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Collapsar Accretion and the Gamma-Ray Burst X-Ray Light Curve. Chris Lindner Milos Milosavljevic , Sean M. Couch, Pawan Kumar. Gamma Ray Bursts. High Energy (foe) Highly Variable Two Types Short Duration – Associated with compact object mergers - PowerPoint PPT Presentation
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Accretion Powered Core Collapse Supernovae
Chris Lindner Milos Milosavljevic, Sean M. Couch,
Pawan Kumar, Rongfeng Shen
The University of Texas at Austin
FLASH Code
Gamma Ray Bursts
• High Energy (Bethes)• Highly Variable• Two Types– Short Duration: Associated
with compact object mergers
– Long Duration: Associated with Core-Collapse supernova
• Observable in multiple wavelengths
The SN – GRB Connection
Woosley & Bloom, 2006
The temporal and spatial coincidence of GRB and core collapse supernovae has
been extensively confirmed
The End of a Massive Star:Supernova
GRB events are believed to be linked to the collapse of the core of massive, rapidly rotating stars
How does this happen?
The End of a Massive Star:Core Collapse
• Massive stars ( > 10 Msun ) will fuse elements up to iron
• Iron fusion is an endothermic process – iron fusion cannot provide more energy to support the star
• The onset of fusion to iron will inevitably lead to the collapse of the core in a massive star
The End of a Massive Star:Core Collapse
Once electron degeneracy pressure fails to support the core of the star, there are two possible
scenarios:
• Collapse to a neutron star – Neutron degeneracy pressure and the nuclear strong force can support a neutron star
• Direct collapse to a black hole – High masses and high infall velocities may lead to direct collapse into a black hole at the center of the star
The End of a Massive Star:Core Bounce
• In a non-rotating star, radial collapse will occur• After the core initially collapses, the equation
of state stiffens• This may lead to a “bounce,” which can be
reenergized by neutrinos emitted by the neutron star
This is a potential supernova mechanism, but is only marginally effective
e.g. Wilson & Mayle 1988; Herant et al. 1994; Burrows, Hayes, & Fryxell 1995;Janka & Mueller 1996; Fryer 1998 ...
Is it possible that the rapid rotation of LGRB progenitors
contributes to their subsequent supernovae?
Stellar Collapse with Rotation•Material with low angular momentum will be able to fall directly into the black hole
•However, high angular momentum material may encounter a centrifugal barrier and form a rotationally supported torus
•Further evolution will be determined by angular momentum and energy transport
Core Collapse with Rotation
Lindner, Milosavljevic, Couch, Kumar 2010
Log(Density)
• 14 solar mass presupernova model 16TI of Heger & Woosley: Wolf-Rayet – high rotation – low metallicity
• Explicit α shear viscosity• Equation of state includes contributions
from radiation, ions, and degenerate/relativistic electrons and positrons
• Inner boundary at ~ 108 cm ; simulation box extends outside of stellar surface
• Ran simulations for up to 2000 s
Accretion Powered Supernovae
• When material first begins to circularize around the black hole, an accretion shock forms
• Once the shock begins travelling outwards, convention is able to carry energy dissipated near the black hole to shock front
• Protons and light elements freed from photodisintegration are also diffused to the shock front
• The energized shock may unbind stellar material at high velocities• Originally proposed in Milosavljevic, Lindner, Shen, and Kumar 2010
Accretion Shock
Thick Disk
Convective WindNeutrino-Cooled
Disk
StellarEnvelope
ShockwaveA hot accretion shock may form, and infalling
material must pass through this shock
vff(r = 107 cm) ~ 8 x 109 cm/s
ρ ~ 107 g/cm^3ρ v2 ~ a T4
T(r = 107 cm) ~ 2 x 1010 KTpairs ~ 6 x 109 K
Tnuc ~ 4 x 109 K
Neutrino Cooling
Beloborodov 2008
• At times when the accretion rate is high, a thin, neutrino-cooled disk is formed near the black hole
Photodisintegration
• At T > 4 x 109 heavy elements will be broken down into lighter elements via photodisintegration, cooling the disk• Convective mixing can bring these light elements to the shock front where they may be fused again
Timmes et al.
