Download Astronomy 201 Cosmology

Physics 270 – The Universe:
Astrophysics, Gravity and Cosmology
•Andris Skuja, May 9, 2006 -- Physics 270
The History of Cosmology
• Mythology vs the scientific method
• Cosmos = Earth  solar system  Milky
Way  Hubble sphere
• Copernicus, Brahe, Kepler, Galileo
•Andris Skuja, May 9, 2006 -- Physics 270
Newton: Cosmology
as a Science
• Galileo: The Scientific method & the
universality of scientific laws
• Newton’s laws
• Newton’s gravity: The heavens and the
Earth follow the same scientific principles
• Galileo: Relativity before Einstein
•Andris Skuja, May 9, 2006 -- Physics 270
Einstein’s Theories of
Special and General
Relativity
• Principle of Relativity
• Giving up absolute space and time
• Space and time: where common sense
makes no sense
• what is here and there or now and then ?
•Andris Skuja, May 9, 2006 -- Physics 270
Special Relativity
• All inertial frames of reference are
equivalent
• The speed of light is absolute (invariant)
• Maxwell’s equations are invariant under
Lorentz transformation
• Newton’s laws, which are based on
absolute space and time, need to be
modified
•Andris Skuja, May 9, 2006 -- Physics 270
Some open problems
• How to treat accelerations ?
• How to deal with gravity ?
• Newton’s gravity acts instantaneously, i.e. it
is inconsistent with special relativity’s
conclusion that information cannot be
communicated faster than the speed of light.
• Distance is relative, so which distance to
use in computing the gravitational force ?
•Andris Skuja, May 9, 2006 -- Physics 270
Non-inertial reference frame
• Non-inertial frames  fictitious forces
– centrifugal force
– Coriolis force
•Andris Skuja, May 9, 2006 -- Physics 270
Why is the Space Shuttle orbiting?
 The space Shuttle is continuously falling
towards the Earth
•Andris Skuja, May 9, 2006 -- Physics 270
Is there no gravity in space ?
No, there is
gravity (actually Earth’s
gravity at the
orbit of the
Shuttle is still
~80-90% of
its strength on
the ground
 So why do astronauts appear
to be weightless ?
•Andris Skuja, May 9, 2006 -- Physics 270
What effect does mass have?
• Gravity: tendency of massive bodies to
attract each other
• Inertia: resistance of a body against changes
of its current state of motion
•Andris Skuja, May 9, 2006 -- Physics 270
Is gravity and inertia the same
thing ?
• No. They are completely different physical
concepts.
• There is no a priori reason, why they should
be identical. In fact, for the electromagnetic
force (Coulomb force), the source (the
charge Q) and inertia (m) are indeed
different.
• But for gravity they appear to be identical
 Equivalence Principle
•Andris Skuja, May 9, 2006 -- Physics 270
Eötvös experiment
Gravity
Coriolis
•Andris Skuja, May 9, 2006 -- Physics 270
Result of the Eötvös experiment
• Gravitational and inertial mass are identical
to one part in a billion
• modern experiments: identical to one part in
a hundred billion
•Andris Skuja, May 9, 2006 -- Physics 270
What effect does mass have?
• Source of gravity
F G
M mgravity
r
2
• Inertia
F  minertia  a
•Andris Skuja, May 9, 2006 -- Physics 270
Principle of Equivalence
F  minertial  a  G
M mgravity
r
2
 mgravity 
M
  G 2
 a  
m
r
inertial


=1
•Andris Skuja, May 9, 2006 -- Physics 270
Weak equivalence principle
The laws of mechanics are precisely
the same in all inertial and freely
falling frames. In particular, gravity is
completely indistinguishable from
any other acceleration.
Strong equivalence principle
The laws of physics are precisely the
same in all inertial and freely falling
frames, there is no experiment that
can distinguish them.
•Andris Skuja, May 9, 2006 -- Physics 270
Consequences of the equivalence
principle: mass bends light
Observer in freely falling reference frame
•Andris Skuja, May 9, 2006 -- Physics 270
Consequences of the equivalence
principle: mass bends light
Outside Observer
•Andris Skuja, May 9, 2006 -- Physics 270
Examples for light bending
•Andris Skuja, May 9, 2006 -- Physics 270
Some effects predicted by the
theory of general relativity
•
•
•
•
gravity bends light
gravitational redshift
gravitational time dilation
gravitational length contraction
•Andris Skuja, May 9, 2006 -- Physics 270
Least action principle
• light travels on a path that minimizes the
distance between two points
 for flat space: straight line
• a path that minimizes the distance between
two points is called a geodesic
• Examples for geodesics
– plane: straight line
– sphere: great circle
•Andris Skuja, May 9, 2006 -- Physics 270
What is the shortest way to Europe?
•Andris Skuja, May 9, 2006 -- Physics 270
Spacetime
• Fourth coordinate: ct
• time coordinate has different sign than
spatial coordinates
• spacetime distance:
s   c t   ct x   x
2
2
2
• , ,  : metric coefficients
•Andris Skuja, May 9, 2006 -- Physics 270
2
Weak equivalence principle
The laws of mechanics are precisely
the same in all inertial and freely
falling frames. In particular, gravity is
completely indistinguishable from
any other acceleration.
Strong equivalence principle
The laws of physics are precisely the
same in all inertial and freely falling
frames, there is no experiment that
can distinguish them.
•Andris Skuja, May 9, 2006 -- Physics 270
General relativity
• Mass tells space how to curve
• Space tells mass how to move
•Andris Skuja, May 9, 2006 -- Physics 270
Why does space curvature result
in attraction ?
•Andris Skuja, May 9, 2006 -- Physics 270
Euclidean (flat) geometry:
• Given a line and a point not on the line,
only one line can be drawn through that
point that will be parallel to the first line
• The circumference of a circle of radius r is
2 r
• The three angles of a triangle sum up to
180
•Andris Skuja, May 9, 2006 -- Physics 270
Spherical geometry:
• Given a line and a point not on the line, no
line can be drawn through that point that
will be parallel to the first line
• The circumference of a circle of radius r is
smaller than 2 r
• The three angles of a triangle sum up to
more than 180
•Andris Skuja, May 9, 2006 -- Physics 270
Hyperbolic geometry:
• Given a line and a point not on the line, an
infinite number of lines can be drawn
through that point that will be parallel to the
first line
• The circumference of a circle of radius r is
larger than 2 r
• The three angles of a triangle sum up to less
than 180
•Andris Skuja, May 9, 2006 -- Physics 270
Tidal forces (I)
•Andris Skuja, May 9, 2006 -- Physics 270
Tidal forces (II)
•Andris Skuja, May 9, 2006 -- Physics 270
Tidal forces (III)
•Andris Skuja, May 9, 2006 -- Physics 270
Tidal forces (IV)
•Andris Skuja, May 9, 2006 -- Physics 270
So does the existence of tidal forces
violate the equivalence principle ?
• there is no freely falling frame of reference
in which gravity vanishes globally
• there is a freely falling frame of reference in
which gravity vanishes locally
• equivalence principle holds for small labs,
“small” in comparison to distances over
which the gravitational field changes
significantly.
• spacetime is locally flat
•Andris Skuja, May 9, 2006 -- Physics 270
Towards a new theory for gravity ...
Requirements:
• it should locally fulfill the equivalence
principle
• it should relate geometry of space to the
distribution of mass and energy
• it should be locally flat
• it should reduce to Newtonian gravity for
small velocities (compared to c) and for
weak gravitational fields
•Andris Skuja, May 9, 2006 -- Physics 270
The entire Universe in one line
G

