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```Midterm exam:
astrophysics
• date: March 17, 2006, 8:15 a.m.
• 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

• 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?
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
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?
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 .
Rnow

emitted
Rthen
Cosmological redshift

General definition of redshift:
z
emitted
 for cosmological redshift:
1 z 
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
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’
```
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