Relativistic radiation mediated shocks: application to GRBs

Amir Levinson Tel Aviv University Levinson+Bromberg PRL 08 Bromberg et al. ApJ 11 Levinson ApJ 12 Katz et al. ApJ 10 Budnik et al. ApJ 10 Nakar+Sari ApJ 10,11

Motivation • In GRBs a considerable fraction of the outflow bulk energy may dissipate beneath the photosphere. - dissipation mechanism: shocks? magnetic reconnection ? other ? In this talk I consider sub-photospheric shocks •Strong shocks that form in regions where the Thomson depth exceeds unity are expected to be radiation dominated.

Structure and spectrum of such shocks are vastly different than those of collisionless shocks.

Other examples: shock breakout in SNs, LLGRB, etc accretion flows

Photospheric emission

GRB090902B

Collapsar simulations

Lazzati et al. 2009 Substantial fraction of bulk energy dissipates bellow the photosphere via collimation shocks

A model with magnetic dissipation Magnetic jets may be converted to HD jets above the collimation zone Levinson & Begelman 13

t Internal shocks Bromberg et al. 2011 Sub-photospheric shocks Morsony et al. 2010 collisionless shocks G

What is a

R

adiation

M

ediated

S

hock?

Shock mechanism involves generation and scattering of photons  downstream energy dominated by radiation  upstream plasma approaching the shock is decelerated by scattering of counter streaming photons Scattered photons Upstream

u u

Radiation dominated fluid Shock transition mediated by Compton scattering downstream

u d

Under which conditions a RMS forms ?

Radiation dominance downstream: aT d 4 > n d kT d From jump conditions: n u m p c 2  u 2  aT d 4   u > 4 × 10 -5 (n u /10 15 cm -3 ) 1/6 In addition, photon trapping requires: Diffusion time t D ≈ shock crossing time t sh  t > 1/  u

RMS versus RRMS

• • Non-relativistic RMS small energy gain: De/e<<1 diffusion approximation holds. Used in most early treatments Zeldovich & Raiser 1967; Weaver 1976; Blandford & Pyne 1981; Lyubarsky & Sunyaev 1982; Riffert 1988 Relativistic RMS • • • • photon distribution is anisotropic energy gain large: De/e >1 optical depth depends on angle: t a (1- cos q) copious pair production Levinson & Bromberg 08; Katz et al. 10; Budnik et al. 10; Nakar & Sari 10,11; Levinson 12

Photon source: two regimes

• Photon production inside the shock (dominant in shock breakouts from stellar envelopes, e.g., SN, LLGRBs..) • Photon advection by upstream fluid (dominant in GRBs; Bromberg et al ‘11) Photon advection Upstream

u

Photon production - ff

Velocity profile for photon rich upstream Levinson + Bromberg 2008

Solutions: cold upstream (eg., shock breakout in SN) Numerical solutions – Budnink et al. 2010 Analytic solutions - Nakar+Sari 2012 Shock width (in shock frame) D s =0.01(  T n u ) -1  u 2 Optical depth inside shock is dominated by e  pairs Velocity profile

Collisionless shocks versus RMS collisionless Plasma turbulence • Scale: c/  p ~ 1(n 15 ) -1/2 cm , c/  B ~ 3 e (B 6 ) -1 cm • can accelerate particles to non-thermal energies.

Upstream

u u

downstream Shock transition mediated by collective plasma processes

u d

RMS Scattered photons • scale: (  T n  s ) -1 ~ 10 9 n 15 -1 cm • microphysics is fully understood Upstream

u u

•

cannot accelerate particles

Radiation dominated fluid Shock transition mediated by Compton scattering downstream

u d

Detailed structure

• • • Shock transition – fluid decelerates to terminal DS velocity Immediate DS – radiation roughly isotropic but not in full equilibrium Far DS – thermodynamic equilibrium is established Upstream

u

shock transition Immediate downstream T s , e rs Thermalization layer T d < T s • • Very hard spectrum inside shock Thermal emission with local temp. downstream

Thermalization depth

Photon generation: Bremst. + double Compton Free-free: τ′ ff = 10 5 Λ ff −1 (n u15 ) −1/8 γ u 3/4 Double Compton: τ′ DC = 10 6 Λ DC −1 (n u15 ) −1/2 γ u −1 Thermalization length >> shock width

Temperature profile behind a planar shock (no adiabatic cooling) Thermalization by free-free + double Compton Levinson 2012 T s t = 0 T d < T s

Spectrum inside the shock (cold upstream) shock frame T s  200 keV h  /m e c 2 Budnik et al. 2010 • • Temperature in immediate downstream is regulated by pair production T s is much lower in shocks with photon rich upstream (as in GRBs)

Prompt phase in GRBs: shock in a relativistically expanding outflow shock D s /r ph = (r/ r ph ) 2 G -2 Γ Shocked plasma photosphere

Breakout and emission photosphere • shock emerges from the photosphere and eventually becomes collisionless • shells of shocked plasma that reach the photosphere start emitting • time integrated spectrum depends on temperature profile behind the shock • at the highest energies contribution from shock transition layer might be significant

Upstream conditions

Example: adiabatic flow  

L



c

2 ;

η c

  

σ T LΓ

0 4

πR

0

mc

3   1

/

4 ~

N



n r n b

 2  10 5

(η /η c )R

0 1

/

4

Γ

0 1

/

4

Computation of single shock emission Integrate the transfer eq. for each shocked shell to obtain its photospheric temperature r ph r 0 r s ~

N

T s local spectrum of a single shell  I  a (h  /kT ph ) 4 e -(h  /kT ph ) T ph (r s )

Time integrated SED: a single relativistic shock Uniform dissipation  u =2  u =5 Contribution from the shock transition layer is not shown  u =10  u = const t 0 =10 R 6 =10 2 0.01

0.1

1 10 From Levinson 2012

Dependence on dissipation profile  u =10( t / t 0 ) 1/2  u =10, t 0 =100 0.01

0.1

1 10

Mildly relativistic shocks Uniform dissipation (  u =const) 0.001

0.01

0.1



u

> (

r ph

/

r

) 1 / 3 (  / 

c

) 4 / 3

Dependence on optical depth Uniform dissipation 0.01

0.1

1

Multipole shock emission

• Single shock emission produces thermal spectrum below the peak. • Multiple shock emission can mimic a Band spectrum

Several shocks with different velocities Keren & Levinson, in preparation  E  10 -3 10 -2 10 -1 h  (MeV) 10 0 10 1

 E  Sum of 4 shocks (uniform velocity, equal spacing) Keren & Levinson in preparation 10 -2 10 -1 h  (MeV) 10 0 10 1

Non-equal spacing

photosphere

post breakout

Shock becomes collisionless: • particle acceleration • nonthermal emission from accelerated particles • possible scattering of photospheric photons by nonthermal pairs To be addressed in future work

Conclusions • Relativistic radiation mediated shocks are expected to form in regions where the Thomson optical depth exceeds unity.

• Time integrated SED emitted behind a single shock has a prominent thermal peak. The location of the peak depends mainly on upstream conditions and the velocity profile of the shock.

• The photon spectrum inside the shock has a hard, nonthermal tail extending up to the NK limit, as measured in the shock frame. Doesn’t require particle acceleration!

• Multiple shock emission can mimic a Band spectrum