Magneto-hydrodynamic Simulations of Collapsars

1. Magneto-hydrodynamic Simulations of Collapsars • Shin-ichiro Fujimoto • (Kumamoto National College of Technology), • Collaborators: • Kei Kotake(NAOJ), • Sho-ichi Yamada (Waseda Univ.), • and Masa-aki Hashimoto (Kyusyu Univ.) EANAM2006 at Daejeon Nov. 03 2006

2. Collapsar ? = a rotating massive star collapsing to a black hole. Collapsar model of gamma-ray bursts (GRBs) • During gravitational collapse of a rotating massive star ( > 20 – 25 Msun) • The central core collapses to a black hole (BH) • Outer layersform an accretion disk around the BH because of high angular momentum. • Jets from an inner part of the disk. • The jets are accelerated to relativistic velocities. • We can observe a GRB if we locate on directions to jet propagation.

3. The collapsar model • Just a scenario • Whether such relativistic jets can be ejected from a collapsar or not ? • Multi-dimensional hydrodynamic simulations in light of the collapsar model • 2D MHD simulations of a 25 Msun collapsar (Proga et al. 2003) • magnetically driven jets can be ejected • for a single set of initial distributions of angular momentum and magnetic fields • the distributions are highly uncertain due to the uncertainty in the models of rotating stars.

4. The present study • 2D MHD simulations of collapsars • Two initial angular momentum distributions • Three magnetic field distributions • Properties of accretion disks and jets for 6 collapsars • Nucleosynthesis inside the jets from the collapsars, based on results of the MHD simulations • High densitiesand temperatures enough to operate nuclear reactions • the jets may produce heavy neutron-rich nuclei, whose origin is still uncertain. ApJ 644, 1040, 2006 (MHD, Astro-ph/0602457), Astro-ph/0602460 (Nucleosynthesis, ApJ Accepted)

5. Numerical code • ZEUS code (Stone & Norman 1992, Kotake et al. 2003) • 2D axisymmetric, Newtonian MHD code • Neutrino cooling • simplified two stream approximation (DiMatteo et al. 2002) • Realistic equation of state(Shen et al. 1998) • familiar in supernova community • important for MHD simulations and nucleosynthesis, in which precious evaluation of temperature is required. (rates for neutrino cooling (∝T^6) & nuclear reaction (∝exp(T)) • BH gravity using the pseudo-Newtonian potential as well as self gravity of a star

6. Initial setup Rapid core case Slow core case • profiles of density and temperature Profiles of spherical model of a 40Msun massive star just before the core collapse(Hashimoto 1995) • magnetic fields Uniform, vertical fields of 10^8G, 10^10G, or 10^12G • angular momentum distribution analytical distribution, two cases: rapidly or slowly rotating iron core > the Keplerian angular momentum at 50km of 3 Msun BH • The onset of the core collapse:t = 0 sec

7. Model parameters Rapid core Slow core

8. 40Msun collpsar before the core collapse Vertical and uniform magnetic fields 10^8,10 or 12 G Computational domain and initial setup Rapidly or slow rotating iron core

9. Density evolution of a collapsar: R10 Log density: 1000km X 1000km • Central parts collapse to a black hole (BH). • While outer layers form an accretion disk around the BH. • Magnetic fields amplified inside the disk. • Jets driven via magnetic pressure. the onset of collapse: t = 0 sec

10. High density & temperature disk 100km 1000km 10,000km radius 100km 1000km 10,000km radius Convective disk Pgas > Pmag 100km 1000km 10,000km 100km 1000km 10,000km 1.66s 1.66s 1.66s 1.66s 1.66s 1.66s 1.66s Quasi-steady disk Quasi-steady disk Quasi-steady disk Quasi-steady disk Quasi-steady disk Quasi-steady disk Quasi-steady disk Convective disk Convective disk Convective disk Convective disk Convective disk Convective disk Convective disk Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Properties of accretion disk: R10 Radial profiles of physical quantities near the equatrial plane 1.66s 1.66s 1.66s 1.66s Quasi-steady disk Quasi-steady disk Quasi-steady disk Quasi-steady disk Convective disk Convective disk Convective disk Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Pgas > Pmag, Prad, Pdeg Convective disk Pgas > Pmag, Prad, Pdeg

11. R8 R10 5×10^51erg/s R12 Neutrino-cooled dense & hot disk 1×10^51erg/s S10 S8 S12 time(sec) 1.0 2.0 Neutrinos from collapsars Neutrino luminosity: all models Neutrino flux: R10 2000km x 2000km The disks are mainly cooled via neutrino emission due to the large neutrino luminosities.

12. Jets from a collapsar：R12 Ｄｅｎｓｉｔｙ 3000km x3000km 0.199s 0.254s Jets: magnetically driven from R12,S12 & S10 in addition to R10 Pmag/Pgas • Magnetically-driven jets of 0.1c • High density jets can be ejected the onset of collapse: t = 0 sec

13. Propeties of the jets compared with GRB jets • Vjet～ 0.1c <<V(GRB)～ c • Mjet > 10^-3 Msun >> M(GRB) ～ 10^-5 Msun • Ejet ～10^50 erg < E(GRB) ～ 10^51 erg To produce GRB jets Acceleration mechanism ? • neutrino interactions (e.g. Nagataki et al. 2006) • general relativistic effects (e.g. Koide’s talk) • magnetic reconnection (e.g. Shibata’s talk) …..

14. Similar to solar r-pattern Scaled solar r-elements collapsar jets: R12 Chemical composiotion of thejets from the collapsar: R12 • The disk hashigh density (>10^11g/cc) and temperature (> 10^10K) • Photo-disintegration reactions destroy all elements • heavier than He to produce protons and neutrons in the disk. • The disk becomes neutron-rich due to e- capture on p ( e- + p  n) • A central part of the disk can be ejected through the jets. • Rapid neutron capture process (r-process) operates in the jets. • Heavy neutron capture elements, such as U & Th in the jets.

15. Summary We have performed two dimensional MHD simulations of 40 Msun collapsars for 2 angular momentum distributions and 3 magnetic field distributions. • Quasi-steadyaccretion disk is formed around the black hole • Cooled by not radiation but neutrino emission,Lnu > 10^51 erg/s • Bphi >> Br, Bth, Bphi ～ 10^15 G • Jetscan be ejected from 4 collapsars (R10, R12, S10 & S12) • The jets can be diriven by magnetic pressure, amplified inside the accretion disk • The jets are too slow (0.1c) and too heavy (>0.001Msun) to drive GRB neutrino interactions, GR effects, reconnection…. ? • R process operates in the jets from a collapsar (R12) to eject heavy neutron-rich nuclei, which could be an origin of the r-process elements in the solar system.