The Collapsar Model

A. MacFadyen
(Caltech)
W. Zhang, S. Woosley (UCSC), A. Heger (LANL)
R. Blandford (Stanford)
D. Proga (Colorado)
“Supernovae & Gamma-ray Bursts”, Seattle (INT-04-2) July 14, 2004

• central engine
requirements
• 1 st collapsar
simulations
– disks, jets, winds
• fallback
• relativistic flow
• magnetic fields
• PPM hydrodynamics
• MHD ZEUS
• SRHD w/ AMR
• Force-Free
Relativistic Plasma
Dynamics
(Pseudospectral)

GRB Light Curve
ms variability + non-thermal spectrum
Compactness Г 100
Superbowl Burst
M = E/ c 2 ~ 10 -6 M
Ultrarelativistic
Ultra-clean

• Relativity (SR & GR)
• Rotation
• Magnetic Fields
• Nuclear Physics
• Neutrinos
• EOS
• Turbulence
• 2D/3D
• Range of Lengthscales

Burrows (2001)
“Delayed” SN Explosion
Accretion vs. Neutrino heating
a
c
Muller (1999)

Pre-Supernova Density Structure
Woosley & Weaver (1995)
Bigger
stars:
Higher
entropy
Shallower
density
gradients

Stellar Rotation
Mass loss
no mass loss
Fukuda
(1982)
Heger
(2000)
No B
fields

IF Two conditions occur (sometimes):
1. Failure of neutrino powered
SN explosion
a. complete
b. partial (fallback)
2. Rotating stellar cores
j 3 x 10 16 cm 2 /s
THEN
Rapidly accreting black hole, (M~0.1 M /s)
fed by collapsing star (t dyn ~ 446 s/ ½ ~ 10 s)
Disk formation
COLLAPSAR

st
• pre-SN 15 Msun Helium star
• Newtonian Hydrodynamics (PPM)
• alpha viscosity
• rotation
• photodisintegration (NSE alpha, n, p)
• neutrino cooling, thermal + URCA optically thin
• Ideal nucleons, radiation, relativistic degenerate
electrons, positions
• 2D axisymmetric, spherical grid
• self gravity
• R in = 9 R s R out = 9000 R s
MacFadyen & Woosley (1999):

= 0.1 = 0.07 M sun /s = 1.3 x 10 53 erg/s

spin
mass
Use 1D
neutrino
cooled
“slim” GR
disk models
from
Popham et
al (1999).

Thermal
energy
deposition
focused by
toroidal
funnel
structure
T = 5.7 ms
E = 5 x 10 50 erg/s
E dep = 2.8 x 10 48 erg
Jet Birth
. .
E jet = f M acc c 2
MHD
f max ~ .06 - .4

Zhang, Woosley & MacFadyen (2003, ApJ)

What made SN1998bw+GRB980425?
1. Accretion powered
hypernova w/ Nickel wind
MacFadyen (2002)
E~ 10 52 erg, M(Ni)~0.5 M
2. “Brief” jet t engine t jet
Engine dies before jet breakout.
Mildly relativistic shock breakout
=> cosmo. GRB = 980425-like GRB + jet GRB
GRB from ~3 shock breakout
(Tan et al 2001, Perna & Vietri 2002)
MacFadyen (1999)

GRB030329/SN2003dh
SN1998bw M(Ni-56) ~ 0.5-0.6 M
SN2003dh M(Ni-56) ~ 0.35 M
see also: Hjorth et al , Fox et
al Nature, Stanek et al
(2003)

t=7.598s
t=7.540s
.
M in
. ~ 1/2
M out
=> Outflows
MacFadyen & Woosley (1999)

“Nickel Wind”
T > 5 x 10 9 K

Si 28
He 4
O 16
T = 10 10 K
C 12
Outflow
- 10 19 erg/gm
"afterburner"
"Nickel Wind"
BH or NS
n, p
10 19 erg/gm
Ni 56
He 4
R (j) = j
kep 2 7 2
/GM = 2.5 x 10 (j17 /m3 ) cm
Disk is replenished by collapsing star
t accrete = t collapse or t fallback
t accrete t drain = m disk/ m

