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Astro 6590: Galaxies and the Universe
See http://www.astro.cornell.edu/academics/courses/astro6590
• Professors Martha Haynes & Riccardo Giovanelli
• MW 1:25-2:40 SSB 301
• 4 credits
• Some ability to solve straightforward numerical problems
• Background in astronomy helpful, but not required
• Books:
• “Galactic Astronomy”, Binney & Merrifield
• “Galactic Dynamics”, Binney & Tremaine
• Papers from the literature available electronically through
CU library
• Regular assignments will include problems, in class presentations
and a final (major) project
• All subject to change/negotiation
Astro 6590: Galaxies and the Universe
See http://www.astro.cornell.edu/academics/courses/astro6590
Find
lecture
notes by
clicking
on date
Readings/Refs
Read the sections
in the textbooks;
You should read
all the papers… at
least, someday
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Astro 6590: Galaxies and the Universe
See http://www.astro.cornell.edu/academics/courses/astro6590
Part B:
For Your Eyes Only
Astro 6590: Galaxies and the Universe
See http://www.astro.cornell.edu/academics/courses/astro590
Part B:
For Your Eyes Only
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Constituents of the Milky Way
The Milky Way is
known in a fair
amount of detail,
and both the gas and
stars split cleanly
into different
populations or
phases.
Stars:
Disk: 5 x 1010 M
Bulge: ~ 1010 M
Halo: ~109 M
Globulars: ~108 M
Gas:
Dark matter:
H2 clouds: ~109 M
Halo: 2 x 1012 M
HI gas: 4 x 109 M
HII regions: ~108 M
Definition: what is a galaxy?
• A galaxy is a self-gravitating collection of about 106 to 1011
stars, plus an amount up to 1/2 of as much by mass of gas,
and about 10X as much by mass of dark matter. The stars
and gas are about 70% hydrogen by mass and 25% helium,
the rest being heavier elements (called "metals").
• Typical scales are: masses between 106 to 1012 M (1 solar
mass is 2 x 1030 kg), and sizes ~ 1-100 kpc (1 pc = 3.1 x 1016
m). Galaxies that rotate have Prot ~ 10-100 Myr at about 100
km/s. The average separation of galaxies is about 1 Mpc.
• Between galaxies there is very diffuse hot gas, called the
intergalactic medium (IGM); in clusters this is called the
intracluster medium (ICM). It was much denser in the past
before galaxies formed, accreted the gas and converted it
into stars.
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Cosmic Inventory
Fukugita & Peebles 2004, ApJ 616, 643
73 % - dark energy or cosmological constant
23 % - dark matter, probably CDM
Ωbaryons = 0.045+/-0.004 ~ (1/6) Ωmatter
Coronal + diffuse IG gas ~0.037
Cluster IGM ~ 0.002
Stars ~ 0.003
Cold Gas ~ 0.0008
(~2/3 atomic)
“HI contributes only a piffling
fraction of cosmic matter”
R. Giovanelli, 2008
Key points about galaxies
J.E. Gunn, 1981, “Astrophysical Cosmology” Vatican Symposium
1. Galaxies are easily discernible as discrete entities whereas
groups and clusters are not.
2. The specific angular momenta of galaxies correlate closely with
optical morphology.
• Scaling relations (Fundamental plane/Tully-Fisher relation)
3. The morphological types of galaxies are related to the density
of galaxies in their immediate neighborhood.
• Morphology-density relation
4. The luminosity function (LF) of galaxies is distinctly nonGaussian with a long tail extending to low luminosities.
5. There are large peaks in the density distribution of matter and
these in turn surround the visible portions of galaxies.
• Dark matter!
4
Properties of galaxies and clusters of galaxies which
must be explained.
1. Galaxies are easily discernible as discrete entities, whereas
groups and clusters are not.
• Characteristic sizes?
• Topologies?
• Origin?
• On what scale does the cosmological principle hold?
If we select a star at random in the universe, it would nearly
always be possible to identify its parent galaxy with significant
confidence. The same is not true of galaxies and “parent”
groups of galaxies.
Virial Theorem:
-2<K.E.> = <P.E.>
Free-fall time: tff =
3π
1
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Gρ
½
Hierarchical models
• How did the structures we
see today form and
evolve?
• Do hierarchical models
predict this behavior?
