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: ) Pe’er et. al., ApJ., 664, L1 Ryde & Pe’er (in preparation)

Outline I. Evidence for a thermal component in GRBs prompt emission Characteristic behavior: T~t -0.6 ; F bb ~t -2 II. Understanding the temporal behavior High latitude emission in optically thick expanding plasma III. Implications a. Analysis of spectra b. Direct measurement of outflow parameters: Lorentz factor  and base of the flow radius r 0

Part I: Evidence for thermal component in GRBs I. Low energy index inconsistent with synchrotron emission: GRB Crider et al. (1997) Preece et al. (2002) Ghirlanda et al. (2003) E 2/3 N E versus E  synchrotron emission gives a horizontal line

II: “Band” function fit to time resolved spectra: Low energy spectral slope varies with time; E p decreases Spectral Evolution: The time resolved spectra evolves from hard to soft ; E p decreases and  gets softer. Band model fits Crider et al. (1997)  Time [s] GRB Time resolved spectral fits: (  = low energy power law index) 20 keV 2 MeV

Ryde 2004, ApJ, 614, 827 Alternative interpretation of the spectral evolution: Alternative interpretation of the spectral 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

In some cases the hybrid model gives the best fits GRB GRB GRB

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) temperature decay

Some more…. Ryde & Pe’er (2008) Temperature broken power law behavior is ubiquitous !!

Characteristic behaviour of the thermal component (2) Thermal flux decay The thermal flux also shows broken power law behaviour Ryde & Pe’er (2008) Late time: F BB ~ t -2

Histograms of late-time decay power law indices (32 bursts) T~t F BB ~t -2 Power law decay of Temperature and Flux are ubiquitous !!! Ryde & Pe’er (2008)

The ratio between F bb and  T 4 : R  t ,  0.3 – 0.7: Characteristic behaviour of the photosphere (3) Ryde & Pe’er (2008)

Part II: Understanding the results Key: Thermal emission must originate from the photosphere High optical depth:  >1Low optical depth:  <1 Photospheric radius: r ph = 6* L 52  2 -3 cm We know the emission radius of the thermal component

Photosphere in relativistically expanding plasma is  - dependent Photon emission radius Relativistic wind Abramowicz, Novikov & Paczynski (1991) Thermal emission is observed up to tens of seconds ! Pe’er (2008)

Extending the definition of r ph -Photons are traced from deep inside the flow until they escape. Thermal photons escape from a range of radii and angles

Photons escape radii and angles - described by probability density function P(r,  ) Isotropic scattering in the comoving frame: P(  ’)~sin(  ’) Extending the definition of r ph

Late time temporal behavior of the thermal flux F(t)  t -2 Thermal flux decays at late times as t -2 Pe’er (2008)

Photon 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 2 nd electron is lower than in rest frame of 1 st electron !

Temporal behavior of T and R Temperature decays as T ob. (t)  t -2/3 -t -1/2 ; R =(F/T 4 ) 1/2  t 1/3 -t 0 Pe’er (2008)

( Model: T ob.  t -2/3 R  t 1/3 ) Model in excellent agreement with observed features R  t 0.4 T ob.  t -0.5 Temporal behavior: observations (Histograms:  t -2/3 ;  t -2 ;  R  t 1/3 )

Part 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 R : (Thermal) emission from wind inside a ball Observed flux: Intensity of thermal emission: The wind moves relativistically; The Photospheric radius is constant ! Effective transverse size due to relativistic aberration

Measuring physical properties of GRB jets - I Known: 1) F ob. 2) T ob. 3) redshift (d L ) Emission is dominated by on-axis photons Dominated by high- latitude emission Pe’er et. al. (2007) Photospheric radius: r ph = 6* L 52  2 -3 cm Unknown:

Measuring physical properties of GRB jets - II Specific example: GRB (z=0.96)  =305  28 r 0 =(2.9  1.8)  10 8 cm Pe’er et. al. (2007) Measuring quantities below the photosphere - model dependent Using energy + entropy conservation: r 0 = size at the base of the flow

Summary GRB (z=0.96)  =305  28 r 0 =(2.9  1.8)  10 8 cm  The prompt emission contains a thermal component  The time evolution of this component can be explained as extended high-latitude emission  r ph 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 r 0 Ryde & Pe’er (in preparation); Pe’er, ApJ, in press (arXiv0802:0725); Pe’er et. al., ApJ, 664, L1 (2007)