8 G 
 4 T
c
Geometry of
spacetime
(Einstein tensor)
Distribution of
mass and energy
in the universe
(stress-energy tensor)
•Andris Skuja, May 9, 2006 -- Physics 270
Why is general relativity (GR)
difficult ?
• conceptually difficult (relativity of space
and time, curvature of spacetime)
• set of 10 coupled partial differential
equations
• non linear (solutions do not superpose)
• space and time are part of the solution
 exact solution known only for a very few
simple cases
•Andris Skuja, May 9, 2006 -- Physics 270
Checklist
• How to deal with accelerations ? 
• How to deal with gravity ? 
• Newton’s gravity acts instantaneously, i.e. it
is inconsistent with special relativity’s
conclusion that information cannot be
communicated faster than the speed of light. 
• Distance is relative, so which distance to use
in computing the gravitational force ? 
•Andris Skuja, May 9, 2006 -- Physics 270
So what is left to do ?
• Show that general relativity provides a
consistent and accurate description of nature
 test it by experiment/observation
•Andris Skuja, May 9, 2006 -- Physics 270
Some open problems
• How to deal with accelerations ?
• How to deal with gravity ?
• Newton’s gravity acts instantaneously, i.e. it
is inconsistent with special relativity’s
conclusion that information cannot be
communicated faster than the speed of light.
• Distance is relative, so which distance to
use in computing the gravitational force ?
•Andris Skuja, May 9, 2006 -- Physics 270
Boost factor
• special relativity:

1
1
v2
c2
• general relativity:
1
1


2
2 GM
v
esc
1  Rc2
1  c2
•Andris Skuja, May 9, 2006 -- Physics 270
First test: bending of light
• Star light should be bend as it passes
through the gravitational field of the Sun,
i.e., it should be possible to see a star
behind the Sun
•Andris Skuja, May 9, 2006 -- Physics 270
First test: bending of light
• Star light should be bend as it passes
through the gravitational field of the Sun,
i.e., it should be possible to see a star
behind the Sun
• General relativity predicts an angle of
1.75”, twice as big as that predicted by
Newtonian gravity
• measured by Arthur Eddington in 1919. Key
event for Einstein’s elevation to a celebrity.
•Andris Skuja, May 9, 2006 -- Physics 270
Test 2: Perihelion shift of Mercury
• Planets do not move on perfect ellipses, but
ellipses are precessing. This effect is due to
the gravitational force exerted by the other
planets
•Andris Skuja, May 9, 2006 -- Physics 270
Test 2: Perihelion shift of Mercury
• Planets do not move on perfect ellipses, but
ellipses are precessing. This effects is
caused by the perturbing effect of the other
planets gravitational field.
• Mercury’s precession amounts to 5600” per
century, but only 5557” can be explained by
Newtonian gravity, leaves a discrepancy of
43” per century.
• General relativity predicts exactly this
additional precession
•Andris Skuja, May 9, 2006 -- Physics 270
Test 3: gravitational time dilation
and redshift
• Can be measured by experiments on Earth
(challenging, but feasible)
• Better: White Dwarfs (very compact objects;
mass comparable to that of the Sun, radius
comparable to that of the Earth), because they
have a stronger gravitational field
• Even better: Neutron Stars and Pulsars (very
compact objects; mass comparable to that of
the Sun, radius only 10-100 km), because
they have a very strong gravitational field
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Pulsar: a rapidly rotating highly magnetized
neutron star that emits radio pulses at
regular intervals
• Discovered by Bell and Hewish in 1967
• Nobel Prize in physics (1974)
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Pulsar:
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Binary pulsar: two
pulsars orbiting
each other
• Orbital time: 7.75h
• Discovered by
Hulse and Taylor in
1974
• Nobel Prize in
physics (1993)
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Precession: 4.2º
per year
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Time delay: Clocks tick slower in strong
gravitational fields
•Andris Skuja, May 9, 2006 -- Physics 270
Test 4: Binary pulsar PSR 1913+16
• Gravitational Waves: Orbital decay due to
emission of gravitational radiation
data points
Prediction of GR
•Andris Skuja, May 9, 2006 -- Physics 270
Tests to come: Gravity Probe B
•Andris Skuja, May 9, 2006 -- Physics 270
Gravitational time dilation and
redshift
• Can be measured by experiments on Earth
(challenging, but feasible)
• Better: White Dwarfs (very compact objects;
mass comparable to that of the Sun, radius
comparable to that of the Earth), because they
have a stronger gravitational field
• Even better: Neutron Stars and Pulsars (very
compact objects; mass comparable to that of
the Sun, radius only 10-100 km), because
they have a very strong gravitational field
•Andris Skuja, May 9, 2006 -- Physics 270
Flash-back: Newtonian gravity
• What velocity is required to leave the
gravitational field of a planet or star?
vesc
2G M

R
• Example: Earth
– Radius: R = 6470 km = 6.47106 m
– Mass: M = 5.97 1024 kg
 escape velocity: vesc = 11.1 km/s
•Andris Skuja, May 9, 2006 -- Physics 270
Flash-back: Newtonian gravity
• What velocity is required to leave the
gravitational field of a planet or star?
vesc
• Example: Sun
2G M

R
– Radius: R = 700 000 km = 7108 m
– Mass: M = 21030 kg
 escape velocity: vesc = 617 km/s
•Andris Skuja, May 9, 2006 -- Physics 270
Flash-back: Newtonian gravity
• What velocity is required to leave the
gravitational field of a planet or star?
vesc
2G M

R
• Example: a solar mass White Dwarf
– Radius: R = 5000 km = 5106 m
– Mass: M = 21030 kg
 escape velocity: vesc = 7300 km/s
•Andris Skuja, May 9, 2006 -- Physics 270
Flash-back: Newtonian gravity
• What velocity is required to leave the
gravitational field of a planet or star?
vesc
2G M

R
• Example: a solar mass neutron star
– Radius: R = 10 km = 104 m
– Mass: M = 21030 kg
 escape velocity: vesc = 163 000 km/s  ½ c
•Andris Skuja, May 9, 2006 -- Physics 270
Flash-back: Newtonian gravity
• Can an object be so small that even light
cannot escape ?  Black Hole
2G M
vescRS  2
cR
RS: “Schwarzschild Radius”
• Example: for a solar mass
– Mass: M = 21030 kg
 Schwarzschild Radius: RS = 3 km
•Andris Skuja, May 9, 2006 -- Physics 270
Some definitions ... and Black Holes
• The Schwarzschild radius RS of an object of
mass M is the radius, at which the escape
speed is equal to the speed of light.
• The event horizon is a sphere of radius RS.
Nothing within the event horizon, not even
light, can escape to the world outside the
event horizon.
• A Black Hole is an object whose radius is
smaller than its event horizon.
•Andris Skuja, May 9, 2006 -- Physics 270
Sizes of objects
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s do it within the context of
general relativity — spacetime
• spacetime distance (flat space):
s  c t  R
2
2
2
time
2
space
• Fourth coordinate: ct
• time coordinate has different sign than
spatial coordinates
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s do it within the context of
general relativity — spacetime
• spacetime distance (curved space of a point
mass):
RGM
11

2

2
S  2 2 2 2
ss  11 2  c ctt 

R
2GM
1

 cR R 
1  RS c/2 RR
22
time
•Andris Skuja, May 9, 2006 -- Physics 270
space
What happens if R  RS
1
 RS  2 2
2
s  1   c t 
R
R
1  RS / R

