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