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Temporal evolution of thermal emission in GRBs. Based on works by Asaf Pe’er (STScI) in collaboration with Felix Ryde (Stockholm) & Ralph Wijers (Amsterdam), Peter Mészáros (PSU), Martin J. Rees (Cambridge). Pe’er, ApJ., in press (arXiv:0802.0725) Pe’er et. al., ApJ., 664, L1 - PowerPoint PPT Presentation
Temporal evolution of thermal emission in GRBs
Based on works by
Asaf Pe’er (STScI)
in collaboration with
Felix Ryde (Stockholm)&
Ralph Wijers (Amsterdam), Peter Mészáros (PSU),
Martin J. Rees (Cambridge)
June 2008
Pe’er, ApJ., in press (arXiv:0802.0725)
Pe’er et. al., ApJ., 664, L1
Ryde & Pe’er (in preparation)
OutlineOutline
I. Evidence for a thermal component in GRBs prompt emission Characteristic behavior: T~t-0.6; Fbb~t-2
II. Understanding the temporal behavior High latitude emission in optically thick expanding plasma
III. Implicationsa. Analysis of spectra
b. Direct measurement of outflow parameters: Lorentz factor and base of the flow radius r0
Part I: Evidence for thermal component in Part I: Evidence for thermal component in GRBsGRBsI. Low energy index inconsistent with synchrotron I. Low energy index inconsistent with synchrotron emission:emission:
GRB 970111
Crider et al. (1997)Preece et al. (2002)
Ghirlanda et al. (2003)
E2/3 NE versus E synchrotron emissiongives a horizontal line
II: “Band” function fit to II: “Band” function fit to time resolvedtime resolved spectra: spectra:
Low energy spectral slope Low energy spectral slope varies with timevaries with time; E; Epp decreases decreases
0 5 10 15
• Spectral Evolution: The time resolved spectra evolves from hard to soft; Ep decreases and gets softer.
Band model fits
Crider et al. (1997)
Time [s]
GRB 910927Time resolved spectral fits:
) = low energy power law index(
20 keV 2 MeV
Ryde 2004, ApJ, 614, 827
Alternative interpretation of the spectral Alternative interpretation of the spectral evolution:evolution:
Planck spectrum + power law (4 parameters)
In this case, index s = -1.5 (cooling spectrum).
3 parameter model
Temperature evolution in time
0.94
Interpretation:-Photospheric and non-thermal synchrotron/IC emission overlayed. -Apparent evolution is an artifact of the fitting.
Hybrid model: 2 = 0.89 (3498)
Band model:2 = 0.92 (3498)GRB 910927
In some cases the hybrid model gives the best fitsIn some cases the hybrid model gives the best fitsGRB911031 GRB960925
GRB 960530
The temperature decreases as a broken power law with a characteristic break.
The power-law index before the break is ~-0.25; after the break ~-0.7
Characteristic behaviour of the thermal component (1)Characteristic behaviour of the thermal component (1)temperature decaytemperature decay
Some moreSome more.….…
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Ryde & Pe’er (2008)
Temperature broken power law behavior is ubiquitous!!
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Characteristic behaviour of the thermal component (2)Characteristic behaviour of the thermal component (2)Thermal flux decayThermal flux decay
The thermal flux also shows broken power law behaviour
Ryde & Pe’er (2008)
Late time: FBB ~ t-2
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Histograms of late-time decay power law indices Histograms of late-time decay power law indices (32 bursts) (32 bursts)
T~t-0.66 FBB~t-2
Power law decay of Temperature and Flux are ubiquitous!!!
Ryde & Pe’er (2008)
The ratio between Fbb and T4 : R t, 0.3 – 0.7:
Characteristic behaviour of the photosphere (3)Characteristic behaviour of the photosphere (3)
Ryde & Pe’er (2008)
Part II: Understanding the resultsPart II: Understanding the results
Key: Thermal emission must originate from the photosphere
High optical depth: >1 Low optical depth: <1
Photospheric radius: rph = 6*1012 L52 2-3 cm
We know the emission radius of the thermal component
Photosphere in relativistically expanding plasmaPhotosphere in relativistically expanding plasma is is - dependent- dependent
€
for θ <<1;Γ >>1→
rph (θ) ≈Rd2π
1
Γ 2+θ 2
3
⎛
⎝ ⎜
⎞
⎠ ⎟
Photon emission radius
Relativistic wind
cm1034
1252
17 −Γ×=≡ Lcm
MR
p
Td
&
€
rph (θ) =Rdπ
θ
sin(θ)−β
⎡
⎣ ⎢ ⎤
⎦ ⎥
Abramowicz, Novikov & Paczynski (1991)
€
Δt ob. ≈rphc
⎛
⎝ ⎜
⎞
⎠ ⎟θ 2
2=Rd3πc
θ 2
2
⎛
⎝ ⎜
⎞
⎠ ⎟
2
≈ 30L52Γ2−1θ−1
4 s
Thermal emission is observed up to tens of seconds!