2
time
space
• R > RS: everything o.k.: time: +, space:  but
gravitational time dilation and length contraction
• R  RS: time  0 space  
• R < RS: signs change!! time: , space: +
 “space passes”, everything falls to the center
 infinite density at the center, singularity
•Andris Skuja, May 9, 2006 -- Physics 270
Structure of a Black Hole
•Andris Skuja, May 9, 2006 -- Physics 270
What happens to an astronaut
who falls into a black hole?
• Far outside: nothing special
• Falling in: long before the astronaut reaches
the event horizon, he/she is torn apart by
tidal forces
• For an outside observer:
– astronaut becomes more and more redshifted
– The astronaut’s clock goes slower and slower
– An outside observer never sees the astronaut
crossing the event horizon.
•Andris Skuja, May 9, 2006 -- Physics 270
What happens, if an astronaut
falls into a black hole?
• For the astronaut:
– He/she reaches and crosses the event horizon in
a finite time.
– Nothing special happens while crossing the
event horizon (except some highly distorted
pictures of the local environment)
– After crossing the event horizon, the astronaut
has 10 microseconds to enjoy the view before
he/she reaches the singularity at the center.
•Andris Skuja, May 9, 2006 -- Physics 270
Cosmic censorship
• Singularity: a point at which spacetime
diverges
–
–
–
–
infinite forces are acting
laws of physics break down
quantum gravity may help ?
no problem as long as a singularity is shielded
from the outside world by an event horizon
• Hypothesis: Every singularity is surrounded
by an event horizon.
There are no naked singularities
•Andris Skuja, May 9, 2006 -- Physics 270
Near a black hole: bending of light
•Andris Skuja, May 9, 2006 -- Physics 270
The Photon sphere
The photon sphere is a sphere of radius 1.5 RS.
On the photon sphere, light orbits a black hole
on a circular orbit.
•Andris Skuja, May 9, 2006 -- Physics 270
Structure of a rotating black hole
Within the ergosphere (or static sphere)
nothing can remain at rest. Spacetime is
dragged around the hole
•Andris Skuja, May 9, 2006 -- Physics 270
No-Hair theorem
• Properties of a black hole:
–
–
–
–
it has a mass
it has an electric charge
it has a spin (angular momentum)
that’s it. Like an elementary particle, but much
more massive
Black holes have no hair
•Andris Skuja, May 9, 2006 -- Physics 270
Hawking Radiation
• Heisenberg uncertainty principle:
Et > h/2
Energy need not be conserved over short
periods, only on average
• Virtual particles: particle-antiparticle pairs
created from vacuum energy fluctuations
which quickly disappear
• Virtual particles that can "steal" energy
from elsewhere become real
•Andris Skuja, May 9, 2006 -- Physics 270
Hawking Radiation
• Virtual pairs near a black hole can steal
energy from the gravitational field
– Tidal stresses accelerate one particle outward,
one drops into event horizon
– Energy of new particle comes from gravitational
energy of BH, so BH mass must decrease
– Black hole evaporates!
•Andris Skuja, May 9, 2006 -- Physics 270
Hawking Radiation
• Energy for new particles comes from tidal
stresses
– Tidal effects must be large over short path
lengths of virtual pairs
– Smaller black holes have steeper gravitational
gradients
=> Smaller black holes evaporate more quickly
tevap = 1010(MBH /1012 kg)3 yr
tevap(1Msolar) ~ 1065 yr
•Andris Skuja, May 9, 2006 -- Physics 270
Hawking Radiation
• Black holes emit as black bodies
– Temperature of black hole proportional to rate of
radiation
– TBH = 10-7 (Msolar / MBH)
– T(1 Msolar) ~ 10-7 K
– T(106 Msolar) ~ 10-13 K
•Andris Skuja, May 9, 2006 -- Physics 270
Exotica
• White holes - a phenomenon analogous to a
black hole from which light can only escape.
No obvious way to make or power one
• Wormholes - conduits between two points in
spacetime. Unstable, difficult to avoid
singularity without going faster than c,
solutions with timelike paths only size of
elementary particles. If they exist, probably
not useful for travel since stable solutions
require "exotic matter"
•Andris Skuja, May 9, 2006 -- Physics 270
A Practical Perspective
• Two main types of black hole in the universe
– Stellar mass black holes: created by the collapse
of a massive star at the end of its life,
~3-100? Msolar
– Supermassive black holes (SMBH): found in the
centers of galaxies, power quasars and AGN,
~a few times 106 - 109 M
•Andris Skuja, May 9, 2006 -- Physics 270
Stellar Black Holes
• Created from stars of more than ~30 Msolar
• Detectable in binary systems
– Normal or evolved star transfers mass to black
hole via accretion disk
– Measure orbital period and velocity of
companion and use Kepler's laws to derive lower
limits on mass
– Neutron stars < 3 Msolar so any larger invisible
companion must be black hole or unknown
physics
•Andris Skuja, May 9, 2006 -- Physics 270
Stellar Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Stellar Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Stellar Black Holes
• X-Ray Binaries
– Viscosity (friction) of gas in disk heats up disk
– A few to 40% of gravitational potential energy (=
rest mass energy) liberated
– Temperatures of ~105-106 K in inner disk
– Spectrum peaks in soft x-rays
– Optically thin material in corona or inner disk at
>107 K gives hard x-ray emission
– Some with relativistic jets
– Luminosities of order 105 Lsolar
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
• Active Galactic Nuclei (AGN)
– Many types; most commonly discussed are radio
galaxies, Seyferts, quasars, and QSOs
– Large black holes at the centers of galaxies form
at early epochs, possibly from collapse of dense
stellar clusters, and grow by accretion over
lifetime of universe
– Luminosity from accretion disks as in X-ray
binaries, but larger BH = lower temperature
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
• AGN structure
– Accretion disk at a few x 104 K, peak emission in
UV (R ~ 100AU ~100 RS)
– Hot, rarefied gas in x-ray halo or corona (R ~ 110 AU ~ RS)
– Broad emission line region (BLR); clouds with
velocities of 104 kms-1, indicate strong
gravitational field (R ~ 0.01pc)
– Dusty molecular torus in plane of disk (R ~ 0.11pc) IR emission
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
• AGN structure continued
– Narrow emission line region (NLR); clouds of
ionized gas with widths of a few hundred kms-1
Seen in cones extending from ~50pc to 15kpc
– Relativistic jets - accelerated by magnetic fields
in disk to significant fraction of c. Looking headon into quasar jets, see OVVs and BL Lacs
– Jets in radio galaxies may extend ~1 Mpc
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
• AGN characteristics
– Emission over 21 orders of magnitude in
frequency - from radio to -rays
– Range of luminosities, from barely discernable to
> 1015 Lsolar, 10,000 times the luminosity of a
bright galaxy
– Radio quiet and radio loud
– Often associated with starbursts, interacting
galaxies, Luminous Infrared Galaxies (LIRGs,
ULIRGs, HLIRGs)
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
• Evidence
– Kinematic evidence
•
•
•
•
Stellar motions in center of Milky Way
Stellar and gas motions in other galaxies
OH masers in NGC 4258
All imply tremendous mass in a tiny area
– Images of dusty torii and accretion disks
– Only way of producing enough energy to make a
quasar in so little space
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive
Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Supermassive Black Holes
•Andris Skuja, May 9, 2006 -- Physics 270
Questions:
• Do they really exist ? (Observe gravitational
effects )
• How do we observe something that does not
emit light? (Light bends around them)
•Andris Skuja, May 9, 2006 -- Physics 270
The cosmic distance ladder
• Parallax
– solar neighborhood (< 1 kpc)
• Main sequence fitting
– distances within the Galaxy (<100 kpc)
• Cepheids
– nearby galaxies (< 20 Mpc)
• Tully-Fisher relation
– distant galaxies (< 500 Mpc)
• Type 1a supernovae
– cosmological distances (~ 1 Gpc)
•Andris Skuja, May 9, 2006 -- Physics 270
Nature of spiral nebulae and the
Milky Way (MW)
Curtis
• MW is 10 kpc across
• Sun near center
• spiral nebulae were other
galaxies
– high recession speed
– apparent sizes of nebulae
– did not believe van
Maanen’s measurement
 Milky Way = one galaxy
among many others
Shapley
• MW is 100 kpc across
• Sun off center
• spiral nebulae part of the
Galaxy
– apparent brightness of
nova in the Andromeda
galaxy
– measured rotation of
spirals (via proper motion)
by van Maanen
 Milky Way = Universe
•Andris Skuja, May 9, 2006 -- Physics 270
Solution
• Role of dust
– obscuration: Kapteyn/Curtis could only see a
small fraction of the Milky Way disk
– dimming: stars appear to be dimmer 
Shapley, ignoring dust, concluded that globular
clusters are farther away than they actually are.
 Milky Way is 30 kpc across, Sun is 8.5 kpc off
center.
 Spiral nebulae are galaxies like the Milky
Way. Distance: millions of parsec.
•Andris Skuja, May 9, 2006 -- Physics 270
•Andris Skuja, May 9, 2006 -- Physics 270
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
•Andris Skuja, May 9, 2006 -- Physics 270
The Hubble classification
•Andris Skuja, May 9, 2006 -- Physics 270
The Hubble classification
• Elliptical galaxies (E0-E7)
– classified according to their flattening: 10(1-b/a)
• Spiral galaxies (S0, Sa-Sd)
– classified according to their bulge-to-disk ratio
– Sa: large bulge, Sd: small bulge
– S0: transition spiral to elliptical
• Barred spiral galaxies (SB0, SBa-SBd)
– classified according to their bulge to disk ratio
• Irregular galaxies (Irr)
•Andris Skuja, May 9, 2006 -- Physics 270
THE EXPANDING UNIVERSE:
Using the Doppler Effect to Measure Velocity
T4 T3
T2
T1
Redshift
Blueshift
•Andris Skuja, May 9, 2006 -- Physics 270
Galaxy Spectroscopy
 Spectra
of a nearby star
and a distant galaxy
 Star is nearby,
approximately at rest
 Galaxy is distant,
traveling away from us at
12,000 km/s
Stellar Spectrum
Sodium
Magnesium
The larger the redshift:
the greater the distance
from us
Galaxy Spectrum
Calcium
•Andris Skuja, May 9, 2006 -- Physics 270
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
•Andris Skuja, May 9, 2006 -- Physics 270
red shift
Doppler effect
redshift:
1 v / c
1 z 
1 v / c
z=0: not moving
z=2: v=0.8c
z=: v=c
•Andris Skuja, May 9, 2006 -- Physics 270
The redshift-distance relation
•Andris Skuja, May 9, 2006 -- Physics 270
The redshift-distance relation
•Andris Skuja, May 9, 2006 -- Physics 270
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 = 70 km/s/Mpc
•Andris Skuja, May 9, 2006 -- Physics 270
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. If the velocity of recession is
proportional to distance, then any point is at
the center of the expansion
•Andris Skuja, May 9, 2006 -- Physics 270
The great synthesis (1930)
• Meeting by Einstein, Hubble and Lemaître
– Einstein: theory of general relativity
– Friedmann and Lemaître: expanding universe
as a solution to Einstein’s equation
– Hubble: observational evidence that the
universe is indeed expanding
• Consequence:
– Universe started from a point
 The Big Bang Model
•Andris Skuja, May 9, 2006 -- Physics 270
History of the Universe (with
Inflation)
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s apply Einstein’s equation to
the Universe
• What is the solution of Einstein’s equation
for a homogeneous, isotropic mass
distribution?
– As in Newtonian dynamics, gravity is always
attractive
– a homogeneous, isotropic and initially static
universe is going to collapse under its own
gravity
– Alternative: expanding universe (Friedmann)
•Andris Skuja, May 9, 2006 -- Physics 270
Einstein’s proposal: cosmological
constant 
• There is a repulsive force in the universe
 vacuum exerts a pressure
 empty space is curved rather than flat
• The repulsive force compensates the attractive
gravity  static universe is possible
• but: such a universe turns out to be unstable:
one can set up a static universe, but it simply
does not remain static
• Einstein: “greatest blunder of his life”, but is it
really … ?
•Andris Skuja, May 9, 2006 -- Physics 270
initial distance: 1 length unit
final distance: 2 length units
recess velocity: 1 length unit per time unit
initial distance: 2 length units
final distance: 4 length units
recess velocity: 2 length units per time unit
•Andris Skuja, May 9, 2006 -- Physics 270
A metric of an expanding Universe
• Recall: flat space
s  ct   x  y  z
2
2
2
2
2
• better: using spherical coordinates (r,,)
s  ct   r  r   r sin  
2
2
2
2
•Andris Skuja, May 9, 2006 -- Physics 270
2
2
2
2
A metric of an expanding Universe
• But, this was for a static space. How does
this expression change if we consider an
expanding space ?