Exploding star Supernovae
• Radioactive decay of Ni56
• tail of Type II, ALL of Type I
• Type I compact star WD or W-R
•E exp -> adiabatic expansion not light
• no Ni56 -> no Supernova
• SN 1998bw & 2003dh need 0.5 M sun

Do all collapsars make observable
supernovae
No.
If Nickel is made,
It depends on angular momentum of star.
1. j isco < j < j efficient cooling GRB only
2. j < j < j semi-efficient cooling GRB + supernova
3. j > j inefficient cooling supernova only
j < j isco nothing

Fallback in weak SN explosions
Shock
reaches
surface of
star but
parts of
star are not
ejected to
infinity.
MacFadyen, Woosley & Heger (2001)

Fallback accretion
Same star
exploded with a
range of
explosion
energies.
Significant
accretion for
thousands of
seconds to days.

Principle Results
• Sustained accretion .1 Msun/s for>10s
• “Relativistic” Jet formation and collimation
• Sufficient energy for cosmo. GRB
• Neutrino cooling & photodissociation allows
accretion
• Massive bi-conical outflows develop
• Time-scale set by He core collapse
• Fallback -> v. long GRB in WR star or
asymmetric SN in SG

Ultrarelativistic Outflows
•GRBs
•Massive star death (Eta Car?)
•micro-quasars
•Pulsar Wind Nebulae
•AGN Jets
1.RAM - Relativistic Hydrodynamics w/
Adaptive Mesh
2.Force-Free Electodynamics SR GR
Pseudo-Spectral

Blandford & McKee (1976)
n = 1000 cm^-3
P = 10^-4 rho
10^54 erg
eta = E/m = 100

density
need R R/2Г 2
Lorentz Factor

progenitor:
15 Msun MS
HE15B3
1/10 solar
no B
Heger et al
(03,in prep)

R star ~ 10 11 cm (3 lt-s) R hole ~ 10 6 cm (3e-5 lt-s)

Early Collapse with j = 3e16 cm 2 /s

Zoom into inner disk

Free Nucleon fraction in disk and early jet

Early Jet Propogation

lower viscosity higher viscosity
= 10 -3 = 10 -1

st
Proga & MacFadyen, Armitage & Begelman (ApJL, 2004)

Proga, MacFadyen, Armitage & Begelman (ApJL, submitted)

Proga et al (2003)

B 2 /8π > ρc 2 for B 10 12 G

Force-Free Relativistic
Electrodynamics
ρ m Dv/Dt = -P + ρE + JxB
if
P

EM stress accelerates EM energy
density
∂ t ((E 2 +B 2 )/2) + ·(ExB) = 0
∂ t (ExB) – ·(E i E j +B i B j - ij (E 2 +B 2 )/2) = 0
Flows are ultrarelativistic but “subsonic”

FORM
FOrce-free Relativistic MHD
• Pseudospectral
– Fourier, Chebyshev, Legendre
• 1,2,3 Dimensional
• Arbitrary coordinates
• Periodic, fixed bc (PML)
• Parallel
–MPI,OpenMP

Colliding Alfven packets
S
E
E S

Conclusions
• long GRBs from rotating WR stars. t engine >t escape
• Need SN failure & angular momentum
– Low metallicity, binary can help
• SN IF nickel is made. GRB/SN association. Type
Ibc.
• SN/GRB ratio may depend on angular momentum.
• “Nickel wind” can explode star -> hypernova
– H env. Type II (no GRB), no H Type I + GRB
• Relativity important for death of stars like Eta
Car. – needs high resolution.
• Magnetic processes may power jet/explosion.
• Fallback -> asymmetric SN, very long GRBs.