Simulations of Accretion Powered Supernovae in the Progenitors of

Gamma Ray Bursts

Chris Lindner

Milos Milosavljevic

Sean M. Couch, Pawan Kumar, Rongfeng Shen

The University of Texas at Austin

FLASH Code

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It has long been hypothesized that winds from collapsar accretion disks could power supernovae.

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Collapsar Wind Powered Supernovae?

E.g.: • MacFadyen, Woosley 1999• Narayan, Piran, Kumar 2000 • Pruit, Woosley, Hoffman 2003• Pruit, Thompson, Hoffman 2004• Kohri, Narayan, Piran 2005• Sekiguchi, Shibata 2010

The collapsing stellar envelope feeds an accretion disk, which launches a wind, which then expels the envelope. This seems dangerously self-limiting. What is the 2D structure of the flow? How much accretion energy is deposited before central accretion shutoff?

MacFadyen 2003

Post-Core Collapse with Rotation

Lindner, Milosavljevic, Couch, Kumar 2010Log(Density)

• Rotating 2D simulations using the FLASH AMR Code

• 14 solar mass presupernova model 16TI of Heger & Woosley: Wolf-Rayet – high rotation – low metallicity

• Explicit α shear viscosity

• Inner boundary at ~ 108 cm ; simulation box extends outside of stellar surface

• Ran simulations for 1000 s

• Rotationally-supported torus contains only 1% of the mass outside the black hole; the rest remains in a hot, pressure supported, outflowing atmosphere

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4Lindner, Milosavljevic, Couch, Kumar 2010Specific Entropy

Post-Core Collapse with Rotation• Circularization gives rise to an accretion shock

• Fluid traversed by the shock is convective; energy generated in the inner accretion disk is either convected outwards or advected inwards

• The disk drains into the black hole and gets partially replenished by accretion from the shocked atmosphere

• Energy dissipated in the disk drives a massive outflow at the top of the atmosphere (cf. ADAF paradigm)

Accretion Powered Supernovae

• We assume that no prompt explosion has taken place (no bounce, the core collapses directly into a black hole)

• A shock wave forms when infalling stellar layers hit the centrifugal barrier

• Some of the accretion energy dissipated in the rotationally-supported inner torus advects into the black hole; the rest convects outward following the shock

• The amount of energy delivered to the stellar envelope is sensitive the location of the ADAF/CDAF boundary

• Heat transport by convection (potentially in the transonic limit), as well as cooling and heating by disintegration and fusion in the presence of compositional mixing, govern the energetics of the flow: strong time dependence!

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Milosavljevic, Lindner, Shen, Kumar 2010

• Spherically symmetric calculations with rotation (1.5D) and shear α-viscosity (Thompson, Quataert, Burrows 2005) with FLASH

• Again, we use the 14 solar mass presupernova model 16TI of Heger & Woosley

• Resolve from the inner neutrino-cooled disk to stellar surface: 5 x 106 cm < r < 4 x 1010 cm

• Smooth transition to NSE for T > 3 x 109 K; neutrino cooling; mixing length theory convective energy flux and compositional mixing; a pseudo-Newtonian gravitational potential; thin-disk corrections

• Simulations were run for 100 s

Simulations of Accretion Powered Supernovae

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Shock Dynamics and EnergeticsViscous HeatingFusionPhotodisintegrationNeutrino Cooling

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vshock ~3,000 km s-1

ADAF CDAF

Shock Dynamics and EnergeticsViscous HeatingFusionPhotodisintegrationNeutrino Cooling

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vshock ~3,000 km s-1

ADAF CDAF

Central Accretion Rate – Central Engine Activity?First few 100 s from Swift 2.5D Simulation: dMBH/dt 1.5D Simulation: dMBH/dt

• The mass accretion rate in each of our simulations over the first ~> 100 s contains a prompt, steady accretion phase, followed by steeply declining phase. This resembles the prompt gamma-ray and the early X-ray light curves of LGRBs

• The “prompt” steady accretion phase ends when the accretion shock starts traveling outward

• The steepness of the accretion rate decline is governed by the rapid readjustment of the shocked, convective envelope. Neutrino cooling quickly shuts off!

dMBH/dt ~ t−2.8

shock

shock

Lindner et al. 2010 Lindner et al. 2011, in prep.