s  ct   R 2 (t ) r 2  r 2  2  r 2 sin 2   2
2
2
• R(t) is the so-called scale factor
•Andris Skuja, May 9, 2006 -- Physics 270

Example: static universe
R(t)
t
•Andris Skuja, May 9, 2006 -- Physics 270
Example: expanding at a constant
rate
R(t)
t
•Andris Skuja, May 9, 2006 -- Physics 270
Example: expansion is
slowing down
R(t)
t
•Andris Skuja, May 9, 2006 -- Physics 270
Example: expansion is
accelerating
R(t)
t
•Andris Skuja, May 9, 2006 -- Physics 270
Example: collapsing
R(t)
t
•Andris Skuja, May 9, 2006 -- Physics 270
How old is the universe?
• A galaxy at distance d recedes at velocity
v=H0  d.
• When was the position of this galaxy
identical to that of our galaxy? Answer:
d
1
t Hubble  
v H0
• tHubble: Hubble time. For H0 = 65 km/s/Mpc:
tHubble = 15 Gyr
•Andris Skuja, May 9, 2006 -- Physics 270
How big is the universe?
• We can’t tell. We can only see (and are affected
by) that part of the universe that is closer than
the distance that light can travel in a time
corresponding to the age of the Universe
• But we can estimate, how big the observable
universe is:
c
d Hubble  ct Hubble 
H0
• dHubble: Hubble radius. For H0 = 65 km/s/Mpc:
dHubble = 4.6 Gpc
•Andris Skuja, May 9, 2006 -- Physics 270
A metric of an expanding Universe
• But, so far, we only considered a flat space.
What, if there is curvature ?
2


r
2
2
2
2
2
2
2
2
s  ct   R (t )
 r   r sin   
2
 1  kr

• k is the curvature constant
– k=0: flat space
– k>0: spherical geometry
– k<0: hyperbolic geometry
•Andris Skuja, May 9, 2006 -- Physics 270
A metric of an expanding Universe
• But, so far, we only considered a flat space.
What, if there is curvature ?
k>0
k=0
• k is the curvature constant
– k=0: flat space
– k>0: spherical geometry
– k<0: hyperbolic geometry
•Andris Skuja, May 9, 2006 -- Physics 270
k<0
Cosmological redshift
• While a photon travels from a distance
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 
changes.
received
Rnow

emitted
Rthen
•Andris Skuja, May 9, 2006 -- Physics 270
Cosmological redshift
• General definition of redshift:
received  emitted
z
emitted
 for cosmological redshift:
1 z 
received
emitted
Rnow

Rthen
•Andris Skuja, May 9, 2006 -- Physics 270
Cosmological redshift
• Examples:
– z=1  Rthen/Rnow = 0.5
• at z=1, the universe had 50% of its present day size
• emitted blue light (400 nm) is shifted all the way
through the optical spectrum and is received as red
light (800 nm)
– z=4  Rthen/Rnow = 0.2
• at z=4, the universe had 20% of its present day size
• emitted blue light (400 nm) is shifted deep into the
infrared and is received at 2000 nm
– most distant astrophysical object discovered so
far: z=5.8
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s switch to general relativity
• Friedmann equation
8 G
2
2
v 
 R  kc
3
2
• k is the curvature constant
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s switch to general relativity
• Friedmann equation
8 G
2
2
v 
 R  kc
3
2
• k is the curvature constant
– k=0: flat space, forever expanding
– k>0: spherical geometry, eventually recollapsing
– k<0: hyperbolic geometry, forever expanding
•Andris Skuja, May 9, 2006 -- Physics 270
k>0
k=0
•Andris Skuja, May 9, 2006 -- Physics 270
k<0
Can we predict the fate of the
Universe ?
• Friedmann equation:
v8 G8 G2
kc
2
H v  2   R  kc
 2
R 3 3
R
2
2
22
0
• k=0:
 crit
2
0
3H

8 G
•Andris Skuja, May 9, 2006 -- Physics 270
Can we predict the fate of the
Universe ?
• If the density  of the Universe
–  =crit: flat space, forever expanding
–  >crit: spherical geometry, recollapsing
–  < crit: hyperbolic geometry, forever expanding
• so what is the density of the universe?
– We don’t know precisely
–  >crit very unlikely
– currently favored model:   0.3crit
•Andris Skuja, May 9, 2006 -- Physics 270
How big is crit ?
• crit = 810-30 g/cm3  1 atom per 200 liter
• density parameter 0
3H 

