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Midterm exam:
astrophysics
• date: March 17, 2006, 8:15 a.m.
• location: Conrad Naber Hall
• bring pocket calculator
• NO text books, notes laptops etc.
• do NOT bring your own paper
• write on exam sheets directly
Spacephysics: see web site
Sir Isaac Newton:
(1643-1727)
Cosmology as a
Science
• Mathematical description
of the Universe
• The same physical laws
apply to earth and Universe
Newton: Fundamental contributions
•Mathematics: - series expansions
- differential calculus
- approximation methods
-…
• Optics:
- spectral analysis of white light
• Physics:
- ‘Principia mathematica…’
• Astronomy: - derive Kepler’s laws from
gravitational forces
• …..
A toy universe
constant density
(homogeneous)
boundary
According to Newton, what is going to happen ?
 The model Universe is going to collapse under
its own gravity
Newton’s Conclusion:
In order to avoid collapse
 homogeneous
 isotropic
 infinite size
 no center
 infinite in time
 has always been
 will always be
 perfect cosmological principle

The perfect cosmological principle
homogeneous: the universe looks the same
everywhere on large scales
 there is no special place (center)
 isotropic:
the universe looks the same in
all directions on the sky
 there is no special direction
 unchanging:
The universe looks the same at
all times
 there is no special epoch

Olber’s Paradox
• If the universe is i) eternal
ii) (more or less) uniformly filled
with stars
iii) infinite
• then there is a star along each line of sight
so:
Why is the night sky dark ?
Problems with an infinite universe

Olber’s Paradox: Why is the night sky dark?
Shell of radius r312:= 4r
2r1 :
r12 1)2
Surface: S321=4 (4r
(2r
2x
r12x
Volume: V321=4 (4r
)
(2r
1
2x
r12x
# of stars: N321= 4  (4r
)
(2r
1
luminosity per star: l*/16
/4
luminosity of shell:
2x
r12x
L321 = 4  (4r
)
(2r
/4
1 l* l*/16
= 4  r12x l* = L1
Olber’s Paradox:
Each shell contributes
L1 = 4  r12x l*
infinite number of shells
 infinite luminosity
(at least) one of the assumptions must be wrong !
How to solve Olber’s paradox ?
Universe is finite
 Universe has finite age
 The distribution of stars throughout space is
not uniform
 The wavelength of radiation increases with
time

Note: for the big bang model, all these
conditions are satisfied
Einstein:
• speed of light = const
relativity of
simultaneity,
special relativity
• general relativity:
space-time is curved
• prediction of black holes
• prediction of gravitational waves
Einstein
• Universe has to be static!
• only possible if extra-term is included in
equations to counter-balance attraction
cosmological constant
• Einstein’s “biggest blunder”
Edwin Hubble
(1889-1953)
Four major accomplishments
in extragalactic astronomy
 The establishment of the
Hubble classification
scheme of galaxies
 The convincing proof that galaxies are island
“universes”
 The distribution of galaxies in space
 The discovery that the universe is expanding
Doppler effect (for light)
The light of an approaching source is shifted to the
blue, the light of a receding source is shifted to the
red
Doppler effect
The light of an approaching source is shifted to the blue,
the light of a receding source is shifted to the red.
blue shift
red shift
Doppler effect
redshift:
obsem
z
em
z=0: not moving
z=2: v=0.8c
z=: v=c
The redshift-distance relation
Key results
Most galaxies are moving away from us
 The recession speed v is larger for more
distant galaxies. The relation between recess
velocity v and distance d fulfills a linear
relation:
v = H0  d
 Hubble’s measurement of the constant H0:
H0 = 500 km/s/Mpc
 today’s best fit value of the constant:
H0 = 71 km/s/Mpc (WMAP)

Question:
If all galaxies are moving away from us,
does this imply that we are at the center?
Answer:
Not necessarily, it also can indicate that the
universe is expanding and that we are at no
special place.
Einstein’s General Relativity +
observation of expanding Universe:
Universe started from a point:
“Big Bang Model”
Big Bang Model
Big Bang in a nutshell:
Cosmological redshift

While a photon travels from a distant source
to an observer on Earth, the Universe
expands in size from Rthen to Rnow.

Not only the Universe itself expands, but
also the wavelength of the photon .
received
Rnow

emitted
Rthen
Cosmological redshift

General definition of redshift:
received  emitted
z
emitted
 for cosmological redshift:
1 z 
received
emitted
Rnow

Rthen
A large redshift z implies ...
The spectrum is strongly shifted toward red
or even infrared colors
 The object is very far away
 We see the object at an epoch when the
universe was much younger than the present
day universe
 most distant astrophysical object discovered
so far: z= 6.3 (in 2005)
 z>5.8: “dark ages”

Are there any indications that this
picture is correct?

Yes !

Primordial Nucleosynthesis

Cosmic Microwave background
Primordial Nucleosynthesis
Georgy Gamov (1904-1968)



If the universe is expanding, then
there has been a big bang
Therefore, the early universe must
have been very dense and hot
Optimum environment to breed the elements by
nuclear fusion (Alpher, Bethe & Gamow, 1948)
 success: predicted that helium abundance is 25%
 failure: could not reproduce elements more massive
than lithium and beryllium ( formed in stars)
The Cosmic Microwave
Background (CMB)
Last scattering surface
transparent
opaque
Penzias and Wilson 1965
Working at Bell labs
 Used a satellite dish to measure radio
emission of the Milky Way
 They found some extra noise in the receiver,
but couldn’t explain it
 discovery of the background radiation
 Most significant cosmological observation
since Hubble
 Nobel prize for physics 1978

The cosmic microwave
background radiation (CMB)
Temperature of
2.728±0.004 K
 isotropic to
1 part in 100 000
 perfect black body
 1990ies: CMB is
one of the major tools to study cosmology
 Note: ~1% of the noise in your TV is from
the big bang

More results from the CMB

The Earth is moving
with respect to the
CMB  Doppler shift

The emission of the
Galaxy

Fluctuations in the
CMB
•Fluctuations in CMB responsible for
structure formation in the universe
Cosmic Structure formation
New developments:
Science discovery of the year 1998
fainter
q0 = 0
q0 = 0.5
Data indicates:
q0 < 0
 Expansion
is accelerating
more distant
From Supernova observations:
The expansion of the universe is
accelerating !!!
 But gravity is always attractive, so it only
can decelerate


Revival of the cosmological constant 
The fate of the Universe for >0
k=+1
>0
=0
Wilkinson Microwave
Anisotropy Probe (WMAP) (2003)
COBE (1992)
WMAP (2003)
Summary of most important results of
WMAP
• Age of the Universe: 13.7 billion years
• First stars:
200 million years
after Big Bang
• CMB:
decoupled 379 000 years
after Big Bang
• Hubble constant:
H0= 71 (km/s)/Mpc
• Content of the Universe:
- 4% Atoms
- 23 % cold, dark matter
- 73 % ‘Dark Energy’