Formation of Earth, Moon, and planets (cont’d) Part 1 Origin of the elements Part 2 Geochronometry: Age of Earth Formation of Earth and Moon. Differentiation of core and mantle. Isotope tracing: sequence of events.
What have we learned so far? • Universe expanding • Age 13.5 Gyr • Alpher, Bethe and Gamow’s calculations suggest only H and He synthesized in early Universe • Test of model cosmic background noise
4 Fundamental forces in physics. • Gravity • Weak (holds neutron together): Note that free neutron is not stable n -> p + e + νe • Electromagnetic (holds atoms together) • Strong (holds nuclei) • When temperature and energy density in Universe decrease, nuclei become stable. Then as Universe gets colder atoms become stable and electromagnetic radiation does not interact with matter any more. Remnant electromagnetic radiation from time of decoupling is cosmic background radiation
Elements abundance • The term nucleosynthesis refers to the formation of heavier elements, atomic nuclei with many protons and neutrons, from the fusion of lighter elements. • The Big Bang theory predicts that the early universe was a very hot place. One second after the Big Bang, the temperature of the universe was roughly 10 billion degrees and was filled with a sea of neutrons, protons, electrons, anti-electrons (positrons), photons and neutrinos. As the universe cooled, the neutrons either decayed into protons and electrons or combined with protons to make deuterium (an isotope of hydrogen). During the first three minutes of the universe, most of the deuterium combined to make helium. Trace amounts of lithium were also produced at this time. This process of light element formation in the early universe is called “Big Bang nucleosynthesis” (BBN). • The predicted abundance of deuterium, helium and lithium depends on the density of ordinary matter in the early universe, as shown in the figure at left. These results indicate that the yield of helium is relatively insensitive to the abundance of ordinary matter, above a certain threshold. We generically expect about 24% of the ordinary matter in the universe to be helium produced in the Big Bang. This is in very good agreement with observations and is another major triumph for the Big Bang theory.
Blackbody radiation Stefan’s law Flux radiated by surface of a black body ~ σ T4 (5.6 10-8W m-2 K-4) Distribution of energy / frequency (wavelength) of radiation depends on temperature. By determining power spectrum of radiation, we can determine temperature.
Radiation and the expansion of the Universe • Cosmic background radiation left when Universe was 3000K • Electromagnetic radiation in expanding universe. • Energy inversely proportional to wavelength (E=hν=hc/λ) • Wavelength of radiation increases in expanding universe. • Energy density decreases (Total energy conserved) • Temperature decreases: Present temperature ~3K
Summary CMB radiation • The existence of the CMB radiation was first predicted by George Gamow in 1948, and by Ralph Alpher and Robert Herman in 1950. It was first observed inadvertently in 1965 by Arno Penzias and Robert Wilson at the Bell Telephone Laboratories in Murray Hill, New Jersey. The radiation was acting as a source of excess noise in a radio receiver they were building. Coincidentally, researchers at nearby Princeton University, led by Robert Dicke and including Dave Wilkinson of the WMAP science team, were devising an experiment to find the CMB. When they heard about the Bell Labs result they immediately realized that the CMB had been found. The result was a pair of papers in the Physical Review: one by Penzias and Wilson detailing the observations, and one by Dicke, Peebles, Roll, and Wilkinson giving the cosmological interpretation. Penzias and Wilson shared the 1978 Nobel prize in physics for their discovery. • Today, the CMB radiation is very cold, only 2.725° above absolute zero, thus this radiation shines primarily in the microwave portion of the electromagnetic spectrum, and is invisible to the naked eye. However, it fills the universe and can be detected everywhere we look. In fact, if we could see microwaves, the entire sky would glow with a brightness that was astonishingly uniform in every direction. The temperature is uniform to better than one part in a thousand! This uniformity is one compelling reason to interpret the radiation as remnant heat from the Big Bang; it would be very difficult to imagine a local source of radiation that was this uniform.
Evolution of early universe (first 3 minutes) • Universe expands: it gets less dense and colder • Particles become stable (p+ p- <->γ) (e+ e-<->γ) (p++ e- <->n + ν) • Free neutrons are unstable • Nuclei form: neutrons fixed and stable in nuclei • At 3000K, atoms become stable. No more interaction between electromagnetic radiation and matter (atoms) • Radiation cools down in expanding universe
Element abundance in solar system Note peak of Fe
Origin of elements: Stardust. • Elements other than H and He do not come from Big Bang. (Sun is a second generation star!) • Nucleosynthesis in stars. (reactions H + H -> D (H2) • D+H > He3He3 + He3 -> He4 + H + H … etc. liberate energy) • Note the peak of Fe • It corresponds to minimum energy /nucleon • Synthesizing elements heavier than Fe requires that energy is provided • Available in stars, but if heavy elements are not removed, they will react to return to minimum energy • 2 ways to remove heavy elements. Reaction in star atmosphere and expulsion in space. • Explosion of the star (Nova, Super nova)
Star formation and evolution • Gravitational collapse yields energy (~3GM2/5R) • When pressure and temperature increase in the collapsing star, there is enough energy to start nuclear fusion reactions which yield more energy • Balance between pressure and gravity maintains the interior of the star in (non-equilibrium) steady-state. • At the end of the life of star, fuel is burned, star collapses, with several possible scenarios depending on mass of star: it will collapse and end as white dwarf, neutron star, black hole, or explode as nova or super nova) • Nova explosion allows elements heavier than Fe to be removed from reactions and preserved.
