Download Cosmology and Astrophysics II

Expansion of Universe is governed by the
FRIEDMAN EQUATION
1 2 GmM Flat
Universe
mv 

energy  0
2
r
v
M
v
r
M
m
v
dr
v
 r
dt
r 2
2
r
4 3 
 r 2
3
c
8G
 2 
3c
and the
CONTINUITY EQUATION
dE  pdV  TdS  0
4 3
E   r
3
r
  3(   p)  0
r
4 3
V  r
3
Reversible
Expansion
Types of matter energy
in our universe
p  0,
p   ,
matterhas,
1
~ 3,
r
dark energy,
 ~ 1,
a~t
2
3
a ~ et
Dark energy
contribution to energy density in rhs of
Einstein-Friedman equation
cannot be differentiated
from
cosmological constant
on lhs.
kind of matter
equation of state ρ = ρ(a)
a = a(t)
Hagedorn
p=ρ
1/a**6
t**(1/3)
Radiation
p = ρ/3
1/a**4
t**(1/2)
Matter/Dust
p=0
1/a**3
t**(2/3)
Cosmic Strings
p = -ρ/3
1/a**2
t
1/a**2
t
Space Curvature
Cosmic Walls
p = -2ρ/3
1/a
t**2
Dark Energy or
p = -ρ
1
exp(t)
1
exp(t)
Cosmological
Constant
Dark Matter = Matter in the universe which we cannot see.
Black holes
Brown dwarfs
Massive Neutrinos
Axions
WIMP
Gravitinos
BLACK HOLE
c
m cannot escape from M even if it is
thrown with speed of light c
m
r
M
GMm 1 2

 mc  0
r
2
r
2GM
 black hole radius
2
c
Colliding
Black Holes
Images from the
National Science
Foundation's Very
Large Array (VLA)
radio telescope
have uncovered
compelling
evidence that
supermassive
black holes at the
hearts of large
galaxies collide
when their host
galaxies merge.
August 1, 2002
11 pointings from
September 21, 1999
through
June 04, 2002
Lobes of hot gas
(red) surround
the Milky Way
center.
The black hole is
located inside
the white region of inte
X-ray
emission.
(energy uncertainity)x(time uncertainity) = h
speed of light = c = 300 Mm/s
conversion factor c2 = 1017 J/kg
conversion factor hc = 1240 eV.nm
1eV = (1240nm) -1
eV =
-1
(μm)
A galaxy is a massive, gravitationally bound system that
consists of stars and stellar remnants, an interstellar medium
of gas and dust, and an important but poorly understood
component tentatively dubbed dark matter, contains 107 to
1012 stars
A star is a massive, luminous ball of plasma that is held
together by gravity, ½ to 20 times the mass of sun.
A supernova (plural supernovae) is a stellar explosion.
A white dwarf, is a small star composed mostly of electrondegenerate matter. They are very dense; a white dwarf's mass
is comparable to that of the Sun and its volume is comparable
to that of the Earth.
The Crab Nebula is a pulsar wind nebula associated with the 1054 supernova.
SN 1994D in the NGC 4526 galaxy (bright spot on the lower left). Image by NASA, ESA,
The Hubble Key Project Team, and The High-Z Supernova Search Team
A Type Ia supernova results from the violent explosion of a
white dwarf star when it reaches 1.4 times the sun’s mass.
These supernova always explode with fixed luminosity and
thus are the standard candles of the universe. By measuring
their redshift and brigtness we conclude how universe has
expanded in the past and how it is expanding now.
A neutron star is a type of remnant that can result from the
gravitational collapse of a massive star during a supernova
event. Such stars are composed almost entirely of neutrons. If
the exploding star leaves a core remnant between 1.4 to 2
solar masses the remnant is a neutron star. If the remnant is
more than 5 times the mass of the sun it becomes a black
hole. In between it may be a quark star which are yet
hypothetical.
Süpernova SN1997ff
The Farthest Known Supernova: Support for an Accelerating Universe and a
Glimpse of the Epoch of Deceleration
Riess et. al. Astrophys.J. 560 (2001) 49-71
Karanlık madde: Yıldızların içinde bulundukları galaksinin
merkezi etrafında dönüş hızlarını ölçerek varlığını bulduğumuz
ama şu anda gözlemleyemediğimiz madde.
Bugünkü evrendeki toplam madde-enerji’nin %22 si karanlık
maddedir.