0 

 crit 8 G
2
0
– 0 =1: flat space, forever expanding (open)
– 0 >1: spherical geometry, recollapsing (closed)
– 0 <1: hyperbolic geometry, forever expanding
• currently favored model: 0 = 0.3
•Andris Skuja, May 9, 2006 -- Physics 270
How can we measure 0 ?
• Count all the mass we can “see”
– tricky, some of the mass may be hidden …
• Measure the rate at which the expansion of
the universe is slowing down
– a more massive universe will slow down faster
• Measure the geometry of the universe
– is it spherical, hyperbolic or flat ?
•Andris Skuja, May 9, 2006 -- Physics 270
Let’s try to measure the
deceleration
• Acceleration according to Newton:
M
4 G
a  G 2  
R
R
3
• deceleration parameter
aR  0
q0   2 
v
2
•Andris Skuja, May 9, 2006 -- Physics 270
So what’s the meaning of q0 ?
• deceleration parameter q0
– q0>0.5:
– 0<q0<0.5:
deceleration is so strong that
eventually the universe stops
expanding and starts collapsing
deceleration is too weak to stop
expansion
• What’s the difference between q0, 0 and k ?
– k:
– 0:
– q0:
curvature of the universe
mass content of the universe
kinematics of the universe
•Andris Skuja, May 9, 2006 -- Physics 270
So let’s measure q0 !
• How do we do that?
– Measure the rate of expansion at different
times, i.e. measure and compare the expansion
based on nearby galaxies and based on high
redshift galaxies
• Gravity is slowing down expansion 
expansion rate should be higher at high
redshift.
•Andris Skuja, May 9, 2006 -- Physics 270
So let’s measure q0 !
q0 = 0
q0 = 0.5
fainter
Data indicates:
q0 < 0
 Expansion
is accelerating
more distant
•Andris Skuja, May 9, 2006 -- Physics 270
Science discovery of the year 1998
• The expansion of the universe is
accelerating !!!
• But gravity is always attractive, so it only
can decelerate
 Revival of the cosmological constant 
•Andris Skuja, May 9, 2006 -- Physics 270
Friedmann’s equation for >0
8 G
R
2
2
v 
 R  kc 
3
3
2
2
• k is the curvature constant
– k=0: flat space
space, flat universe
– k>0: spherical geometry
geometry, closed universe
– k<0: hyperbolic geometry,
geometry open universe
• but for sufficiently large  a spherically curved
universe may expand forever
•Andris Skuja, May 9, 2006 -- Physics 270
Deceleration parameter q for >0
• Acceleration according to Newton:
4 G

a
R R
3
3
• deceleration parameter
with
aR  0
q0   2 
 
v
2

 
2
3H 0
•Andris Skuja, May 9, 2006 -- Physics 270
The fate of the Universe for >0
k=+1
>0
=0
•Andris Skuja, May 9, 2006 -- Physics 270
Is the fate of the Universe well
determined ?
• deceleration:
– ½0 –  > 0: decelerating
– ½0 –  < 0: accelerating
• curvature
– 0 +  = 1: flat
– 0 +  < 1: hyperbolic
– 0 +  > 1: spherical
• two equations for two variables  well
posed problem
•Andris Skuja, May 9, 2006 -- Physics 270
Cosmology: the quest for three
numbers
• The Hubble constant H0
 how fast is the universe expanding
• The density parameter 0
 how much mass is in the universe
• The cosmological constant 
 the vacuum energy of the universe
• current observational situation:
• H0 = 65 km/s/Mpc
• 0 = 0.3; = 0.7  flat space
•Andris Skuja, May 9, 2006 -- Physics 270
How old is the Universe?
• A galaxy at distance d recedes at velocity
v=H0  d.
• When was the position of this galaxy
identical to that of our galaxy? Answer:
d
1
t Hubble  
v H0
• tHubble: Hubble time. For H0 = 65 km/s/Mpc:
tHubble = 15 Gyr
•Andris Skuja, May 9, 2006 -- Physics 270
The age of the Universe revisited
• So far, we have assumed that the expansion
velocity is not changing (q0=0, empty
universe)
• How does this
estimate change,
if the expansion
decelerates, i.e.
q0>0 ?
now
• An 0>0, =0 universe is younger than 15 Gyr
•Andris Skuja, May 9, 2006 -- Physics 270
The age of the Universe revisited
• So far, we only have considered
decelerating universes
now
• How does this
estimate change,
if the expansion
accelerates, i.e.
q0<0 ?
• An >0 universe can be older than 15 Gyr
•Andris Skuja, May 9, 2006 -- Physics 270
The age of the Universe revisited
• 0=0, =0: tHubble =1/H0 = 15 Gyr
• 0=1, =0: tHubble =2/(3H0)= 10 Gyr
• open universes with 0<0<1, =0 are
between 10 and 15 Gyr old
• closed universes with 0>1, =0 are less
than 10 Gyr old
• >0 increases, <0 decreases the age of the
universe
• 0=0.3, =0.7: tHubble =0.96/H0 = 14.5 Gyr
•Andris Skuja, May 9, 2006 -- Physics 270
Can we measure the age of the
Universe ?
• not directly
• but we can constrain the age of the
Universe. It must not be younger than the
oldest star in the Universe.
• How do we measure the age of stars?
– radioactive dating
– stellar evolution models
• Result: age of the oldest star ~12-14 Gyr
• 0>~1 strongly disfavored
•Andris Skuja, May 9, 2006 -- Physics 270
The life of a universe – key facts
• Unless  is sufficiently large (which is
inconsistent with observations) all
cosmological models start with a big bang.
• An universe doesn’t change its geometry. A
flat universe has always been and will
always be flat, a spherical universe is
always spherical and so on.
• Two basic solutions:
– eventual collapse for large 0 or negative 
– eternal expansion otherwise
•Andris Skuja, May 9, 2006 -- Physics 270
Some common misconceptions
• The picture that the Universe expands into a
preexisting space like an explosion
• The question “what was before the big
bang?”
• Remember: spacetime is part of the solution
to Einstein’s equation
• Space and time are created in the big bang
•Andris Skuja, May 9, 2006 -- Physics 270
So is the big crunch the same as
the big bang run in reverse ?
• No. The Universe has meanwhile formed
stars, black holes, galaxies etc.
• Second law of thermodynamics:
The entropy (disorder) of a system at best
stays the same but usually increases with
time, in any process. There is no perpetual
motion machine.
• Second law of thermodynamics defines an
arrow of time.
•Andris Skuja, May 9, 2006 -- Physics 270
Friedmann’s equation for =0, 0<1
8 G
kc
H
 2
3
R
2
Expansion rate
Falls off like Falls off like
of the Universe
the cube of R the square of R
• At early epochs, the first term dominates
 the early universe appears to be almost flat
• At late epochs, the second term dominates
 the late universe appears to be almost empty
•Andris Skuja, May 9, 2006 -- Physics 270
Friedmann’s equation for >0, 0<1
8 G
kc

H
 2 
3
R
3
2
Expansion rate
of the Universe
Falls off like Falls off like
the cube of R the square of R
constant
• At early epochs, the first term dominates
 the early universe appears to be almost flat
• At late epochs, the third term dominates
 the late universe appears to be exponentially
expanding
•Andris Skuja, May 9, 2006 -- Physics 270
A puzzling detail
• =0: for most of its age, the universe looks
either to be flat or to be empty
• >0: for most of its age, the universe looks
either to be flat or to be exponentially
expanding
• Isn’t it strange that we appear to live in that
short period between those two extremes ?

