Download Lecture 33

ASTR 200 : Lecture 33
The very early, and the very late universe
1
Announcements
• Solutions for HW1-8 already on website. HW9 solutions tonight.
• HW9 (last homework) will be graded by middle of next week.
• Final exam: Tuesday, Dec 13 7 PM, room LSK 200 (locate before!)
• I will hold two review/Q&A sessions :
– Homework review. Monday Dec 5, noon. Henn 202
• Email me questions about the HW solutions.
• I will answer them Monday.
– Open questions review. ?? AM Dec 12. Henn ???
• There will be many open office hours between Dec 5 and 12
– Listed on website now.
– You can always email me or a TA for a private appointment also
• Suggestion: form small study groups and discuss concepts and
terminology. Explain them, and associated formulae, to each other.
2
At the time of decoupling, the CMB tells us that the universe
was very uniform, but that there were 10-5 fluctuations
• Known because of tiny temperature fluctuations in the CMB
- The fluctuations just occur because some places are by chance
denser, and thus some areas nearby are less dense
3
These fluctuations are essentially just noise in a uniform background
• However, they can grow with time if they are large enough
• It is in fact the growth of these density perturbations that eventually
makes the universe more and more non-uniform.
4
• In an expanding universe, the first thing that happens is that dark
matter forms small clumps that lie along `filaments'
The matter clumps
• This leads to the matter (both dark and normal) concentrating onto
these filaments, with big densities at filament intersections.
5
• These correspond to large galaxy clusters
Different kinds of matter clump on different scales
gas
normal matter
dark matter
• Gas (which has pressure support) stays with largest scales
• Normal matter drops to smallest scales
6
• Dark matter has not clumped as much as luminous matter –> halos
Dark matter halos
• These surround galaxies luminous
galaxies
• The properties of the dark matter
(that is, what it is made of) influence
on what scale it clumps, and also
whether the visible matter collects
into lots of little dwarf galaxies or
fewer (relative to the big galaxies)
• At right, the dark and visible matter
structure around a galaxy for
different assumed properties of the
dark matter.
7
So after decoupling, it takes time before stars and galaxies form
• It took hundreds of millions of years for the matter to become clumped
enough that the first stars and clusters of stars could form.
• It probably took a billion or so years before galaxies to scale of the
Milky Way could form
8
• But spirals might be the assembly of many small clumps
Once there were stars, there were now `factories' that created
heavy elements via fusion of hydrogen and helium
• Recall that The solar system is about 74% H, 24% He,
and 2% everything else
• Can we understand why H and He are so dominant in
the universe?
– Where did they come from?
– Like when we thought about the epoch of recombination
and decoupling, we have to consider even further back in
time towards the Big Bang
– At t~300,000 years, the temperature T~3000 K
• What about before that?
9
Pushing backwards in time, the density and temperature of
matter and radiation continue to rise
• Back at t~1 minute, the T exceeded one billion K and
the thermal energies (of motion) of the particles exceed
their rest-mass (mc2) energies.
• At the very high densities, collisions between particles
were very frequent, keeping all `species' of particles
very close to thermal equilibrium (same amount of mass
energy per particle)
• A few seconds after the Big Bang, the main particle
species present were protons, neutrons, neutrinos, and
photons
10
What was going on in that period (few sec < t< 1 minute)?
• Neutrons and protons can convert to each other via the
weak nuclear interactions
• Here there are electron neutrinos and anti-neutrinos
• Neutrons have a slightly higher rest mass than protons,
so have more mass energy. Therefore their abundance
ends up being lower than protons
– The ratio can be calculated from the Boltzmann
equation:
• Because the mass difference is small, when T is large
11 the number of n and p ~1 but decreases with time
Freeze out of the protons and neutron
• As the universe rapidly expanded and the density drop, the
interaction rate decreased
• When the p<--->n reaction rate became less than the expansion
rate (determined by H(t) at that time) the reactions stopped
• Thus, the n/p ration become frozen at the value set by the
temperature at that time, which turns out to be : p/n ~ 7
• So for every neutron there were 7 protons
• After the first second this was set, but it was too hot for protons
and neutrons to combine to form nuclei, it was just a sea of free
subatomic particles
12
If you don't like the Universe, just wait a minute.... :-)
• The universe had to expand by more than another order of
magnitude in order to cool so that neutrons and protons could
combine; before that any that formed were immediately broken
apart again by high-energy photons.