Karanlık enerji: Evren genişledikçe yoğunluğu sabit kalan bir
“madde-enerji” türü.
Bugünkü evrendeki toplam madde-enerji’nin %75 ii karanlık
enerjidir.
Görünen madde: %3
The Microwave Sky, c. 1996
The all-sky image produced by the COBE Satellite. It is a low resolution image of
the sky (7 degree resolution), but obvious cold and hot regions are apparent in
the image. The large red band is the microwave emissions from our own galaxy.
• Empirical foundations of the Big Bang theory.
– Cosmic Microwave Background.
– Physical and chemical composition of the
Universe.
Cosmic Microwave Background
•
•
•
The cosmic microwave
background was discovered as
a background “noise” a real
problem for
telecommunication satellites
(1965)
Wherever Penzias and Wilson
pointed their antenna they
would detect a microwave
signal, very uniform across the
sky
This signal is now called the
cosmic microwave
background…
Cosmic Microwave Background
•
•
•
The CMB was already visible in
the data taken by Dunham and
Adams of the properties of CN
in the interstellar medium
…back in 1937
The saw that CN was excited as
if it was immersed in a thermal
bath of radiation of
temperature T~3K…
But nobody realized it.. So the
Nobel Prize went to Penzias &
Wilson… and not to Dunham
and Adams.. Such is life..
Cosmic Microwave Background
•
•
A group of physicist (initially
Gamow (1948) and then Alpher
and Hermann (1950) and then
Dicke and his group at Princeton)
had predicted such radiation, from
the so-called big bang
nucleosynthesis theory (later in
the class..)
The CMB was predicted to be:
–
–
–
Thermal
At a temperature of about 5K
Isotropic
Dicke was devising a CMB
search when the discovery was
made. His paper with Peebles,
Roll, and Wilkinson presented
the cosmological interpretation
along-side the Penzias and
Wilson paper.
Cosmic Microwave Background.
Thermal “Blackbody” Radiation
•
•
•
We know Penzias and
Wilson detected isotropic
radiation, so that was
consistent with the Big
Bang model and the
copernican principle
The theory predicted it to
be thermal, i.e. a
blackbody.
But what is really a
blackbody? 1. Matter and radiation in equilibrium
2. Characteristic spectral shape
3. Wien’s Law - hotter body produces higher energy
photons
Is the Microwave Background Radiation a Blackbody?
COBE got the answer
Cosmic Microwave Background. The
temperature is 2.725 K..
Cosmic Microwave Background.
Anisotropies from WMAP
The CMB sky, circa 2002…
What is the universe made of?
“normal” matter
•
•
•
•
Ordinary matter is made for
the most part of protons and
neutrons, i.e. quarks up and
down.
For this reason we refer to
ordinary matter as baryonic
matter
Neutrinos should not have
mass in the standard model,
but they do (neutrino
oscillations)
No antimatter is observed!
What baryons? Chemical composition
of stars.
•
•
•
•
•
•
The sun is made of:
Hydrogen (74% by mass)
Helium (25%)
Heavier elements (1%)
commonly referred to as
“metals” by astrophysicists
This is way more He than
expected from a universe
initially made of Hydrogen
where Helium is produced in
stars…
This is a common problem:
Helium abundance is always
~25%
Helium abundance.
The Big Bang solution
•
•
•
He is produced in the
early Universe when T
was high enough (above
~109 K) to allow for
nuclear fusion.
Why do you need high
temperature to do
fusion?
The Big Bang theory
predicts exactly the
abundance of all heavy
elements.
Big Bang nucleosynthesis predicts a primordial abundance of about 25% helium-4 by
mass, irrespective of the initial conditions of the universe. As long as the universe was
hot enough for protons and neutrons to transform into each other easily, their ratio,
determined solely by their relative masses, was about 1 neutron to 7 protons (allowing
for some decay of neutrons into protons). Once it was cool enough, the neutrons quickly
bound with an equal number of protons to form helium-4. Helium-4 is very stable and
neither decays nor combines easily to form heavier nuclei. So out of every 16 nucleons
(2 neutrons and 14 protons), 4 of these (25%) combined into one helium-4 nucleus. One
analogy is to think of helium-4 as ash, and the amount of ash that one forms when one
completely burns a piece of wood is insensitive to how one burns it.
