The Collapsar Model
The Collapsar Model
The Collapsar Model
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A. MacFadyen<br />
(Caltech)<br />
W. Zhang, S. Woosley (UCSC), A. Heger (LANL)<br />
R. Blandford (Stanford)<br />
D. Proga (Colorado)<br />
“Supernovae & Gamma-ray Bursts”, Seattle (INT-04-2) July 14, 2004
• central engine<br />
requirements<br />
• 1 st collapsar<br />
simulations<br />
– disks, jets, winds<br />
• fallback<br />
• relativistic flow<br />
• magnetic fields<br />
• PPM hydrodynamics<br />
• MHD ZEUS<br />
• SRHD w/ AMR<br />
• Force-Free<br />
Relativistic Plasma<br />
Dynamics<br />
(Pseudospectral)
GRB Light Curve<br />
ms variability + non-thermal spectrum<br />
Compactness Г 100<br />
Superbowl Burst<br />
M = E/ c 2 ~ 10 -6 M <br />
Ultrarelativistic<br />
Ultra-clean
• Relativity (SR & GR)<br />
• Rotation<br />
• Magnetic Fields<br />
• Nuclear Physics<br />
• Neutrinos<br />
• EOS<br />
• Turbulence<br />
• 2D/3D<br />
• Range of Lengthscales
Burrows (2001)<br />
“Delayed” SN Explosion<br />
Accretion vs. Neutrino heating<br />
a<br />
c<br />
Muller (1999)
Pre-Supernova Density Structure<br />
Woosley & Weaver (1995)<br />
Bigger<br />
stars:<br />
Higher<br />
entropy<br />
Shallower<br />
density<br />
gradients
Stellar Rotation<br />
Mass loss<br />
no mass loss<br />
Fukuda<br />
(1982)<br />
Heger<br />
(2000)<br />
No B<br />
fields
IF Two conditions occur (sometimes):<br />
1. Failure of neutrino powered<br />
SN explosion<br />
a. complete<br />
b. partial (fallback)<br />
2. Rotating stellar cores<br />
j 3 x 10 16 cm 2 /s<br />
THEN<br />
Rapidly accreting black hole, (M~0.1 M /s)<br />
fed by collapsing star (t dyn ~ 446 s/ ½ ~ 10 s)<br />
Disk formation<br />
COLLAPSAR
st<br />
• pre-SN 15 Msun Helium star<br />
• Newtonian Hydrodynamics (PPM)<br />
• alpha viscosity<br />
• rotation<br />
• photodisintegration (NSE alpha, n, p)<br />
• neutrino cooling, thermal + URCA optically thin<br />
• Ideal nucleons, radiation, relativistic degenerate<br />
electrons, positions<br />
• 2D axisymmetric, spherical grid<br />
• self gravity<br />
• R in = 9 R s R out = 9000 R s<br />
MacFadyen & Woosley (1999):
= 0.1 = 0.07 M sun /s = 1.3 x 10 53 erg/s
spin<br />
mass<br />
Use 1D<br />
neutrino<br />
cooled<br />
“slim” GR<br />
disk models<br />
from<br />
Popham et<br />
al (1999).
<strong>The</strong>rmal<br />
energy<br />
deposition<br />
focused by<br />
toroidal<br />
funnel<br />
structure<br />
T = 5.7 ms<br />
E = 5 x 10 50 erg/s<br />
E dep = 2.8 x 10 48 erg<br />
Jet Birth<br />
. .<br />
E jet = f M acc c 2<br />
MHD <br />
f max ~ .06 - .4
Zhang, Woosley & MacFadyen (2003, ApJ)
What made SN1998bw+GRB980425?<br />
1. Accretion powered<br />
hypernova w/ Nickel wind<br />
MacFadyen (2002)<br />
E~ 10 52 erg, M(Ni)~0.5 M <br />
2. “Brief” jet t engine t jet<br />
Engine dies before jet breakout.<br />
Mildly relativistic shock breakout<br />
=> cosmo. GRB = 980425-like GRB + jet GRB<br />
GRB from ~3 shock breakout<br />
(Tan et al 2001, Perna & Vietri 2002)<br />
MacFadyen (1999)
GRB030329/SN2003dh<br />
SN1998bw M(Ni-56) ~ 0.5-0.6 M <br />
SN2003dh M(Ni-56) ~ 0.35 M <br />
see also: Hjorth et al , Fox et<br />
al Nature, Stanek et al<br />
(2003)
t=7.598s<br />
t=7.540s<br />
.<br />
M in<br />
. ~ 1/2<br />
M out<br />
=> Outflows<br />
MacFadyen & Woosley (1999)
“Nickel Wind”<br />
T > 5 x 10 9 K
Si 28<br />
He 4<br />
O 16<br />
