Radiative transfer and photospheric emission in GRB jets

Radiative transfer
and photospheric emission
in GRB jets
Indrek Vurm
(Columbia University)
in collaboration with
Andrei M. Beloborodov (Columbia University)
Tsvi Piran (Hebrew University)
Yuri Lyubarsky (Ben-Gurion University)
Romain Hascoet (Columbia University)
Moscow 2013
Outline



Prompt emission: optically thin vs. thick
Photospheric emission from dissipative jets:

Photon number and spectral peaks

Non-thermal spectra
GeV emission

GeV flash from pair-loaded progenitor wind

Example: 080916C
GRB prompt emission:
optically thin vs. thick
Internal
shocks
Photospheric
emission
R0~107 cm
heating
L~1051 erg/s
τT=1
?
Γf
Γs
Hardness problem
a =-3/2
a=-2/3
cooling
deathline
synchrotron
deathline
FORBIDDEN
Nn~Fn / n ~ n
a
EFE
a
E

Preece et al. (2000)
Optically thin + radiatively efficient
 a > -1.5 (synch. or IC)
Peak sharpness and position
Blazars
GRB 990123
Ghisellini (2006)
Briggs et al. (1999)

GRB spectra narrow

Peak energies cluster
Synch. peak
2
Gg peak
B
Epeak µ
(1+ z)
Epk
Goldstein et al. (2012)
Photospheric emission

Spectral peaks



Narrow: can be as narrow as Planck
Position

Natural scale

Observed

photon production
Non-thermal shape: Dissipation
Dissipative jets
“Disturbed” jet

Jets could be dissipative throughout
their expansion
Recollimation
Internal
shocks
Collisional
Magnetic

shocks
dissipation
reconnection
Recollimation
shocks
Emerging radiation shaped over a
broad range of radii, i.e. knows about
expansion history
Morsony, Lazzati, Begelman (2007)
Photon production and
spectral peaks
T=1
R0
PHOTON GENERATION
Eph~5 MeV
Epk~500 keV
Observed photons must be produced in the jet
Thermalization

Thermalization/photonproduction location

(e.g. Thompson, Meszaros, Rees 2007,
Pe’er et al. 2007, Eichler & Levinson 2000)
Blackbody relation


Observations
“Yonetoku”
- jet launch radius
Photons from the central engine insufficient
Thermalization
abs=1
T=1
y~10
rbb
R0
PLANCK
nFn
BB
W I E N
BB
nFn
IC
em/abs
em/abs
4kTe
hn
4kTe
hn
Thermalization
T=1
T
y~10
~102
abs=1
rbb
R0
PLANCK
nFn
BB
W I E N
nFn
BB
Wien
IC
em/abs
em/abs
4kTe
hn
hn
Neither T»1 nor y»1 are sufficient conditions for thermalization
Photon sources

Non-magnetized flows:



Bremsstrahlung
Double-Compton scattering
- thermal
Magnetized flows

Cyclotron

Synchrotron
Ne()
3kTe
nth
Photon production: summary
bremsstrahlung
double Compton
cyclotron
synchrotron
T=1
rWien
R0
PLANCK
1010 cm
T~104
y~103
W I E N
~10
1012 cm
T~102
y~10

Photon production occurs in a limited range of radii, at T»1

Observed Epk -s  modest ~10 at r~1011 cm

Most efficient mechanism: synchrotron

Number of photons at the peak established below/near the Wien radius
Spectral shape
Photospheric emission from a dissipative jet
does NOT resemble a Planck spectrum

Spectrum broadened by:

Large-angle emission

`Fuzzy` photosphere

Diffusion in frequency space
Low-energy slope: dissipative jet
PLANCK
W I E N
y~1
τT=
nFn
1
n
Low-energy spectrum is shaped in an extended region
between the Wien radius and the Thomson photosphere
nFn
n
Low-energy slope: dissipative jet
WIEN


Wien/Planck spectrum at y»1
is broadened by the combined
effect of Comptonization
and adiabatic cooling
Photospheric spectrum
substantially softer than Planck
y~1
τT=1
nFn  n 2
Low-energy slope: dissipative jet;
with a soft photon source

α=-1 slope is a slow
attractor
a  0.9
photon injection
saturated Comptonization
Dissipative jet: high-energy spectrum


Non-thermal spectrum above the peak: dissipation near τT~1
Possible mechanism: collisional heating (Beloborodov 2010)
 Proton and neutron flows decouple at T20

Drifting neutron and proton flows  nuclear collisions:


