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