Download - Relativistic Winds from Collapsars
![Page 1: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/1.jpg)
Relativistic Winds from Collapsars
Enrique Gómez
Phil Hardee
December 15, 2005
![Page 2: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/2.jpg)
Why are we seeing secondary flares and
spikes in long GRB and XRF light curves?
![Page 3: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/3.jpg)
Outline
• Collapsar Model
• KH Stability in jet
• Relativistic wind evolution
• Internal shock production in wind
![Page 4: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/4.jpg)
Review of the Collapsar Model
![Page 5: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/5.jpg)
Stages of Development
• Progenitor (He Star)
• Collapse
• Jet Production
• Jet Evolution
• Optically Thick Relativistic Wind
• Optically Thin Relativistic Wind
• Momentum Conserving Stage
![Page 6: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/6.jpg)
After SN shock
Stellar Envelope He Core 1011 cm
Axis of Rotation
Free-Fall Material
Fe Core
![Page 7: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/7.jpg)
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
![Page 8: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/8.jpg)
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
![Page 9: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/9.jpg)
Jet Stability Study
![Page 10: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/10.jpg)
What Jet Structures Are There?
Pinch Body Modes From K-H Instabilities.
![Page 11: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/11.jpg)
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
![Page 12: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/12.jpg)
Jet Profiles
![Page 13: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/13.jpg)
Pinch Mode Solutions
![Page 14: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/14.jpg)
Lorentz Factor
Theory (Jet Radius = 1) 1st +2nd Body Modes
Simulation C51(Jet Radius = 2.3 108 cm )
![Page 15: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/15.jpg)
Energy Density
Theory (Jet Radius = 1) 1st +2nd Body Mode
Simulation C51(Jet Radius = 2.3 108 cm )
![Page 16: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/16.jpg)
KH Instability Body Modes
![Page 17: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/17.jpg)
Relativistic Wind Evolution
![Page 18: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/18.jpg)
Velocity Enhancements
C50
5.24 s
![Page 19: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/19.jpg)
Wind EquationsMass
Momentum
Energy Bernulli
![Page 20: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/20.jpg)
Thermodynamic Condition
![Page 21: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/21.jpg)
Optical Depth To Pair Production
![Page 22: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/22.jpg)
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
![Page 23: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/23.jpg)
Relativistic Wind Shocks
![Page 24: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/24.jpg)
Shock Evolution
![Page 25: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/25.jpg)
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
![Page 26: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/26.jpg)
Shock Timing
021 zz 1 zzm
![Page 27: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/27.jpg)
Shock Location
021 zz 1 zzm
![Page 28: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/28.jpg)
Conversion Efficiency
U=i Mic2
![Page 29: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/29.jpg)
Lamb, Donaghy, Graziani 2003
![Page 30: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/30.jpg)
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.
![Page 31: Relativistic Winds from Collapsars](https://reader036.vdocument.in/reader036/viewer/2022062519/5681504c550346895dbe4903/html5/thumbnails/31.jpg)
Thank You
Questions?