مقدمه ای بر کیهان شناسی و اختر فیزیک نوین
مقدمه ای بر کیهان شناسی و اختر فیزیک نوین
مقدمه ای بر کیهان شناسی و اختر فیزیک نوین
سمینار آقای دکتر عباسی (دکترای اختر شناسی از دانشگاه فردوسی مشهد)
Introduction to Cosmology and
Modern Astrophysics
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Introduction to Cosmology and
Modern Astrophysics
The Story so far...
2005 is Einstein Year!
(Most) Significant figure in Modern Physics
2005
100 years since the 3 “key papers” were published
50 years since his death
Galileo
Major contributions in many areas of physics
Theories can be tested by conducting experiments.
Also used thought experiments
Isaac Newton
“Nature and Nature’s laws lay hid by night;
God said, Let Newton be! And all was light.”
Alexander Pope - intended Epitaph
“Mortals, congratulate yourselves that so great a man has lived for the honour of the human race”
Translation of the inscription on Newton’s tombstone in
Westminster Abbey
“Nearer to gods no mortal may approach”
Edmund Halley “Ode to Newton”
“If I have seen further (than others) it is by standing upon the shoulders of Giants”
Isaac Newton in a letter to Robert Hooke, 1675
Newton’s Principia
Isaac Newton
Most famous for gravity but also:
laid down 3 laws of motion
much work on optics
invented calculus independently of Leibniz
First scientist to be knighted
(in 1705 by Queen Anne)
Albert Einstein
Born in Ulm, Germany (1879)
Well-documented that he was not a brilliant pupil!
Managed to get into ETH in Zurich, graduated as a teacher in maths and physics in 1900
Became Swiss citizen in 1901
Employed in patent office 1902-1909
Einstein - 1905
Published ‘5’ papers in Annalen der Physik
Photoelectric effect (led to Nobel Prize in 1921)
Brownian Motion (proved existence of atoms)
Special Relativity
Special Relativity 2 (E=mc2)
Molecular dimensions (PhD)
How to describe gravity: General Relativity
Dynamics takes place in a four dimensional spacetime
Mass induces warping or curvature of spacetime
Spacetime curvature may also exist in the absence of mass (cosmological constant)
A sermon on General Relativity
In some contexts, spacetime curvature becomes pronounced, and space and time become inextricably linked or “coupled”. One example is black holes. Another is the universe as a whole. When we look on cosmological scales c/H0, you cannot view the universe as three dimensional, with time as a parameter. The universe exists as a 4D entity with strong curvature effects. You can’t even qualitatively understand what is going on if you stick to a 3D view
An analogy
The surface of the Earth is a 2D surface embedded in a 3D space. Locally, the surface of the Earth looks purely 2D. On scales of the radius of the Earth, the curvature is unavoidable.
Cosmology
The study of the structure and evolution of the Universe as a whole.
Seeks to answer questions such as:
How big is the Universe?
What shape is it?
How old is it?
How did it form?
What will happen to it in the future?
Distribution of Galaxies
Galaxies appear to be distributed throughout the Universe
Galaxies clump together into clusters and superclusters.
Distant galaxies appear to be moving away from us.
We know this from the redshifts in the spectrum of galaxies.
Newton’s Universe
According to Newtonian cosmology, we live in a static, infinitely old and infinitely large universe with stars randomly scattered throughout the universe.
In the early 1800s , the German astronomer Heinrich Olbers pointed out that something was wrong with this picture - Olbers’s Paradox.
Olbers’s Paradox
If the Universe is infinite, why isn’t the sky bright at night?
We should be able to have a line of sight to galaxy or star in any direction we look, if the line of sight extends far enough.
But sky is dark, so there must be an end.
End is due to expansion of Universe and resulting cosmic horizon - some of light from Universe has not reached us yet.
Expansion of the Universe
Einstein’s relativity gave an entirely different picture of spacetime and gravity.
His calculations showed that the universe must expand or contract, so he included a fudge factor into his equations - Cosmological Constant - so that his theory would support a static universe.
Later, when it was established that the Universe is indeed expanding, he said that it was the biggest blunder in his life.
Expansion of the Universe
While some disagree about how the universe came into existence, no one argues that the Universe is expanding.
The first person to discover this was Edwin Hubble. He observed that all remote galaxies are moving away from us.
Hubble’s Law - The further away something is from us, the faster it is receding from us.
v = H0 * d v = recession velocity, H = Hubble’s constant, d = distance
Conceptualizing the expansion of the Universe
What does it actually mean to say that the universe is expanding?
Think of small coins representing the galaxies glued on a balloon as it is blown up.
As the balloon expands, the the amount of space between the coins gets larger and large.
