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Relativistic Winds from Collapsars

Exploring the phenomena of secondary flares and spikes in long GRB and XRF light curves, focusing on the Collapsar Model, KH stability in jets, and relativistic wind evolution.

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Relativistic Winds from Collapsars

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  1. Relativistic Winds from Collapsars Enrique Gómez Phil Hardee December 15, 2005

  2. Why are we seeing secondary flares and spikes in long GRB and XRF light curves?

  3. Outline • Collapsar Model • KH Stability in jet • Relativistic wind evolution • Internal shock production in wind

  4. Review of the Collapsar Model

  5. Stages of Development • Progenitor (He Star) • Collapse • Jet Production • Jet Evolution • Optically Thick Relativistic Wind • Optically Thin Relativistic Wind • Momentum Conserving Stage

  6. Fe Core Axis of Rotation Free-Fall Material Stellar Envelope He Core 1011 cm After SN shock

  7. Recollimation Shock Mach Disk Jet Cocoon Bow Shock Jet Propagation r<rHe Density Profile for   r -3/2 Radiation Dominated Pressure p   4/3 r –2 . ~1 =Lj /Mc 2 ~ 10 2 Meszaros & Rees ApJ 556:L37–L40

  8. Jet Break out r~rHe Relativistic Gas Bubble Internal Shocks Recollimation Shock Causal Contactj j≤ (aj/c)2 At Saturation j 100 Jet Relativistic Wind External Shock

  9. Jet Stability Study

  10. What Jet Structures Are There? Pinch Body Modes From K-H Instabilities.

  11. Collapsar Simulations Aloy et al ApJ 531:L119–L122 C50 dE/dt = 1050 ergs s-1 0 = 30° 0 = 1 C51 dE/dt = 1051 ergs s-1 0 = 30° 0 = 1 Zhang, Woosley & McFadyen 586 (2003) 356-371 A dE/dt = 1051 ergs s-1 0 = 20° 0 = 50 B dE/dt = 1051 ergs s-1 0 = 5° 0 = 50

  12. Jet Profiles

  13. Pinch Mode Solutions

  14. Lorentz Factor Simulation C51(Jet Radius = 2.3 108 cm) Theory (Jet Radius = 1) 1st +2nd Body Modes

  15. Energy Density Simulation C51(Jet Radius = 2.3 108 cm) Theory (Jet Radius = 1) 1st +2nd Body Mode

  16. KH Instability Body Modes

  17. Relativistic Wind Evolution

  18. Velocity Enhancements C50 5.24 s

  19. Mass Momentum Energy Wind Equations Bernulli

  20. Thermodynamic Condition

  21. Optical Depth To Pair Production

  22. Wind After Breakout 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).

  23. Relativistic Wind Shocks

  24. Shock Evolution

  25. Collision of Inelastic Shells Conversion efficiency of shell kinetic energy to internal energy Lorentz factor of merged shell: Kobayashi et al. ApJ 492,92, Daigne & Mochkovitch MNRAS 196, 275

  26. Shock Timing

  27. Shock Location

  28. Conversion Efficiency U=Gi Mic2

  29. Lamb, Donaghy, Graziani 2003

  30. 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.

  31. Thank You Questions?

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