Handout by jizhen1947


									                                 The Milky Way
The Milky Way (our galaxy) is a fairly typical spiral galaxy

                             • About 2 x 1010 stars
                             • Flat-ish disc of stars:
                                 ~300 pc thick,
                                 ~30 kpc diameter
                             • Bright, roughly spherical
                               central bulge
                             • Spiral “arms” or orbiting stars
                             • Huge “halo” containing old
                               stars (Globular Clusters)
Spiral Density Waves
       Spiral arms are not “solid”
       but rotating density waves
       caused by mis-alignment of
       slightly elliptical orbits
       Star formation occurs in
       higher-density regions
                                  Other Galaxies
Not all galaxies are Spirals like our own.
In 1925 Hubble produced a classification sequence called the
“Hubble Sequence” or “Tuning Fork Diagram ”
Basic types:
   • Elliptical – sub-grouped by ellipticity
   • Spiral – sub-grouped by dominance of bulge
   • Barred-spiral – like spirals but with elongated bulge
   • Irregulars – everything else!
Sizes vary from few 1000 stars to > 1011 stars.
Note: This is not an evolutionary        sequence!
Hubble Sequence
                         Galaxy Types cont.
Ellipticals generally contain old stars and very little dust or
gas. Light is dominated by Red Giants.
The largest and smallest galaxies are elliptical.
The bulges of spirals and barred-spirals are similar to
ellipticals, but the spiral arms contain more dust and gas and
contain new stars.
The light of the arms is, therefore, dominated by hot, massive
blue stars .
                        Clusters of Galaxies
Just as stars group together
to form clusters, so do
Clusters of galaxies vary in
size from a handful of
galaxies to several
thousand .
We live in a small cluster
called the Local Group .

                                   Hubble’s Law
As noted in Distance Estimation section, galaxies appear to
be moving away from us and the speed of the recession is
proportional to their distance .
This was discovered by Edwin Hubble in 1929
             (See the website for a brief history)
Apparent recession due to the Expansion of the Universe

Although Hubbles’ original measurements were rather
inaccurate (not his fault!), the result has held.
Hubble’s Law cont.
                   Recession Velocities
Recession velocities measured using doppler shift in galaxy
Redshift z is given by:

Where l is the observed wavelength, l0 is the rest-frame
wavelength and Dl = l – l0
For small z:

Where v is the recession velocity and c is the speed of light
                                       Hubble’s Law
Hubble’s relationship is, therefore:

 Where d is the distance to the galaxy and H0 is called Hubble’s
 Constant     .
 The exact value for H0 is subject to debate!
 The latest value (from WMAP results) is:
                           71 km/s/Mpc
 Note the weird units!
The discovery of the expansion of the Universe, coupled
with Einsteins development of General Relativity marked
the beginning of Cosmology
Cosmology is based on the assumptions that:
   • Structure (ie galaxies, stars etc) are negligible on
     large enough scales:
         Æ The universe is Homogeneous
   ÆOur position in the universe is not special
         Æ Assumption of Isotropy
Without these assumptions, cosmology would get nowhere!
                          The Scale Factor
In this simple universe, we can represent any distance by a
dimensionless number multiplied by a universal Scaling
Factor     which changes with time.
The distance between two points s then becomes s=xR(t)
where x is the dimensionless distance (a constant for any
two points) and R(t) is the Scale Factor.
                        Recession Velocity
From this, the recession velocity is given by:


This demonstrates the linear nature of Hubble’s Law, but
note that the Hubble “constant” actually varies with time!
                       Age of the Universe
If H0 were a true constant, the age of the Universe would be
given by 1/H
However, the gravitational effect of all the mass in the
Universe will tend to slow down the expansion.
Therefore the 1/H0 value will be an upper     limit to the age.
The rate of change of R(t) is governed by the average
density of the universe.
If the density is low, the universe will expand for ever.
If it is high, the expansion will eventually be stopped and
The Cosmological Parameter that governs this is W0
           The Density Parameter - W0
 W0 is defined as:

Where r0 is the current density of the universe and rc is the
critical density – the density that sits on the border between an
infinitely expanding universe and a re-collapsing one.
      • W0 < 1 gives infinite expansion – called an Open Universe
      • W0 = 1 on the balance point - a Flat   Universe
      • W0 > 1 re-collapse will occur - a Closed   Universe
The Density Parameter - W0

                  The fate of the
                               So, what is W0?
The obvious way to estimate W0 is to add up all the mass we
can see and divide it by the volume we are looking at!
This gives W0 ~ 0.003
If this was all there was, the universe would expand for ever.
However, there is evidence for a lot of matter that we cannot
see making W0 much larger (close to 1)
This is the so-called Dark   Matter
               Evidence for Dark Matter
The idea that most of the mass in the Universe is something
we cannot see is a bold one!
Without a lot of evidence, it is going to be very difficult to
However, the nature of Dark Matter is such that we can only
see its gravitational effects.
One example is the rotation       curves of galaxies
                              Rotation Curves
The rotational velocity V of an object at radius R from an
object of mass M is given by

