1. 2014 TALENT Lectures III. Nucleosynthesis – NSE Freeze-Out:
entropy and BBN
2014 TALENT Lectures
George M. Fuller
Department of Physics, UCSD

2. . . . because of the advent of . . .
VERY EXCITING FUTURE . . .
because of the advent of . . .
(1) comprehensive cosmic microwave background (CMB)
observations (e.g., Planck, PolarBear, ACT, SPT, CMBPol)
(e.g., high precision baryon number and
cosmological parameter measurements, Neff, 4He, n mass limits)
(2) 10/30-meter class telescopes, adaptive optics, and orbiting observatories
(e.g., precision determinations of deuterium abundance,
dark energy/matter content, structure history etc.)
(3) Laboratory neutrino mass/mixing measurements
is setting up a nearly over-determined situation where new
Beyond Standard Model neutrino physics
likely must show itself!

3. My main point about the exciting developments . . .
Five developments which will set up sensitivity to new (dark sector) sector physics:
Currently degeneracy between these;
broken by phasing of acoustic peaks,
E-mode polarization?

4. baryon number of universe
From CMB acoustic peaks, and/or
observationally-inferred primordial D/H:
three lepton numbers
From observationally-inferred 4He and large scale structure
and using collective (synchronized) active-active neutrino oscillations
(Abazajian, Beacom, Bell 03; Dolgov et al. 03):

5. First the results!

6. Standard
BBN
Nao Suzuki (Tytler group) 2006

7. So, where do we stand in comparing the observationally-determined
light element abundances with BBN predictions ??
(1) only really complete success is deuterium
– and this is very good! (see Ryan Cook’s recent work!)
(2) Helium is historically problematic, but promising with CMB
From compact blue galaxy linear regression, extrapolation to zero metallicity
Izotov & Thuan (2010) get helium mass fraction
Using the CMB-determined baryon-to-photon ratio the standard BBN prediction is
Best bet may be future CMB determinations via the Silk damping tail,
very tricky – Neff and 4He almost degenerate
(3) Lithium is a mess:

9. NSE Freeze Out

10. Thermonuclear Reaction Rates
Rate per reactant is the thermally-averaged
product of flux and cross section.
Rates can be very temperature sensitive,
especially when Coulomb barriers are big.

11. At high enough temperature the forward and reverse
rates for nuclear reactions can be large and equal
and these can be larger than the local expansion rate.
This is equilibrium. If this equilibrium encompasses
all nuclei, we call it Nuclear Statistical Equilibrium (NSE).
In most astrophysical environments NSE sets in for T9 ~ 2.

12. In general, abundance relative to baryons for species i
Electron Fraction
In general, abundance relative
to baryons for species i
mass fraction
mass number

13. Freeze-Out from Nuclear Statistical Equilibrium (NSE)
In NSE the reactions which build up and tear down nuclei
have equal rates, and these rates are large compared to
the local expansion rate.
Z p + N n A(Z,N) + g
nuclear mass A is the sum
of protons and neutrons A=Z+N
Z mp + N mn = mA + QA
Binding Energy
of Nucleus A
Saha Equation

14. Typically, each nucleon is bound in a nucleus by ~ 8 MeV.
For alpha particles the binding per nucleon is
more like 7 MeV.
But alpha particles have mass number A=4,
and they have almost the same
binding energy per nucleon as heavier nuclei
so they are favored whenever there is a competition
between binding energy and disorder (high entropy).

15. Neutrino-Driven Wind (S/kb~102)
FLRW Universe (S/kb ~1010)
Neutrino-Driven Wind (S/kb~102)
Temperature
co-moving fluid element in the early universe
Outflow from Neutron Star
Weak Freeze-Out
T~ 0.7 MeV
T~ 0.9 MeV
Weak Freeze-Out
n/p>1
n/p<1
Alpha Particle Formation
T~ 0.1 MeV
T~ 0.75 MeV
Alpha Particle Formation
Time
PROTON
NEUTRON

16. 3H n 11C 12C 13C 6Li 7Li 8Li 3He 4He p 2H 13N 14N 8Be (a,g) (a,g) 8B
Cococubed.asu.edu/code-pages/net_bigbang.shtml

17. 2nd order Runga-Kutta integration
Nuclear Abundance Evolution – nuclear reactions
Wagoner-Kawano Code
2nd order Runga-Kutta integration
many variants with different integrators and weak rate
See bigbangonline.org hosted and led by Michael Smith
prescriptions
at ORNL
for example
Where , with a simple
2-to-2 strong interaction,
as in the example above,

18. Saha equation would have given
Full network BBN
What NSE and the
Saha equation would have given
M. Smith, L. Kawano, R. Malaney

