At the beginning of the 20 th century, what we now call spiral galaxies were referred to as
“ spiral nebulae ” and most astronomers believed them to be clouds of gas and stars associated with our own Milky Way. The breakthrough came in 1924 when Edwin
Hubble was able to measure the distance to the
“ Great Nebula in Andromeda ” (M 31, at right) and found its distance to be much larger than the diameter of the Milky Way. This meant that
M 31, and by extension other spiral nebulae, were galaxies in their own right, comparable to or even larger than the Milky Way.
Edwin P. Hubble (1889-1953)
(NOAO/AURA Photo)

• Star systems like our Milky Way
• Contain a few thousand to tens of billions of stars.
• Large variety of shapes and sizes

a) Cepheid Method: Using Period – Luminosity relation for classical Cepheids:
Measure Cepheid ’ s Period

Find its luminosity

Compare to apparent magnitude

Find its distance b) Type Ia Supernovae (collapse of an accreting white dwarf in a binary system):
Type Ia Supernovae have well known standard luminosities

Compare to apparent magnitudes

Find its distances
Both are “ Standard-candle ” methods:
Know absolute magnitude (luminosity)
 compare to apparent magnitude
 find distance.

Repeated brightness measurements of a Cepheid allow the determination of the period and thus the absolute magnitude.

Distance

At very large distances, only the general characteristics of galaxies can be used to estimate their luminosities
 distances.
Cluster of galaxies at ~ 4 to 6 billion light years

The analogous phenomenon on Earth occurs with sound waves from a moving object, such as the police siren below.
The stationary observer hears the pitch change from high to low as the siren passes.

Christian Doppler, in 1842, published an equation describing this change in pitch. In the equation, f s siren ’s pitch when stationary and f d is the pitch an is the observer (themselves moving at speed v d
) hears when the siren is moving at a speed v s
. v is the speed of sound.

But sound waves can change speed! So, when the analogy was made for the Doppler shift to apply to light, because light could not change speed, it was the wavelength (color) of light that would change.
In the equation above, v rad is the radial (direct-line) velocity of an object, c is the speed of light, λ rest is the wavelength of a color measured in a stationary (laboratory) frame and
λ shift is the wavelength of the same color measured from the moving object. Key point: if λ shift
> λ rest
, the object looks redder when moving, so this is called a red shift . In this case, then v rad from us.
is positive, and the object is moving away

Note that, for a really fast object, the wavelength emitted by that moving object can be so shifted that λ shift
– λ rest
> λ rest
, in which case the ratio on the right side is greater than one, which means that (on the left side) the object is moving faster than the speed of light . This is impossible!

Special relativity states that no object can exceed the speed of light, and the equation for the Doppler shift applied to light can be modified:
You can check this yourself, but even when the ratio on the left side is greater than one, v r
< c, so no object moves faster than the speed of light. Indeed, it is Δλ = λ shift (obs)
λ rest that is the critical measurement.
–

In 1912, Vesto Slipher discovered that with few exceptions, every galaxy is receding from us, i.e., its spectral lines are shifted from their normal (laboratory) position towards the red end of the spectrum. These spectra lines are said to exhibit redshift .
Quantitatively, redshift is defined by the equation: z =
Dl/l
High z objects are those that have z > 1

Kennicutt (1992)
These are what galactic spectra look like; wavelength is along the x-axis and intensity is along the y-axis.

• In the 1920s, Edwin Hubble determined the distances to dozens of galaxies using the
Cepheid variable method.
Combining that with Slipher’s redshift data, Hubble and
Humason discovered that more distant galaxies are receding faster (have larger redshifts).
• This relationship, well-fit by a straight line, is called Hubble ’ s
Law.
Hubble ’ s Law is written:
Recessional velocity (km/s) = H o
 distance (Mpc)
Or: V = H o
D where H o is Hubble ’ s constant (slope of the line). So are we the center of the universe!? No reason to think so, so why is everything leaving us??

