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Temporal evolution of thermal emission in GRBs

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  1. 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 Ryde & Pe’er (in preparation) June 2008

  2. Outline • I. Evidence for a thermal component in GRBs prompt emission Characteristic behavior: T~t-0.6; Fbb~t-2 • II. Understanding the temporal behaviorHigh 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

  3. Part I: Evidence for thermal component in GRBs I. Low energy index inconsistent with synchrotron emission: GRB 970111 Crider et al. (1997) Preece et al. (2002) Ghirlanda et al. (2003) E2/3 NE versus E  synchrotron emission gives a horizontal line

  4. II: “Band” function fit to time resolved spectra: Low energy spectral slope varies with time; Ep decreases Time resolved spectral fits: GRB 910927 Crider et al. (1997) a 0 5 10 15 Time [s] (a = low energy power law index) 20 keV 2 MeV Band model fits • Spectral Evolution: The time resolved spectra evolves from hard to soft; • Ep decreases and a gets softer.

  5. Alternative interpretation of the spectral evolution: Planck spectrum + power law (4 parameters) In this case, index s = -1.5 (cooling spectrum). c2 3 parameter model Hybrid model: c2 = 0.89 (3498) Band model: c2 = 0.92 (3498) GRB 910927 0.94 Temperature evolution in time • Interpretation: • Photospheric and non-thermal synchrotron/IC emission overlayed. • Apparent a evolution is an artifact of the fitting. Ryde 2004, ApJ, 614, 827

  6. In some cases the hybrid model gives the best fits GRB 960530 GRB911031 GRB960925

  7. Characteristic behaviour of the thermal component (1)temperature decay 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

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

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

  10. Histograms of late-time decay power law indices (32 bursts) T~t-0.66 FBB~t-2 Power law decay of Temperature and Flux are ubiquitous !!! Ryde & Pe’er (2008)

  11. Characteristic behaviour of the photosphere (3) The ratio between FbbandsT4 : R  t, 0.3 – 0.7: Ryde & Pe’er (2008)

  12. High optical depth: >1 Low optical depth: <1 Photospheric radius: rph = 6*1012 L522-3 cm Part II: Understanding the results Key: Thermal emission must originate from the photosphere We know the emission radius of the thermal component

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

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

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

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

  17. Photon energy loss below the photosphere Photons lose energy by repeated scattering 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 ! Comoving energy decays as’(r) r-2/3 below the photosphere

  18. Temporal behavior of T and R Temperature decays as Tob.(t) t-2/3-t-1/2;R=(F/T4)1/2t1/3-t0 Pe’er (2008)

  19. Tob.t-0.5 Rt0.4 Temporal behavior: observations (Histograms: <Tob.>t-2/3 ; <FBB>t-2;Rt1/3) (Model:Tob.t-2/3Rt1/3) Model in excellent agreement with observed features

  20. 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 scatteringReal life spectra is not easy to model !! (NOT simple broken Power law)

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

  22. Measuring physical properties of GRB jets - I Dominated by high- latitude emission Emission is dominated by on-axis photons Unknown: Known:1) Fob.2) Tob.3) redshift (dL) Photospheric radius: rph = 6*1012 L522-3 cm Pe’er et. al. (2007)

  23. Measuring physical properties of GRB jets - II Measuring quantities below the photosphere - model dependent Using energy + entropy conservation: r0 = size at the base of the flow Specific example: GRB970828(z=0.96) =30528 r0=(2.91.8)108 cm Pe’er et. al. (2007)

  24. Summary • The prompt emission contains a thermal component • The time evolution of this component can be explained as extended high-latitude emissionrph 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 GRB970828(z=0.96) =30528 r0=(2.91.8)108 cm Ryde & Pe’er (in preparation); Pe’er, ApJ, in press (arXiv0802:0725); Pe’er et. al., ApJ, 664, L1 (2007)