Summary: origin of elements • Big Bang nucleo synthesis (H, He) • Stellar nucleo synthesis elements -> Fe • Explosive nucleo synthesis Heavier elements in Nova Supernova (Models have been confirmed by direct observation of a supernova explosion) • Note also cosmic ray interaction (e.g. 10Be in the upper atmosphere)
Hypotheses Solar system formation Constraints 3 proposed mechanisms • Constraints • Sun = 99% of mass • Planets = 99 % of angular momentum • Bode’s law • Distribution of Elements • Recent cosmochemical data (isotopes, etc.) • Planets extracted from sun by passing star (Jeans-Jeffreys) • Sun formed then captured planets from cloud • Sun and planets formed together (Laplace)
Other clues to the formation of the Solar System • Inner planets are small and dense • Outer planets are large and have low density • Satellites of the outer planets are made mostly of ices • Cratered surfaces are everywhere in the Solar System • Saturn has such a low density that it can't be solid anywhere • Formation of the Earth by accretion: Initial solar nebula consists of mixtures of grains (rock) and ices. The initial ratio is about 90% ices and 10% grains • The sun is on so there is a temperature gradient in this mixture:
Earth and Planets formed by accretion from meteorites • There are small differences in composition between Earth and chondritic meteorites because of the accretion processes • Accretion by collisions gives a lot of heat => some “volatile elements” are lost.
Geochronometry-Isotope tracingAge and early evolution of the Earth Geochronometry (methods) Age of nuclear synthesis synthesis Meteorites Age of the Earth accretion The moon Formation of the core Formation of crust Plate tectonics starts
Dating the synthesis of elements • Direct estimate • Indirect dating • Age of Earth • Determining how long after nucleo-synthesis did Earth form
Geochronometry is based on development of mass spectrometry Mass spectrometer allow to determine the ratio of different isotopes of an element. Sample is ionized and ions are accelerated into a magnetic field Deflection of ion by field (i.e. acceleration) inversely proportional to mass. Recent technical improvements allow precise measurements on samples with extremely low concentration of analyzed elements.
Geochronometry • Radiogenic isotopes • Decay mechanisms (α decay, β decay, electron capture) • Main isotopic systems for dating • Rb-Sr • K-Ar • U-Pb • Th-Pb • Other isotopes used mainly for “tracing” (Sm-Nd, Re-Os, …) • Another implication of the radio-isotopes is that their decay gives energy.
Geochronometry (hypotheses) • Parent -> daughter decay probability λ • Mineral closes at temperature (depends on type: zircons 800 deg, feldspars 350, …) • No daughter present at closure (or it can be accounted for) • No loss or gain of parent or daughter after mineral closes • Counting P/D gives the time that elapsed since the system closed
Geochronometry (particulars) • K->Ar is a branching decay K40 -> Ar 40 or Ca 40 • U -> Pb two different isotopes of same element give two independent age estimates (must be concordant) • Rb/Sr requires different minerals with variable Rb/Sr ratios (same for Sm-Nd). Methods yield initial isotopic ratio of Sr87/Sr86 (important for tracing)
K-Ar • No Ar initially • But problem of atmospheric contamination • Correction based on Ar36 • Also Ar is easily lost • Retrace loss by step heating of samples and Ar-Ar ages
Note that the 87Sr/86Sr increases with the concentration in Rb. This provides a useful tracer. • In the Earth, Rb is preferentially concentrated in the crust relative to the mantle. • Present samples from mantle have 87Sr/86Sr ~0.705. Higher ratios would indicate that the source has been enriched in Rb relative to mantle, most likely it is crustal.
Meteorite samples achondrite chondrite Iron
Xe129 • Xe129 product of short half life I129 • Meteorites formed shortly after nucleosynthesis. • Xe129 in earth atmosphere (I129 in primitive earth) comes from degasing of mantle • Earth and meteorites have ~ same age
Meteorites • All meteorites have about the same age 4.55 Ga • Some meteorites that have younger ages come from the moon. They were ejected after impact. • A few are much younger (1.1 Ga). They are assumed to have been ejected by Mars after a large impact