Similarly,as the universe expands, the amount of space between the widely separated galaxies increases.
The Expansion of the Universe
The motion of galaxies away from us is due to the expansion of the Universe.
Like buttons on a balloon which when inflated all move away from one another, so too are all the galaxies moving apart.
The buttons are not moving it is the balloon itself that carries the buttons away.
Space itself is expanding and simply carrying the galaxies with it.
The scientific basis of modern cosmology
Hubble’s Law
V = H0d
The universe is expanding
Red Shift and Distance
Hubble – 1929
Creating space
What is the universe expanding into?
NOTE! The Universe is not expanding into pre-existing space - it “creates” space as it goes (!?), just as the surface of a balloon gets bigger as it is blown up.
There is nothing “beyond” the universe, because there is no beyond.
Asking what is beyond the universe is a meaningless question.
The Big Bang
Since the Universe is expanding it must have been smaller in the past.
At some point in the past the entire Universe must have been packed into some very small size.
In 1927, Abbé George Lemaitre, a Belgian cosmologist and priest proposed that the Universe began as a “Primeval Atom” and estimated its age.
To estimate the age you need to know the expansion rate – in other words Hubble’s Constant, H.
H is 71 +/- 4 km/sec/Mpc giving an age to the Universe of 13.7 +/- 0.2 Billion years.
The Cosmic Horizon
There is a limit to how deep in the Universe we can peer. We are at the center of the limits of our vision (a.k.a. the Cosmic Particle Horizon)
limit set by how old Universe is and speed of light: light from distant galaxies must have had time to reach us
our cosmic horizon is different from other galaxies - they are at their own center
This solves the Olbers’s Paradox. We do not receive light from galaxies beyond our horizon.
The cosmic horizon
The Cosmic Singularity
At the moment of the Big Bang:
A state of infinite density filled the universe
A condition of infinite curvature existed, giving rise to a situation where space and time were jumbled.
Therefore, we cannot apply laws of physics to describe the moment of the Big bang.
This is very similar to the condition at the center of a black hole - i.e. at the black hole singularity
For this reason we refer to the black hole as the Cosmic Singularity.
Plank Time
Due to the state of the universe during the BB, we cannot use laws of physics to describe this event.
Nor can science answer what existed before the BB - these are fundamentally unknowable things.
In fact, from the beginning of the BB until 10-43 seconds after The BB, space & time was so jumbled-up that laws of Physics fails us
This time interval tP = 10-43 sec. is referred to as the Plank time.
Arno Penzias & Robert Wilson
Skip Forward to 1964
Cosmic microwave background radiation (CMB)
This radiation is blackbody radiation and depends on the temperature, just like the radiation from the Sun.
This radiation which fills all space is referred to as the Cosmic Microwave background radiation (CMB).
It was discovered by Arno Penzias & Robert Wilson in the early 60s.
Why 2.7 K?
Original temperature about 1013 Kelvin and density 1010 g/cm3, but expansion has cooled it.
Cooling occurs as space is stretched by expansion, and wavelengths get longer - redshift.
The redshift caused by the expansion of the universe is called the cosmological redshift.
The Big Bang happened EVERYWHERE in space - right here included!!
Will the universe expand forever?
What is the shape of the Universe?
The density of the Universe
Hard question to answer - requires knowing how much matter and radiation is in the Universe (equivalently: Energy density)
Which plays a more important role in the Universe; Matter or energy?
Depends on when!
At present the matter & radiation densities:
Radiation density r rad= 4.6 x 10-31 kg/m3
Matter density r m = 2 to 4 x 10-27 kg/m3 ( 1 to 2 H atoms in 1 m3)
The density of the Universe
Today, mater prevails over radiation in the Universe - matter-dominated Universe
However, as you go back in time towards the BB, as the universe was more compressed, both densities were higher, but in addition photons were not so redshifted => higher energy.
Early universe was a radiation-dominated Universe
The transition from radiation dominated to matter dominated universe happened about 2500 yrs. after the BB
History of the Universe
Very exciting in the beginning, very dull now. Hot early, cool later.
Radiation dominated: At first, Universe very hot. Exotic forms of matter present, but were quickly destroyed. Mostly EM radiation like gamma rays present. Would see brightness everywhere.
Matter dominated: (Like now) Universe dark, cooler. Matter forms and stays formed.
Transition between two eras is where CMB came from
What shape is the Universe?
Open Universe: Will expand forever. Negative curvature. Parallel lines always diverge.
Closed Universe: Stops expanding and collapses again. Positive curvature. Parallel lines always converge.
Flat Universe: exactly stops expanding but doesn’t collapse (really doesn’t exactly stop until infinite time). Zero curvature. Parallel lines remain parallel
What shape is the Universe?