• Can they give us any
insight into what is going
on?
timeÆ
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cluster
halo
Wechsler et al.
‘Milky Way’ halo
Cosmic hierarchies
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Coma Cluster = A1656
cz ~ 7000 km/s => D ~ 100 Mpc
Often used as “prototypical rich cluster”
Identifying clusters of galaxies
1 RA = Abell radius ~ 1.5 h-1 Mpc
RG et al. 1997 (SCI)
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The redshift dimension
Not only do redshifts help the identification of group or cluster
members, they also prove useful to indicate masses, identify
substructure and detail evolutionary processes at work
e.g. use Virial Theorem to estimate mass of cluster of galaxies
2
Observe many radial velocities: vr P(x,μ,σ) = 1 exp - 1 x – μ
2
σ
σ√2π
[
( )
]
Properties of galaxies and clusters of galaxies which
must be explained.
2. The specific angular momenta of galaxies correlate closely with
optical morphology.
• Bare spheroid: ~ 240 kms-1 kpc <= elliptical
• Spheroid in disk: ~ 600 “
<= bulge
• Disk galaxy:
~4000
a. Elliptical galaxies do not rotate fast enough to explain their
flattening.
b. Scaling relations: Radii and internal velocities correlate with L
Ellipticals
Spirals
Faber-Jackson relation
“Fundamental plane” (later)
Tully-Fisher relation
L ∝ σ4
log Re = 0.36(<I>e/μB) + 1.4 log σ0
n
L∝
L ∝Vrot n~4
γ ~ 2 (~const SB)
Rγ ,
Why?
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Spiral Galaxies: Tully-Fisher Relation
Why?
W ~ 2 Vrot
Giovanelli et al. 1997
Template Rotation Curves
Catinella et al. 2006
ApJ
Not just the
amplitude, but the
shape is correlated
with luminosity
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Morphological Classification
Morphological classification schemes
10
Galaxy Zoo
Ellipticals: E0 to E7
Type E0
Type E3
Type E6
En, n=0 to 7, where n = 10 (1 – b/a)
Hubble 1936, “The Realm of the Nebulae”
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Spiral sequence
To first order, the tightness of a spiral galaxy’s arms is correlated
with the size of its nuclear bulge.
Type Sa
Type Sb
Type Sc
• In addition: Sa’s are usually brighter, rotate faster and have
less current SFR than Sc’s
• Sa’s show a diversity of B/D ratios; Sc’s only small ones.
The barred spiral sequence
• Origin of bars: do all spirals have bars? Why/why not?
• Relationship to SMBH
Type SBa
Type SBb
Type SBc
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Spiral arms
• We easily see these spiral arms because they
contain numerous bright O and B stars which
illuminate dust in the arms.
• However, stars in total seem to be evenly
distributed throughout the disk.
• The density contrast is only of order 10%.
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.
The nearby spiral galaxy M83 in blue light (L)
and at 2.2μ (R)
Variations in spiral morphology
• Spiral structure varies greatly in detail.
• The cause of this is not really
understood
• Grand design spirals seem to have
nearby companions – driven by
interactions
Flocculent spirals
(fleecy)
Grand-design spirals
(highly organized)
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Properties of galaxies and clusters of galaxies which
must be explained.
3. The morphological mix is related to the density of galaxies in
the local surroundings.
=> Morphological segregation
Morphology-density relation
Dressler, 1980
Holds over 6 orders of
magnitude of galaxy density
Field:
E:S0:Sp = 10:10:80
Why?
Hierarchical simulations
show a clear correlation
between
color/morphology
and density, in
qualitative
agreement with
observations
Kauffmann et al. 1999
VIRGO/GIF simulations
see also
Benson et al. 2001;
Springel et al. 2001
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Elliptical versus Spiral
Ellipticals
Smooth light distribution
Brightest stars are red
Little/no star formation
Little/no cool/cold gas
Random motions
Spirals
Arms, disk, bulge
Brightest are blue
On-going star formation
Molecular + atomic gas
Circular rotation in disk
Found in cluster cores
Avoid cluster cores
Morphological segregation:
Initial conditions or evolution?
