GRB prompt emission:
spectral energy distribution and
light curve profile
Francesco Massaro
Harvard (SAO – CfA)
Barcellona
June 2011
Thanks to:
J. Grindlay, R. Preece, N. Omodei
Modeling GRBs
Since the discovery of GRBs…
Two major descriptions of their SEDs have been used:
Band fucntion and Blackbody+powerlaw
while
the lightcurves have been described with the Norris profile
We propose a new view for both the
1.  Spectral Energy Distributions (SEDs)
and
2.  Light Curves (LCs)
FACTS…and NOT ARTIFACTS
Observational evidences (random order):
1. SEDs curved and broadly peaked
2. Single pulse or Spiky lightcurves
3. Cosmological distances
4. Variability classes (long and short GRBs)
5. Presence of afterglows
6. Relativistic effects
7. Supernova connection
8. HIC during the LC decay phase
9. GeV emission (not all of them)
10. Presence of X-ray flares (not all of them)
Spectral Energy Distribution of the
GRB prompt emission
AIMS
We aim to find a model for the SED that:
1.  Could describe at least 90% of GRBs
2.  Must describe the TIME RESOLVED SPECTRA
(not only the time integrated)
3.  Must interpret the majority of the observed FACTS
4.  Must work directly on the observed spectra
(not on the “deconvolved” SED)
5.  Must have a strong physical background
6.  MUST NOT IMPROVE THE NUMBER OF PARAMETERS
Ockham Razor
(Frustra fit per plura quod fieri potest per paucior)
Since 1992…The Band Function
SWIFT, Fermi GBM, Multifrequency ToO obs.
new planned missions (we hope) … but still …
Since 1992…The Band Function
Band et al. 1993
Tavani et al. 1996
The SED shape is well described by this phenomenological model
The thermal emission
Physical background !!!
(Ryde 2004)
1. 
2. 
3. 
4. 
5. 
6. 
7. 
My view…it still has some problems
No signatures exponential cutoff
Power-law always necessary
Extrapolation of the power-law
No BB photon index at low energies
Connection low-high energies
It cannot describe all GRBs
No high values of curvature
The log parabolic spectral shape
Massaro, Grindlay & Paggi 2010
Log-parabola
Energy dependent photon index
A new physical parameter: the spectral curvature b
The log parabolic spectral shape
Log-parabolic means log-normal
Parabola is the natural way to approximate functions around a
minimum or a maximum --> e.g. Taylor series
The physics!!!
Since Kardashev 1962
The general solution of the kinetic equation is well
approximated by a log-parabolic function when:
1.  Not only Systematic but also stochastic acceleration
2.  Radiative cooling + adiabatic expansion ……etc. etc.
Similar ideas: Ellison et al. 2001, Pelletier et al. 2003, Stawarz & Petrosian 2006.
The log-parabolic synchrotron
spectra
N(γ)=N0(γ/γ0)- s - r Log γ/γ0
Curvatures
b ~ r/5
F(ν)=F0(ν/ν0)- a - b Log ν/ν0
b (BL Lacs): 0.05 – 0.5
b (GRBs): 0.2 – 1.2
(time resolved spectra)
GRB 090902B
GRB 090902B
GRB 090902B
GRB 090902B
GRB 090902B
Adiabatic expansion
Hp. Self similar scenario:
Possible interpretation of the
hardness intensity correlation (HIC):
so
The HIC has a peak index of ~ 1.6
Massaro & Grindlay 2011
Using the log-parabola….
We can test this idea
Spectral curvature behavior
Simulated spectral evolution
Observed spectral behavior
We do not see drastic
variations of the curvature
during GRB single pulses
Massaro & Grindlay 2011
Adiabatic losses do not change
the shape of the SED
A new feature of GRBs
No high values of spectral curvature (Blackbody expected b~10)
A note on the synchrotron scenario
Synchrotron: line of death or small pitch angle?
Photon index
A clear signature of
Synchrotron emission
Then LCs….
Llody & Petrosian 2002
Light curves of the
GRB prompt emission
Since 1996 and 2005…
The Norris profile
Single long pulse GRBs
Norris et al. 2005
It is always asymmetric
The LC profile can be described by this phenomenological model
Since 1996 and 2005…
The Norris profile
An example of an artifact…..
Rise and decay time ratios is ~ 1/2
1,000,000 of
Montecarlo simulations
with uniform distribution
Massaro & Grindlay 2011 in prep.
Modified
Beta
Function
Vetere et al. 2006
3C 273 Abdo et al. 2010
Massaro & Grindlay 2011 in prep.
FACTS
Observational evidences:
1. SEDs curved and broadly peaked
2. Spiky lightcurves
3. Cosmological distances
4. Fast variability (long and short GRBs)
5. Presence of afterglows
6. Relativistic effects
7. Supernova connection
8. HIC during the LC decay phase
9. No large variations of the spectral curvature
10. GeV emission (not all of them)
11. Presence of X-ray flares (not all of them)
12. Modified Beta profile to describe LCs
(symmetric and asymmetric profiles)
CONCLUSIONS
1. Log-parabola vs Band
From the statistical point of view 4 or 5 vs 3 parameters
(in agreement with Fermi LAT GRBs detections)
From the physical point of view a priori physical background
2. Time resolved spectra are very well described in terms of
log-parabolic model (up to now no exceptions)
3. No drastic variation of the spectral curvature
during GRB single pulses (CAREFUL must be tested)
(signatures of adiabatic expansion)
4. A new idea to describe the LCs: modifed Beta function
More versatile than the exponential profile and without
degeneracies or biases
AIMS for the SED model
And we came out with a model
1.  Could describe at least 90% of GRBs
2.  Must describe the TIME RESOLVED SPECTRA
(not only the time integrated)
3.  Must interpret the majority of the observed FACTS
4.  Must work directly on the observed spectra
(not on the “deconvolved” SED)
5.  Must have a strong physical background
6.  MUST NOT IMPROVE THE NUMBER OF PARAMETERS
Ockham Razor
(Frustra fit per plura quod fieri potest per paucior)
And thanks for your attention
Backup slides
GRB conference in Rome 2004
R. Blandford concluding remarks
Curved spectra in jets
Vela plerion (Mangano et al. 2005)
Cygnus A (FR II)
(Carilli et al. 1991)
Crab Pulsar (Campana et al. 2008)
Curved spectra in jets
Mrk 501
BL Lacs
(Massaro et al. 2006, 2008)
Mrk 501
Log-parabolic model
Mrk 421
Curved spectra in jets
Radio galaxies (Katz-Stone et al. 1993)
GPS radio sources
(Ostorero et al. 2009)
High Frequency Peakers
(Maselli et al. 2009)
The synchrotron line of death
Preece et al. 1998
The synchrotron line of death
Asymmetric log-parabola
X-ray flares in GRB afterglows
SWIFT
time resolved spectral analysis
1.  No drastic variations of b
2. Inconsistent with thermal
(i.e. Blackbody) emission
3. Same model adopted for GRB
prompt emission