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