Pe’er (2008)
Extending the definition of rExtending the definition of rphph
-Photons are traced from deep inside the flow until they escape.
Thermal photons escape from a range of radii and angles
€
r0 ≡ rph (θ = 0) =Rd
2πΓ 2
Photons escape radii and angles - described by probability density function P(r,)
€
r0 ≡ rph (θ = 0) =Rd
2πΓ 2
€
P(r) =r0r2e
−r0r
€
P(θ) =sin(θ)
2Γ 2[1−β cos(θ)]2;
u ≡1−β cos(θ)
⇒ P(u) =1
2Γ 2βu2
Isotropic scattering in the comoving frame:
P(’)~sin(’)€
(r) ~ r−1 → Psc (r..r + δr) =1− e−δτ ≈ δτ ~δr
r2
Extending the definition of rExtending the definition of rphph
Late time temporal behavior of the thermal fluxLate time temporal behavior of the thermal flux
F(t)t-2
Thermal flux decays at late times as t-2
€
F(t)∝ P(r)dr P(u)duδ t ob. =ru
βc
⎛
⎝ ⎜
⎞
⎠ ⎟∫∫ ∝ t−2
€
u =1−β cos(θ)
€
tN = r0(1−β ) /c
Pe’er (2008)
Photon energy loss below the photospherePhoton energy loss below the photosphere
Photons lose energy by repeated scattering below the photosphere
Comoving energy decays as ’(r) r-2/3 below the photosphere
Local comoving energy is not changed
Photon energy in rest frame of 2nd electron is lower than in rest
frame of 1st electron !
Temporal behavior of T and Temporal behavior of T and RR
Temperature decays as Tob.(t) t-2/3-t-1/2; R=(F/T4)1/2t1/3-t0
Pe’er (2008)
€
T(t)∝ P(r)dr P(u)duT '(r)Dδ t ob. =ru
βc
⎛
⎝ ⎜
⎞
⎠ ⎟∫∫ ∝ t−2 / 3
€
u =1−β cos(θ)
€
D ≡Doppler factor
=1
Γ(1−βμ)
)Model: Tob.t-2/3 Rt1/3(
Model in excellent agreement with observed features
Rt0.4Tob.t-0.5
Temporal behavior: observationsTemporal behavior: observations
)Histograms: <Tob.>t-2/3 ; <FBB> t-2 ;Rt1/3(
Part III: Implication of thermal componentPart III: Implication of thermal component
Pe’er, Meszaros &Rees 2006
There is “Back reaction” between e Thermal photons serve as seed photons for IC scattering
Real life spectra is not easy to model !! (NOT simple broken Power law)
Why Why RR: (Thermal) emission from wind inside a ball: (Thermal) emission from wind inside a ball
Observed flux:
€
F ob. =2π
dL
2dμμ × rph
2 I∫
I = dνIν =∫ D 4 σT '4
π
D ≡ Doppler factor =1
Γ(1−βμ)
Intensity of
thermal emission:
The wind moves relativistically ;
The Photospheric radius is constant!
Γ∝⎟⎟
⎠
⎞⎜⎜⎝
⎛≡ ph
Lob
ob r
dT
F 12/1
4.
.
σR
Effective transverse size due to relativistic aberration
Measuring physical properties of GRB jets - IMeasuring physical properties of GRB jets - I
4
2/1
4.
. 11
iso
L
ph
Lob
ob Ld
rdT
F∝
Γ∝⎟⎟
⎠
⎞⎜⎜⎝
⎛≡R
Known: 1) Fob.
2) Tob.
3) redshift (dL)
Emission is dominated by on-axis photons
Dominated by high- latitude emission
€
1) Liso = 4πdL2F
2) η ∝ 1+ z( )2dLF
R
⎡
⎣ ⎢
⎤
⎦ ⎥
1/ 4
3) rph
Pe’er et. al. (2007)Photospheric radius: rph = 6*1012 L52 2-3 cm
Unknown:
Measuring physical properties of GRB jets - IIMeasuring physical properties of GRB jets - II
( )
R
R
20
4/1
2
)1(
1
z
dr
Fdz
L
L
+∝
⎥⎦
⎤⎢⎣
⎡+∝η
Specific example:
GRB970828 (z=0.96)
=30528
r0=(2.91.8)108 cm
Pe’er et. al. (2007)
Measuring quantities below the photosphere - model dependent
Using energy + entropy conservation:
€
T ob = DT '(rph )∝ L1/ 4η 2 / 3rph
−2 / 3r01/ 6
r0 = size at the base of the flow
SummarySummary
GRB970828 (z=0.96)
=30528
r0=(2.91.8)108 cm
The prompt emission contains a thermal component
The time evolution of this component can be explained as extended high-latitude emissionrph dependes on Photons escape described by P(,r) Photon energy loss: ’~r-2 /3
Thermal emission is required in understanding the spectrum
Observations at early times allow a direct measurement of the Lorentz factor and of r0
Ryde & Pe’er (in preparation); Pe’er, ApJ, in press (arXiv0802:0725); Pe’er et. al., ApJ, 664, L1 (2007)