Pair-Instability Black Hole Formation and You!Simon PorterSeptember 21, 2007Hyper-Large Pop III Stars• Population III may have been home to a number of ridiculously large stars (100-10,000 M☼)• Such stars would have practically zero metallicity, and thus loose little mass during main sequence• Internal pressures high enough to create pair-instabilityPair InstabilityMain Sequence FusionIncreased Gamma EmissionPair ProductionIncreased FusionNeutrinosNeutrinosFeedback LoopFeedback LoopPair InstabilityInitial Stellar Mass > 100 M☼e-/ e+Pair InstabilityISM < 260 M☼ISM > 260 M☼Pair Instability SupernovaNeutrino Burst and Black Hole FormationScience Objective• Goal of Nakazato et al. was to model the spherically symmetric gravitation collapse of Pop III massive stars• From this, a relic neutrino background flux can estimated, providing a direct measurement of Population IIIPop III Stars Modeled• 18 ISMs modeled• ISM > 260 M☼(Black hole formation)• ISM < 1600 M☼(GR < Pair Instability)The Numerical Model• Model uses spacetime metric from Misner& Sharp (1964):• Energy equation:Neutrino ReactionsCore Collapse• Start with a reference hydrodynamic/GR model for density and temperatureCore Collapse• Core is divided into two parts:– Subsonic inner core (U ~ r)– Supersonic outer core (U ~ r -1/2)Apparent Horizon• To chart black hole formation, the model tracks the trapped surfaces described by:• Which is satisfied by:Importance of Neutrino Cooling• Neutrino cooling has a massive effect on core collapseImportance of Neutrino Cooling• With neutrino cooling, core shock disappears and entropy dropsElectron Fraction• The high entropy in the core prevents the core from reaching electron degeneracy pressure.• The positron capture rate is slower than electrons.• Equilibrium is reached where β / inverse βreaction rates equal outElectron FractionNeutrino Luminosity• Because of the high reaction rates, the neutrino luminosity peaks near ~1054erg/s, 10 times higher than a normal supernova• But the apparent horizon closes within 100 ms, so total energy emitted is only ~1053erg, comparable to a supernovaNeutrino Luminositye-neutrinoe+ neutrinoτ, µneutrinoTotalneutrinoNeutrino Luminositye-neutrino,t = -12.3 mse+ neutrino,t = -12.3 msτ, µneutrino,t = -12.3 msτ, µneutrino,t = -1.52 msNeutrino Spectrum• Because of the high reaction rates, the neutrino luminosity peaks near ~1054erg/s, 10 times higher than a normal supernova• But the apparent horizon closes within 100 ms, so total energy emitted is only ~1053erg, comparable to a supernovaNeutrino Energy Spectrume-neutrinoe+ neutrinoτ, µneutrinoTotalneutrinoInitial Mass Dependence (or lack thereof)Initial Mass Dependence(or lack thereof)10,500 M☼375 M☼Initial Mass Dependence(or lack thereof) • The spectrum does not change drastically over the mass rangeRelic Neutrino Flux• The net flux is an integral over the number density of Pop III stars and their redshift:• Substituting for redshift and adding a normalizing factor Ψ(z):Relic Neutrino Flux• Using a Pop III mass distribution from Nakamura & Umemura (2001)• So,Relic Neutrino Flux• Putting it all together:• But we still need a Ψ(z)!Relic Neutrino Flux• Model A assumes reionization at z = 17 ± 5 based on WMAP data (Spergel 2003)• Model B assumes reionization at z ~ 10 (Scannapieco et al., 2003)• Model C just assumes continuous Pop III formation across z = 4-12 (Yonetoku, 2004)Results!• Assuming Model A (WMAP):Results!• Anti-electron neutrino flux is relatively high!Detection?• Solar neutrinos will overwhelm electron neutrinos below 18 MeV, and ordinary supernovas above 10 MeV• Terrestrial nuclear reactors will dominate anti-electron neutrinos below 10 Mev• So, no possible detection, yet…Summary• Pop III stars greater than 260 M☼would form black holes due to pair instability• Such a process would produce an intense neutrino burst, with an energy distribution independent of initial mass• These neutrinos would create a relic background source• But which is below current limits of