· You can think of space as the surface of a balloon. As the balloon expands, the space between galaxies stretches.
· This means that the wavelength of light photons emitted by galaxies are also stretched as space expands. That is to say, the wavelengths are expanded, i.e. redshifted.

If the rate of expansions stays constant over time, and all objects are together at t=0, current distance between two objects is d = v t o where t o is current age of Universe
Then, v = (1/t o
)d
Same as Hubble ’ s law with identification H o
= 1/t o
Where 1/H o is called the Hubble Time  age of the
Universe if expansion is constant ( which is unlikely as we will see..
)
H o has units of km/s/Mpc to express velocity and distance in convenient units (btw, Hubble ’ s first estimate of H o km/s/Mpc, pretty far from the current value of around 70!) was 500

How to determine the Hubble Constant
We need to get accurate distances to the most distant galaxies we can see to measure the expansion rate of the Universe. Galaxy velocities must be dominated by the Hubble flow , not the random motions caused by gravitational attractions to nearby galaxies in groups, clusters, etc.
Cepheids
With their high luminosities (~10,000 L sun
),
Cepheid variables extend the distance scale to nearby galaxies, out ~25 Mpc (80 million light years).

Type 1a SN
Type-I supernova result from the detonation of white dwarf stars when their mass (slightly) exceeds
1.4 M sun
.
The brightness of the explosion should be (roughly) the same for every Type-1 supernova.
Type-I Supernovae are standard candles . Knowing their luminosity, and comparing to their measured flux, yields the distance via the inverse-square law.
Useful for determining distances out to (3 billion light years - 1 Gpc).

Tully-Fisher Relation
(a broadened line)
• Galaxy rotation is often measured via the 21cm atomic hydrogen line.
• Rotation speed (line width) is proportional to the galaxy ’ s mass.
• Galaxy luminosity is also proportional to galaxy mass (number of stars).
• The correlation between luminosity and rotation speed is referred to as the Tully-Fisher relation.

Extending the distance scale allows us to put more galaxies on the Hubble
Diagram and determine
Hubble ’ s constant with greater accuracy.
Type 1a SN

Each distance technique has uncertainties which then add to the error in determining the Hubble Constant
Current values hover around 70 km/s/Mpc with an error of
+/- 8 km/s/Mpc

The Cosmic
Distance Ladder
Hubble ’ s law allows us to measure distances to the “ ends of the visible universe, ”
(~13 billion light years).
It is less accurate for distances
< 100 Mpc because of the
“ peculiar ” velocities of galaxies
(i.e. motions affected by local gravitational fields).

• Many galaxies are typically millions or billions of parsecs from our galaxy.
• Typical distance units:
Mpc = Megaparsec = 1 million parsec
Gpc = Gigaparsec = 1 billion parsec
• Distances of Mpc or even Gpc  The light we see left the galaxy millions or billions of years ago!!
• “ Look-back times ” of millions or billions of years

Vastly different sizes and luminosities:
From small, lowluminosity irregular galaxies (much smaller and less luminous than the
Milky Way) to giant ellipticals and large spirals, a few times the Milky Way ’ s size and luminosity

Observe frequency of spectral lines across a galaxy.
From blue / red shift of spectral lines across the galaxy
 infer rotational velocity
Plot of rotational velocity vs. distance from the center of the galaxy: Rotation Curve

The Doppler effect permits us to measure the speed of material orbiting around the center of a galaxy. Photographs of galaxies show that luminous material appears to be concentrated towards the center and drops off with increasing distance.
Observed
Expected
Distance from galaxy center
If matter were really concentrated in this fashion, we would see
“ rotation curves ” following the “ expected ” path in the diagram at right. What is invariably observed instead is that rotation curves tend to remain high as far out as they can be measured. This implies the existence of massive halos of dark matter in galaxies.
The nature of the material comprising this dark matter is completely unknown at present, making this one of the greatest problems of contemporary astronomy.

