Prompt emission spectra from the photosphere of a GRB

1
Prompt emission spectra from the photosphere of a
GRB

• Dimitrios Giannios
• RTN Meeting
• Antalya 31/03/06

2
Introduction

• Prompt emission mechanisms are poorly understood
• CLUES
• GRB flows are ultrarelativistic (?gt100 e.g.
  Piran 1999)
• The spectra have non-thermal appearance (Band et
  al. 1993 Preece et al. 1998)
• Acceleration, emitted spectra need explanation

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Acceleration

• Key feature to be explained low baryon loading
  or ?E/mbc2gtgt1
• Efficient acceleration can lead to ??
• Two types of models proposed for E
• Thermal form ? thermal acceleration (fireball
  Paczynski 1986 Goodman 1986 Sari Piran 1991)
• Magnetic form ? magnetic acceleration (Thompson
  1994 Drenkhahn Spruit 2002 Lyutikon
  Blandford 2003)
• All models predict (to some extent) photospheric
  emission of the flow

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Fireballs

• Go though fast acceleration
• Most of the energy is in the bulk motion of the
  baryons further out
• Radiation and matter decouple when t1
• Photospheric emission takes place
• Internal shocks are believed responsible for the
  prompt emission (Rees Meszaros 1993 Sari
  Piran 1997)

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Photosphere of a fireball

• The photospheric emission is rather strong
• If thermal, it peaks in the BATSE range and is
  hard to hide (e.g. Daigne Mochkovitch 2002)
• Shocks at rph lead to non-thermal spectra (Rees
  Meszaros 2000 Peer et al. 2005)

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Magnetic (Poynting) models

• Acceleration is more gradual (Drenkhahn Spruit
  2002 (DS02) Vlahakis Koenigl 2003)
• Field can be axisymmetric (DC flow) or highly
  asymmetric (AC flow)
• Gradual magnetic dissipation because of
  instabilities (Giannios Spruit 2006) or
  reconnection (DS02) leads to efficient
  acceleration and radiation
• Here, I focus on the photospheric emission from
  an AC flow

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AC model

• Magnetic field changes polarity on small scales
  ?2pc/O
• Magnetic reconnection proceeds with a fraction
  e0.1 of the Alfvén speed (Lyutikov Uzdenski
  2003 Lyubarky 2005)
• The dynamics of the flow have been studied by
  Drenkhahn (2002) and DS02 through solving the
  steady, 1-D relativistic MHD equations

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AC model (continued)

• Much below rsr , a self-similar solution can
  describe the characteristics of the flow
• One arrives to the following scaling for various
  physical quantities
• Parameters of the model L, s0, (eO) with
  reference values 1052erg/s/sterad, 102, 103
  rad/s-1 respectively
• Notation (L1052 L52 erg/s/sterad)

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The photospheric radius rph

• Important quantity rph
• dt ?(1-ß cos?)ns?ds
• Integrating from r to infinity
• Defining rph t(rph)1

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Radiative transfer analytical estimates

• Deep in the flow radiation particles are in
  thermal equilibrium
• The temperature of the flow is (Giannios Spruit
  2005)
• Characteristic temperatures of a few 100 eV at
  the photospheric region indicate the importance
  of Comptonization there

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The equilibrium radius req

• At req radiation and electrons drop out of
  equilibrium
• Assuming a fraction fe 1 of the dissipated
  energy rate goes to the electrons and balancing
  it with the Compton cooling rate
• One solves for the electron temperature

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Equilibrium radius (continued)

• Equilibrium between radiation and electrons is
  achieved up to the radius where TfTe
• The Thompson optical depth of the flow is high
• Comments
• The equilibrium radius lies a factor of 10 below
  the photosphere
• The electron temperature increases and reaches
  values 40 keV there
• ? Inverse Compton scattering can greatly modify
  the emitted spectrum

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Numerical study

• But inverse Compton leads to deviations from
  black body distribution for the photons assumed
  in the analytics
• A detailed calculation asks for self consistent
  determination of the photon distribution and the
  electron temperature at different radii in the
  flow
• To this end, I implemented a Monte Carlo
  Comptonization code (Pozdniakov et al. 1983)
• A thermal distribution of photons is injected at
  req (inner boundary)
• The scattering path of a large number of photons
  is followed in the flow until t0.1 (outer
  boundary)
• Special relativistic effects related to bulk
  motion and scattering cross section are taken
  into account

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Numerical study (continued)

• Procedure of computation
• The flow is divided into (100) shells
• The electron temperature is assumed to have a
  power law dependence with radius
• T0 and the exponent s are iterated until heating
  approximately balances Compton cooling of the
  electrons at every radius of the flow
• Parametric study of the model

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Results cooling and heating

• The initial guess for T0 and s is given by the
  analytical estimate
• The iteration converges to values close the
  analytical estimates (Giannios 2006)
• T0Tf(req), s3/2
• Overall heating balances cooling except the very
  inner region of the flow
• ?power law modeling of the temperature
  dependence satisfactory

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The electron temperature

• In the inner region radiation and matter are in
  thermal equilibrium
• Triangles electrons depart from equilibrium
• Stars location of the photosphere
• Circles saturation radius
• Note that curves follow parallel tracks!
• ?similar temperatures at the same optical depths
  indicate similar Comptonization spectra

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Spectra

• Characteristic peak at 1 MeV (CE frame)
• Flat power law high energy tails (unsaturated
  Comptonization)
• When fitted with the Band model one gets slopes
  and Epeak close to the observed values
• For high baryon loadings the spectrum is
  quasi-thermal
• May be relevant for a sub-group of bursts (Ryde
  2004 2005)

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Energetics

• How strong is the photospheric component?
• Defining the radiative efficiency eph
• It peaks for moderate loadings
• Overall it ranges from 3 to 20

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Discussion

• Is pair creation significant?
• Not in the photospheric region (maybe further out
  in the flow)
• What happens in the Thompson thin region?
• For low baryon loadings dissipation continues in
  the Thomson thin region
• Thermalization of the electrons is no more
  justified
• Synchrotron emission may not be ignored (Giannios
  Spruit 2005)
• Here we focused in the AC reconnection model but
  similar consideration can be applies to other
  dissipative models (internal shocks MHD
  instabilities)

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Summary-Conclusions

• GRB models predict a photospheric component to
  some extent
• Comes from the region that radiation and matter
  decouple
• If thermal, it typically peaks in the sub-MeV
  energy range
• Energy dissipation in this region can lead to
  highly non-thermal spectra (Rees Mészaros 2000
  2005 Peer et al. 2006)
• Here I focus on the photospheric appearance of a
  Poynting flow
• Analytical and numerical study of the electron
  energy balance is performed
• The flow develops a hot photosphere
• Inverse Compton leads to nonthermal spectra close
  to the observed ones
• The photospheric component is rather strong (10
  of that of the flow)