The curvature (Shape) of the universe depends on the combined matter + radiation density - r 0
Critical Density r C :
If r 0 = r C the universe is flat
If r 0 > r C the universe is closed
If r 0 < r C the universe is open
Using H0 = 70 km/s/Mpc we get
r C = 9.2 x 10-27 kg/m3
5.5 hydrogen atoms per cubic meter
What shape is the Universe?
Astronomers prefer to use the Density parameter instead of density:
W 0 = r 0 / r C
Therefore, the shape of the universe can be understood in terms of W 0 .
Critical Density r C :
If W 0 = 1 the universe is flat
If W 0 > 1 the universe is closed
If W 0 < 1 the universe is open
Flat space
Curved space
Measurements of open vs. closed universe
These measurements are underway with a new generation of telescopes
From current observations astrophysicists find that W 0 = 1.0 with an uncertainty of 10%.
This means that the universe is flat.
The flatness of the universe presents a major dilemma.
Dark Energy
The matter & Radiation density parameter W m/R lies between 0.2 - 0.4.
But W 0 = 1.0 and if there is only matter & radiation in the Universe then W 0 = W m/R!!
The source of the missing density must be some form of energy that we cannot detect from its gravitational effects (like astronomers do with dark matter) nor does it emit any radiation.
This mysterious energy is called Dark Energy
Dark Energy
Therefore, the density parameter of the universe has two components: W 0 = W m/R + W L , where W L is the dark energy density parameter.
W L should be between 0.6 & 0.8 (since W m/R = 0.2 to 0.4 and W 0 = 1.0).
That is dark energy accounts for 60% to 80% of the contents of the universe!!
It is believed that this dark energy to be a form of energy that provides an anti-gravity like effect that cause the universe to accelerate mare rapidly.
This concept goes back to Einstein and his cosmological constant.
Dark Matter
Recent measurements: Is the expansion speeding up?
Recently published measurements of velocity vs. distance using supernovae as distance indicators suggest that the rate of expansion is increasing.
Where is the energy driving this rate of increase coming from? Dark Energy?
The First Few Moments
Initially the Universe was incredibly hot.
Matter and energy were freely transforming into one another through Einstein’s Mass-Energy relation.
The mass formed were in matter anti-matter pairs. Matter and anti-matter destroy one another when they come into contact but just enough matter existed to survive.
This remaining matter is what fills the Universe.
Composition of the Early Universe
As the Universe cooled Hydrogen nuclei began to form.
Conditions were still hot enough for fusion reactions to occur forming Helium.
Nearly all elements heavier than Helium however were formed later by stars.
We notice that the oldest stars have much less heavy elements than the Sun. This is further evidence for the Big Bang theory.
After neutral atoms formed the radiation that filled the Universe was allowed to freely propagate.
Steady State Theory
Bondi, Gold, Hoyle – 1948
The same laws of physics are valid at all times
The Universe does not change in time
Continuous creation of matter balances the expansion of the Universe
There are more bright radio sources at greater distances => the Universe is changing
The discovery of CMBR killed the idea of a static Universe
Steady State Universe
Bondi, Gold, Hoyle - 1948
NEUTRON STARS AND BLACK HOLES
NEUTRON STAR
Mass is between 1.4 and 3 solar masses
A star about the size of a city
Smallest, densest star known in the Universe
Density is about 1014 gm/cm3
One teaspoon of material would weigh 109 tons.
Surface gravity is 7 x 109 Earth's
Magnetic field is 1012 Earth's.
Rotation period ranges from 0.001 to 100 seconds.
Electrons are crushed into protons forming neutrons (inverse beta decay).
INVERSE BETA DECAY
PULSARS
Pulsars are rapidly rotating neutron stars detected by radio pulses.
Pulsars are like cosmic lighthouses beaming their radiation toward Earth.
PULSAR MODEL
CRAB NEBULA IN X-RAYS
STELLAR BLACK HOLES
For stars greater than about 3 solar masses, neutron pressure (nuclear force) will not stop the core's gravitational collapse.
Gravity wins the final battle.
No known force in the Universe can stop the contraction.
A black hole in space-time is formed, where the force of gravity is so great that not even light can escape from this bottomless gravitational well.
When escape velocity reaches the speed of light on a collapsing neutron star, a black hole is formed.
SCHWARTZCHILD RADIUS
A LEAP INTO A BLACK HOLE
Time dilation
Length contraction
Gravitational red shift
Strong tidal forces
JETS AND ACCRETION DISKS
Bipolar flows are seen ejecting matter perpendicular to the accretion disk.
High speed jets have matter moving near the speed of light.
SS 433
The End
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