Radiative transferRadiative transferand photospheric emissionand photospheric emission

in GRB jetsin GRB jets

Indrek VurmIndrek Vurm((Columbia UniversityColumbia University))

in collaboration within collaboration with

Andrei M. Beloborodov (Columbia University)Andrei M. Beloborodov (Columbia University)Tsvi Piran Tsvi Piran ((Hebrew UniversityHebrew University))

Yuri Lyubarsky Yuri Lyubarsky ((Ben-Gurion UniversityBen-Gurion University))Romain Hascoet (Columbia University)Romain Hascoet (Columbia University)

MoscowMoscow 201 20133

OutlineOutline

Prompt emission: optically thin vs. thickPrompt emission: optically thin vs. thick Photospheric emission from dissipative Photospheric emission from dissipative

jets:jets: Photon number and spectral peaksPhoton number and spectral peaks Non-thermal spectraNon-thermal spectra

GeV emissionGeV emission GeV flash from pair-loaded progenitor windGeV flash from pair-loaded progenitor wind Example: 080916CExample: 080916C

RR00~10~107 7 cmcm

ττTT=1=1L~10L~1051 51 erg/serg/s

ΓΓff

ΓΓss

InternalInternalshocksshocks

PhotosphericPhotosphericemissionemission

heatingheating

GRB prompt emission:GRB prompt emission:optically thin vs. thickoptically thin vs. thick

??

Hardness problemHardness problem

N~F / ~

EFEFEE

EE

Preece et al. Preece et al. ((20002000))

FORBIDDEN

=-2/3=-3/2

coolin

g

death

line

syn

chro

tron

death

line

Optically thin + radiatively Optically thin + radiatively

efficientefficient

> -1.5 (synch. or IC)> -1.5 (synch. or IC)

Peak sharpness and positionPeak sharpness and positionGhisellini (2006)Ghisellini (2006)BlazarsBlazars

Briggs et al. (1999)Briggs et al. (1999)

GRB 990123GRB 990123

GRB spectra narrowGRB spectra narrow

Peak energies clusterPeak energies cluster

EEpkpk

Synch. peakSynch. peak

Goldstein et al. Goldstein et al.

(2012)(2012)

Photospheric emissionPhotospheric emission

Spectral peaksSpectral peaks Narrow: Narrow: cancan be as narrow as be as narrow as

PlanckPlanck PositionPosition

Natural scale Natural scale

Observed Observed

Non-thermal shape:Non-thermal shape:DissipationDissipation

photon productionphoton production

Morsony, Lazzati, Begelman (2007)Morsony, Lazzati, Begelman (2007)

““Disturbed” jetDisturbed” jet

Dissipative jetDissipative jetss

RecollimationRecollimationshocksshocks

Jets could be dissipative Jets could be dissipative throughout their expansionthroughout their expansionRecollimation shocksRecollimation shocksInternal shocksInternal shocksCollisional dissipationCollisional dissipationMagnetic reconnectionMagnetic reconnection

Emerging radiation shaped over Emerging radiation shaped over a broad range of radii, i.e. knows a broad range of radii, i.e. knows about expansion historyabout expansion history

Photon production and Photon production and spectral peaksspectral peaks

RR00

PHOTON PHOTON GENERATIONGENERATION

TT=1=1

EEphph~5 MeV~5 MeV

Observed photons must be produced in the jetObserved photons must be produced in the jet

EEpkpk~500 keV~500 keV

Thermalization/photon- production locationThermalization/photon- production location

Blackbody relationBlackbody relation

ObservationsObservations

ThermalizationThermalization

Photons from the central engine insufficientPhotons from the central engine insufficient

(e.g. Thompson, Meszaros, Rees 2007,(e.g. Thompson, Meszaros, Rees 2007,Pe’er et al. 2007, Eichler & Levinson 2000)Pe’er et al. 2007, Eichler & Levinson 2000)

““Yonetoku”Yonetoku”