ADAF vs. CDAF
• In the ADAF regime, accretion occurs via a geometrically thick disk, and energy is advected inwards
• In the CDAF regime, energy transport is dominated by convection, and energy can be efficiently transported outwards
• Understanding where the transition between these regimes occurs is vital to our project, as it determines how much energy can contribute to a possible supernova– The location of this transition is ultimately a competition
between α and convective mixing length
Accretion Powered Supernovae• Spherical hydrodynamic calculations• Resolve from the inner neutrino-cooled disk to star
surface: 2.5 x 106 cm < r < 1012 cm
• Necessary physics– Rotation and explicit alpha viscosity– Mixing length convection treatment for energy transport and
species diffusion in the shock downstream– Neutrino cooling calculations (Urca and pairs)– A nuclear statistical equilibrium network including 47 species
and heating/cooling from fusion and photodisintegration (Seitenzahl et al. 2008)
– Thin disk considerations• Explored the parameter space using 9 simulations of
varying rotation, viscosity, and convective efficiency
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
Results:Accretion
Base run α=0.1
α=0.025
α=0.2
2.5x convection 0.25x convection
0.5x convection 0.5x rotation 3x convective mixing
Results:Energy Transport
Results:Prospects forexplosion
Base run α=0.1
α=0.025
α=0.2
2.5x convection
0.25x convection
0.5x convection
0.5x rotation
3x convective mixing
Results:Shock
Base run α=0.1
α=0.025
α=0.2
2.5x convection 0.25x convection
0.5x convection 0.5x rotation 3x convective mixing
t=0 s t=20 s t=30 s t=50 s
Results:Nucleosynthesis
Conclusions
• Accretion-induced supernovae may have the potential for low energy, low-velocity (vshock =2-5 x 103 km/s) supernovae
• The most important parameter in determining explosion likelihood is convective efficiency
• Future work: – 3D hydrodynamic studies of convective efficiency – More detailed studies of nucleosynthesis– 3D GRMHD with a full nuclear network (wishful
thinking)
Entropy
Funnel Outflow, Thick Disk Accretion
Structure of the Convective Envelope
gravity
rotation
pressure
The GRB Collapsar model
• Observational evidence directly links Long Duration GRB to core-collapse of a star (Woosley & Bloom, 2006)
• Some models predict that X-ray Luminosity is modulated by central object accretion rate (Kumar, Narayan, & Johnson 2008)
• Others predict a magnetar model for long duration bursts (Duncan & Thompson 1992;Wheeler et al. 2002)
http://www.tls-tautenburg.de/research/klose/GRB.review.htmlSimulation from MacFadyen
Results: Mass Accretion
• The end of the prompt phase occurs at the onset of shock formation • During the steep decay: dM/dt ~ t–2.8 • A break in the power law decay occurs at ~ 200 s
Lindner, Milosavljevic, Couch, Kumar 2010 (ApJ, in press)
Viscous Heating
• In a rapidly rotating star, large quantities of energy can be generated in the inner accretion disk
• However, the energy must make it out of the disk to unbind the star– Cannot be lost to cooling processes– Cannot be advected into the black hole
• Therefore, the energy must be transported far from the black hole
ADAF
• Geometrically and optically thick, advection dominated flows
• High viscosity accretion flows suppress convective instabilities; most of the energy advects into the black hole (e.g. Igumenshchev, Chen, and Abramowicz 1995)
Convection Convection can carry energy out of the disk,
and into the stellar envelope
Convection also results in
compositional mixing
Photodisintegration and Nuclear Fusion
• At high temperatures (T ~ 4 x 109 K), high energy photons can break down the nucleus of heavy isotopes into lighter ones, sapping energy from the radiation field
• This can cause an inversion of typical compositional stratification
• Convection may smooth out these compositional gradients, carrying lighter isotopes to cooler regions where they can be fused again
Neutrino Cooling and Heating
• The two dominant neutrino cooling processes in core collapse SN are the Urca process and pair production– Urca– Pair Annihilation
• Neutrino heating
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
Accretion Powered SupernovaeAccretion HeatNSE HeatNSE CoolNeutrino Cool
r shoc
k (cm
)
Time (s)
5,000 km/s
r shoc
k (cm
)
Time (s)
5,000 km/s
Vshock = 5,000+ km/s !Unbound Mass = 7+ Msun !!!
Composition
Composition
Nickel
Woosley & Bloom 2006
Pruet, Thompson, & Hoffman 2003
Considerations
• α = .01 - .35• Mixing Length Convection ..?• Rotation?• Progenitor?• Nickel?• Rmin?
Future Work
• More simulations• Analytic Work• Better Nuclear Physics
• Supermassive Stars (Begelman)
Conclusions• In the absence of rotation, the collapse of the
core of a massive star can lead to a supernova via core bounce and neutrino heating
• In the presence of rotation, an accretion disk may form inside of the stellar envelope– Accretion onto the central black hole may explain
the early evolution of the GRB X-ray light curve– Accretion energy may be able to reach the
accretion shock front and unbind large portions the star at high velocities
AcknowledgementsI would like to acknowledge the essential contributions of my co-authors Milos, Sean, Pawan, and Rongfeng.
