# Presentation: 475638

## Toward Understanding the Central Engine of Long GRBs

- Kyoto University, Stanford University
- S. Nagataki

- 23th Feb 2007,  ASPEN

- Kinkaku-Temple, Kyoto, Japan

- Stanford University, CA, USA

## Collaborators

- R. Blandford (KIPAC)
- A. Mizuta (Chiba)
- R. Takahashi (U. of Tokyo)
- S. Mineshige (Kyoto)
- T. Yamasaki (CEA Saclay)

- T. Takiwaki (U. of Tokyo)
- S. Yamada (Waseda)
- H. Takabe (Osaka)
- M. Hashimoto (Kyusyu)
- K. Sato (U. of Tokyo)

## § Introduction 

## Some GRBs are Accompanied by Hypernovae

- GRB030329/SN2003dh

**Explosion energy of a hypernova is estimated to be ****~****1E+52ergs****, which cannot be explained by the standard scenario of a normal collapse-driven supernova.**

- GRB980425/SN1998bw

- Other explosion mechanism is required.

## Promising candidates for the energy scales

- (b) Rotation Energy of
- a central BH (magnetar).
- Duration is ~ (1-10) sec?
- Blandford-Znajek Process

- (a) Gravitational Binding
- Energy of Accreted Matter
- onto a central BH.
- Duration is ~10sec.

**MacFadyen and woosley (1999)**

## § (a) Gravitational BindingEnergy (collapsar model)

## Progenitor: Model E25 in Heger et al. (2000) that is modified so that inner most core has collapsed to form a BH with 1.7Mo.
2-D Ideal MHD (r,)=(150,30) is solved by ZEUS code. 
Initial rotation is same with MacFadyen and Woosley (1999).
Realistic EOS (Blinnikov et al. 1996).
Photo-disintegration (N, P, He, O, Ni).
Newton Gravity (Including self gravity; MBH =1.7Mo).
Neutrino Cooling (Leakage scheme).
Neutrino Heating (optically-thin limit).
Magnetic Field     (Vertical + Dipole field: ON・OFF). 

- 2-D Ideal MHD (r,)=(150,30) is solved by ZEUS code.
- Initial rotation is same with MacFadyen and Woosley (1999).
- Realistic EOS (Blinnikov et al. 1996).
- Photo-disintegration (N, P, He, O, Ni).
- Newton Gravity (Including self gravity; MBH =1.7Mo).
- Neutrino Cooling (Leakage scheme).
- Neutrino Heating (optically-thin limit).
- Magnetic Field     (Vertical + Dipole field: ON・OFF).

- Input Physics

## Neutrino Processes

- Cooling Process

- Electron and positron Capture on free nucleons
- (Epstein and Pethick 1981)
- Pair annihilations
- (Itoh et al. 1999)
- Plasmon decays
- (Itoh et al. 1989)

****

- Heating Process
- Electron-type neutrino capture on free nucleons
- (Epstein and Pethick 1981)
- Neutrino pair annihilations
- (Goodman et al. 1987)

## § Results of collapsar model  

## Case of Neutrino Heating (no B-Field)

- Density contour with velocity fields,
- Final time is 4.8sec.

- Neutrino cooling  Rate [erg/s/cc] at
- t = 2.2 sec. The rate correlates with
- Nucleon density.

## Case of Neutrino Heating (no B-Field)

- Energy Deposition Rate [erg/s/cc]
- By neutrino absorption on free nucleons
- At t = 2.2 sec. The rate correlates with
- Nucleon density.

- Energy Deposition Rate [erg/s/cc]
- By neutrino pair annihilation
- at t = 2.2 sec.

- Energy is deposited globally, but
- With low efficiency

- Energy is absorbed at the accretion disk

## Energetics

**Pair-**
**annihilation**

**Absorption**
**On nucleons**

**Thermal**

**kinetic**

**total**

**Mdot**

**From above:**
**Total**
**e- capture**
**e+ capture**
**e+e- pair**
**plasmon**

**After the shock passage, the released energy was shared by kinetic and thermal**
**Energy  almost equally (****~****1E+52erg). Most of thermal energy was lost by neutrino**
**Cooling. About 10% was absorbed at the accretion disk (****~****1E+51erg). Efficiency**
**Of neutrino pair annihilarion is as low as ****0.1%**** ****(****~****1E+49erg).**** **

## Simulations with Magnetic Fields 

- Simulations with Magnetic Fields

- 9

- Density contour
- Final time is 2.2sec.

- Jet is launched by B_phi, which is
- amplified by winding-up effect.

