1 Physics of GRB Prompt emission Asaf Pe’er University of Amsterdam September 2005.

1

Physics of GRB Prompt emission

Asaf Pe’er

University of Amsterdam

September 2005

2

Outline

Dynamics Basic facts Why relativistic expansion ? Constraints on the expansion Lorentz factor Fireball hydrodynamics: Time evolution The 4 different phases

Radiative Processes Spectrum I: Simplified analysis Complexities Spectrum II: Modified analysis Some open issues

3

Basic Facts

- ray flux: f ~ 10-7 -10-5 erg cm-2 s-1

ob. MeV

Cosmological distance: z=1 dL = 1028 cm

Liso, = 4 f dL2 1050 – 1052 erg s-1

Duration: few sec.

Variability: t~ ms

Example of a lightcurve

(Thanks to Klaas Wiersema)

4

Why relativistic expansion?

♦ Variability: t ~ 1ms Source size: R0 = ct ~ 107 cm

♦ Number density of photons at MeV:

♦ Optical depth for pair production e±:

cR

Ln

204

1MeV

16

0

TT0 10

4~

cR

LnR

Creation of e±, fireball !

-152 s erg10L

5

Why relativistic expansion ?

► Photons accelerate the fireball.

► In comoving frame: co. = ob./

►Photons don’t have enough energy to produce pairs.

6

Estimate of

Mean free path for pair production ) e±( by photon of comoving energy

,,(') 1

2

11

Th dd

ndddl

:/' 11

100 MeV photons were observed

Idea: Optical depth to ~100 MeV photons ≤ 1

22 BATSEU

d

dn

T1 16

3(,,)

221

T11

()2

'

16

3

2

1(')

cm

Ul

e

BATSE

The )comoving( energy density in the BATSE range )20 keV – 2 MeV(: cR

LU BATSE 224

1

2

'

()

cos1

2 2

cme

Th

7

Estimate of (2)

Constraint on source size in expanding plasma:

22

(cos1)2

2

RRRR

R

-

1

c

Rt

22

tcmc

L

e

6222

1T

()512

3

6/112

152, MeV100

250

tL

RRco

1

Rt relation:

l

RcocRcm

Ll

e2222

1T1

1

4()2

'

16

3

2

1(')

QxQ/10x

8

Some complexities

♦ The observed spectrum is NOT quasi-thermal

♦ Small baryon load )enough >10-8 M( High optical depth to scattering

Conclusion: Explosion energy is converted to baryons kinetic energy,

which then dissipates to produce -rays.

9

Stages in dynamics of fireball evolution

Acceleration Coasting Self-similar:

(Forward )shock

Dissipation )Internal collisions,Shock waves(

Transition)Rev. Shock(

R

R-3/2 )R-1/2(

R0

10

Stages in dynamics of fireball evolution

Acceleration Coasting Self-similar:

(Forward )shock

Dissipation )Internal collisions,Shock waves(

Transition)Rev. Shock(

R

R-3/2 )R-1/2(

R0

11

Scaling law for an expanding plasma: I. Expansion phase

Conservation of entropy in adiabatic expansion:

Conservation of energy )obs. Frame(:

Combined together:

.

3

4 ()

30

2

4

02

ConstTRR

Tu

p

RRVT

puVS co

co

.40

2

..

ConstTRR

uVE cocoob

33

11 ;()()

;()

RnRV

RRRT

RR

coco

12

Stages in dynamics of fireball evolution

Acceleration Coasting Self-similar:

(Forward )shock

Dissipation )Internal collisions,Shock waves(

Transition)Rev. Shock(

R

R-3/2 )R-1/2(

R0

13

Scaling law for an expanding plasma: II. Coasting phase

Fraction of energy carried by baryons:

Baryons kinetic energy:

Entropy conservation equation- holds

1/21 EcM b

0

2

RR

EcME

s

bk

2

3/2

30

2

;()

()

Rn

RRT

ConstR

ConstTRR

co

024 RRVco

14

Extended emission: Shells collisions

cRtTGRB /0

22 22

c~v~For

c

The kinetic energy must dissipate. e.g.:

Magnetic reconnection

Internal collisions (among the propagating shells)

External collisions (with the surrounding matter)

Slow heating Expansion as a collection of shells each of thickness R0

cm1062 22

2122

ttcRcollisions

R0=ct

v1, 1 v2,2

15

Stages in dynamics of fireball evolution

Acceleration Coasting Self-similar:

(Forward )shock

Dissipation )Internal collisions,Shock waves(

Transition)Rev. Shock(

R

R-3/2 )R-1/2(

R0

16

Radiation

─ Characteristic )synchrotron( observed energy -

─ Characteristic inverse Compton )IC( energy-

cR

LuuB iso

B 222/1

4 ;(8)

MeV1.0

2

3

13

22

2/152,

2/15.0,

25.0,

2.

tL

cm

qB

isoBe

me

obsyn

fm

m

e

pem

1

.2. obsynm

obIC

f~few

Dissipation process: Unknown physics !!!