The helium-4 abundance is important because there is far more helium-4 in the universe
than can be explained by stellar nucleosynthesis. In addition, it provides an important
test for the Big Bang theory. If the observed helium abundance is much different from
25%, then this would pose a serious challenge to the theory. This would particularly be
the case if the early helium-4 abundance was much smaller than 25% because it is hard
to destroy helium-4. For a few years during the mid-1990s, observations suggested that
this might be the case, causing astrophysicists to talk about a Big Bang nucleosynthetic
crisis, but further observations were consistent with the Big Bang theory.[
Theories which govern Particles and Cosmology:
Special Relativity depends on the absoluteness of light velocity. In simple
terms velocity of light “added to” any other velocity still gives velocity of light.
Quantum Field Theory unifies quantum physics whose basis is the
uncertainity principle with special relativity. Standard Model incorporates the
known particles: leptons, quarks and the electromagnetic, weak and strong
force carriers in a consistent Quantum Field Theory .
General Relativity generalizes Newtoniain Gravity such that it is consistent
with Special Relativity. Both Newtonian Gravity and Special Relativity are
noncoinciding special cases of General Relativity. General Relativity
depends on the principle that matter-energy curves space-time.
As yet no Quantum Field Theory which is consistent with General Relativity
exists. A solution to this problem may be that basic entities are not point
particles but are strings.
Cosmology Astrophysics and Particles: a Postlude
1 : a closing piece of music; especially : an organ voluntary at the end of a church service
2 : a closing phase (as of an epoch or a literary work)
God and Physics
Newton, in his book “Principia mathemetica” explicitly
refers to God and says his work is proof that god exists:
God and the Universe
This most beautiful system of the sun, planets, and comets could
only proceed from the counsel and dominion of an intelligent and
powerful Being. And if the fixed stars are the centers of other like
systems, these, being formed by the like wise counsel, must be all
subject to the dominion of One, especially since the light of the
fixed stars is of the same nature with the light of the sun and from
every system light passes into all the other systems; and lest the
systems of the fixed stars should, by their gravity, fall on each
other mutually, he hath placed those systems at immense
distances from one another.
This Being governs all things not as the soul of the world, but as Lord over all; and on
account of his dominion he is wont to be called "Lord God" . . . or "Universal Ruler." . . .
It is the dominion of a spiritual being which constitutes a God. . . And from his true
dominion it follows that the true God is a living, intelligent and powerful Being. . . he
governs all things, and knows all things that are or can be done. . . He endures forever,
and is everywhere present; and by existing always and everywhere, he constitutes
duration and space. . . In him are all things contained and moved; yet neither affects the
other: God suffers nothing from the motion of bodies; bodies find no resistance from the
omnipresence of God. . . As a blind man has no idea of colors so we have no idea of the
manner by which the all-wise God preserves and understands all things. He is utterly
void of all body and bodily figure, and can therefore neither be seen, nor heard, nor
touched; nor ought to be worshipped under the representation of any corporeal thing.
We have ideas of his attributes, but what the real substance of any thing is we know
not.... Much less, then, have we any idea of the substance of God. We know him only by
his most wise and excellent contrivances of things. . . We reverence and adore him as
his servants, and a god without dominion, providence, and final causes, is nothing else
but Fate and Nature. Blind metaphysical necessity, which is certainly the same always
and everywhere, could produce no variety of things. All that diversity of natural things
which we find suited to different times and places could arise from nothing but the ideas
and will of a Being necessarily existing. . . And thus much concerning God, to discourse
of whom from the appearances of things does certainly belong to Natural Philosophy.
On the other hand Newton’s belief in an
eternal nonchanging heaven may have
prevented him from discovering the Big
Bang model. The Friedman equation
which governs the expansion of
universe was first derived using
General Relativity but we have seen
that they can be derived from Newton’s
equations.
After the discovery of expansion of the universe but before the discovery of
CMBR there were two competing theories:
1. The Big Bang model
2. The Steady State model which depended on the perfect cosmological
principle. The perfect cosmological principle states that the univerese looks
the same at all times as well as it looks the same when observed from
different points in all directions. In this model to make up for the expanding
univerese matter was constantly created to repair the decreasing density.
Some Steady State believers accused the Big Bang believers by being
influenced by their belief that God created the universe at Big Bang.
CMBR proved that The Big Bang theory was the correct one.
Although the Steady State believers accused the Big Bang believers of
being too religous, it is a fact that Steady State model is more in
concordance with Newton’s ideas.