ASTR 200 : Lecture 33 Structure formation & Cosmic nuceleosynthesis 1
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 2
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. 3 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 the big densities at filament intersections. 4 These correspond to large galaxy clusters
The local universe does look like this, in the luminous mass 5
Different kinds of matter clump on different scales gas normal matter dark matter Gas (which has pressure support) often has the 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. The number of small galaxies varies. 7
So, review of what we've talked about Normal galaxies & planetary systems CMB Growth of structure It took hundreds of millions of years for the matter to become clumped enough that the first stars and globular clusters of stars could form. It probably took a billion or so years before galaxies the scale of the Milky Way could form 8 Spirals may be the assembly of many small clumps, so ~2-3 Gyr?
What about BEFORE recombination?? Normal galaxies & planetary systems CMB Growth of structure We discussed that before the epoch of recombination (when the CMB photons were liberated), matter and radiation existed in a highly coupled hot state in equilibrium 9 We said there were dominantly photons, electrons, protons (hydrogen nuclei) and helium nuclei (2p+2n)
Once there were stars, there were now `factories' that created heavier nuclei via fusion of hydrogen and helium Recall that the solar system is about 74% H, 24% He, and 2% everything else. So there must have been less `metals' (everything >He) in the past Can we understand why H and He are so dominant in the universe? (and still now...) Where did they come from? 10
Once there were stars, there were now `factories' that created heavier nuclei via fusion of hydrogen and helium Recall that the solar system is about 74% H, 24% He, and 2% everything else. So there must have been less `metals' (everything >He) in the past Can we understand why H and He are so dominant in the universe? (and still now...) 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 11 What about before that?
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 (the same amount of mass-energy per particle) Thus, a few seconds after the Big Bang, the main particle species present were protons, neutrons, neutrinos, and photons (Protons and neutrons not combined in nuclei) 12
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 13 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 at that time to combine to form nuclei, it was just a sea of free subatomic particles 14
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 nuclei that formed were immediately broken apart again by high-energy photons. Thus, starting at t~1 minute, the cooling universe started to permit 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 15
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 were there very many neutrons to use up 16
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, nearly all ending up in helium-4 nuclei A tiny amount of Li and Be were created too...nothing heavier 17
Cosmic nucleosynthesis 18
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 nuclei (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. That's what the universe made! 19
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 concordant Major success of big bang model 20
Announcements Solutions for HW1-8 already on website. HW9 solutions before Friday. HW10 (last homework) may not be graded before final. We'll try. The solutions will be posted Friday evening. Final exam: Thursday, Dec 7, 8:30 AM, room LSK 201 (locate before!) I will give a Q&A session : ASTR 200 Q&A. Monday Dec 4, 2-3:30 pm. Henn 318. Email me questions about content and/or HW before 8 PM Sunday Dec 3rd. I will answer them until I run out of time. There will be many open office hours Dec 4, 5, 6 Check the course website for times/places 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. 21
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