Flatness problem
•Andris Skuja, May 9, 2006 -- Physics 270
The life of a universe – key facts
• Unless  is sufficiently large (which is
inconsistent with observations) all
cosmological models start with a big bang.
• An universe doesn’t change its geometry. A
flat universe has always been and will
always be flat, a spherical universe is
always spherical and so on.
• Two basic solutions:
– eventual collapse for large 0 or negative 
– eternal expansion otherwise
•Andris Skuja, May 9, 2006 -- Physics 270
General acceptance of the big
bang model
• Until mid 60ies: big bang model very
controversial, many alternative models
• After mid 60ies: little doubt on validity of
the big bang model
• Four pillars on which the big bang theory is
resting:
–
–
–
–
Hubble’s law 
Cosmic microwave background radiation
The origin of the elements
Structure formation in the universe
•Andris Skuja, May 9, 2006 -- Physics 270
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)
•Andris Skuja, May 9, 2006 -- Physics 270
Hoyle’s ”Big Bang”
•Andris Skuja, May 9, 2006 -- Physics 270
What are the consequences (Gamow)?
• In order to form hydrogen and helium at the right
proportions, the following conditions are required:
– density:   10-5 g/cm-3
– temperature:
T  109 K
• Radiation from this epoch should be observable as an
isotropic background radiation
• Due to the expansion of the universe to
  310-30 g/cm3, the temperature should have dropped
to T  5 K (-450 F)
• Can we observe this radiation ?
•Andris Skuja, May 9, 2006 -- Physics 270
The discovery of the relic
radiation
• Gamov’s result on the background radiation
was not well recognized by the scientific
community
• Result was rediscovered by Dicke and
Peebles in the early sixties. They started
developing an antenna to search for the
background radiation
• T  5 K  microwaves
• but …
•Andris Skuja, May 9, 2006 -- Physics 270
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
•Andris Skuja, May 9, 2006 -- Physics 270
A quote ...
• John Bahcall: "The discovery of the cosmic
microwave background radiation changed
forever the nature of cosmology, from a
subject that had many elements in common
with theology to a fantastically exciting
empirical study of the origins and evolution
of the things that populate the physical
universe."
•Andris Skuja, May 9, 2006 -- Physics 270
The Big Bang and the Creation of
the elements (Hoyle + Saltpeter)
• Atoms are mostly empty space
• Atoms consist of protons (+), neutrons (o) and
electrons (-)
• protons and neutrons
form the atomic
nucleus
• # of protons determines the element
• electrons in the outskirts determine chemistry
•Andris Skuja, May 9, 2006 -- Physics 270
The structure of matter
• Neutrons and protons are very similar, but
– Protons are electrically charged, neutrons are not
– Neutrons have a slightly higher mass
• Electrons are much less massive than
nucleons  most of the mass of an atom is in
its nucleus
• If charges of the same sign repel, and the
nucleus is made of protons, why don’t the
protons fly apart ?
•Andris Skuja, May 9, 2006 -- Physics 270
The four forces of nature
• gravity
• electromagnetism
• strong nuclear force
– keeps atomic nuclei together
• weak nuclear force
– decay of free neutrons into protons
 + n  p+ + e•Andris Skuja, May 9, 2006 -- Physics 270
The structure of matter
•Andris Skuja, May 9, 2006 -- Physics 270
Abundance of elements
• Hydrogen and helium
most abundant
• gap around Li, Be, B
•Andris Skuja, May 9, 2006 -- Physics 270
Thermal history of the universe
• When the universe was younger than
300 000 yrs, it was so hot that neutral atoms
separated into nuclei and electrons. It was
too hot to bind atomic nuclei and electrons
to atoms by the electromagnetic force
• When the universe was younger than
~1 sec, it was so hot that atom nuclei
separated into neutrons and protons. It was
too hot to bind protons and neutrons to
atomic nuclei by the strong nuclear force
•Andris Skuja, May 9, 2006 -- Physics 270
Formation of helium in the big bang
• Hydrogen: 1 nucleon (proton)
• Helium: 4 nucleons (2 protons, 2 neutrons)
• In order to from helium from hydrogen one
has to
– bring 2 protons and 2 neutrons close together, so
the strong nuclear force can act and hold them
together
– close together: Coulomb repulsion has to be
overcome  high velocities  high temperatures
• but: 4 body collisions are highly unlikely
•Andris Skuja, May 9, 2006 -- Physics 270
Transforming hydrogen into helium
• Hot big bang: neutrons and protons
• Use a multi step procedure:
–
–
–
–
p + n  2H
p + 2H  3He
n + 2H  3H
3He + 3He  4He + 2 p
• some side reactions:
– 3He + 3H  7Li
– 3He + 3He  7Be
•Andris Skuja, May 9, 2006 -- Physics 270
Mass gap/stability gap at A=5 and 8
• There is no stable atomic nucleus with 5 or
with 8 nucleons
• Reaction chain stops at 7Li
• So how to form the more massive elements?
• There exist a meta-stable nucleus (8B*). If
this nucleus is hit by another 4He during its
lifetime, 12C and other elements can be
formed
•Andris Skuja, May 9, 2006 -- Physics 270
Mass gap/stability gap at A=5 and 8
• Reaction chain:
– 4He + 4He  8B*
– 8B* + 4He  12C
• so-called 3-body reaction (Saltpeter)
• in order to have 3-body reactions, high
particle densities are required
– densities are not high enough in the big-bang
– but they are in the center of evolved stars
• Conclusion: big bang synthesizes elements up
to 7Li. Higher elements are formed in stars
•Andris Skuja, May 9, 2006 -- Physics 270
Primordial nucleosynthesis
Consistent with
abundance
of H, He and Li
Result:
• abundance of
H,He and Li is
consistent
• but: b ~0.04
•Andris Skuja, May 9, 2006 -- Physics 270
How far can we see ?
• Naked eye: 2 million Light years
(Andromeda galaxy)
• Large telescopes: 14 billion Lyr (z=5.8)
• What are the limiting factors ?
– there are no bright sources at high z
– light is redshifted into the infrared
– absorption
• The universe appears to be fairly
transparent out to z=5.8
•Andris Skuja, May 9, 2006 -- Physics 270
When does a gas become opaque?
• A gas appears opaque (e.g. fog) if light is
efficiently scattered by the atoms/molecules
of the gas
The three important factors are thus
– the density of the gas
(denser  more particles  more scattering)
– the efficiency with which each individual
particle can scatter light
– wavelength of the light
•Andris Skuja, May 9, 2006 -- Physics 270
The transition from a transparent
to an opaque universe
• At z=0 the universe is fairly transparent
• At higher z, the universe becomes denser
( = 0(1+z)3) and hotter (T=T0(1+z))
• At z=1100, the universe is so dense that its
temperature exceeds 3000K. In a fairly
sharp transition, the universe becomes
completely ionized and opaque to visible
light. (last scattering surface)
• At z=1100, the universe is ~300 000 yrs old
•Andris Skuja, May 9, 2006 -- Physics 270
Black body radiation
• A hot a body is brighter than a cool one
(LT4, Stefan-Boltzmann’s law)
• A hot body’s spectrum is bluer than that of a
cool one (max1/T, Wien’s law)
•Andris Skuja, May 9, 2006 -- Physics 270
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
•Andris Skuja, May 9, 2006 -- Physics 270
Should the CMB be perfectly
smooth ?
• No. Today’s Universe is
homogeneous and
isotropic on the largest
scales, but there is a fair
amount of structure on
small scales, such as
galaxies, clusters of
galaxies etc.
•Andris Skuja, May 9, 2006 -- Physics 270
Should the CMB be perfectly
smooth ?
• We expect some
wriggles in the CMB
radiation, corresponding
to the seeds from which
later on galaxies grow
•Andris Skuja, May 9, 2006 -- Physics 270
The Cosmic Background Explorer
(COBE)
Main objectives:
• To accurately
measure the
temperature of the
CMB
• To find the expected
fluctuations in the
CMB
•Andris Skuja, May 9, 2006 -- Physics 270
Main results from COBE
•Andris Skuja, May 9, 2006 -- Physics 270
More results from the CMB
• The Earth is moving
with respect to the
CMB  Doppler shift
– Earth’s motion around
the Sun
– Sun’s motion around
the Galaxy
– Motion of the Galaxy
with respect to other
galaxies (large scale
flows)
•Andris Skuja, May 9, 2006 -- Physics 270
More results from the CMB
• The Earth is moving
with respect to the
CMB  Doppler shift
• The emission of the
Galaxy
•Andris Skuja, May 9, 2006 -- Physics 270
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
•Andris Skuja, May 9, 2006 -- Physics 270
The BOOMERANG mission
• COBE was a satellite mission, why ?
– Measure at mm and sub-mm wavelengths
– Earth atmosphere almost opaque at those wavelengths due to water vapor
– satellite missions take a
long time and are expensive
• What can be done from the
ground ?
– Balloon experiment
– desert  South Pole
•Andris Skuja, May 9, 2006 -- Physics 270
The BOOMERANG mission
•Andris Skuja, May 9, 2006 -- Physics 270
The BOOMERANG mission
•Andris Skuja, May 9, 2006 -- Physics 270
How can we measure the
geometry of the universe
• We need a yard stick on the CMB
• For different curvatures, a yard stick of
given length appears under different angles
•Andris Skuja, May 9, 2006 -- Physics 270
Measuring the Curvature of the
Universe Using the CMB
•Andris Skuja, May 9, 2006 -- Physics 270
Measuring the Curvature of the
Universe Using the CMB
• Recall: with
supernovae, one
measures
q0 =½0 – 
• CMB fluctuations
measure curvature
 0 + 
• two equations for
two variables
 problem solved
•Andris Skuja, May 9, 2006 -- Physics 270
What comes next ?
WMAP
•Andris Skuja, May 9, 2006 -- Physics 270
Planck
Can we see the sound of the
universe ?
• Compressed gas heats up
 temperature fluctuations
•Andris Skuja, May 9, 2006 -- Physics 270
Acoustic Oscillations in the CMB