T = 10 10 K<br />
C 12<br />
Outflow<br />
- 10 19 erg/gm<br />
"afterburner"<br />
"Nickel Wind"<br />
BH or NS<br />
n, p<br />
10 19 erg/gm<br />
Ni 56<br />
He 4<br />
R (j) = j<br />
kep 2 7 2<br />
/GM = 2.5 x 10 (j17 /m3 ) cm<br />
Disk is replenished by collapsing star<br />
t accrete = t collapse or t fallback<br />
t accrete t drain = m disk/ m
Exploding star Supernovae<br />
• Radioactive decay of Ni56<br />
• tail of Type II, ALL of Type I<br />
• Type I compact star WD or W-R<br />
•E exp -> adiabatic expansion not light<br />
• no Ni56 -> no Supernova<br />
• SN 1998bw & 2003dh need 0.5 M sun
Do all collapsars make observable<br />
supernovae<br />
No.<br />
If Nickel is made,<br />
It depends on angular momentum of star.<br />
1. j isco < j < j efficient cooling GRB only<br />
2. j < j < j semi-efficient cooling GRB + supernova<br />
3. j > j inefficient cooling supernova only<br />
j < j isco nothing
Fallback in weak SN explosions<br />
Shock<br />
reaches<br />
surface of<br />
star but<br />
parts of<br />
star are not<br />
ejected to<br />
infinity.<br />
MacFadyen, Woosley & Heger (2001)
Fallback accretion<br />
Same star<br />
exploded with a<br />
range of<br />
explosion<br />
energies.<br />
Significant<br />
accretion for<br />
thousands of<br />
seconds to days.
Principle Results<br />
• Sustained accretion .1 Msun/s for>10s<br />
• “Relativistic” Jet formation and collimation<br />
• Sufficient energy for cosmo. GRB<br />
• Neutrino cooling & photodissociation allows<br />
accretion<br />
• Massive bi-conical outflows develop<br />
• Time-scale set by He core collapse<br />
• Fallback -> v. long GRB in WR star or<br />
asymmetric SN in SG
Ultrarelativistic Outflows<br />
•GRBs<br />
•Massive star death (Eta Car?)<br />
•micro-quasars<br />
•Pulsar Wind Nebulae<br />
•AGN Jets<br />
1.RAM - Relativistic Hydrodynamics w/<br />
Adaptive Mesh<br />
2.Force-Free Electodynamics SR GR<br />
Pseudo-Spectral
Blandford & McKee (1976)<br />
n = 1000 cm^-3<br />
P = 10^-4 rho<br />
10^54 erg<br />
eta = E/m = 100
density<br />
need R R/2Г 2<br />
Lorentz Factor
progenitor:<br />
15 Msun MS<br />
HE15B3<br />
1/10 solar<br />
no B<br />
Heger et al<br />
(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<br />
= 10 -3 = 10 -1
st<br />
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<br />
Electrodynamics<br />
ρ m Dv/Dt = -P + ρE + JxB<br />
if<br />
P
EM stress accelerates EM energy<br />
density<br />
∂ t ((E 2 +B 2 )/2) + ·(ExB) = 0<br />
∂ t (ExB) – ·(E i E j +B i B j - ij (E 2 +B 2 )/2) = 0<br />
Flows are ultrarelativistic but “subsonic”
FORM<br />
FOrce-free Relativistic MHD<br />
• Pseudospectral<br />
– Fourier, Chebyshev, Legendre<br />
• 1,2,3 Dimensional<br />
• Arbitrary coordinates<br />
• Periodic, fixed bc (PML)<br />
• Parallel<br />
–MPI,OpenMP
Colliding Alfven packets<br />
S<br />
E<br />
E S
Conclusions<br />
• long GRBs from rotating WR stars. t engine >t escape<br />
• Need SN failure & angular momentum<br />
– Low metallicity, binary can help<br />
• SN IF nickel is made. GRB/SN association. Type<br />
Ibc.<br />
• SN/GRB ratio may depend on angular momentum.<br />
• “Nickel wind” can explode star -> hypernova<br />
– H env. Type II (no GRB), no H Type I + GRB<br />
• Relativity important for death of stars like Eta<br />
Car. – needs high resolution.<br />
• Magnetic processes may power jet/explosion.<br />
• Fallback -> asymmetric SN, very long GRBs.