Post on 12-Jan-2016
description
Maxim BarkovSpace Research Institute, Russia,
University of Leeds, UK
Serguei KomissarovUniversity of Leeds, UK
GRBs CENTRAL ENGINES AS MAGNETICALLY DRIVEN
COLLAPSAR MODEL
21/04/23 1MFoGRBP, SAO, Bukovo
Plan of this talk
• Gamma-Ray-Bursts – very brief review,• BH driven Models of Central Engines,• Numerical simulations I: Magnetic flux,• Magnetic Unloading,• Realistic initial conditions,• Numerical simulations II: Collapsar model,• Common Envelop and X-Ray flairs, • Conclusions
21/04/23 2MFoGRBP, SAO, Bukovo
II. Relativistic jet/pancake model of GRBs and afterglows:
jet at birth(we are here) pancake later
21/04/23 3MFoGRBP, SAO, Bukovo
(1.1) Merger of compact stars – origin of short duration GRBs?
Neutron star + Neutron starNeutron star + Black holeWhite dwarf + Black hole
Black hole + compact disk
Paczynsky (1986);Goodman (1986);Eichler et al.(1989);
Burst duration: 0.1s – 1.0s
Released binding energy:
21/04/23 4MFoGRBP, SAO, Bukovo
(1.2) Collapsars– origin of long duration GRBs?
Woosley (1993)MacFadyen & Woosley (1999)
Iron core collapses into a black hole: “failed supernova”. Rotating envelopeforms hyper-accreting disk
Collapsing envelope
Accretion shock
Accretion disk
The disk is fed by collapsing envelope.
Burst duration > few seconds21/04/23 5MFoGRBP, SAO, Bukovo
(1.3) Mechanisms for tapping the disk energy
BB
Neutrino heating Magnetic braking
fireballMHD wind
Eichler et al.(1989), Aloy et al.(2000) MacFadyen & Woosley (1999) Nagataki et al.(2006), Birkl et al (2007) Zalamea & Beloborodov (2008) (???)
Blandford & Payne (1982)Proga et al. (2003)Fujimoto et al.(2006)Mizuno et al.(2004)
21/04/23 6MFoGRBP, SAO, Bukovo
Setup
v
B
v
B
v
v
v
(Barkov & Komissarov 2008a,b)(Komissarov & Barkov 2009)black hole
M=3Msun a=0.9
Uniform magnetization R=4500km
= 4x1027-4x1028Gcm-2
outer boundary, R= 2.5x104 km
free fallaccretion
(Bethe 1990)
• 2D axisymmetric GRMHD;• Kerr-Schild metric;• Realistic EOS;• Neutrino cooling;• Starts at 1s from collapse onset. Lasts for < 1s
Rotation:
rc=6.3x103kml0 = 1017 cm2 s-1
230 1,/minsin crrll
III. Numerical simulations
21/04/23 7MFoGRBP, SAO, Bukovo
Free fall model of collapsing star (Bethe, 1990)
radial velocity:
mass density:
accretion rate:
Gravity: gravitational field of Black Hole only (Kerr metric); no self-gravity;Microphysics: neutrino cooling ; realistic equation of state, (HELM, Timmes & Swesty, 2000); dissociation of nuclei (Ardeljan et al., 2005); Ideal Relativistic MHD - no physical resistivity (only numerical);
1
2/11
1 1011.0
sM
M
M
s
tCM sun
sun
21/04/23 8MFoGRBP, SAO, Bukovo
magnetic field lines, and velocity vectors
unit length=4.5km t=0.24s
Model:AC1=9; Bp=3x1010 G
log10 (g/cm3) log10 P/Pmlog10 B/Bp
21/04/23 9MFoGRBP, SAO, Bukovo
magnetic field lines, and velocity vectors
unit length=4.5km t=0.31s
Model:AC1=9; Bp=3x1010 G
log10 (g/cm3)
21/04/23 10MFoGRBP, SAO, Bukovo
Model:AC1=9; Bp=3x1010 G
log10 (g/cm3)
magnetic field lines
21/04/23 11MFoGRBP, SAO, Bukovo
Model:CC1=3; Bp=1010 G
velocity vectors
log10 P/Pm
21/04/23 12MFoGRBP, SAO, Bukovo
Jets are powered mainly by the black hole via the Blandford-Znajek mechanism !!