Elastic: Thermal heating of e± via Coulomb collisions
Inelastic: Injection of relativistic e± with ~300
via pion production and decay
m c 2  140 MeV
  ,  ,
     n  ;      n  ;  0    
0
   e n e n  ;    e n e n 
Other models:
Thompson (1994)
Pe’er, Mészáros & Rees (2005)
Giannios & Spruit (2006)
Ioka et al. (2007)
etc.
Spectra: non-magnetized flows
ELE  n a  2
MeV
Pairs
GeV
Heating-cooling
balance
kT=15 keV
cooling,
pair cascades
injection
Thermal
Compton
Non-thermal
Compton
γγ - absorption
Dissipative jet: summary
~10
R0
SPE CTRUM FORMATION
PH. GENERATION
D
I
S
T=1
T~102
y~10
S
I
P
A
T
I
O
N
rWien
nFn
Wien
4kTe
hn
nFn
nFn
Epk
hn
Epk
hn
Generic model for a dissipative jet
W I E N

Continuous dissipation
throughout the jet

rcoll
(rcoll)~10
τT=1
Thermal and non-thermal
channels:

Acceleration:

Magnetization:

Initial radius rcoll=1011 cm
- terminal Lorentz factor
Radiative transfer
- intensity
- photon angle
Processes: Compton, synchrotron,
pair-production/annihilation
Spectral formation
rcoll
rWien
τT=1
W I E N

Initial spectrum: Wien

Peak shifted to lower energies
due to photon production

Broadening starts near
the Wien radius, proceeds
through the photosphere

Final spectrum: Band
rcoll=1011 cm
Parameters:
T(rcoll)=400
(rcoll)~50
=300
Spectra at different stages of expansion
Spectra: varying LF at the base
W I E N

Canonical Band shape

Low-energy slope stays near a1

Spectral peak sensitive to (rcoll)
via photon production efficiency
rcoll=1011 cm
B= 10-2
rcoll
τT=1
Summary

Photospheric emission typically NOT thermal-looking

Dissipative jets


Naturally lead to Band-like spectra

Photon index a=-1 is an attractor for the Comptonization problem
Typical Epk -s require

efficient dissipation at r~1011 cm. Recollimation shocks?

bulk Lorentz factor ~10 at the same radii

At least moderate magnetization B>10-3
Continuous dissipation throughout the jet?
GeV flashes
with
Andrei Beloborodov and Romain Hascoet
Observations: GRB 080916C
GRB 080916C
GBM
LAT
Fermi collaboration (2013)
Observations: LAT lightcurves

‘Regular’ behaviour:


LAT emission peaks during the prompt:


external origin (forward shock)?
likely not assoc. with deceleration
Lasts well beyond T95
080916C
T95 (GBM)
090926A
Fermi LAT collaboration (2013)
090902B
Emission mechanism

Synchrotron?

Kumar & Barniol Duran (2009)
Asano et al. (2009)
Razzaque et al. (2010)
Ghisellini (2010)
Theoretical limit: a few 10 MeV (comoving)
 ~ 10 GeV (observed); limit tighter at late times
e.g. Nakar & Piran (2010)


Observed: 95 GeV (GRB 130427A)
Inverse Compton

GeV peak during prompt  intense IC cooling by prompt radiation
Number of IC photons
Bright GeV flashes:
No. of emitted IC photons:
Photon multiplicity
Wind velocity
Required pair multiplicity:
Proposed mechanism: inverse Compton scattering
of prompt MeV radiation in the forward shock
in a pair-enriched external medium
Forward shock
GeV
EXTERNAL
MEDIUM
Pair-enrichment of the external medium
e±
ee.g Thompson & Madau (2000)
Beloborodov (2002)
Kumar & Panaitescu (2004)
FS
Z±,pre
1. ISM particle scatters a prompt photon
2. Scattered photon pair-produces with another prompt photon
3. New pairs scatter further photons etc.
Prompt radiation pair-loads and pre-accelerates the
ambient medium ahead of the FS
Loading and pre-acceleration controlled by
the column density of prompt radiation
e-
GRB 080916C:
pair-loading and pre-acceleration
Pair loading at the forward shock
Pre-acceleration and blastwave Lorentz factors
Beloborodov, Hascoet, IV (2013)
GRB 080916C:
thermal injection Lorentz factor
Thermal heating:

Flash peaks when:
- pair loading

Early decay due to fast
evolution of inj and Z±
GRB 080916C: lightcurve
Flux above 100 MeV
T95 (GBM)



Delayed rise
Peak during the prompt
Persists well after T95
Wind parameter
Peak radius R1016 cm
Non-thermal acceleration NOT required
GRB 080916C: spectra
LAT photon index
Spectra
-2
-2
Fermi LAT collaboration (2013)
Summary



Proposed mechanism: GeV flashes from FS
running into pair-loaded external medium
Radiative mechanism: IC of prompt MeV
photons
Standard wind medium consistent with
observations

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