Download - Photosphere Emission in Gamma-Ray Bursts
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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
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Temporal Characteristics
light curve profiles
complicated
durations~ ms - 1000 s
variabilities~ 1ms , even ~ 0.1ms
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photon energies : 10keV – 10GeV non-thermal
GRB090510 GRB090902B
multi-colorblackbody
Spectral Characteristics
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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)
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Fγ ~ 10-6 erg/cm2
DL ~ 3 Gpc
Eisotropic = 4DL2 Fγ
~ 1051 erg
EGRB970228 ~ 1051 erg
EGRB990123 ~ 1054 erg
unisotropic
Jet?
GRBs : energy bugget
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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
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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
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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
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Seminal papers on GRB fireball models
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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 )
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Scaling laws of accelerating fireball
radiation-dominated epoch
matter-dominated epoch
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0r
Characteristic radii of GRB
fireball-photosphere-internal shocks
0sR r phR 2int 0R r
R
0rphphRr /
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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
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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
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Static Photosphere(un-relativistic)
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Relativistic Photosphere
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Assumptions :( 1 ) do not consider the Equal Arrival Time Surface Effect ;( 2 ) impulsive photosphere; ( 3 ) uniform fireball
Relativistic Photosphere
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Relativistic Photosphere
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Approximation :
Relativistic Photosphere
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Relativistic Photosphere
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Thermal Spectrum from a Relativistic Photosphere
wider than Planck function !we call it“relativistic Planck function”
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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)
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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
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Analytical Approach of mBB Model
For m<-1
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mBB Model: Analytical vs. Accurate
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Light Curve of GRB081221
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Time-Resolved Spectra in 081221
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Summary of Time-Resolved Spectral Fit
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Time-Integrated Spectrum of 081221
Time-resolved spectral models are not self-consistent with time-integrated spectrum !
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~ (9.9 keV)^4
~ 7.1 keV
For 081221:
Moments of temperature of mBB
See Hou Shujin’s Poster
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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 !
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Relativistic Photosphere
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0r
High efficiency photosphere
0sR r 2int 0R r
R
0r0r
phR
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0r
0sR r 2int 0R r
R
0r0r
phR
High efficiency photosphere
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0r
0sR r 2int 0R r
R
0r0r
phR
High efficiency photosphere
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
Constraint-1
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
Constraint-2
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
Constraint-3
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0r
0sR r phR 2int 0R r
R
0rphphRr /
Low efficiency photosphere
Constraint-1,2 & 3
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GRB 970828
GRB 081221
GRB 090510
GRB 090618
GRB 090902B
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Correlations in Luminosities
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Luminosity – Lorentz Factor Correlations
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Lv et al 2012; Fan et al 2012
Gamma - Luminosity Relation
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Temperature-Related Correlations
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Ghirlanda et al 2012
Gamma - Epeak Correlation?
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Lu et al 2012
Yonetoku Relation ?
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Thank You