Amir Levinson Tel Aviv University Levinson+Bromberg PRL 08 Bromberg et al. ApJ 11 Levinson ApJ 12...
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Transcript of Amir Levinson Tel Aviv University Levinson+Bromberg PRL 08 Bromberg et al. ApJ 11 Levinson ApJ 12...
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