Based on rotation curves, use Kepler ’ s 3 rd law to infer

Property Spirals Ellipticals Irregulars
Mass/M of Sun 10 9 to 4x10 11
Luminosity/L of Su 10 8 to 2x10 10
10 5
3x10 to 10
5
13 to 10 11
Diameter (light years) 16x10 3 to 8x10 5 3x10 3 to 7x10 5
%-age of galaxies 77% 20%
10 8 to 3x10 10
10 7 to 3x10 9
3x10 3 to 3x10
3%
4
National Optical Astronomy Observatory images
From this table, you should take note of which galaxies are the most and least massive, most and least luminous, and largest and smallest in size.

From the measurement of stellar velocities near the center of a galaxy:
Infer mass in the very center
 central black holes!
Several million, up to more than a billion solar masses!


Adding “ visible ” mass in:
• stars,
• interstellar gas,
• dust,
…etc., we find that most of the mass is “ invisible ” !
• The nature of this “ dark matter ” is not understood at this time.
• Some ideas: brown dwarfs, small black holes, exotic elementary particles.

Rich clusters:
1,000 or more galaxies, diameter of ~ 3 Mpc, condensed around a large, central galaxy
Poor clusters:
Less than 1,000 galaxies
(often just a few), diameter of a few Mpc, generally not condensed towards the center

As predicted by Einstein ’ s General Theory of Relativity, a compact intervening object is bending and distorting light from individual members of this cluster so that we see a halo effect.
Hubble Space Telescope Image

An intervening galaxy between us and this distant quasar is causing light from the quasar to be bent along curved paths that give rise to an Einstein cross , a phenomenon predicted by
Einstein ’ s General Theory of
Relativity.
National Optical Astronomy Observatories Image

Space between galaxies is not empty, but filled with hot gas (observable in X-rays)
That this gas remains gravitationally bound provides further evidence for dark matter.
Visible light
Coma Cluster of Galaxies
X-rays

Milky Way
Andromeda galaxy
Small Magellanic
Cloud
Large Magellanic
Cloud

Some galaxies of our local group are difficult to observe because they are located behind the center of our Milky
Way, from our view point.
Spiral Galaxy Dwingeloo 1

Cartwheel Galaxy Particularly in rich clusters, galaxies can collide and interact.
Galaxy collisions can produce ring galaxies and tidal tails.
NGC 4038/4039
Often triggering active star formation: starburst galaxies

Example for galaxy interaction with tidal tails:
The Mice

Numerical simulations of galaxy interactions have been very successful in reproducing tidal interactions like bridges, tidal tails, and rings.

NGC
7252:
Probably result of merger of two galaxies,
~ a billion years ago:
Radio image of M 64: Central regions rotating backward!
Small galaxy remnant in the center
Multiple nuclei in giant is rotating elliptical backward!
galaxies

NGC 5194
• Collisions of large with small galaxies often result in complete disruption of the smaller galaxy.
• Small galaxy is
“ swallowed ” by the larger one.
• This process is called
“ galactic cannibalism ”

M 82
Starburst galaxies are often very rich in gas and dust; bright in infrared: ultraluminous infrared galaxies
Cocoon Galaxy






 Half of all galaxies are in clusters (higher density; more Es and S0; mass > few times 10 14 -10 15 ) or groups (less dense; more Sp and Irr; less than 10 14 M sun
)
Clusters contain 100s to 1000s of gravitationally bound galaxies
Typically ~few Mpc across
Central Mpc contains 50 to 100 luminous galaxies (L > 2 x 10 10 L sun
)
Abell ’ s catalogs (1958; 1989) include 4073 rich clusters
Both luminous Es and dEs more concentrated in clusters than mid-size Es (?)
 Nearest rich clusters are Virgo and Fornax
(containing 1000 ’ s of galaxies; d=15-20 Mpc)
 Richer cluster, Coma, at d=70 Mpc and 7 Mpc across
 Clusters filled with hot gas (T=10 7 – 10 8 K X-ray bright – strips away cool gas of infalling galaxies
Coma Cluster