- jet launch radius- jet launch radius

FF

hh4kT4kTee

em/absem/abs

ICIC

BBBB

ThermalizationThermalization

absabs=1=1

RR00

TT=1=1

y~10y~10

FF

hh4kT4kTee

em/absem/abs

BBBB

PLANCPLANCKK

WIENWIEN

rrbbbb

FF

hh

BBBB WieWienn

ICIC

em/absem/abs

ThermalizationThermalization

absabs=1=1

RR00

TT=1=1

y~10y~10

FF

hh4kT4kTee

em/absem/abs

BBBB

PLANCPLANCKK

WIENWIEN

rrbbbb

Neither Neither TT»1 nor y»1 are sufficient conditions for »1 nor y»1 are sufficient conditions for thermalizationthermalization

TT~10~1022

Photon sourcesPhoton sources

Non-magnetized flows:Non-magnetized flows: BremsstrahlungBremsstrahlung Double-Compton Double-Compton

scatteringscattering Magnetized flowsMagnetized flows

CyclotronCyclotron

Synchrotron Synchrotron

- thermal- thermal

NNee(())

3kT3kTeenthnth

Photon production: summaryPhoton production: summary

RR00

TT=1=1

~10~1010101010 cm cm

10101212 cm cm

synchrotronsynchrotronbremsstrahlungbremsstrahlung

double Comptondouble Compton

cyclotroncyclotron

TT~10~1022

TT~10~1044

y~10y~1033

y~10y~10

rrWienWien

Photon production occurs in a limited range of radii, at Photon production occurs in a limited range of radii, at TT»1»1

Observed EObserved Epkpk -s -s modest modest ~10 at r~10~10 at r~101111 cm cm

Most efficient mechanism: synchrotronMost efficient mechanism: synchrotron

Number of photons at the peak established below/near the Wien radiusNumber of photons at the peak established below/near the Wien radius

PLANCPLANCKK

WIENWIEN

Spectral shapeSpectral shape

Spectrum broadened by:Spectrum broadened by: Large-angle emissionLarge-angle emission `Fuzzy` photosphere`Fuzzy` photosphere Diffusion in frequency space Diffusion in frequency space

Photospheric emission from a dissipative jetPhotospheric emission from a dissipative jetdoes NOT resemble a Planck spectrum does NOT resemble a Planck spectrum

Low-energy slope: dissipative Low-energy slope: dissipative

jetjet

PLANCPLANCKK

WIENWIEN

DISSIPATIONDISSIPATION

ττTT==

11

Low-energy spectrum is shaped in an extended Low-energy spectrum is shaped in an extended

region between the Wien radius and the Thomson region between the Wien radius and the Thomson

photospherephotosphere

FF

FF

y~1y~1

Low-energy slope: dissipative jetLow-energy slope: dissipative jet

2 F

Wien/Planck spectrum at y»1Wien/Planck spectrum at y»1is broadened by the combinedis broadened by the combinedeffect of Comptonizationeffect of Comptonizationand adiabatic coolingand adiabatic cooling

Photospheric spectrumPhotospheric spectrumsubstantially softer than Plancksubstantially softer than Planck

ττTT=1=1

WIENWIEN

DISSIPATIONDISSIPATION

y~1y~1

Low-energy slope: dissipative Low-energy slope: dissipative jet; with a soft photon sourcejet; with a soft photon source

photon injectionphoton injection

αα=-1 slope is a slow =-1 slope is a slow attractorattractor

saturated Comptonizationsaturated Comptonization

9.0

Dissipative jet: high-energy Dissipative jet: high-energy spectrumspectrum

Non-thermal spectrum above the peak: dissipation near Non-thermal spectrum above the peak: dissipation near ττTT~~11

Possible mechanism: collisional heating (Beloborodov Possible mechanism: collisional heating (Beloborodov 2010)2010) Proton and neutron flows decouple at Proton and neutron flows decouple at TT2020

Drifting neutron and proton flows Drifting neutron and proton flows nuclear collisions:nuclear collisions: Elastic: Thermal heating of eElastic: Thermal heating of e±± via Coulomb collisions via Coulomb collisions

Inelastic: Injection of relativistic eInelastic: Injection of relativistic e± ± with with ~300~300via pion production and decayvia pion production and decay Other models:Other models:

Thompson (1994)Thompson (1994)Pe’er, MPe’er, Méészszááros & Rees ros & Rees

(2005)(2005)Giannios & Spruit (2006)Giannios & Spruit (2006)Ioka et al. (2007)Ioka et al. (2007)etc.etc.

