Photosphere Emission in Gamma-Ray Bursts

Xuefeng Wu

Purple Mountain Observatory

Chinese Center for Antarctic Astronomy

Chinese Academy of Sciences

Collaborators: Shujin Hou, Zigao Dai,

Bing Zhang, Enwei Liang, Tan Lu et al.

4th Fermi Asian Network Workshop, HKU, July 8-12, 2013

Temporal Characteristics

light curve profiles

complicated

durations～ ms - 1000 s

variabilities～ 1ms , even ～ 0.1ms

photon energies ： 10keV – 10GeV non-thermal

GRB090510 GRB090902B

multi-colorblackbody

Spectral Characteristics

GRBs ： stellar explosions

δT ～ ms

Ri ≤ cδT = 300 km (Ri: emission size)

Blackhole ： R = 2GM/c2

MM ≤ 100 M≤ 100 M⊙⊙

 

GRBs: stellar objectsstellar objects (compact stars)

Fγ ~ 10-6 erg/cm2

DL ~ 3 Gpc

Eisotropic = 4DL２ Fγ

~ 1051 erg

EGRB970228 ~ 1051 erg

EGRB990123 ~ 1054 erg

unisotropic

Jet?

GRBs ： energy bugget

Initial fireball: optically thick Initial energy Initial size

E0 = 1051 ergs Ri ≤ cδ T = 300 km

fireball optical depthτ γ γ (for γ γ → e+e-):

1)ms10

()Gpc3

)(ergs/cm10

(108 2227p

13

2e

2

2Tp

TDFf

cmR

FDf

i

fp : f racti on of photons pai rs sati sfyi ng 2e21 cmEE ,

E1、E2 are energi es of photon pai rs;

F, GRB fl uence; D, di stance of GRB

Expanding Fireball

The fireball will expand and accelerate to be ultra-relativistic driven by the high radiation temperature and pressure, while the optical depth decreases from extremely thick to thin and produce non-thermal emission.

Ri ≤ cδT non-thermal spectrum

optically thick solution optical thin

ultra-relativisticultra-relativistic

Lorentz factor: Lorentz factor: >>1>>1

Compactness Lorentz factor γ :

Ri ≤ cδ T ～ Re ≤ γ 2cδ T

fp ～ fp/ γ 2α

2227p)24(

13

2e

2e

2Tp )

ms10()

Gpc3)(

ergs/cm10(

108

TDFf

cmR

FDf

1 (optically thin) ～ >102

ME/ <10-5(E / 2× 1051 ergs)M⊙

～ baryon contamination problem

Seminal papers on GRB fireball models

Acceleration of GRB baryonic fireballIdeal hydrodynamic assumption ：(1)outside is vacuum (environmental density is low)(2)Photons are coupled (optical depth > 1)(3)Baryons and photons are coupled (lepton-photon scattering depth > 1)

Conservations of energy, momentum and particle number ：

( energy )

( momentum )

( particle number )

Scaling laws of accelerating fireball

radiation-dominated epoch

matter-dominated epoch

0r

Characteristic radii of GRB

fireball-photosphere-internal shocks

0sR r phR 2int 0R r

R

0rphphRr /

Long Way in Discovery of GRB Fireball Emission

Since 1997 ， cosmological GRB internal-external shocks models have been confirmed by many observations ；

No thermal emission was detected from the energetic GRB 080916C (Fermi GBM/LAT) – evidence of highly magnetization of the initial fireball of this burst!

Zhang & Pe’er 2009

Thermal emission from GRB fireball photosphere was first discovered (with high confidence level) in GRB 090902B by Fermi

Thermal emission have been found in a few GRBs, such as 970828 、 081221 、 090510 、 090618

GRB 090902B

Ryde et al. 2009 Hou et al. 2013

GRB 081221

Long Way in Discovery of GRB Fireball Emission

Static Photosphere(un-relativistic)

Relativistic Photosphere

Assumptions ：（ 1 ） do not consider the Equal Arrival Time Surface Effect ；（ 2 ） impulsive photosphere; （ 3 ） uniform fireball

Relativistic Photosphere

Relativistic Photosphere

Approximation ：

Relativistic Photosphere

Relativistic Photosphere

Thermal Spectrum from a Relativistic Photosphere

wider than Planck function ！we call it“relativistic Planck function”

Realistic Relativistic Photosphere

（ 1 ） fireball is not isotropic（ 2 ） there are many fireballs in a GRB（ 3 ） equal arrival time surface effect

multi-color black body (mBB)

Model of multi-color black body (mBB)

4

4 /

8.0525( )

( ) 1E kT

k EEF E

kT e

Single black body

max

min

41

2 /( )

1

T mE E kTT

EEF C kT dT

e

multi-color black body

1( ) ( )mA T A kT

max

min

4

/

( )

1

T

E E kTT

E dA TEF C dT

e dT

see Ryde et al. (2009)

A(>Tmin) =1, normalization

Analytical Approach of mBB Model

For m<-1

mBB Model: Analytical vs. Accurate

Light Curve of GRB081221

Time-Resolved Spectra in 081221

Summary of Time-Resolved Spectral Fit

Time-Integrated Spectrum of 081221

Time-resolved spectral models are not self-consistent with time-integrated spectrum ！

~ (9.9 keV)^4

~ 7.1 keV

For 081221:

Moments of temperature of mBB

See Hou Shujin’s Poster

Comparison with 090902B(time-integrated spectrum)

GRB 090902B

GRB 081221

m ~ -2Rayleigh – Jeans part not observed

Ryde et al. 2009 Hou et al. 2013

m ~ -4Rayleigh – Jeans part observed !

Relativistic Photosphere

0r

High efficiency photosphere

0sR r 2int 0R r

R

0r0r

phR

0r

0sR r 2int 0R r

R

0r0r

phR

High efficiency photosphere

0r

0sR r 2int 0R r

R

0r0r

phR

High efficiency photosphere

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

Constraint-1

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

Constraint-2

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

Constraint-3

0r

0sR r phR 2int 0R r

R

0rphphRr /

Low efficiency photosphere

Constraint-1,2 & 3

GRB 970828

GRB 081221

GRB 090510

GRB 090618

GRB 090902B

Correlations in Luminosities

Luminosity – Lorentz Factor Correlations

Lv et al 2012; Fan et al 2012

Gamma - Luminosity Relation

Temperature-Related Correlations

Ghirlanda et al 2012

Gamma - Epeak Correlation?

Lu et al 2012

Yonetoku Relation ？

Thank You