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

. . . 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!

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?

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):

First the results!

Standard BBN Nao Suzuki (Tytler group) 2006

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:

NSE Freeze Out

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.

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.

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

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

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).

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

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

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,

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

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

N. Suzuki (Tytler group) (2006)

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

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

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.

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

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

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

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)

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:1308.3240

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?

Two ways to make 7Li

Can we add new physics? Decaying particles?

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

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

but the steriles have rest masses ~ GeV OOPS!

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

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

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

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

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