I appreciate the incredibly informative discussions with Craig Wheeler, Rodolfo Barniol Duran, and Manos Chatzopoulos.
I am lucky to have an excellent and supportive committee consisting of Milos Milosavljevic, Pawan Kumar, Craig Wheeler, Volker Bromm, and Chris Sneden.
I thank the NSF for their support through the NSF Graduate Research Fellowship.
These simulations were conducted using the FLASH astrophysical code. The software used in this work was in part developed by the DOE-supported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago
[[[ EXTRA SLIDES HERE ]]]]
Gamma Ray Bursts
• High Energy (>1051 erg)• Highly Variable• Two Types– Short Duration –
Associated with compact object mergers
– Long Duration – Associated with Core-Collapse supernova
• Observable in many wavelengths
Viscous HeatingIn a Shakura-Sunyaev α-viscosity prescription, angular
momentum transport and viscous heating are parameterized
X-ray Light CurveTypically, long
duration GRB exhibit 3 distinct phases in the first 103 s
• Phase 0 - 101 s – Prompt Phase
• Phase I – 102 s – Fast Decay
• Phase II – 103 s – Plateau PhaseThe x-ray light curve for GRB 050315 from
Vaughan et al. 2006
The Collapsar model• Outer H layers stripped
away off of a massive Wolf-Rayet progenitor
• Center of star collapses into a neutron star or black hole
• Rotation causes a disk (torus) to form
• Magnetic (?) Jets form and are able to push through the star
• Luminosity is modulated by central object accretion rate
http://www.tls-tautenburg.de/research/klose/GRB.review.htmlSimulation from MacFadyen
Lindner, Milosavljevic, Couch, Kumar 2010
(Accepted to ApJ)
• 2D Hydrodynamic (HD) simulation of collapsar model using FLASH AMR HD code
• Start with same 14 Solar Mass Heger & Woosley model (16TI) WR – high rotation – low metalicity
• Use an explicit shear viscosity (modified α model)• Set up a modified outflow inner boundary at
(Rmin=5.0E7 to 2E8 cm)• Ran simulations for up to 1000 s
Results: Mass Accretion
Phase 0: Quasiradial accretion
Phase I: Funnel and Thick Disk Accretion
Phase II: Funnel Outflow, Thick Disk Accretion
Future Work
• 1D Simulations– Explore the Neutrino-Cooled disk– Look at the possibility for Accretion-Induced
collapse
• Super Massive Stars / Quasistars
Conclusions• The three initial phases of the GRB X-ray light
curve fit well with the three phases of accretion history in the collapsar model– Phase 0: Quasiradial Accretion– Phase I: Funnel and Thick Disk Accretion– Phase II: Funnel Outflow, Thick Disk Accretion
Future Work• 1D Simulations– Explore the Neutrino-Cooled disk– Look at the possibility for Accretion-Induced
collapse• Super Massive Stars / Quasistars
Phase II: Funnel Outflow, Thick Disk Accretion
Kumar, Narayan, & Johnson 2008
• Constructed an analytical model of collapsar accretion
• Use 14 solar mass progenitor star from Woosley & Heger 2006
• Use a basic power law model for rotation profile
• Used α-model viscosity (α=.1)
• Compute onset of accretion shock (~102 s), a steep decline phase, and plateau phase
Basic Equations of Hydrodynamics
Momentum Continuity:
Conservation of Energy:
Continuity of Mass:
Poisson Equation:
-Each grid point contains a full set of fluid variables
-Hydrodynamic equations allow grid coordinates to ‘talk’ to each other
The End of a Massive Star:Hydrostatic Equalibrium
Stars are in hydrostatic equilibrium
Pressure comes in many forms
In stars, greater and greater amounts of pressure are required as you move towards
the center of the star
The End of a Massive Star:Pressure Support
In massive stars, most of the pressure support comes from radiation pressure.
This radiation pressure is provided by the vast quantities of energy
produced as light elements are fused into heavier ones.
The End of a Massive Star:Nuclear Fusion
However, once iron is produced, energy can no longer be gained via fusion in the interior layers.
The End of a Massive Star:Electron Degeneracy
Electron degeneracy pressure must account for the additional pressure needed to support interior layers
against collapse.
The End of a Massive Star:Core Collapse
However, for masses greater than 1.4 MSun,
electron degeneracy
pressure fails, and further collapse will
result
The End of a Massive Star:Core Collapse
Once the core of the star collapses, the layers above the core lose their pressure support.
As these layers also collapse, a runaway infall process propagates at the sound speed, as each layer falls in,
removing the support for the layer above it.
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole
The End of a Massive Star:Core Collapse
What happens from here is depends on the specifics of the progenitor star.
If there is no rotation in the star, the rest of the star will simply collapse into the black hole