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

Collapsar ? During gravitational collapse of a rotating massive star ( > 20 – 25 Msun) The central core collapses to a black hole (BH) Outer layers form 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. = a rotating massive star collapsing to a black hole. Collapsar model of gamma-ray bursts (GRBs)

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.

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 densities and 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/ ), Astro-ph/ (Nucleosynthesis, ApJ Accepted)

ZEUS code ( Stone & Norman 1992, Kotake et al ) 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 Numerical code

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 Initial setup Rapid core case Slow core case

Model parameters Model A ngular momentum distribution R12 rapid12 R10 rapid10 R8 rapid8 S12 slow12 S10 slow10 S8 slow8 Rapid core Slow core

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

1.Central parts collapse to a black hole (BH). 2.While outer layers form an accretion disk around the BH. 3.Magnetic fields amplified inside the disk. 4.Jets driven via magnetic pressure. Log density: 1000km X 1000km Density evolution of a collapsar: R10 the onset of collapse: t = 0 sec

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

Neutrinos from collapsars Neutrino flux: R km x 2000km Neutrino-cooled dense & hot disk Neutrino luminosity: all models The disks are mainly cooled via neutrino emission due to the large neutrino luminosities. 5×10^51erg/s R1 2 S12 S10S8 R1 0 R8 time(sec) ×10^51erg/s

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

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) …..

Chemical composiotion of the jets from the collapsar: R12 The disk has high 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. Similar to solar r-pattern collapsar jets: R12 Scaled solar r-elements

Summary Quasi-steady accretion 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 Jets can 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. We have performed two dimensional MHD simulations of 40 Msun collapsars for 2 angular momentum distributions and 3 magnetic field distributions.