Transcript ppt

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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Collapsar Wind Powered Supernovae?
It has long been hypothesized that winds from collapsar accretion
disks could power supernovae.
E.g.:
• MacFadyen, Woosley 1999
• Narayan, Piran, Kumar 2000
• Pruit, Woosley, Hoffman 2003
• Pruit, Thompson, Hoffman 2004
• Kohri, Narayan, Piran 2005
MacFadyen 2003
• 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?
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Post-Core Collapse with Rotation
• 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
Lindner, Milosavljevic, Couch, Kumar 2010
Log(Density)
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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)
Specific Entropy
Lindner, Milosavljevic, Couch, Kumar 2010
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Accretion Powered Supernovae
Milosavljevic, Lindner, Shen, Kumar 2010
• 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 rotationallysupported 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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Simulations of Accretion Powered
Supernovae
• 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
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Shock Dynamics and Energetics
Viscous Heating
Fusion
Photodisintegration
Neutrino Cooling
vshock ~3,000 km s-1
ADAF
CDAF
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Shock Dynamics and Energetics
Viscous Heating
Fusion
Photodisintegration
Neutrino Cooling
vshock ~3,000 km s-1
ADAF
CDAF
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Central Accretion Rate – Central Engine Activity?
First few 100 s from Swift
2.5D Simulation: dMBH/dt
1.5D Simulation: dMBH/dt
shock
dMBH/dt ~ t−2.8
shock
Lindner et al. 2010
Lindner et al. 2011, in prep.
• 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!
Total Energy
• 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
Base run α=0.1
4.5 Mʘ Unbound
α=0.2
4.3 Mʘ Unbound
α=0.025
1.3 Mʘ Unbound
2.5x convection
2.3 Mʘ Unbound
0.5x convection
No mass Unbound
0.25x convection
3.3 Mʘ Unbound
0.5x rotation
4.4 Mʘ Unbound
3x convective mixing
5.1 Mʘ Unbound
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Nucleosynthesis
t=1 s
t=15 s
t=25 s
t=50 s
• Hydrostatic elements disintegrate into 4He and nucleons in the innermost, hottest
regions of the accretion flow
• Convective mixing transports disintegration products into the shocked, quasihydrostatic 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.
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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 DOEsupported ASC / Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. Portions of this work were supported by
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an NSF Graduate Research Fellowship.
[Supplemental Slides]
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ADAF/CDAF Transition
Understanding 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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Neutrino cooling
• Pair capture on free nucleons (the Urca process):
• Pair annihilation:
MRI motivated α-viscosity prescription
(Thompson et al. 2005)
(Shakura & Sunyaev 1973)
Pseudo-Newtonian gravitational acceleration
(Artemova et al. 1996)
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47 Isotope Nuclear Statistical Equilibrium (NSE)
calculations (Seitenzahl et al. 2008)
• 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
Equation of state (EOS) includes contributions to P and
ε from radiation, ions, electrons, positrons, and
Coulomb Corrections (Timmes & Swesty 2000)
• 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 the
shock 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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