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)