAR 249
phone 6488 4756
email [email protected]
References
Binney & Tremaine: Galactic Dynamics (1987, 2008).
The dynamical lectures are partly based on this book, which
is the best book on the subject. It covers far more ground
than we can cover in these lectures.
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
13.7 Gyr
Two important timescales
1) 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
Ý
rÝ = - 
where
 2  = 4 G 
is Poisson’s 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
Question: do these fluctuations have a significant effect on
the star’s 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 B&T I:187-190)
TR / Tdyn ~ 0.1 N / ln N where N is the total number of stars in
the system
In galactic situations, usually TR >> age
eg in the solar neighborhood, m = 1 M, n = 0.1 pc-3
v = 20 km s -1 so TR = 5.10 12 yr >> 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, which makes galaxy dynamics much simpler.
For real disk galaxies, we can calculate the potential
of the stars and
the gas from the observed surface density distribution of stars and gas in the
disk, and then calculate the expected rotation curve from
Quick Time™a nd a
dec ompr esso r
ar e nee ded to see this pictur e.
QuickTime™ and a
decompressor
are needed to see this picture.
This is not usually a good fit to the observed rotation curve, because most of the
mass of disk galaxies is in the form of dark matter
Surface Brightness
HI Rotation Curve
(out to 11 scale lengths)
Dark matter is
important here
If E and Lz are the only two integrals of the motion, then the orbit would visit
all points within ints zero-velocity curve.
E
E = E max
locus of const rmax
L
circular orbits
A rosette orbit is the vector superposition of these two components:
the epicycle + the circular guiding centre motion.
Now take ez
NGC 1300
Define the convective derivative in phase space
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTi me™ and a
decompressor
are needed to see t his pict ure.
Then we can show that
Quick Time™a nd a
dec ompr esso r
ar e nee ded to see this pictur e.
for a collisionless system. This is the collisionless Boltzmann equation: the convective
derivative of the phase space density is zero.
These two equations are coupled:
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Rotation of the Galaxy
Merrifield (1992)
Stromberg’s asymmetric drift
-30
-20
-10
1250
2500
RR2 (km s -1) 2
absorbs
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 the merger is often an elliptical galaxy.
NGC 5907: debris of small accreted galaxy
Our Galaxy has a similar structure from the disrupting Sgr dwarf
APOD
The “field of streams” seen in SDSS star counts in the halo of our Galaxy
north galactic pole
l = 180, b = 25
Accretion of small galaxies is more important than major mergers for the evolution
of the Milky Way: look now at the two main processes involved in accretion.
Recent HST proper motion measurements for the LMC indicate that the LMC
is not in a circular orbit around the Galaxy and may not even be bound to the
Galaxy.
The HI Magellanic Stream (Putman 2002),
believed to come from interaction of the
Galaxy and the Magellanic Clouds. Seen
only in HI, not in stars.
The pioneering work on this problem was done by Quinn & Goodman 1986)
Decay of
a prograde
satellite
orbit
The satellite sinks
into the plane of the
galaxy in < 1 Gyr.
The disk provides
about 75% of the
torque on the satellite:
dynamical friction
against the dark halo
Provides the rest
Some background to the paper “Panoramic High Resolution Spectroscopy”
and galactic archaeology
Chemical Evolution
Elements lighter than ~ Be are built in the hot universe, shortly after the big bang
Elements heaver than Be are built in stars, and ejected back into the interstellar gas
by supernovae and AGB stars - many cycles of enrichment give chemical evolution
up to the present level of chemical abundance - SN and AGB stars
Two main kinds of supernovae:
SNII (progenitor M > 8M) produce -elements (O, Mg, Si, Ca,Ti), some Fe-peak
elements (V … Zn), and r-process elements (eg Eu) all on timescales ~ 107 years
SNIa (lower mass progenitors, probably white dwarf binaries) produce mainly
Fe-peak elements but on longer timescales ~ 109 years
AGB stars over wide range of mass produce s-process elements (Sr, Zr,Ba), again on
longer timescales ~ 109 years
If we see stars which are rich in -elements relative to iron, this means that the chemical
evolution of the gas from which they formed happened quickly (~ 108 yr), before there
was time for the SNIa to generate a lot of iron etc
To measure the abundances of chemical elements accurately, we need high resolution
spectra with R > 30,000. Until now, high resolution spectrographs can measure only
one star at a time. In the near future, we will be able to measure hundreds a a time.
Stellar Moving Groups in the Disk
The galactic disk shows kinematical substructure in the solar
neighborhood: groups of stars moving together, usually called
moving stellar groups (Kapteyn, Eggen)
• Some are associated with dynamical resonances (eg Hercules
group): don't expect chemical homogeneity
• Some are debris of star-forming aggregates in the disk (eg
HR1614 group). Might expect chemical homogeneity; these
could be useful for reconstructing the history of the galactic disk.
• Others may be debris of infalling objects, as seen in CDM
simulations: eg Abadi et al 2003 (Arcturus Group, Navarro
et al 2004)
The Hercules group is associated with local resonant kinematic
disturbances by the inner bar : OLR is near solar radius
(Hipparcos data) : Dehnen (1999), Fux (2001), Feast (2002)
Sirius and Hyades
streams - mainly
earlier-type stars
Hercules disturbance from OLR
-mainly later-type
stars
U
(U,V are relative to the LSR)
Dehnen 1999
Hercules group
• o field stars
The abundances of
Hercules Group stars
cannot be distinguished
from the field stars. This
is a dynamical group, not
the relic of a star forming
event.
