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

Very long GRBs

21.04.23 1HEA-2008, IKI

I. Gamma-Ray-Bursts

Discovery: Vela satellite (Klebesadel et al.1973);

Konus satellite (Mazets et al. 1974); Cosmological origin: 1. Beppo-SAX satellite – X-ray afterglows (arc-minute resolution) , optical afterglows – redshift measurements – identification of host galaxies (Kulkarni et al. 1996, Metzger et al. 1997, etc)

2. Compton observatory – isotropic distribution (Meegan et al. 1992);

Supernova connection of long duration GRBs: 1. Association with star-forming galaxies/regions of galaxies; 2. Few solid identifications with supernovae, SN 1998bw, SN 2003dh and others... 3. SN bumps in light curves of optical afterglows. 4. High-velocity supernovae ( 30,000km/s) or hypernovae (1052erg).

21.04.23 2HEA-2008, IKI

Bimodal distribution (two types of GRBs?):

Spectral properties: Non-thermal spectrum from 0.1MeV to GeV:

long durationGRBs

short durationGRBs

very long duration GRBs21.04.23 3HEA-2008, IKI

Relativistic jet/pancake model of GRBs and afterglows:

jet at birthpancake later

21.04.23 4HEA-2008, IKI

II. Models of central engines

(1) Potential of disk accretion onto stellar mass black holes:

disk binding energy:

thin disk life time:

Ultra-dense Hyper-Eddington neutrino cooled disks !!!

- gravitational radius

- disk outer radius

- accreted mass

Shakura–Sunyaev parameter

21.04.23 5HEA-2008, IKI

GRBs Jet magnetic acceleration:

•We get MHD acceleration of relativistic jet up to ≈300•Conversion of magnetic energy to kinetic one more than 50%•Acceleration have place on long distance req≈2rlc

•Jet is very narrow θ<2 (Astro-ph:0811.1467)

21.04.23 6HEA-2008, IKI

(???)1/ 2 cMEBZ

III. Magnetic Unloading

22

227

50106.3 MafEBZ

22

2

11 a

aaf

That is criteria ofexplosion start?How it happens?

21.04.23 7HEA-2008, IKI

The disk accretion makes easier the explosion conditions. The MF lines shape reduce local accretion rate.

10/1/ 2 cMEBZ

MNRAS (2008) 385L, 28 and arxiv:0809.1402 21.04.23 8HEA-2008, IKI

IV. 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 9HEA-2008, IKI

)~(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 10HEA-2008, IKI

Power low density distribution model

3 r

21.04.23 11HEA-2008, IKI

Realistic model

M=35 Msun, MWR=13 Msun

Heger at el (2004)

21.04.23 12HEA-2008, IKI

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 13HEA-2008, IKI

Uniform magnetization R=150000km

B0= 1.4x107-8x107G

v

B

v

B

v

v

v

V. Numerical simulations: 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 14HEA-2008, IKI

Griped MF and angular momentum

3/42

00 1

sin,

fft

t

r

RlRl

mtffmm

mtffmr

rRifttRr

rRifttRBB 3/2

,13

3/4,

20

/1

/1cossin

mtffmm

mtffm

rRifttRr

rRifttRBB 3/5

,23

3/1,

20

/1

/12

2

sin

)(9

2

1

3

,

3/2

,

m

mffm

ffmmmt

rGM

rt

ttrr

21.04.23 15HEA-2008, IKI

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

21.04.23 16HEA-2008, IKI

VI. 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;

± All Collapsar model need high angular momentum, common envelop stage could help.

21.04.23 17HEA-2008, IKI

IV. 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 18HEA-2008, IKI

• 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 19HEA-2008, IKI

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. Zhang & Fryer 2001 ). In both cases the hydrogen envelope is dispersed leaving a bare helium core.

21.04.23 20HEA-2008, IKI

Required magnetic flux , =1028 Gcm-2, still exceeds 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 =1027 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 21HEA-2008, IKI

log10 (g/cm3), magnetic field lines, and velocity vectors 21.04.23 50HEA-2008, IKI

log10 21.04.23 51HEA-2008, IKI

log10 B/Bplog10 B21.04.23 52HEA-2008, IKI