Temporal evolution of thermal emission in GRBs

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.….…

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Ryde & Pe’er (2008)

Temperature broken power law behavior is ubiquitous!!













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


Late time: FBB ~ t-2





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!!!


The ratio between Fbb and T4 : R t, 0.3 – 0.7:

Characteristic behaviour of the photosphere (3)Characteristic behaviour of the photosphere (3)


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)

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Temporal evolution of thermal emission in GRBs