Bensby et al 2007
Now look at the HR1614 group (age ~ 2 Gyr, [Fe/H] = +0.2).
Studied by Feltzing & Holmberg (2000) who argued for its reality
as a relic group.
De Silva et al (2007) measured very precise chemical abundances
for many elements in HR1614 stars, and finds a very small
spread in abundances.
The Wolf 630 group was recently found to be similarly homogeneous
in its element abundances
• HR 1614
o field stars
The HR 1614 stars
(age 2 Gyr)
are chemically
homogeneous.
They are
probably the
dispersed relic
of an old star
forming event.
De Silva et al 2007
Most spirals (including our Galaxy) have a second thicker disk
component . In some galaxies, it is easily seen
The thin disk
The thick disk
NGC 4762 - a disk galaxy with a bright thick disk (Tsikoudi 1980)
Our Galaxy has a significant thick disk
• its scaleheight is about 1000 pc, compared to
300 pc for the thin disk
• its surface brightness is about 10% of the thin disk’s.
• it rotates almost as rapidly as the thin disk
• its stars are older than 12 Gyr, and are
• significantly more metal poor than the thin disk
(-0.5 > [Fe/H] > -2.2) and
• alpha-enriched
The galactic thick disk
• its mass is about 10% of the thin disk’s
• it is old (> 12 Gyr) and significantly more metal poor than the thin disk:
mean [Fe/H] ~ -0.7 and -enhanced
• its rotation lags the thin disk by only ~ 50 km/s
thick disk
thin disk
higher [/Fe] 
more rapid formation
The Galactic element abundance data are consistent with
a time delay between formation of thick disk stars and the
onset of star formation in the current thin disk.
Most disk galaxies have thick disks:
(eg Yoachim & Dalcanton 2006)
The fraction of baryons in the thick disk is typically small
(~ 10-15%) in large galaxies like the MW but rises to
~ 50% in smaller disk systems
Baryonic mass ratio: thick disk/thin disk
Yoachim & Dalcanton 2006
How do thick disks form ?
• a normal part of early disk settling (Samland et al 2003,
Brook et al 2004)
• accretion debris (Abadi et al 2003, Walker et al 1996)
• early thin disk, heated by accretion events - eg the  Cen
accretion event (Bekki & KF 2003): Thin disk formation
begins early, at z = 2 to 3. Partly disrupted during merger
epoch which heats it into thick disk observed now, The rest
of the gas then gradually settles to form the present thin disk
Disks have a roughly exponential light distribution in R and z:
I(R,z) = Io exp (-R/hR) exp (-z/hz)
out to R = (3 to 5) hR, then often truncated
M33 (Ferguson et al)
The truncations are not understood: may be associated with
•
•
•
•
the star formation threshold
angular momentum redistribution by bars and spiral waves
the hierarchical accretion process
bombardment by dark matter subhalos (de Jong et al 2007)
Roskar et al (2008) - SPG simulation of disk formation from cooling
gas in an isolated dark halo : includes star formation and feedback.
The break is seeded by rapid radial decrease in surface density of
cool gas : break forms within 1 Gyr and gradually moves outwards
as the disk grows. The outer exponential is fed by secularly
redistributed stars from inner regions (Sellwood & Binney 2002)
so its stars are relatively old.
stellar surface density
gas surface density
star formation rate
mean stellar age
Roskar et al (2008)
break
Secular radial distribution of stars via spiral arm interaction
into outer (break) region of truncated disk
Redistribution of stars by orbit swapping will affect the
galactic abundance gradient
Roskar et al (2008)
The galactic disk shows an abundance gradient
(eg galactic cepheids: Luck et al 2006) ....
Background to the final section ….
Using dispersed star clusters for galactic archaeology: finding fossil remains
of the star forming events which built up our Galaxy
Galaxies like the Milky Way are believed to form by
• the infall of gas which then turns gradually to stars (most of which form in the
disk of the Galaxy, in open star clusters which quickly dissolve), and also by
• the accretion of smaller galaxies which become absorbed in the larger system.
A major goal is to determine how important these accretion events were in
building up the Galactic disk and the bulge.
Our current galaxy formation theory based on Cold Dark Matter predicts a very high
level of accretion activity which conflicts with many observed properties of disk galaxies.
By now, the star clusters and the small accreted galaxies have broken up and
be unrecognisable: their debris will be dispersed right around the Galaxy. But …
We can use their chemical signatures over many chemical elements to identify their debris:
• stars from a common cluster have similar chemical signatures, and their chemical
properties vary from cluster to cluster
• stars from a small accreted galaxy have chemical patterns that are very different
from those we see in the open clusters which formed in the disk.
Using chemical signatures to identify stars having
a common origin is called chemical tagging
This will be one of the big things of the next decade
in galactic astronomy
Cluster abundance patterns
Ba
Na
Si
Mn
Zr
Hyades
Coll 261
HR1614
Ca
Mg
De Silva 2007
Clusters
vs
nearby
field stars
Hyades
Coll 261
HR1614
Clusters have small
abundance spread:
The mean is
different from cluster
to cluster
De Silva 2007
Galactic Archaeology with HERMES
Simulations show that a chemical tagging program
to reconstruct the fossils of the star forming aggregates
that built up our Galaxy
needs high resolution spectra of about a million stars
We are building a large multi-object spectrometer
(HERMES) for the AAT to do this survey.
It will acquire high resolution spectra of
about 400 stars at a time, and the survey
will take about 400 clear nights.
Expect to start work in 2012