the astrophysical formation of the elements

the astrophysical formation of the elements Rebecca Surman Union College Second Uio-MSU-ORNL-UT School on Topics in Nuclear Physics 3-7 January 2011

the astrophysical formation of the elements lecture 1: some preliminaries lecture 2: big bang nucleosynthesis lecture 3: fusion in main sequence stars lecture 4: stellar evolution and supernovae lecture 5: neutron-capture nucleosynthesis

but first, some cosmology an expanding Universe v = H r v r galaxy's recessional velocity distance between galaxy and observer H Hubble's constant

but first, some cosmology an expanding Universe v = H r Hubble s Law is a natural result of an expansion that is isotropic and homogeneous v r galaxy's recessional velocity distance between galaxy and observer H Hubble's constant

Hubble expansion Look at the expansion kinematics Write the interparticle distances as: r (t) = a(t) r today a(t) space independent universal scale factor r today time independent comoving coordinate So the expansion velocity is: v (t) = d dt ( today ) = a(t) r a r today = a a a r today = a a H(t) = a a r (t) = cosmic expansion rate

Hubble expansion Look at the expansion dynamics Consider an arbitrary point, in a homogeneous universe with density ρ ρ r The test particle sees an enclosed mass: M = 4π 3 r3 ρ Assuming Newtonian dynamics and Euclidian (flat) geometry, we see: H 2 = a a 2 = 8π 3 Gρ

Looking farther back R Surman, Union College Introduction to Nuclear Astrophysics, Lecture 2 5 January 11

cosmic microwave background

cosmic microwave background Max s Cosmic Cinema http://space.mit.edu/home/tegmark/cmb/movies.html

hot big bang cosmology

hot big bang cosmology R Surman, Union College Introduction to Nuclear Astrophysics, Lecture 2 5 January 11

hot big bang cosmology big bang nucleosynthesis

big bang nucleosynthesis: the conditions space homogeneous, isotropic hot, radiation dominated ρ early ρ radiation T γ 4 dark matter, dark energy present but not interacting adiabatic expansion with fixed baryon-to-photon ratio T = T 0 a η = n b n γ composition γ, e, e +, ν, ν, p, n

back-of-the-envelope BBN Reactions coupling radiation and matter are initially in equilibrium γ +γ e + e + ν + ν p + e ν e + n n +e + ν e + p and so the neutron-to-proton ratio can be calculated as n n n p = e Q / kt, where Q = (m n m p )c 2 =1.293 MeV As the temperature falls, so do the interaction rates Weak equilibrium fails when T~10 10 K, so the neutron-to-proton ratio is frozen at: n n = e Q / kt = e (1.293 MeV)/(8.617 10 11 MeV/K 10 10 K ) 0.223 n p Composition is therefore ~223 n for every 1000 p

back-of-the-envelope BBN At T~10 10 K, still too hot for D to form: p + n D + γ Below T~10 9 K, the reverse reaction slows, and D can survive. From T~10 10 K to T~10 9 K, roughly 176 s have passed, and the composition has evolved due to the decay of the neutron: N n = 223e t /τ = 223e 176 / 885.7 =183 neutrons remaining N p =1000 + (223 183) =1040 protons If we now assume all of the neutrons combine with an equal number of protons to make D, and that all of the D combines to 4 He, we can estimate the mass fraction of helium as: X He ~ 4N He N p + 4N He ~ 4(91) 858 + 4(91) ~ 0.298

a full BBN network Includes: All relevant nuclear species, reactions, and decays Dynamically evolving T, ρ Adjustable physics inputs http://cococubed.asu.edu/code_pages/net_bigbang.shtml

time evolution of BBN abundances http://cococubed.asu.edu/code_pages/net_bigbang.shtml

time evolution of BBN abundances one free parameter η, the baryon to photon ratio Predicts primordial abundances of four observable species: D, 4 He, 3 He, 7 Li http://cococubed.asu.edu/code_pages/net_bigbang.shtml

variation of BBN abundances with η Observations with statistical and systematic uncertainties Particle Data Group (2008)

variation of BBN abundances with η WMAP value of η Range of η consistent with observations of 4 He, D, 7 Li Particle Data Group (2008)

variation of BBN abundances with η agreement with 4 He (but not a strong constraint) excellent agreement with D???? Mathews, Kajino, Shima (2005)

variation of BBN abundances with η excellent agreement with D Mathews, Kajino, Shima (2005) Cyburt, Fields, Olive (2008)

nuclear physics sensitivities 12 key reactions: Coc & Vangioni (2010)

nuclear physics sensitivities 12 key reactions: theory experiment Coc & Vangioni (2010)

nuclear physics uncertainties neutron lifetime Mathews, Kajino, Shima (2005) X 4 He PDG value Serebrov et al Paul (2009)

nuclear physics uncertainties 3 He(α,γ) 7 Be can count the resulting 7 Be activity or the prompt γ rays Gyuyrky (2007) Brown et al (2008)

nuclear physics uncertainties with modern rates for 1 H(n,γ) and 3 He(α,γ) with older values Coc & Vangioni (2010)

nuclear physics uncertainties with modern rates for 1 H(n,γ) and 3 He(α,γ) with older values A nuclear physics solution to the 7 Li problem is unlikely Coc & Vangioni (2010) An astrophysical solution??

lithium observations Both 7 Li and 6 Li are observable and can be resolved in the local interstellar medium Krauth et al (2003) But in metal-poor halo stars, the lines are blended fits to the lineshape are required to extract elemental information Asplund et al (2006)

lithium observations Plot by V.V. Smith

lithium observations Lots of scatter at high metallicity Li easily destroyed via nuclear burning in stars, can be synthesized via spallation reactions on CNO nuclei Plot by V.V. Smith

lithium observations Plateau at low metallicity likely a measure of primordial Li Spite plateau (Spite & Spite 1982) But observations of Li/H are a factor of ~3 lower than predicted Plot by V.V. Smith

nuclear physics uncertainties with modern rates for 1 H(n,γ) and 3 He(α,γ) with older values A nuclear physics solution to the 7 Li problem is unlikely An astrophysical solution is also unlikely Points to physics beyond Standard Model??? Coc & Vangioni (2010)

if you want to play check out some of the available online BBN tools Big Bang Online http://bigbangonline.org Frank Timmes site http://cococubed.asu.edu/code_pages/net_bigbang.shtml