Transcript class1-2_SolarSystemhx

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 10-8 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.
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 > He3 He3 + 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
 Planets extracted from sun by
 Sun = 99% of mass
passing star (Jeans-Jeffreys)
 Sun formed then captured planets
from cloud
 Sun and planets formed together
(Laplace)
 Planets = 99 % of angular
momentum
 Bode’s law
 Distribution of Elements
 Recent cosmochemical data
(isotopes, etc.)
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 (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 SmNd). 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
Same equations and method for other systems (U-Pb, Sm-Nd)
 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.
Evolution of the Pb/U as a function of time
Meteorite samples
chondrite
Iron
achondrite
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
Martian meteorites (?)
Moon samples
Nasa has collected samples for dating
Ages range between 3.0 and 4.5 Ga
(see PDF document)

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.
Dating core formation
 Hafnium Hf and Tungsten W
 Hf182 -> W182 (half life 9 Myears)
 Hf180 reference
 Hf stays in mantle
 W goes in core
 Initial ratio Hf182/Hf180 in solar system different from that of mantle
 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).
 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.
 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.

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.
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
He
 It is assumed that volatiles were lost during accretion
 Very little He in atmosphere (too light, lost to space)
 He in mantle
 He3 is primitive, He4 primitive + decay of radioelements
 He4/He3 ratio (initial ratio same as that of universe)
 He4/He3 ratio grows with time
 Some degasing
 Shows mantle is not well mixed
Tracing with isotopes
 Crust
 Mantle
 Rb/Sr high
 Rb/Sr low
 Sm/Nd low
 Sm/Nd high
 Sr87/Sr86 increases
 Nd143/Nd144 decreases compared
with mantle
Anisotropy in CMB very weak
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.