Luke Roberts UCSC w/ Stan Woosley and Rob Hoffman Neutrino Driven - PowerPoint PPT Presentation

Luke Roberts UCSC w/ Stan Woosley and Rob Hoffman

 Neutrino Driven Wind Models  Integrated Nucleosynthesis  2 Models  Effects of varying neutrino luminosities  Secondary heating source  Neutron to seed ratio variation  Acoustic power

 Initial studies found wind to be promising r‐process site (Woosley et al. 1994)  Wind nucleosynthesis determined by Y e, s, and t dyn  Proton rich wind may also contribute to nucleosynthesis  How does standard NDW nucleosynthesis fit in the context of full stellar models? Sneden et al. 2007

 Neutron and alpha particle abundances after nucleon recombination: Y n = (1 − 2 Y e ) Y α = Y e /2  Rate of seed production given by: ≈ dY 12 C dY seed ∝ ρ 3 Y α 3 Y n dt dt  Giving a neutron to seed ratio: 3 Y n τ dyn ( ) Y e − 3 Y seed ∝ S f 2 3 + 10 ∝ S f ⇒ N n N seed τ dyn Hoffman et al. (1997)

Analytic NDW Nucleosynthesis Predictions  Assuming 4 L ν ∝ T ν  Large neutrino anti‐ neutrino asymmetry required in “standard model”  Likely in N=50 Regime

Kepler massive stellar evolution code y t i c o (cf. Weaver, Zimmerman, l e V & Woosley 1978) Spherically symmetric  Implicit Lagrangian  hydrodynamics Nuclear network for energy Entropy  generation Adaptive nuclear network for Energy Deposition  nucleosynthesis to ~3000 isotopes X heavy Thermal neutrino losses  Integrates ejected  Y e nucleosynthesis as mass flows off the grid Post Newtonian corrections to  gravitational potential

Kepler updates for wind models New neutrino interaction rates  Coupled to both reaction  networks Nucleon capture rates include  first order corrections in the nucleon mass Gravitational redshifts  “Lightbulb” transport  approximation Includes bending of null  geodesics in Schwarzschild geometry Different neutrino sphere radii  Mass recycling  Artificial energy deposition 

L nu (10 51 erg s -1 ) S/100, Y e , and 10 t d s Mass Loss Rate Y e ν µ / τ <E nu > (MeV) ν e ˙ M τ d ν e Time (s) Time (s) Luminosity histories from Woosley et al. (2004) Original models had successful r-process, but entropies were too high

Integrated Wind Nucleosynthesis: 20 Msun  Total ejected mass: 18.4 Msun Production Factor  No significant p‐ process production  Reverse shock doesn’t affect A nucleosynthesis

Production Factor A Integrated wind yields combined with yields from 20 Msun model of Woosley & Weaver (1995)

Production Factor Production Factor A A Anti-neutrino energy reduced No weak magnetism by 15% corrections

Without neutrino With neutrino interaction interaction corrections corrections

 Fall off at low metallicity  Inconsistent with NDW nucleosynthesis predictions  [Sr/Fe]=0.8 in 20 Msun model  Evidence for increased SN fallback at low metallicity? Lai et al. (2008)

L nu (10 51 erg s -1 ) S/100, Y e , and 10 t d Mass Loss Rate s <E nu > (MeV) Y e ν ν µ / τ e ν e ˙ τ d M Time (s) Time (s) Luminosity histories from Huedepohl et al. (2009) Proton rich throughout, nup-process?

 Total ejected mass: 7.4 Msun Production Factor  All weighted production factors at or below one  No significant p‐process production  Reverse shock not expected to be strong, doesn’t affect A nucleosynthesis

• Temperature structure of the protoneutron star atmosphere set by: ˙ e ≈ ˙ q ε ν 1/ 6 T − 1/ 3 L ν ,51 1/ 3 ⇒ T atm ≈ 3 R 6 MeV ν ,5 MeV • Mass loss rate set near surface • Volumetric energy deposition source doesn’t effect atmosphere, deposits energy after mass loss rate is set • Increases entropy of material, decreases dynamical timescale, conditions more favorable for r- process (Qian & Woosley 96, Suzuki & Nagataki 05)

Neutron-to-Seed Ratio  Volumetric energy deposition source with constant damping: L 0 ˙ q = ρ l d r 2 exp[( r − r 0 )/ l d ]  Optimal damping length: Seed Abundance l d ≈ 10 6 cm (see Suzuki & Nagataki 2005)  Conditions at 10 sec in Woosley (1994) model: Y e = 0.44  Is this reasonable? Total Energy Deposition Rate (erg s -1 )

Suzuki & Nagataki argue it is reasonable for high  magnetic fields, give Alfven waves and non‐linear damping Other possibility, purely acoustic power (Qian &  Woosley 1996, Burrows et al 2007) Neutrino damped PNS oscillations (Weinberg &  Quatert 2008) l=1 oscillations have intensity of (see Landau &  Lifshitz) L 0 ≈ 4 × 10 47 ergs − 1       E 1  1.4 M sun ρ ×      10 48 erg 10 12 g / cc M NS       3 R NS 4 6     × 10 9 cm / s   ω       Weinberg & Quatert 2008 10 6 c s   1000 hz      Q‐factor < 1 1  Must be driven by × 1 + ( ω R / c s ) 4 /4 accretion

 How do these acoustic waves damp?  Studied in the context of the solar corona (see Stein & Schwartz 1973for references) Mach Number - 1  Steepen into shocks over distance of order the pressure scale height  Energy loss given by weak shock theory as Δ s = 2 γ ( γ − 1) c v 3( γ + 1) 2 m 3 dE s dt = − ρ Tc s Δ s (1 + m /2)  Results in a damping length Height (km) l d ≈ 2.6 × 10 6 cm Stein & Schwartz 1973 1/2 1000 hz 1/2 1/2 1/2      T   s  P ×          MeV   100  3 ε w ω 0    

Temperature (K) Density (g/cc)  Self consistent acoustic T energy input based on weak shock damping ρ length π γ ( γ − 1) c v ρ T ω S 3/ 2 ∂ t S + r − 2 ∂ r ( r 2 v g S ) = − 3 P 3/ 2 Edot (ergs/g/s)  Atmosphere temperature ˙ ε Entropy still set by neutrino fluxes s  Final entropy 285  Dynamical timescale ~2 ms Radius

Abundance Reverse Shock Temperature Density T Time (s) ρ Time (s)

Abundance A

 Integrated NDW Nucleosynthesis  Low mass progenitor wind does not contribute significantly  Higher mass progenitor consistent with yields from the full star  Sensitive to uncertain neutrino spectra  Evolution of N=50 closed shell elements may trace fallback history  See arXiv:1004.4916  Secondary Energy Deposition  Get high neutron to seed ratios for reasonable amount of energy deposition  sound waves from PNS oscillations weak shocks  Volumetric energy deposition at correct radius for r‐process