• Although there are fluctuations on all scales, there is
a characteristic angular scale.
•Andris Skuja, May 9, 2006 -- Physics 270
Acoustic Oscillations in the CMB
WMAP team (Bennett et al. 2003)
•Andris Skuja, May 9, 2006 -- Physics 270
Last scattering surface
transparent
opaque
•Andris Skuja, May 9, 2006 -- Physics 270
Sound Waves in the Early Universe
After recombination:
Before recombination:
Ionized
– Universe is neutral.
– Photons can travel freely
past the baryons.
– Phase of oscillation at trec
affects late-time amplitude.
Recombination
z ~ 1000
~400,000 years
Time
•Andris Skuja, May 9, 2006 -- Physics 270
Neutral
Today
Big Bang
– Universe is ionized.
– Photons provide enormous
pressure and restoring force.
– Perturbations oscillate as
acoustic waves.
Sound Waves
• Each initial overdensity (in DM &
gas) is an overpressure that launches
a spherical sound wave.
• This wave travels outwards at
57% of the speed of light.
• Pressure-providing photons decouple
at recombination. CMB travels to us
from these spheres.
• Sound speed plummets. Wave stalls
at a radius of 150 Mpc.
• Overdensity in shell (gas) and in the
original center (DM) both seed the
formation of galaxies. Preferred
separation of 150 Mpc.
•Andris Skuja, May 9, 2006 -- Physics 270
QuickTime™ and a
GIF decompressor
are needed to see this picture.
A Statistical Signal
• The Universe is a superposition of these shells.
• The shell is weaker than
displayed.
• Hence, you do not
expect to see bullseyes
in the galaxy
distribution.
• Instead, we get a 1%
bump in the correlation
function.
•Andris Skuja, May 9, 2006 -- Physics 270
Cosmological Constraints
Pure CDM degeneracy
2s
1s
Acoustic scale alone
WMAP 1s range
•Andris Skuja, May 9, 2006 -- Physics 270
The History of the Universe
The “Concordance” Model (not yet the “Standard Model”) of
Cosmology:
The Universe is homogeneous and flat (horizon problem
and flatness problem)
The Universe evolved from a quantum fluctuation no bigger
than 10-35 m
in diameter.
Since gravitational energy is negative and the energy of a
massive object is positive, the total energy of the quantum
fluctuation can be zero
If the fluctuation now expands it may become the entire universe
The “Concordance” Model postulates that the initial expansion was
very rapid indeed (cosmic inflation)
•Andris Skuja, May 9, 2006 -- Physics 270
History of the Universe (with
Inflation)
•Andris Skuja, May 9, 2006 -- Physics 270
Inflation (potential)
•Andris Skuja, May 9, 2006 -- Physics 270
Matter era
• The energy of matter is nowadays ~10000
times higher than that of radiation
• but temperature rises like (1+z)
• 2.7K < T < 10000K: matter era
• dominate particles (in order of decreasing
contribution:
– baryons, photons, neutrinos
• dominant forces:
– gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Radiation era
• As the temperature exceeds ~ 10000K,
radiation starts dominating
• 10000K < T < 1010K: radiation era
• dominate particles (in order of decreasing
contribution:
– photons, neutrinos, baryons
• dominant forces:
– electromagnetism, gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Electron-positron annihilation
• As the temperature exceeds ~ 1010K,
creation of electron-positron pairs
– T > 1010K: equilibrium between electronpositron pair creation and annihilation
– T < 1010K: freeze-out. Remaining pairs
annihilate
•Andris Skuja, May 9, 2006 -- Physics 270
Lepton era
• 1010K < T < 1012K
• dominate particles (in order of decreasing
contribution:
– electrons, positrons, photons, neutrinos,
antineutrinos, baryons
• dominant forces:
– electromagnetism, weak nuclear, gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Hadron annihilation
• As the temperature exceeds ~ 1012K,
creation of hadron-antihadron pairs (e.g.
proton-antiproton)
– T > 1012K: equilibrium between hadron pair
creation and annihilation
– T < 1012K: freeze-out. Remaining pairs
annihilate
•Andris Skuja, May 9, 2006 -- Physics 270
Hadron era
• 1012K < T < 1013K
• dominate particles (in order of decreasing
contribution:
– baryons+antiparticles, mesons+antiparticles,
electrons, positrons, photons, neutrinos,
antineutrinos
• dominant forces:
– electromagnetism, strong nuclear, weak nuclear,
gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Still quark era
• 1013K < T < 1015K
• hadrons (baryons, mesons) break into
quarks
• dominate particles (in order of decreasing
contribution:
– quarks, antiquarks, electrons, positrons,
photons, neutrinos, antineutrinos
• dominant forces:
– electromagnetism, strong nuclear, weak nuclear,
gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Electroweak phase transition
• As the temperature exceeds ~ 1015K,
electromagnetism and weak nuclear force
join to form the electroweak force
– T > 1015K: electroweak force
– T < 1015K: electromagnetism, weak nuclear
force
• Limit of what we can test in particle
accelerators.
• Nobel prizes 1979 (theory) and 1984
(experiment)
•Andris Skuja, May 9, 2006 -- Physics 270
Quark era
• 1015K < T < 1029K
• dominate particles (in order of decreasing
contribution:
– quarks, antiquarks, electrons, positrons,
photons, neutrinos, antineutrinos
• dominant forces:
– electroweak, strong nuclear, gravity
•Andris Skuja, May 9, 2006 -- Physics 270
GUT phase transition
• As the temperature exceeds ~ 1029K,
electroweak force and strong nuclear force
join to form the GUT (grand unified
theories)
– T > 1029K: GUT
– T < 1029K: electroweak force, strong nuclear
force
• relatively solid theoretical framework (but
may be wrong), but pretty much no
constraint by experiments
•Andris Skuja, May 9, 2006 -- Physics 270
GUT era
• 1029K < T < 1032K
• dominate particles (in order of decreasing
contribution:
– Zillions of particles, most of them not detected
yet
• dominant forces:
– GUT, gravity
•Andris Skuja, May 9, 2006 -- Physics 270
Planck epoch
• T > 1032K unification of GUT and gravity
• Particles:
– ???
• Forces:
– TOE (theory of everything)
• The last frontier ...
•Andris Skuja, May 9, 2006 -- Physics 270
Structure formation in the Big-Bang
model
•Andris Skuja, May 9, 2006 -- Physics 270
The Hubble sequence of galaxies
•Andris Skuja, May 9, 2006 -- Physics 270
A galaxy census: spiral galaxies
• Most common type among the luminous
galaxies (~75%)
• two major classes, S and SB
– regular spirals (S)
– barred spirals (SB)
• further classified from a to d according to
the bulge-to-disk ratio
– a: very large, prominent bulge
– d: essentially no bulge at all
• The Milky Way is a Sbc or a SBbc galaxy
•Andris Skuja, May 9, 2006 -- Physics 270
A galaxy census: spiral galaxies
• Spiral galaxies are disk like and in
centrifugal equilibrium
• The are “cold”, i.e. the velocity dispersion
(random motion of individual stars) s is
much smaller than the rotation velocity vrot
(Milky Way: s=20 km/s; vrot=220 km/s)
• They mainly consist of stars, but ~10% of
the mass is gas and dust
• They actively form stars (Milky Way: ~ 1
star per year)
•Andris Skuja, May 9, 2006 -- Physics 270
A galaxy census: elliptical galaxies
• ~20% of the luminous galaxies are ellipticals
• classified according to the flattening E0-E7: n=10(1b/a)
– E0: circular
– E7: minor axis only 30% of major axis
• They are “hot”, i.e. the velocity dispersion s is much
larger than the rotation velocity vrot
• flattened by an anisotropic velocity dispersion
• little gas, no recent star formation
• predominantly in clusters of galaxies
•Andris Skuja, May 9, 2006 -- Physics 270
A galaxy census: other galaxies
• Irregular galaxies (~ 5% of the luminous
galaxies)
• dwarf galaxies
–
–
–
–
–
dwarf irregulars
dwarf spheroidals
dwarf ellipticals
blue compact dwarfs
...
•Andris Skuja, May 9, 2006 -- Physics 270
Toomre & Toomre
(mid 70s)
• 11 out of the 4000 galaxies
in the New General Catalog
(NGC) show indications of
recent interactions (e.g. tails)
• Those tidal features last a few 108 years
• Over the age of the universe, several
hundred of those interactions must have
taken place
• There are several hundred elliptical galaxies
in the NGC
•Andris Skuja, May 9, 2006 -- Physics 270
Do ellipticals form by merging
spirals ?
•Andris Skuja, May 9, 2006 -- Physics 270
Younger galaxies should be smaller ...
•Andris Skuja, May 9, 2006 -- Physics 270
How good is the assumption of
isotropy?
• CMB: almost perfect
• but what about the closer neighborhood ?
•Andris Skuja, May 9, 2006 -- Physics 270
How good is the assumption of
isotropy?
• CMB: almost perfect
• but what about the closer neighborhood ?
The great
wall
•Andris Skuja, May 9, 2006 -- Physics 270
The spatial distribution of galaxies
• Galaxies are not randomly
distributed but correlated
• Network of structures
(filaments, sheets, walls)
 “cosmic web”
Courtesy: Huan Lin
•Andris Skuja, May 9, 2006 -- Physics 270
65 Mpc
z=9.00
50 million
particle
N-body
simulation
•Andris Skuja, May 9, 2006 -- Physics 270
65 Mpc
z=4.00
50 million
particle
N-body
simulation
•Andris Skuja, May 9, 2006 -- Physics 270
65 Mpc
z=2.33
50 million
particle
N-body
simulation
•Andris Skuja, May 9, 2006 -- Physics 270
65 Mpc
z=1.00
50 million
particle
N-body
simulation
•Andris Skuja, May 9, 2006 -- Physics 270
65 Mpc
z=0.00
50 million
particle
N-body
simulation
•Andris Skuja, May 9, 2006 -- Physics 270
Does a picture like this look
familiar ?
•Andris Skuja, May 9, 2006 -- Physics 270
Counting all the mass ...
• Obstacle: we want mass, but we see light
• Procedure:
– count all the stars you see and multiply them
with there luminosity  total visible luminosity
– correct for dust absorption  total luminosity
– convert luminosity into mass using a mass-tolight ratio
 M / M sun 


