Amir Levinson Tel Aviv University

Levinson+Bromberg PRL 08 Bromberg et al. ApJ 11Levinson ApJ 12

Katz et al. ApJ 10Budnik et al. ApJ 10Nakar+Sari ApJ 10,11

Relativistic radiation mediated shocks: application to GRBs

MotivationMotivation

• 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

Levinson & Begelman 13

Magnetic jets may be converted to HD jets above the collimation zone

Internal shocksBromberg et al. 2011

Morsony et al. 2010

Sub-photospheric shocks

collisionless shocks

What is a Radiation Mediated Shock?

downstream energy dominated by radiation

upstream plasma approaching the shock is decelerated by scattering of counter streaming photons

Upstream uu

downstream du Shock transition mediated by Compton scattering

Radiation dominated fluid

Scattered photons

Shock mechanism involves generation and scattering of photons

Under which conditions a RMS forms ?

u > 4×10-5 (nu /1015 cm-3)1/6

Radiation dominance downstream: aTd4 > nd kTd

From jump conditions: numpc2u2 aTd

4

In addition, photon trapping requires:

Diffusion time tD ≈ shock crossing time tsh > 1/u

RMS versus RRMSNon-relativistic RMS

• small energy gain: • 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: •optical depth depends on angle: cos• 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)

Upstream u

Photon production - ff

Photon advection

Velocity profile for photon rich upstream

Levinson + Bromberg 2008

Solutions: cold upstream (eg., shock breakout in SN)

Numerical solutions – Budnink et al. 2010Analytic solutions - Nakar+Sari 2012

Shock width

(in shock frame)

s=0.01(Tnu)-1u2

Optical depth inside shock is dominated by e pairs

Velocity profile

Upstreamuu

downstreamdu

Shock transition mediated by collective plasma processes

Upstreamuu

downstreamdu

Shock transition mediated by Compton scattering

Radiation dominated fluid

Scattered photons

Collisionless shocks versus RMS

• Scale: c/p ~ 1(n15)-1/2 cm, c/B~ 3(B6)-1 cm

• can accelerate particles to non-thermal energies.

• scale: (T n s)-1 ~ 109 n15-1 cm

• microphysics is fully understood

• cannot accelerate particles

Plasma turbulence

collisionless

RMS

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 uImmediate downstream Ts, ers

Thermalization layer Td < Ts

shock transition

• Very hard spectrum inside shock• Thermal emission with local temp. downstream

Thermalization depth

Double Compton: τ′DC= 106 ΛDC−1 (nu15)−1/2γu

−1

Free-free: τ′ff = 105Λff−1 (nu15)−1/8γu

3/4

Photon generation: Bremst. + double Compton

Thermalization length >> shock width

Temperature profile behind a planar shock (no adiabatic cooling)

Thermalization by free-free + double Compton

Levinson 2012

Ts Td < Ts

= 0

Spectrum inside the shock (cold upstream)

• Temperature in immediate downstream is regulated by pair production• Ts is much lower in shocks with photon rich upstream (as in GRBs)

Budnik et al. 2010

Ts 200 keV

h/mec2

shock frame

Prompt phase in GRBs: shock in a relativistically expanding outflow

s/rph = (r/ rph )2-2shock

Shocked plasma

Γ

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

Example: adiabatic flow

Upstream conditions

410

410

5 102~ //

cb

r Γ)R/η(ηn

nN

; 2cM

L

41

30

0

4

/

Tc mcπR

LΓση

Computation of single shock emission

Integrate the transfer eq. for each shocked shell to obtain its photospheric temperature

N~

Tph(rs)

rphrs

Ts

r0

local spectrum of a single shell

I (h/kTph)4 e-(h/kTph)

Time integrated SED: a single relativistic shock

u= const

Uniform dissipation

0=10

R6=102

u=2 u=10u=5

Contribution from the shock transition layer is not shown

From Levinson 2012

0.1 10.01 10

Dependence on dissipation profile

u=10, 0=100u=10(/0)1/2

0.10.01 1 10

Mildly relativistic shocks

Uniform dissipation (u=const)

3/43/1 )/()/( cphu rr 0.10.010.001

Dependence on optical depth

Uniform dissipation

0.10.01 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

10-2 10010-1 101h (MeV)

E

10-3

E

Keren & Levinson, in preparation

Sum of 4 shocks (uniform velocity, equal spacing)

10-2 10010-1 101h (MeV)

EE

Keren & Levinson in preparation

Non-equal spacing

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

photosphere

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