 Groups of galaxies are smaller than clusters
 Contain less than ~100 galaxies
 Loosely (but still gravitationally) bound
 Contain more spirals and irregular galaxies than clusters
“ The Local Group ”

Compare relative sizes of groups and clusters

 Distribution of galaxies in a cluster falls as r 1/4 of elliptical galaxies)
(like surface brightness
 May be dynamically relaxed systems
 Crossing time in a typical cluster (galaxy moving at 1000 km/s, cluster size 1 Mpc)  10 9 years
 Thus, clusters must be gravitationally bound systems and have possibly had enough time to “ relax ”
If clusters are relaxed systems, we can use the virial theorem to estimate their masses
M = (5/3)(<v 2 >R/G) eq. 13.47
Using radial velocity component only (Doppler shifts)
M = 5<v r
2 >R/G eq. 13.52
For Coma cluster, v rms what is mass?
= 860 km/s and cluster size 6.1 Mpc,
M = 5 x 10 15 M sun

Clusters have a Dark Matter problem too...
Luminous matter does not make up this mass
L
B
~ 8 x 10
M/L
B
12
~ 250 M
L
B,sun sun
/L
B,sun
Adding up mass in DM halos of spiral galaxies still not enough
Look for mass in hot, intracluster gas - T=10 7 K
Estimate gas mass from diffuse X-ray emission
Significant mass in gas – can be up to 10 times stellar mass
Dynamical (virial) measurements indicate this accounts for about
20% of the mass...

Mass appears to be contained in individual galaxy halos that extend further than we can measure
Clusters seem to have their own Dark Matter halos
M/L ratios for clusters is
200:1
Example of dark matter evidence in clusters (and the exotic nature of DM) 
The Bullet Cluster

Many clusters have a central dominant or cD galaxy at their center (e.g. M87 in Virgo)
•contain multiple nuclei
•could come from merger of central galaxies
•galactic cannibalism
Numerical simulations reveal what happens to the stars and gas when two galaxies collide and merge
Note: most mergers are actually thought to occur in groups rather than clusters. Why? The relative velocities of galaxies in groups are slower (v =
100 to 500 km/s) allowing them to have greater interactions.

Are there structures larger than clusters? YES
Local Supercluster - 10 6 galaxies in 10 23 lyr 3
(30 Mpc across)
•Can ’ t get mass with virial theorem
•Crossing times are too large, systems are not relaxed
•In addition to superclusters, large scale structure of galaxies reveals equally large voids

Redshift surveys of distant galaxies reveal the 3-d largescale structure in the Universe
•Galaxies appear to sit on 3-d surfaces (e.g. bubbles, sponges)
•Voids are ~50 Mpc across
•Survey mag limit appears as galaxy “ thinning ” beyond z=0.15
•Galaxy motions (wrt each other) are sometime organized  attracted by a large mass
•Our own MW and local group are moving towards the Virgo cluster at 300 km/s. Virgo is also moving towards the great attractor.

Where does the structure come from?
Top-down: First largest scale structures form
(superclusters, voids) and then smaller structures form out of the matter
Bottom-up: Smaller scale structures (i.e. galaxies) form first and then come together to form larger scale structures.
Which is it?

Compare large galaxy surveys with simulations designed to model the data. One of the largest simulation recently completed is the
Millenium Simulation.
•Assumes cold dark matter dominates Universe
•N-body simulation with particles interacting gravitationally
•10 10 particles mapped from early times in the
Universe to the present in cubes 500 h -1 Mpc on a side

Galaxies
Dark Matter

The simulation shows that structure forms more along the lines of the “ bottom-up ” model (i.e. galaxies form first), but that these form in the already over-dense regions of the dark matter distribution.
Redshift z=18.3 (t = 0.21 Gyr)
Redshift z=1.4 (t = 4.7 Gyr)
Redshift z=5.7 (t = 1.0 Gyr)
Redshift z=0 (t = 13.6 Gyr)