Lenticulars = S0’s
Ellipticals
Smooth light distribution
Brightest stars are red
Little/no star formation
Little/no cool/cold gas
Random motions
Spirals
Arms, disk, bulge
Brightest are blue
On-going star formation
Molecular + atomic gas
Circular rotation in disk
Found in cluster cores
Avoid cluster cores
S0:
Spiral-like: disk+bulge, rotation
Elliptical-like: little gas/star formation; no
spiral structure
Evolution along the Hubble sequence?
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Properties of galaxies and clusters of galaxies
which must be explained.
4. The luminosity function (LF) of galaxies is distinctly nonGaussian with a long tail extending to low luminosities.
• LF = The number of objects (stars,
galaxies) per unit volume of a given
luminosity (or absolute magnitude)
Φ(L) = dN/dL dV
• Bright galaxies are rare … But can be
detected to large distances.
• Faint galaxies can only be seen nearby.
• Binggeli, Sandage & Tammann:
Compared LFs of Virgo Cluster Catalog
(VCC) and local field
VCC: Virgo Cluster Catalog
Sandage, Binggeli & Tammann
1985AJ 90, 1759
Properties of galaxies and clusters of galaxies which
must be explained.
4. The luminosity function (LF) of galaxies is distinctly nonGaussian with a long tail extending to low luminosities.
LF: Number density of galaxies per unit L
φ(L)dL ~ Lα eL/L* dL
φ(M)dM ~ 10-0.4(α+1)M exp(-100.4(M*-M)) dL
Press-Schechter (1974) formalism plus
CDM fluctuation spectrum predicts faint
end slope α = -1.8
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Luminosity function
• The L.F. gives the number of galaxies per unit volume per
luminosity (or magnitude) interval.
• Schechter (1980) expressed the LF as an analytic function
with both a power law and an exponential:
α = faint end slope
L* = luminosity at “knee” of L.F.
cD’s
too
bright!
ϕ(L)
Bright galaxies are rare.
Low L galaxies only seen nearby.
log L
Elliptical galaxies display a variety of sizes
and masses
• Giant elliptical galaxies can be 20
times larger than the Milky Way
• Dwarf elliptical galaxies are
extremely common and can contain
as few as a million stars
M32
M31 - Andromeda
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Key points of cosmology (later)
The dominant motion in the universe is the smooth linear
expansion known as “Hubble’s Law”.
• Hubble (1923): galaxy spectra are redshifted
• “redshift” = z = ∆ λ / λ
• Hubble’s law (1926): v = H d
where V is the observed recessional velocity
d is the distance in Mpc
The metric for a homogeneous and isotropic model universe is:
R2(t)
dσ2
ds2 = dt2 c2
where R(t) is the scale factor, and dσ2 is the metric for constant
curvature in 3-D space:
k : the
dr2
2 (dθ2 + sin2θ dφ2)
dσ2 =
+
r
curvature
1 – kr2
constant
2/3
k=0 => R(t) ∝ t
=> Einstein-deSitter universe
Quantitative Morphology
Photometric surface brightness
profile (at projected radius R)
“de Vaucouleurs’ profile”:
I(R)= I(Re) exp{-7.67[(R/Re)¼ - 1]}
where Re is the “effective
radius” and L(<Re)=½ Ltotal
Works for ellipticals and for bulges
“exponential profile”:
I(R)= I(0) exp[-R/Rd]
where Rd is the “exponential scale
length”.
Works for spiral disks
Spiral: I(R) = Ibulge(R) + Idisk(R)… [+ Ibar(R)]
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Quantitative Morphology
“Sersic profile”:
I(R)= I(Re) exp{-b[(R/Re)1/n - 1]}
where n is the “Sersic index” =>
n=1 and b=1.67 (disk)
n=4 and b=7.67 (deVauc)
In general, we want to derive the
luminosity density j(r) from the
surface brightness I(R):
For z2 = r2 - R2 and dz = r dr/(r2 - R2)½:
I(R) =
∫
∞
j(r) dz
-∞
= 2
∞
j(r) r dr
R
(r2 - R2)1/2
∫
This is an Abel integral equation with solution:
∞
-1
dI
dR
j(r) =
π R dR (R2 - r2)1/2
∫
For certain I(R), j(r) can be expressed algebraically. For smooth (fitted)
profiles, the integral can be evaluated directly. For noisy data, use the
Richardson-Lucy iterative inversion algorithm (B&M 4.2).
For Monday’s class
I will post the slides tomorrow.
Please look at them in advance of class, so I can
speed through the first half.
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