Maxim Barkov Space Research Institute, Russia, University of Leeds, UK Serguei Komissarov

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

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II. Relativistic jet/pancake model of GRBs and afterglows:

jet at birth(we are here) pancake later

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(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:

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(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)

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Model:AC1=9; Bp=3x1010 G

log10 (g/cm3)

magnetic field lines

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Model:CC1=3; Bp=1010 G

velocity vectors

log10 P/Pm

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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

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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

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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

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Realistic model

M=35 Msun, MWR=13 Msun

Heger at el (2004)

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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

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Normal WRSAnd

Black Hole

black hole spiralling

jets produced

MBH left behind

few seconds

< 1000 seconds

5000 seconds

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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

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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