Relativistic Winds from Collapsars

Enrique Gómez

Phil Hardee

December 15, 2005

Why are we seeing secondary flares and

spikes in long GRB and XRF light curves?

Outline

• Collapsar Model

• KH Stability in jet

• Relativistic wind evolution

• Internal shock production in wind

Review of the Collapsar Model

Stages of Development

• Progenitor (He Star)

• Collapse

• Jet Production

• Jet Evolution

• Optically Thick Relativistic Wind

• Optically Thin Relativistic Wind

• Momentum Conserving Stage

After SN shock

Stellar Envelope He Core 1011 cm

Axis of Rotation

Free-Fall Material

Fe Core

Jet Propagation r<rHe

Density Profile for

r -3/2

Radiation Dominated Pressure

p 4/3 r –2

. ~1 =Lj /Mc 2 ~ 10 2

Bow Shock Cocoon

Jet

Recollimation Shock

Mach Disk

Meszaros & Rees ApJ 556:L37–L40

Jet Break out r~rHe

Causal Contact j j ≤ (aj/c)2

At Saturation

j 100Jet

Recollimation Shock

Internal Shocks

Relativistic Wind

Relativistic Gas Bubble

External Shock

Jet Stability Study

What Jet Structures Are There?

Pinch Body Modes From K-H Instabilities.

Collapsar Simulations

Zhang, Woosley & McFadyen 586 (2003) 356-371

AdE/dt = 1051 ergs s-1

0 = 20°

0 = 50

BdE/dt = 1051 ergs s-1

0 = 5°

0 = 50

Aloy et al ApJ 531:L119–L122

C50dE/dt = 1050 ergs s-1

0 = 30°

0 = 1

C51dE/dt = 1051 ergs s-1

0 = 30°

0 = 1

Jet Profiles

Pinch Mode Solutions

Lorentz Factor

Theory (Jet Radius = 1) 1st +2nd Body Modes

Simulation C51(Jet Radius = 2.3 108 cm )

Energy Density

Theory (Jet Radius = 1) 1st +2nd Body Mode

Simulation C51(Jet Radius = 2.3 108 cm )

KH Instability Body Modes

Relativistic Wind Evolution

Velocity Enhancements

C50

5.24 s

Wind EquationsMass

Momentum

Energy Bernulli

Thermodynamic Condition

Optical Depth To Pair Production

Relativistic flows evolved with the wind equation for the C50 simulation with distance to the jet engine. Top diagrams show the evolution of pressure, photon density, and temperature in the observer frame. Bottom diagrams show the evolution of the bulk Lorentz factor of the flow with distance to the jet engine (solid) and optical depth to pair production (short dash).

Wind After Breakout

Relativistic Wind Shocks

Shock Evolution

Collision of Inelastic Shells

Conversion efficiency of shell kinetic energy to internal energy

VM iii

Lorentz factor of merged shell:

Kobayashi et al. ApJ 492,92,

Daigne & Mochkovitch MNRAS 196, 275

Shock Timing

021 zz 1 zzm

Shock Location

021 zz 1 zzm

Conversion Efficiency

U=i Mic2

Lamb, Donaghy, Graziani 2003

Conclusions

• KH instabilities guarantee velocity enhancements in collapsar jets

• Shells in the wind collide and form shocks at edge of wind not the center

• The kinetic energy to internal energy conversion efficiency is the highest at wide angles from the center of the wind.

Thank You

Questions?