19. Cococubed.asu.edu/code-pages/net_bigbang.shtml

20. N. Suzuki (Tytler group) (2006)

21. There are two neutrons for every alpha particle, so in the limit where
every neutron gets incorporated into an alpha particle the abundance
of alpha’s will be
The alpha mass
fraction at
the  formation
epoch,
T ~ 100 keV,
is then

22. Extra particles or energy density speeds up
earlier (hotter) weak freeze out and, hence,
expansion rate, leading to
more 4He
3.4
3.2
3.0

23. 4He yield sensitive to neutron/proton ratio
very crudely:
4He yield sensitive to neutron/proton ratio
2H sensitive to baryon density
Actually, helium does depend on baryon density,
and deuterium does depend on the n/p ratio
and the expansion rate.

24. C. Smith, G. Fuller, C. Kishimoto, K. Abazajian, PRD 74, 085008 (2006)

25. NSE Freeze-Out for the Deuteron
deuteron is very fragile, bound by only B.E. = 2.2 MeV,
and stays in equilibrium until the neutrons are
locked up in alpha particles at Ta ~ 0.07 to 0.1 MeV . . .
n + p <-> d + g
Deuteron abundance at Freeze-Out
(where the alphas form):
Yd ~ eB.E./Ta

26. Deuteron production reaction
deprived of neutrons because of
alpha formation: goes out of NSE

27. Primordial Deuterium Abundance
From observations of isotope-shifted Lyman lines in the spectra
of high redshift QSO’s.
See for example: J.M. O’Meara, D. Tytler, D. Kirkman, N. Suzuki,
J.X. Prochaska, D. Lubin, & A.M. Wolfe
Astrophys. J. 552, 718 (2001)
D. Kirkman, D. Tytler, N. Suzuki, J.M. O’Meara,
& D. Lubin
Astrophys. J. Suppl. Ser. 149, 1 (2003)

28. Uncertainty in Primordial Deuterium Abundance
arguably ~30% with current data
With the advent of 30m class telescopes
(hence, many more “clean” QSO absorption systems),
might it be possible to get
the uncertainty down to ~2% or even lower ???
- will be limited by n(p,g)D cross section!
M. Pettini & R. Cooke, MNRAS (2012)
R. Cooke et al., arXiv:

29. Lithium evolution is very interesting
BBN predicts factor 3-4 more 7Li (produced as 7Be)
than observed on the surfaces of old, blue halo stars
Problem with BBN, nuclear reaction rates? or
Stellar depletion through rotationally-driven turbulent diffusion
Non-thermal “cascade” nuclear reactions driven by WIMP decay?
(Jedamzik 2007) Or
First stars –very massive?; cosmic rays? or
Physics of BBN itself?

30. Two ways to make 7Li

31. Can we add new physics?
Decaying particles?

32. Consider as an example:
sterile neutrinos with rest masses ~ 1 GeV
and lifetimes ~ seconds
particle decay-induced “dilution” in the early universe

33. Heavy sterile neutrinos with sufficiently large coupling will be in
thermal equilibrium at temperatures T >> 1 GeV
This means that their number densities will be comparable to those of photons
at the BBN epoch, albeit somewhat diluted by loss of degrees of freedom
at the QCD epoch.
Nevertheless, their energy spectra will be a “relativistic Fermi Dirac black body”
just like the decoupled active neutrinos but with a lower “temperature”
number density
prior to decay
photon number density
Fuller, Kishimoto, Kusenko 2011

34. but the steriles have rest masses ~ GeV OOPS!

35. Decay into 7 possible channels No threshold: Non-zero threshold:
Pions and Muons decay
instantaneously:
Non-zero threshold:
List not meant as exhaustive
Pi^+/- decay is 5 neutrino decay
xpio=135 MeV, xpic = 140 MeV, xmuon = 105 MeV

36. heavy “sterile” neutrino decay
Photons thermalize,
but neutrinos may or may not, depending on their energies and the decay epoch

38. Dashed Lines: (ms,s)=(300 MeV, 4.0 s)
Solid Lines: SBBN
Dashed Lines: (ms,s)=(300 MeV, 4.0 s)
Solid curves are SBBN
Dashed curves are with steriles

39. Abundance/Mass Fraction vs. Sterile Lifetime (ms=300 MeV)
Sweet Spot?

40. Conclusions SBBN successfully predicts D abundance, but
has problems with Li and maybe (possibly) Neff
Sterile Neutrino mass/lifetime can be tuned to
preserve primordial abundances
with the exception of Li (Be) and can change Neff
Boltzmann neutrino transport code needed to determine
if sweet-spot solution for Li problem is consistent with
forthcoming constraints on Neff