 Also, the gravitational mass of a galaxy at a particular
 orbital distance is the mass inside that orbit.
               Example Rotation Curve
V µ R ž constant density

          V = const. ž M µ R

                               Flat rotation curve, so mass
                                 must be increasing even
                               outside the “visible” galaxy.
                Cosmological Constant
When all the extra matter is included, W0 ~ 0.2-0.3
However, the theory of Inflation (where the universe
expands very fast in its early history) predicts W0 = 1
Current models provide the extra “density” by adding a
constant to the solution for R(t)
This is the Cosmological Constant L0
Sometimes called a “vacuum energy density” or “dark
energy ”, this term produces a repulsive force which
opposes gravity and is µ distance.
Evidence from Sn Ia “Standard candle” distances.
                  Best Estimate for W0
Current best estimate for W0 come as a result of the
WMAP microwave background measurements (see later):
   W0 from normal matter = 0.04
   W0 from dark matter   = 0.23
   W0 from L0            = 0.73
   W0 total              = 1.0 – Flat Universe
    Standard Hot Big Bang Model
If the universe is expanding, then it follows that by going
back in time, we move towards a moment when the universe
is infinitely dense
This singularity, from which the universe is expanding is the
so-called Big Bang.
The Big Bang model is a theory for the formation,
development and future history of the universe. As with any
theory, it includes assumptions and is developed by testing it.
               Big Bang - Assumptions
 • The universe is homogeneous and isotropic:
      –The Cosmological Principle
 – Gravity dominates on large scales (i.e. General
  Relativity is correct)
 –The same laws of physics apply though all time and

Without assumptions such as these, no theory can even get
Some attempts are begin made to test them, but it is very
                           Big Bang - Tests
The Big Bang theory is considered to be a very successful
This is mainly because it explains three very important
observational facts (tests):
    •   The expansion of the Universe
    •   The relative abundances of light elements
    •   The cosmic microwave background.
We have already discussed the expansion (Hubble’s Law
etc). What about the other two?
          Primordial Nucleosynthesis
For the first 10-15 minutes, the temperature of the universe is
very high – high enough to produce light elements by nuclear
The theory of Primordial Nucleosynthesis combines our
understanding of nuclear physics with the Big Bang model to
predict the relative abundances of the light elements:
   Deuterium (21H), Helium-3 (32He), Helium-4 (42He), Lithium
   -7 (73Li)
These predictions can be tested by studying metal-poor
galaxies (i.e. those where stellar-processing has had very little
          Predictions match observations exactly
 Cosmic Microwave Background
In the early stages of the universe, the temperature was high
enough to keep all matter fully ionized.
Photons scattered on all the free electrons and electrons
collided with ions.
This kept matter and radiation in equilibrium
However, once the temperature of the universe dropped to
~3000K, neutral Hydrogen could form – this was about ½
million years after the Big Bang.
At this point, the number of free electrons dropped
dramatically, and the photons became free to move
independently of matter:
                     Era of Decoupling
                                         CMB cont.
Therefore, at decoupling the universe was filled with
radiation with a blackbody temperature of ~3000K.
Since then expansion has caused the radiation to “cool”.
Big Bang theory, therefore, predicts a “sea” of photons filling
the universe now with a blackbody temperature of ~3K.
A 3K blackbody peaks at ~1mm wavelengths, so it is very
difficult to observe.
However, in 1965 Penzias and Wilson accidentally
discovered the radiation (a Nobel prize was to follow)
Since then, several satellites and other experiments have
produced detailed maps and spectra of the CMB.
CMB Spectrum from CoBE

           Fit to spectrum – giant errorbars
                                          CMB maps
Be the time of Decoupling, some structure had started to form
(by gravitational magnification of small fluctuations)
So, when photons became “free”, some had larger gravitational
wells to climb out of than others.
So, some will have been gravitationally redshifted        .
Therefore, some parts of the CMB will be slightly “cooler” than
By producing a map, we can measure the size and relative
density of the fluctuations at this very early point in the universe
This can then be used to devise further tests for the Big Bang
                                   WMAP Map
WMAP satellite recently produced newer results (Feb.2003).
Higher resolution and less noise.
Still supports Big Bang model
                 Cosmology - Summary
Current evidence favours a slightly modified Hot Big Bang
model of the Universe:
   • Universe started in a singularity ~13-14 billions years ago
   • Expanded since then, forming structure by gravitational
     instability magnifying tiny initial fluctuations
   • Expansion slowed by combination of “normal” matter,
     dark matter and “dark energy”
   • Evidence from: expansion, light element abundances,
     CMB (among others)
   • Still a number of questions…
                Cosmology - Questions
Some of the major outstanding questions:
   • What is the Dark Matter?
   • How do we get from the structure in the CMB to the
     galaxies, stars, planets etc that we see today?
   • What about the very earliest stages of the Big Bang?
     (new physics required)
   • What was there “before” the Big Bang? (this is more
     philosophy than physics!)
   Theories cannot be proved right, only proved wrong!

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