Most commonly used model:Synchrotron + inverse Compton )IC(

A fraction e of the energy is transferred to electronsB - to magnetic field

Characteristic electrons Lorentz factor:

magnetic field:

17

Example of expected spectrum- optically thin case

Synchrotron component

Inverse-Compton Component

18

Some complexities…

• Clustering of the peak energy

• Steep slopes at low energies

Observational:

• Dissipation at mild optical depth ?

• Contribution from other radiative sources .

• Unknown shock microphysics )e,B…(

Theoretical:

From Preece et. al., 2000

19

“The compactness problem”

3'

cRm

Ll

e

T

55.2

145.0,52250'

tLl e

1

11'

sc

l

Optically thin Synchrotron – IC emission model is incomplete ! Synchrotron spectrum extends above ob.

syn~0.1 MeV Possibility of pair production

Compactness parameter:

High compactness Large optical depth

T2'

. ()' cmnRl eco

MeV1.0 14

25.2

2/152

2/15.0,

25.0,

.

tLBe

obsyn

15.0,

35.0,

15.24

2.MeV1.0,250'

Be

obsyn tl

MeV250

'1.0 5/32/1

5.0,5/8

5.0,10/1

5/2.

452

tL

lBe

obsyn

Put numbers:

Or: ob.syn~0.1 MeV

High Compactness !!

20

Example of optically thin spectrum

Synchrotron component

Inverse-Compton Component

21

Physical processes – dissipation phase:

Electrons cool fast by Synchrotron and IC scattering –

♦ Synchrotron )cyclotron(

♦ Synchrotron self absorption

♦ Inverse )+ direct !( Compton

♦ Pair creation: e±

♦ Pair annihilation: e+ + e-

♦ Contribution of protons – production )’, high energy photons(

22

Estimate of scattering optical depth by pairs

Balance between pair production and annihilation

Pair production rate – from energy considerations:

dyne

e

tcmcR

L

dt

dn222

od.Pr

1

4

T2

Ann.

cndt

dn

At steady state: 2/1T. 'lnRco

Pair annihilation rate:

Conclusion: optical depth of (at least)±≥ few is expected due to pairs!

23

Spectrum at mild- high optical depth

IC scattering by pairs:

Steep slopes in keV – MeV : 0.5 < peak ~ MeVHigh optical depth Sharp cutoff at mec2 100 MeV

250'l

2500'l

24

Electron distribution: high compactness

=0.08

Low energy distribution: quasi )but not( Maxwellian

Steep power law above .1/1' pe nnfl

l’ = 250

= elec. temp. )in units of mec2(

25

Spectrum as a function of compactness

500100log100()

log()

1

()3

4exp()

.2

.

.

.2

..

in

sc

el

sc

scelinsc

nn

nn

Spectrum dependence on the Optical depth Compactness

± < few, l’≤few Optically thin spectrum

± >500, l’>105 Spectrum approach thermal

Characteristic values – in between !!

Estimate number of scattering required for thermalization:

26

Summary

Dynamical evolution of GRB’s: different phases

Resulting spectrum : Complicated Low compactness High compactness

Acceleration Coasting Self-similar:

Dissipation

27

Estimate of Full calculation(

• Given: Photons observed up to 1~100 MeV

2

2

2

2~10log

BATSE

BATSE

U

d

dn

AAd

dndU

Ad

dn

d

dndd

dd

dnddl

(cos)16

3

2

1

(,,)(')

T

111

221

T

221

T

2T11

()2

'

16

3

2

1

(cos)1(cos)()2

'

216

3

2

1

2(cos)

16

3

2

1(')

cm

U

dcm

U

Uddl

e

BATSE

e

BATSE

BATSE

TH

T1 16

3(,,)

Photons in the BATSE range )20 keV – 2 MeV(: above MeV

6/112

152,

6222

1T

221

T

MeV100250

1()512

3

()2

'

16

3

2

1

2

tL

tcmc

L

cm

UR

l

R

ee

BATSEco