 L / Lsun 
– The sun has =1 by definition.
•Andris Skuja, May 9, 2006 -- Physics 270
Overall result:
  0.01
Implications:
• less than the nucleosynthesis constraint of =0.04
in baryons  consistent
• Most of the baryons in the universe (~75%) do not
shine [are too dim to be detected]
– gas and dust
– stellar remnants (white dwarfs, neutron stars, black
holes)
– brown dwarfs [failed stars]
•Andris Skuja, May 9, 2006 -- Physics 270
•Andris Skuja, May 9, 2006 -- Physics 270
Evidence of dark matter:
rotation curves of spiral galaxies
•Andris Skuja, May 9, 2006 -- Physics 270
Fritz Zwicky
He measured the
velocities of galaxies
in galaxy clusters
and concluded that
most of the cluster’s
mass must be dark
•Andris Skuja, May 9, 2006 -- Physics 270
Evidence of dark matter:
X-ray clusters
•Andris Skuja, May 9, 2006 -- Physics 270
Evidence of dark matter:
clusters of galaxies
•Andris Skuja, May 9, 2006 -- Physics 270
Evidence of dark matter:
large scale flows
•Andris Skuja, May 9, 2006 -- Physics 270
Overall result:
  0.3
Implications:
• most of the mass in the Universe is dark
• most of it is even of non-baryonic origin
• the perfect Copernican principle
–
–
–
–
The Earth is not at the center of the solar system
The Sun is not at the center of the Milky Way
The Milky Way is not at the center of the Universe
We may not even be made from the most abundant type of
matter in the Universe
•Andris Skuja, May 9, 2006 -- Physics 270
Is the claim that dark matter exist
really so embarrassing ?
• When Leverrier was proposing in
the 1840s that there maybe an
8th planet in the solar system,
Neptune, a planet that can explain
the irregularities of Uranus’ orbit,
this planet was also “dark matter”
• But it was a clear prediction that eventually
could be tested observationally
• The discovery of Neptune by Galle was one
of the finest moments of science
•Andris Skuja, May 9, 2006 -- Physics 270
MACHOs ?
• MAssive Compact Halo Objects
• Brown dwarfs (stars not massive enough to
shine)
• Dim white dwarfs (relics of stars like the
Sun)
• Massive black holes (stars that massive that
even light cannot escape)
• but: if the DM is really in MACHOs,
something with the nucleosynthesis
constraint must be wrong
•Andris Skuja, May 9, 2006 -- Physics 270
How can we see MACHOs ?
• Gravitational lensing:
• If foreground object has only little mass, the
image split is too small to be observed
• But the amplification (brightening) is
observable
•Andris Skuja, May 9, 2006 -- Physics 270
How can we see MACHOs ?
• How likely is it for a star in the Milky Way
to get amplified ?
• Once every 10 million years
•Andris Skuja, May 9, 2006 -- Physics 270
How can we see MACHOs ?
• Solution: monitor 10 million stars
simultaneously
•Andris Skuja, May 9, 2006 -- Physics 270
How can we see MACHOs ?
Magnification due
to gravitational
lensing
There are not
enough brown
dwarfs to account
for the dark matter
in the Milky Way.
Alcock et al. 1993
•Andris Skuja, May 9, 2006 -- Physics 270
WIMPs ?
• Weakly Interacting Massive Particles
• Massive neutrino
– at least we know that it exists
– we don’t know whether it has mass or not
– hot dark matter (hot: moving at speeds near the
speed of light)
• Another (yet undiscovered) particle
predicted by some particle physicists
– cold dark matter (cold: moving much slower
than the speed of light)
•Andris Skuja, May 9, 2006 -- Physics 270
Summary
• The Universe is stranger than Alice’s
Wonderland
• We have only scratched the surface of what
is know
• Many insights and observations still to
come
•Andris Skuja, May 9, 2006 -- Physics 270