Lecture 9: Nucleosynthesis of Light Elements Flashcards
When we talk about nucleosynthesis we mean
the formation of the light elements
the light elements
hydrogen
deuterium
helium-3
helium-4
lithium-7
Heavier elements can be formed through
nuclear fusion in the centres of stars
the abundances of the light elements reflect the
primordial state of the universe
and the conditions that existed at that time.
The theory of primordial nucleosynthesis is able to successfully predict
the abundances over about 9 orders of magnitude
this makes it one of the strongest pieces of evidence for the Hot Big Bang Theory
ratio of neutrons to protons - 4 important facts
- protons lighter than neutrons
- free neutrons decay into protons
- neutrons bound into stable isotopes of the light elements do not decay
- neutrinos decouple from the rest of the cosmic plasma at T=10^10K
which are lighter, protons or neutrons?
protons (938.3MeV to 939.6MeV)
free neutrons decay into protons with a half life of
610s
Consider the period before nuclei form but late enough that protons and neutrons are non-relativistic.
This is equivalent to
kBT «mpc^2
or
T«10^13K
Consider the period before nuclei form but late enough that protons and neutrons
are non-relativistic.
the number density N will be
in a maxwell boltzmann distribution
Nn/Np is approx 1 when
kBT»_space; (mn-mp)c^2
ie the typical thermal energy of photons significantly exceeds the rest-mass
energy of the proton-neutron mass difference
The relevant reactions involve neutrinos, mediated by the weak force:
n + ve <-> p + e-
n + e+ <-> p + anti ve
when kBT is approx 0.8MeV, neutrinos
decouple and the cosmic neutrino background is formed
what does neutrinos decoupling and the cosmic neutrino background forming mean?
the reactions can no longer occur and neutrons freeze out, though free neutrons can still decay
R=
Nn/Np
approx exp(-1.3MeV/0.8MeV)
approx 1/5
(numerator - mass difference, denominator - neutrino decoupling temp)
If it were not possible to ‘lock away’ neutrons in stable nuclei eventually
all of the free neutrons would have decayed into protons.
We’d have a universe consisting only of hydrogen: we would not exist.
why do we not have a universe consisting only of hydrogen
deuterium can be formed via
p+n –> d + gamma
deuterium
one proton + one neutron
deuterium formation: High-energy photons in the tail of the distribution cause
photo-disintegration
of the deuterium d until the temperature of the universe drops to about T=8x10^8K at t=300s
deuterium formation: By the point of photo-disintegration, the ‘frozen-in’ value of R = Rf will have reduced because
of the decay of the free neutrons
model as a radioactive process
R at freeze out
R=Rf=0.2 at freeze out
valid at t=300s
light element abundances in the early universe - assume
that all the free neutrons end up as helium-4 nuclei.
if all free neutrons end up as helium-4 nuceli, NHe=
1/2Nn
Y4 is the
mass abundance ratio
=mass of He4/total mass
for R300=0.135, Y4=
0.24
ie helium-4 makes up around 1/4 of the universe
As well as helium-4 we can predict the abundances of
deuterium (10−4) helium-3 (10−5),
and lithium-7 (10−10) as a function of the density of baryons.
There is an agreement between theory and observed abundances over about
nine orders of
magnitude
caveat of success of 9 order of magnitude
the baryon density be no
more than 4% or 5% of the critical density (for h = 0.7).
ie lots of other stuff (dark matter etc)
the predicted abundances depend on
a number of different parameters
if we tweak the neutron lifetime, we can see how
Y4 changes
baryon to photon ratio, n also influences
the predicted abundances
what other parameters affect the predicted abundances
- neutron half-life
- number of neutrino species
- baryon to photon ratio
- non-degeneracy of neutrinos
neutron half-life: increasing the nurton half life…
increases Y4 because fewer neutrons will have decayed by t=300s which means more neutrons are available to be captured in deuterium nuclei to then form helium
neutrons freeze out earlier so there are even more neutrons available to form helium
number of neutrino species - the standard model predicts 3 neutrino species Nv, increease Nv…
increases Y4 because it increases the relativistic energy density at nucleosynthesis. This means a higher value of H at that time so the neutron freeze out occurs at higher temperature and a higher R
baryon to photon ratio, increasing n causes
an increase in Y4 because it means there are less high-energy photons in the tail of the distribution, resulting in a less severe deuterium bottleneck, thus the build-up of He-4 begins earlier and more of it will form
we expect a decrease in deuterium with an increase in n
non degeneracy of neutrinos: neutrinos are fermions and obey the Pauli Exclusion Principle. At low temps, neutrinos…
fill up states to Fermi level, anti-neutrinos do the same but to different Fermi level. If there are many more neutrinos than anti-neutrinos a chemical potential results from the difference in Fermi levels
so n to p reactions occur more often than p to n so Y4 decreases
comparison with CMBR constraints - there is a discrepancy between planck and observations called
the cosmological lithium problem
due to difficulty in making accurate observations of primordial Li-7
