Magneto-hydrodynamic Magneto-hydrodynamic Simulations of CollapsarsSimulations 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

Collapsar ?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 modelThe 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 studyThe present study2D 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/0602457),Astro-ph/0602460 (Nucleosynthesis, ApJ Accepted)

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

Numerical codeNumerical code

profiles of density and temperatureProfiles of spherical model of a 40Msun massive star just before the core collapse (Hashimoto 1995)

magnetic fieldsUniform, 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 setupInitial setup

Rapid core case

Slow core case

Model parametersModel parameters

ModelAngular

momentum distribution

R12 rapid 12

R10 rapid 10

R8 rapid 8

S12 slow 12

S10 slow 10

S8 slow 8

Rapid core

Slow core

40Msun collpsarbefore the core

collapse

Computational domain Computational domain and initial setupand 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 Density evolution of a collapsar: R10collapsar: R10

the onset of collapse: t = 0 sec

Properties of accretion disk: R10Properties of accretion disk: R10Radial profiles of physical quantities near the equatrial plane

High density & temperature disk

100km 1000km 10,000km

radius

100km 1000km 10,000km

radius

Neutrinos from collapsarsNeutrinos from collapsarsNeutrino flux: R10

2000km x 2000km

Neutrino-cooled dense & hot disk

Neutrino luminosity: all models

The disks are mainly cooled via neutrino emissiondue to the large neutrino luminosities.

5×10^51erg/s

R12

S12

S10

S8

R10

R8

time(sec) 1.0 2.0

1×10^51erg/s

Ｄｅｎｓｉｔ

ｙ

0.199s

0.254s

Pmag/Pgas

3000kmx3000km

• Magnetically-driven jets of 0.1c High density jets can be ejected

Jets from a collapsarJets from a collapsar ：： R12R12

the onset of collapse: t = 0 sec

Jets: magnetically driven from R12,S12 & S10 in addition to R10

Propeties of the jets compared Propeties of the jets compared with GRB jetswith GRB jets

Vjet ～ 0.1c << V(GRB) ～ cMjet > 10^-3 Msun >> M(GRB) ～ 10^-5 MsunEjet ～ 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 theChemical composiotion of the jets from the collapsar: R12jets 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

SummarySummary

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.