• Energy injection into the shocked envelope starts as the shock begins travelling the star and continues for 50 – 100 seconds

• All simulations with the exception of the lowest convective efficiency simulation reached a net positive combined total mechanical and thermal energy on the computational grid by the end of the simulation

• In models which achieved explosion, total unbound masses ranged from 1.3 to 5.1 Mʘ

Total Energy

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4.5 Mʘ Unbound

4.3 Mʘ Unbound

1.3 Mʘ Unbound

2.3 Mʘ Unbound

No mass Unbound

3.3 Mʘ Unbound

4.4 Mʘ Unbound

5.1 Mʘ Unbound

Base run α=0.1

0.5x rotation

3x convective mixing

α=0.025

α=0.2

2.5x convection

0.25x convection

0.5x convection

Nucleosynthesist=1 s t=15 s t=25 s t=50 s

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• Hydrostatic elements disintegrate into 4He and nucleons in the innermost, hottest regions of the accretion flow• Convective mixing transports disintegration products into the shocked, quasi-hydrostatic atmosphere, where they may recombine (we do not simulate non-NSE burning and do not explicitly make 56Ni)• The resulting supernovae should exhibit a high degree of mixing of hydrostatic and explosive elements• Outward convecting 4He may burn into 56Ni, especially if significant neutronization is confined to the ADAF, and Ye remains ~0.5 in the CDAF.

Conclusions• Following circularization around the black hole of the infalling stellar strata, an

accretion shock wave starts to traverse the star.

• The post-shock flow consists of an inner rotationally-supported ADAF containing a small fraction of the mass, which is embedded in an outer, quasi-hydrostatic CDAF containing most of the mass (no thin disk!).

• Convection and convective mixing transport the energy dissipated near the ADAF/CDAF transition outward.

• Over the course of 50-100 seconds, several solar masses of shocked stellar envelope end up with a net positive energy of ~ 0.5×1051 ergs.

• One nucleosynthetic signature of a collapsar-accretion-powered supernova is a high degree of mixing of hydrostatic and explosive elements.

• The central accretion rate resembles the prompt gamma-ray and early X-ray LGRB light curve, suggesting that: (1) the prompt emission phase terminates when the accretion shock starts traveling outward, (2) the subsequent steep decline is a result of the rapid shutting off of central accretion by heating and convective re-adjustment.

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. Portions of this work were supported by

an NSF Graduate Research Fellowship. 12

[Supplemental Slides]

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ADAF/CDAF TransitionUnderstanding where the transition between an

advection dominated flow (ADAF) and a convection dominated flow (CDAF) occurs is vital, as this location 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

Milosavljevic, Lindner, Chen & Kumar 2010

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Shock Location and Velocity

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Results

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Nucleosynthesis

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MRI motivated α-viscosity prescription

(Shakura & Sunyaev 1973)(Thompson et al. 2005)

Pseudo-Newtonian gravitational acceleration (Artemova et al. 1996)

Neutrino cooling• Pair capture on free nucleons (the Urca process):

• Pair annihilation:

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47 Isotope Nuclear Statistical Equilibrium (NSE) calculations (Seitenzahl et al. 2008)

Equation of state (EOS) includes contributions to P and ε from radiation, ions, electrons, positrons, and Coulomb Corrections (Timmes & Swesty 2000)

• Captures photodisintegration and fusion occurring at T > 3 x 109 K

• Relaxed to on a physical timescale (Khoklov 1991)

• Proton to Nucleon ratio (Ye) is held constant

• For stability, the EOS and NSE calculations are solved simultaneously

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Mixing length convection with compositional mixing

• A Gaussian smoothing is applied to the values of P and s used in these calculations• Convective flux is limited to remain behind the shock front, and linearly decay near theshock front

Thin Disk Corrections• Cooling via neutrinos and photodisintegration may result in a thin disk at small radii, enhancing the values of ρ and T• To account for this, the values of ρ and T used in our NSE and neutrino cooling calculations were modified by a geometric factor where the disk was expected to be thin

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Neutrino Cooling

Beloborodov 2008

• At times when the accretion rate is high, a thin, neutrino-cooled disk is formed near the black hole

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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.

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