1. 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.

2. 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

3. 4 Fundamental forces in physics. Gravity Weak (holds neutron together): Note that free neutron is not stable n -> p + e + ν e 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

4. 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).Big Bangisotope 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.density of ordinary matter

6. Blackbody radiation Stefan’s law Flux radiated by surface of a black body ~ σ T 4 (5.6 10 -8 W m -2 K -4 ) Distribution of energy / frequency (wavelength) of radiation depends on temperature. By determining power spectrum of radiation, we can determine temperature.

7. 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

8. 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. absolute zeroelectromagnetic spectrum

9. 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

10. Element abundance in solar system Note peak of Fe

12. 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 (H 2 ) D+H > He 3 He 3 + He 3 -> He 4 + 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)

13. Star formation and evolution Gravitational collapse yields energy (~3GM 2 /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.

14. 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. 10 Be in the upper atmosphere)

16. 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)

20. 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 :

23. 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.

24. 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

25. Dating the synthesis of elements Direct estimate Indirect dating Age of Earth Determining how long after nucleo-synthesis did Earth form

27. 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.

28. 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.

31. 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

32. Geochronometry (particulars) K->Ar is a branching decay K 40 -> 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)

34. K-Ar No Ar initially But problem of atmospheric contamination Correction based on Ar 36 Also Ar is easily lost Retrace loss by step heating of samples and Ar-Ar ages

35. Same equations and method for other systems (U-Pb, Sm-Nd)

37. Note that the 87 Sr/ 86 Sr 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 87 Sr/ 86 Sr ~0.705. Higher ratios would indicate that the source has been enriched in Rb relative to mantle, most likely it is crustal.

40. Evolution of the Pb/U as a function of time

41. Meteorite samples chondrite achondrite Iron

43. Xe 129 Xe 129 product of short half life I 129 Meteorites formed shortly after nucleosynthesis. Xe 129 in earth atmosphere (I 129 in primitive earth) comes from degasing of mantle Earth and meteorites have ~ same age

46. 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

47. Martian meteorites (?)

52. Moon samples Nasa has collected samples for dating Ages range between 3.0 and 4.5 Ga (see PDF document)

53. Time series of a Moon-forming impact simulation. Results are shown looking down onto the plane of the impact at times t = 0.3, 0.7, 1.4, 1.9, 3, 3.9, 5, 7.1, 11.6, 17 and 23 hours (from left to right); the last frame is t = 23 hours viewed on-edge. Colour scales with internal energy (shown on the colour bar in units of 6.67 times 108 erg g-1), so that blue and dark green represents condensed matter, and red particles signify either the expanded phase or a hot, high-pressure condensed phase; pressures at intermediate energies are computed by an interpolation between the Tillotson15 condensed and expanded phases. We form initial impactors and targets in hydrostatic equilibrium by pre-colliding smaller bodies together at zero incidence, resulting in realistically evolved internal energies, stratified densities (basalt mantle + iron core) and consistent pressures. Each particle's internal energy is evolved due to the effects of expansion/compression and shock dissipation, with the latter represented by artificial viscosity terms that are linear and quadratic in the velocity divergence of converging particles; effects of mechanical strength and radiative transfer are ignored. The momentum of each particle is evolved due to pressure, viscous dissipation and gravity. Gravity is computed using a binary tree algorithm, reducing the N2 calculation of particle– particle attractions into an NlogN calculation25. We use a beta spine kernel to define the spatial distribution of material represented by each SPH particle. The scale of each particle, h, is automatically adjusted to cause overlap with a minimum of 40 other particles, ensuring a 'smoothed' distribution of material even in low-density regions. The code is explicit, requiring a Courant-limited timestep Deltat < (c/h) where c is the sound speed. For a full description of the technique, see ref. 26, from whose efforts our present algorithm derives.

56. Dating core formation Hafnium Hf and Tungsten W Hf 182 -> W 182 (half life 9 Myears) Hf 180 reference Hf stays in mantle W goes in core Initial ratio Hf 182 /Hf 180 in solar system different from that of mantle

57. εw values of carbonaceous chondrites compared with those of the Toluca iron meteorite and terrestrial samples analysed in this study. The values for Toluca, Allende, G1-RF and IGDL-GD are the weighted averages of four or more independent analyses. Also included are data from ref. 16 (indicated by a), ref. 30 (b), and ref. 2 (c). For the definition of εw see Table 1. The vertical shaded bar refers to the uncertainty in the W isotope composition of chondrites. Terrestrial samples include IGDL-GD (greywacke), G1-RF (granite) and BB and BE-N (basalts).

58. εw versus 180Hf/184W for different fractions of the H chondrites Ste Marguerite (a) and Forest Vale (b). NM-1, NM-2 and NM-3 refer to different nonmagnetic fractions, M is the magnetic fraction. We interpret the positive correlation of εw with 180Hf/184W as an internal Hf–W isochron whose slope corresponds to the initial 182Hf/180Hf ratio at the time of closure of the Hf–W system.

59. Time of core formation in Myr after CAI condensation for Vesta, Mars, Earth and Moon versus planet radius as deduced from Hf–W systematics. For the Moon, the two data points refer to the endmember model ages. The Moon plots distinctly to the left of the correlation line defined by Vesta, Mars and Earth, suggesting a different formation process.

60. Timing of core formation. The Earth formed through accretion, absorbing planetesimals (lumps of rock and ice) through collisions. Did the Earth accrete undifferentiated material that then separated into shell and core — in which case, did the planet reach its present mass before differentiating, or was it a more gradual process? Alternatively, core formation might have happened rapidly inside growing planetesimals, so that the Earth's core is a combination of these previously formed cores. Isotopic evidence supports the latter model, and now Yoshino et al.1 demonstrate a mechanism for the physical process.

61. Core formation (conservation laws) Gravitational potential energy decreases when core forms Moment of inertia decreases Angular velocity of rotation increases Rotational energy increases Increase in energy of rotation < Decrease in gravitational potential energy Total energy must be conserved Difference goes into heat Estimates: Core formation -> 1000-2000K temperature increase

66. He It is assumed that volatiles were lost during accretion Very little He in atmosphere (too light, lost to space) He in mantle He 3 is primitive, He 4 primitive + decay of radioelements He 4 /He 3 ratio (initial ratio same as that of universe) He 4 /He 3 ratio grows with time Some degasing Shows mantle is not well mixed

68. Tracing with isotopes Crust Rb/Sr high Sm/Nd low Sr 87 /Sr 86 increases Nd 143 /Nd 144 decreases compared with mantle Mantle Rb/Sr low Sm/Nd high

78. The data brings into high resolution the seeds that generated the cosmic structure we see today. These patterns are tiny temperature differences within an extraordinarily evenly dispersed microwave light bathing the Universe, which now averages a frigid 2.73 degrees above absolute zero temperature. WMAP resolves slight temperature fluctuations, which vary by only millionths of a degree. Anisotropy in CMB very weak