0,, MeV1402 cm

0;;

ee ee ;

Spectra: non-magnetized flowsSpectra: non-magnetized flows

ThermalThermalComptonCompton

Non-thermalNon-thermalComptonCompton γγγγ - absorption - absorption

GeVMeV

kT=15 keV

Heating-cooling balance

injection

cooling,pair cascades

2 EEL PairsPairs

Dissipative jet: summaryDissipative jet: summary

FF

hh4kT4kTee

WienWien

RR00

PH. PH. GENERATIONGENERATION

TT=1=1

~10~10

SPECTRUM FORMATIONSPECTRUM FORMATION

TT~10~1022

y~10y~10

DISSIPATIONDISSIPATION

rrWienWien

FF

hhEEpkpk

FF

hhEEpkpk

Generic model for a dissipative jetGeneric model for a dissipative jet

ττTT=1=1rrcollcoll

WIENWIEN

(r(rcollcoll)~1)~1

00

Continuous dissipationContinuous dissipationthroughout the jetthroughout the jet Thermal and non-thermalThermal and non-thermal

channels:channels:

Acceleration:Acceleration:

Magnetization:Magnetization: Initial radius rInitial radius rcollcoll=10=101111 cm cm

DISSIPATIONDISSIPATIONACCELERATION

ACCELERATION

- terminal Lorentz factor- terminal Lorentz factor

Radiative transferRadiative transfer

- intensity- intensity - photon angle- photon angle

Processes: Compton, Processes: Compton, synchrotron, synchrotron,

pair-production/annihilationpair-production/annihilation

Spectral formationSpectral formation

Spectra at different stages of expansionSpectra at different stages of expansion

rrcollcoll=10=101111

cmcm

TT(r(rcollcoll)=40)=40

00

(r(rcollcoll)~50)~50

=300=300

Initial spectrum: WienInitial spectrum: Wien

Peak shifted to lower energiesPeak shifted to lower energies

due to photon productiondue to photon production

Broadening starts nearBroadening starts near

the Wien radius, proceedsthe Wien radius, proceeds

through the photospherethrough the photosphere

Final spectrum: BandFinal spectrum: Band

rrWienWien

ττTT=1=1rrcollcoll

WIENWIEN

Parameters:Parameters:

Spectra: varying LF at the base Spectra: varying LF at the base

ττTT=1=1rrcollcoll

WIENWIEN

(r(rcollcoll))

rrcollcoll=1=1001111

cmcm Canonical Band shapeCanonical Band shape

Low-energy slope stays near Low-energy slope stays near 11

Spectral peak sensitive to Spectral peak sensitive to (r(rcollcoll))

via photon production efficiencyvia photon production efficiency

BB= 10= 10-2-2

Photospheric emission typically NOT thermal-lookingPhotospheric emission typically NOT thermal-looking

Dissipative jetsDissipative jets Naturally lead to Band-like spectraNaturally lead to Band-like spectra

Photon index Photon index =-1 is an attractor for the Comptonization =-1 is an attractor for the Comptonization

problemproblem

Typical ETypical Epkpk -s require -s require

efficient dissipation efficient dissipation at r~10at r~101111 cm. Recollimation shocks? cm. Recollimation shocks?

bulk Lorentz factor bulk Lorentz factor ~10 at the same radii~10 at the same radii

At least moderate magnetization At least moderate magnetization BB>>1010-3-3

SummarySummary

Continuous dissipation throughout the jet?Continuous dissipation throughout the jet?

GeV flashesGeV flashes

withwith

Andrei Beloborodov and Romain HascoetAndrei Beloborodov and Romain Hascoet

Observations: GRB 080916CObservations: GRB 080916C

Fermi collaboration (2013)Fermi collaboration (2013)

LATLAT

GBMGBM

GRB 080916CGRB 080916C

Observations: LAT lightcurvesObservations: LAT lightcurves

080916C080916C

090902B090902B090926A090926A

TT95 95 (GBM)(GBM)

Fermi LAT collaboration Fermi LAT collaboration

(2013)(2013)

‘‘Regular’ behaviour: Regular’ behaviour: external origin external origin ((forward shock)?forward shock)?