• Thus, starting at t~1 minute, the universe started to allow the
creation of the nuclei of atoms
• Hydrogen is just a bare proton, but at this time electrons couldn't
bind to make an atom (that had to wait for decoupling...)
• However, two nuclei of two
isotopes could form (deuterium 2H
and tritium 3H)
• It was also possible to make helium
nuclei
13
Cosmic nucleosynthesis
• Reaction chain that takes free p and n and combines them to
make the nuclei of the light elements
• There was not time to make much else, nor many neutrons
14
Cosmic nucleosynthesis
• It was all over in less than an hour, as T dropped from 3 billion
to <300 million degrees
• It stopped essentially because all the neutrons got used up,
essentially all moving into helium-4 nuclei
• A tiny amount of Li and Be were created too...nothing heavier
15
The outcome of Cosmic nucleosynthesis
• Each Helium-4 nucleus contains 2 n and 2 p. But, there because
there were 7 times as many protons and neutrons, there are
2x7 – 2 = 12 protons left over, which are the normal H nuceli
• (the mass fraction of deuterium and tritium is tiny)
• We can thus predict the helium mass fraction. Since a He
nucleus has about 4 times the mass of a proton, the mass in He
will be
• These predicted initial fractions of the light elements
synthesized in the Big Bang theory were a prediction, but it was
immediately realized that this explained why so much of the
interstellar material is H and He.
• What about the other elements?
16
Abundance of light elements
• Observations of interstellar and
intergalactic matter measure the mass
fraction of Helium, Deuterium and
Lithium-7 (harder)
• Here the observational range (vertical
extent of each black box) constrains
what the density of baryons (normal
matter) must have been at the time of
cosmic nucleosynthesis.
• Despite there being many orders of
magnitude between the different
mass fractions, there is one consistent
value (vertical blue band) of the
baryon density (at about 4% of the
critical density) where the mass
fractions are all concordent.
– Major success of big bang
model
17
We won't talk about what happened in the 1 st second
• Beyond the scope of this course (and requires better knowledge of nuclear
physics)
• But....wait a minute, where did the Z=2% of elements heavier than helium
come from?
18
All elements heavier than atomic mass number 7 come from later stellar
synthesis, either in the cores, or during explosive events
Type II supernova
(death of massive star)
Type Ia supernova
(white dwarf in binary
Passes Chandra limit)
19
Planetary Nebula
(outer layers of main
sequence star puffed of near end of main sequence lifetime)
The elements (Boron and up) are mixed back into the gas in
the galaxy, and then participate in the next generation of stars
The Vela
supernova
remnant
20
The abundance of heavy elements has thus been gradually rising.
21
•
The vertical axis is the
logarithm of the amount of
iron divided by the amount
of hydrogen, normalized to
the Sun. This will be
roughly proportional to Z.
•
When the Sun formed ~4.5
Gyr ago, the metalicity Z
had reached about 2% in
the part of the galaxy
where the Sun formed (in
the disk).
•
Prior to that, there were
less heavy elements (and
old stars show this). Stars
formed more recently are
somewhat more heavy
element rich.
(into past)
The Sun will participate in this.
• In another ~5 Gyr the Sun will become a red giant and return
several tenths of a solar mass of its outer layers to the interstellar
gas.
• It will leave behind a white dwarf core
• Wait a minute... so the net result is to have taken a solar mass of
mostly H and He and leave behind ~0.7 in a carbon white dwarf
(locked up) and return a few tenths of a solar mass.
– That can't continue forever
22
On time scales thousands of times longer than the current
age of the universe, the H and He will become rare
• With our current understanding, the universe will become unable to make
new stars
• The stars will go out, even the long-lived dwarf stars, and no new ones
will light up
• All mass will be locked into degenerate objects (WDs, neutron stars)
• On time scales of 1038 years, they will find each other and turn into black
holes
• On time scales of 10100 years black holes will have consumed all the
mass. The universe will be dark, and dead...
23
OR MAYBE NOT
• Our understanding of the Universe has evolved quickly over the last
100 years
• There is almost certainly more astrophysics that we don't yet know.
24