• No explosion if a=0; • Jets originate from the black hole;• ~90% of total magnetic flux is accumulated by the black hole;• Energy flux in the ouflow ~ energy flux through the horizon (disk contribution < 10%);• Theoretical BZ power:
15122
227
50 1048.0106.3 sergMafEBZ
Model: C
21/04/23 13MFoGRBP, SAO, Bukovo
Preliminary results
1/50 of case a=0.9
21/04/23 14MFoGRBP, SAO, Bukovo
GB
CsMM SUN
10
11
103
315.0
9.0
10 12170
a
scml
9.0
103 12170
a
scml
5.0
10 12170
a
scml
0.0
10 12170
a
scml
21/04/23 15MFoGRBP, SAO, Bukovo
• Jets are formed when BH accumulates sufficient magnetic flux.• Jets power• Total energy of BH • Expected burst duration (?)• Jet advance speed • Expected jet break out time • Jet flow speed (method limitation) • Jets are powered by the Blandford-Znajek mechanism
Summary:
Good news for the collapsar model of long duration GRBs !
15110134.0 serg
cVs 5.01.0
21/04/23 16MFoGRBP, SAO, Bukovo
IV. Magnetic Unloading
(???)1/ 2 cMEBZ
22
227
50106.3 MafEBZ
22
2
11 a
aaf
What is the condition for activation of the BZ-mechanism ?
1) MHD waves must be able to escape from the black hole ergosphereto infinity for the BZ-mechanism to operate, otherwise expect accretion.
or
2) The torque of magnetic lines from BH should be sufficient to stop accretion
(Barkov & Komissarov 2008b)(Komissarov & Barkov 2009)
21/04/23 17MFoGRBP, SAO, Bukovo
The disk accretion makes easier the explosion conditions. The MF lines shape reduce local accretion rate.
10/1/ 2 cMEBZ
21/04/23 18MFoGRBP, SAO, Bukovo
V. Discussion
Magnetically-driven stellar explosions require combination of (i) fast rotation of stellar cores and (ii) strong magnetic fields.
Can this be achieved?
• Evolutionary models of solitary massive stars show that even much weaker magnetic fields (Taylor-Spruit dynamo) result in rotation being too slow for the collapsar model (Heger et al. 2005)
• Low metallicity may save the collapsar model with neutrino mechanism (Woosley & Heger 2006) but magnetic mechanism needs much strongermagnetic field.
• Solitary magnetic stars (Ap and WD) are slow rotators (solid body rotation).
21/04/23 20MFoGRBP, SAO, Bukovo
• The Magnetar model seems OK as the required magnetic field can be generated after the collapse via dynamo inside the proto-NS (Thompson & Duncan 1995)
• The Collapsar model with magnetic mechanism. Can the required magnetic field be generated in the accretion disk?
- turbulent magnetic field (scale ~ H, disk height)
- turbulent velocity of -disk
Application to the neutrino-cooled disk (Popham et al. 1999):
21/04/23 21MFoGRBP, SAO, Bukovo
Inverse-cascade above the disk (Tout & Pringle 1996) may give large-scale field (scale ~ R)
This is much smaller than needed to activate the BZ-mechanism!
• Possible ways out for the collapsar model with magnetic mechanism.
(i) strong relic magnetic field of progenitor, =1027-1028 Gcm-2;
(ii) fast rotation of helium in close binary or as the result of spiral-in of compact star (NS or BH) during the common envelope phase (e.g. Tutukov & Yungelson 1979 ). In both cases the hydrogen envelope is dispersed leaving a bare helium core.
21/04/23 22MFoGRBP, SAO, Bukovo
Required magnetic flux , =1027-28 Gcm-2, close to the highest value observed in magnetic stars.