**B_phi**

**B_r**

**B_the**

## Can the Jet be a GRB?

**Mass, total energy, and terminal bulk lorentz factor of the jet **
**(within 10 degrees, positive total energy, and high velocity(=5E+9cm/s))**
**as a function of the initial amplitude of magnetic fields.**

-  Initial B                   B=1E+10G        B=1E+11 G           B=1E+12G
- Mass                 2.1E-8Msolar     1.2E-5Msolar          1.5E-4Msolar
- Total Energy     9.1E+45erg        1.2E+48erg             1.8E+49erg
**(without rest mass)**
- Lorentz Factor     1.08                       1.05                          1.07

- These jets can not be GRB jets.
- MJ seems to increase with B0, since the jet is launched
- earlier for larger Bo.
- Simulation for longer physical time is required?
-                At least, special relativistic MHD is required.

## § (b) Rotation Energy of a Central BH (BZ-Process Model)

## § Formulation of General Relativistic Magneto-Hydrodynamic Code (GRMHD Code) 

## Gammie, McKinney, Toth 03

- Basic Equations

- Additional Equations

- (Constrained
-  Transport)

- Conserved
- Variables

- Primitive
- Variables

- Newton-Raphson Method

- Solver

- Flux term

- (HLL Method)

- Slope (2nd order in Space, 3rd in time)
- Mimmod or Monotonized Center
- TVD Runge-Kutta

## § Results of GRMHD Simulation

## Fishbone and Moncrief’s Problem

- a=0.938, no-magnetic field

- N×N=150×150

- T=0

- T=1200

- constant

**G=c=M=1**

**c.f.  e.g. McKinney and Gammie 2004, McKinney 2006**

## Fishbone and Moncrief’s Problem (cont’d)

- a=0.938, with-magnetic field

- N×N=150×150

- T=1200

**R**** ****<**** ****60**

**R**** ****<**** ****300**

**G=c=M=1**

**c.f.  e.g. McKinney and Gammie 2004, McKinney 2006**

## § Discussion 

## Effects of Neutrino Pair Annihilationwith General Relativity

- Effects of Neutrino Pair Annihilationwith General Relativity

- R. Takahashi and S.N. (2007) in prep.
- c.f. e.g. Popham et al. (1999)

**Effective Potential**

**Geodesic of Neutrinos**

**Disk structure is also changed.**

## § Brief Comments on Explosive

- Nucleosynthesis in a GRB (Hypernova)

## Results of Explosive Nucleosynthesis including effects of jet like explosion applied for SN1987A

**2D Simulation, 6Msolar He Core**
**Explosion energy is fixed to be 1 times10  erg**
**Nuclear Reaction Network contains 250 nuclei**
**Explosion Energy is injected at the inner boundary**
**with asymmetric injection rate so that jet like explosion occurs.**

- Spherical Explosion

- Jet like Explosion

- Mass Fraction of   Ni

**56**

- Explosive Nucleosyntheis
- occurs aroud the jet region
- very actively

**51**

**S.N. et al. 97, S.N. 00**

- Model S1: Spherical Model
- Model A1: Vp/Ve = 2:1
- Model A2: Vp/Ve = 4:1
- Model A3: Vp/Ve = 8:1

## One of Our Predictions on GRBs in 2000.

- S.N. ApJS 127 (2000) 141-157

- Velocity Distribution of Iron

- Model S1: Spherical Model
- Model A1: Vp/Ve = 2:1
- Model A2: Vp/Ve = 4:1

**c.f. Maeda et al. 2002, 2005**

**S.N. et al. 1998, S.N. 2000**

**Mildly bi-polar Explosion is **
**favored for SN1987A**

## Observations of Line Profiles of  Hypernovae

- Mazzali et al. 05

- Oxygen Line

## Where is Ni  synthesized?

- Where is Ni  synthesized?

**56**

- Duration of Explosion is
- set to be10sec.

- All explosion energy is
- Deposited Initially.

- Abundance
- is small.
- Faint HN will
- Be possible.

- Abundance
- is much

- Origin of     Ni in a hynernova is not unknown.
-      Another possibility: Ejection from the accretion flow.
-                                                (e.g.MacFadyen and Woosley 99)
- (ii) Amount of    Ni synthesized in the jet depends on the duration of
-      the jet, if    Ni is synthesized in the Jet.

**56**

**S.N. et al. ApJ 2003**
**S.N. et al. ApJ 2006**

**56**

**56**

## Faint Hypernova?

**S.N. et al. ApJ 2003**
**S.N. et al. ApJ 2006**
**c.f. Tominaga et al. 2007**

**GRB060614**
**GRB060505**

**Gehrels et al. Nature 2006**
**Gal-Yam et al. Nature 2006**

- Della Valle et al.
- 2006

**Is preferred.**

**Duration?**
**Small ejection**
**From the accretion**
**Disk?**
**Short GRB?**

## § Summary

## Summary

- Effects of general relativity should be important for the formation
- of relativistic jet (BZ-process, Neutrino Heating), which we are
- planning to study using our GRMHD code with microphysics.

- A Jet is launched by magnetic fields, although this jet
- is non-relativistic at present.

- It is found that neutrino heating processes are insufficient to
- launch a jet in this study.

- Neutrino heating processes have been included in the collapsar model.

- Simulations of the order of 10sec may be required to generate
- a powerful jet by special (general) relativistic MHD code.