LAT emission peaks LAT emission peaks duringduring the prompt: the prompt: likely not assoc. with decelerationlikely not assoc. with deceleration

Lasts well beyond TLasts well beyond T9595

Emission mechanismEmission mechanism

Synchrotron?Synchrotron?

Theoretical limit: a few 10 MeV (comoving)Theoretical limit: a few 10 MeV (comoving) ~ 10 GeV (observed); limit tighter at late times ~ 10 GeV (observed); limit tighter at late times

Observed: 95 GeV (GRB 130427A) Observed: 95 GeV (GRB 130427A)

Inverse ComptonInverse Compton GeV peak during prompt GeV peak during prompt intense IC cooling by prompt intense IC cooling by prompt

radiationradiation

e.g. Nakar & Piran (2010)e.g. Nakar & Piran (2010)

Kumar & Barniol Duran (2009)Kumar & Barniol Duran (2009)

Asano et al. (2009)Asano et al. (2009)

Razzaque et al. (2010)Razzaque et al. (2010)

Ghisellini (2010)Ghisellini (2010)

Number of IC photonsNumber of IC photons

Wind velocityWind velocity

Bright GeV flashes:Bright GeV flashes:

No. of emitted IC photons:No. of emitted IC photons:

Photon multiplicityPhoton multiplicity

Required pair multiplicity:Required pair multiplicity:

Proposed mechanism: inverse Compton Proposed mechanism: inverse Compton

scattering of prompt MeV radiation in the scattering of prompt MeV radiation in the

forward shockforward shock

in a pair-enriched external mediumin a pair-enriched external medium

PROMPT RADIATIONPROMPT RADIATION

Forward shockForward shock

GeGeVV

EXTERNAEXTERNAL L MEDIUMMEDIUM

Prompt radiation pair-loads and pre-accelerates Prompt radiation pair-loads and pre-accelerates the ambient medium ahead of the FSthe ambient medium ahead of the FS

Pair-enrichment of the external Pair-enrichment of the external mediummedium

PROMPT RADIATIONPROMPT RADIATION

FSFS

1. ISM particle scatters a prompt photon1. ISM particle scatters a prompt photon

2. Scattered photon pair-produces with another prompt photon2. Scattered photon pair-produces with another prompt photon

3. New pairs scatter further photons etc.3. New pairs scatter further photons etc.

e-

e± e-

Loading and pre-acceleration controlled by Loading and pre-acceleration controlled by

the column density of prompt radiationthe column density of prompt radiation

ZZ±±,,prepre

e.g Thompson & Madau (2000) e.g Thompson & Madau (2000)

Beloborodov (2002)Beloborodov (2002)

Kumar & Panaitescu (2004)Kumar & Panaitescu (2004)

GRB 080916C:GRB 080916C:pair-loading and pre-accelerationpair-loading and pre-acceleration

Pair loading at the forward shockPair loading at the forward shock Pre-acceleration and blastwave Lorentz factorsPre-acceleration and blastwave Lorentz factors

Beloborodov, Hascoet, IV (2013)Beloborodov, Hascoet, IV (2013)

GRB 080916C:GRB 080916C:thermal injection Lorentz factorthermal injection Lorentz factor

Flash peaks when:Flash peaks when:

Early decay due to fast Early decay due to fast evolution of evolution of injinj and Z and Z±±

- pair loading- pair loading

Thermal heating:Thermal heating:

GRB 080916C: lightcurveGRB 080916C: lightcurve

Delayed riseDelayed rise Peak during the Peak during the

promptprompt Persists well after TPersists well after T9595

T95 (GBM)

Flux above 100 MeV Flux above 100 MeV

Wind parameterWind parameter

Peak radius RPeak radius R10101616 cm cm

Non-thermal acceleration NOT requiredNon-thermal acceleration NOT required

GRB 080916C: spectraGRB 080916C: spectra

Fermi LAT collaboration Fermi LAT collaboration

(2013)(2013)

-2

-2

SpectraSpectra LAT photon indexLAT photon index

SummarySummary

Proposed mechanism: GeV flashes from FS Proposed mechanism: GeV flashes from FS

running into pair-loaded external mediumrunning into pair-loaded external medium Radiative mechanism: IC of prompt MeV Radiative mechanism: IC of prompt MeV

photonsphotons Standard wind medium consistent with Standard wind medium consistent with

observationsobservations