• Accretion rate through the polar region can strongly decline several seconds after the collapse (Woosley & MacFadyen 1999), reducing the magnetic flux required for explosion (for solid rotation factor 3-10, not so effective as we want);
• Neutrino heating (excluded in the simulations) may also help to reduce the required magnetic flux;
• Magnetic field of massive stars is difficult to measure due to strong stellar winds – it can be higher than =2x1027 Gcm-2 ; • Strong relic magnetic field of massive stars may not have enough time to diffuse to the stellar surface, td ~ 109 yrs << tevol , (Braithwaite Spruit, 2005) 21/04/23 23MFoGRBP, SAO, Bukovo
VI. Realistic initial conditions
• Strong magnetic field suppress differential rotation in the star (Spruit et. al., 2006).
• Magnetic dynamo can’t generate big magnetic flux (???), relict magnetic field is necessarily?
• In close binary systems we could expect fast solid body rotation.
• The most promising candidate for long GRBs is Wolf-Rayet stars.
21/04/23 24MFoGRBP, SAO, Bukovo
)~(tR
BH
starR
)(rl
If l(r)<lcr then matter falling to BH directly
If l(r)>lcr then matter goes to disk and after that to BH
Agreement with model Shibata&Shapiro (2002) on level 1%
Simple model:
21/04/23 25MFoGRBP, SAO, Bukovo
Power low density distribution model
3 r
21/04/23 26MFoGRBP, SAO, Bukovo
Realistic model
M=35 Msun, MWR=13 Msun
Heger at el (2004)
21/04/23 27MFoGRBP, SAO, Bukovo
Realistic model
M=35 Msun, MWR=13 MsunM=20 Msun, MWR=7 Msun
neutrino limit
BZ limit
Realistic model
Heger at el (2004)
21/04/23 28MFoGRBP, SAO, Bukovo
Uniform magnetization R=150000km
B0= 1.4x107-8x107G
v
B
v
B
v
v
v
VII. Numerical simulations II: Collapsar model
GR MHD 2D
black holeM=10 Msun a=0.45-0.6
Setup
Bethe’s free fall model,T=17 s, C1=23
Initially solid body rotation
Dipolar magnetic field
21/04/23 29MFoGRBP, SAO, Bukovo
a=0.6 Ψ=3x1028 a=0.45 Ψ=6x1028
Model a Ψ28 B0,7 L51 dMBH /dt η
A 0.6 1 1.4 - - -
B 0.6 3 4.2 0.44 0.017 0.0144
C 0.45 6 8.4 1.04 0.012 0.049
152
10
10170
skm
M
M
ergs
EV
bh
sunkick
21/04/23 30MFoGRBP, SAO, Bukovo
Normal WRSAnd
Black Hole
black hole spiralling
jets produced
MBH left behind
few seconds
< 1000 seconds
5000 seconds
21/04/23 31MFoGRBP, SAO, Bukovo
disk formed
VIII Common Envelop (CE):
• During CE stage a lot of angular momentum are transferred to envelop of normal star.
• Accretion of stellar core can give main gamma ray burst.
• BZ could work effectively with low accretion rates.
• Long accretion disk phase could be as long as 10000 s. Good explanation for X-Ray flashes.
see for review(Taam & Sandquist 2000)
st
sMtM
MM
d
sunsun
8000
1
104.1 1
21/04/23 32MFoGRBP, SAO, Bukovo
log 1
0Fx(0
.3
–1
0ke
V)
log10(t/sec)
2 3 4 51
0
1
2 3
4
“Canonical” X-ray afterglow lightcurve (Swift)
Zhang (2007)
5
(Barkov & Komissarov 2009)
IX. Conclusions
+ Black holes of failed supernovae can drive very powerful GRB jets via Blandford-Znajek mechanism if the progenitor star has strong poloidal magnetic field;+ Blandford-Znajek mechanism of GRB has much lower limit on accretion rate to
BH then neutrino driven one (excellent for very long GRBs);
• The Collapsar is promising models for the central engines of GRBs.• Theoretical models are sketchy and numerical simulations are only now beginning to explore them. • Our results suggest that:
- Blandford-Znajek mechanism needs very hight magnetic flux or late explosion (neutrino heating as starter?);
± All Collapsar model need high angular momentum, common envelop stage could help.
Low and moderate mass WR (MWR<8 MSUN ?) more suitable for BZ driven GRB.
21/04/23 33MFoGRBP, SAO, Bukovo