The origin of the prompt GRB spectrum

Abstract

Using a detailed model of the internal shock phase, we discuss the origin of the prompt emission in gamma-ray bursts. We focus on the identification of the dominant radiative process (Fermi-GBM range) and propose an explanation for some features observed by Fermi-LAT at high energy in some GRB lightcurves. Comment: 2009 Fermi Symposium, eConf Proceedings C091122;

Full text

Page 1

arXiv:0912.3743v1 [astro-ph.HE] 18 Dec 2009
2009 Fermi Symposium, Washington, D.C., Nov. 2-5
1
The origin of the prompt GRB spectrum
F. Daigne∗and Z. Bosnjak†
Institut d’Astrophysique de Paris – UMR 7095 Universit´ e Pierre et Marie Curie-Paris 06; CNRS
98 bis bd Arago, 75014 Paris, France
G. Dubus
Laboratoire d’Astrophysique de Grenoble – UMR 5571 Universit´ e Joseph Fourier; CNRS
BP 53, 38041 Grenoble, France
Using a detailed model of the internal shock phase, we discuss the origin of the prompt emission in gamma-ray
bursts. We focus on the identification of the dominant radiative process (Fermi-GBM range) and propose an
explanation for some features observed by Fermi-LAT at high energy in some GRB lightcurves.
1. Introduction
The physical origin of the prompt emission from
Gamma-ray bursts (hereafter GRBs) is still un-
clear. Due to the high variability observed in the
lightcurves, it is usually believed that it is produced
from within the relativistic outflow (internal origin)
and that the variability is due to the activity of
the central engine [Sari and Piran 1997].
the radiated energy can in principle be extracted
from three potential reservoirs :
or magnetic energy.In the first case, radiation
will occur at the photosphere.
cases, an extraction mechanism is needed.
extraction of the kinetic energy of the outflow can
be obtained via shock waves propagating within the
outflow (internal shocks, Rees and M´ esz´ aros [1994])
that accelerate particles, which then radiate.
extraction of magnetic energy can be achieved via
magnetic dissipation due to the reconnection of the
field lines [Lyutikov and Blandford 2003]. This leads
again to particle acceleration.
Then
thermal, kinetic
In the two other
The
The
The first fundamental question is to identify which
of these mechanisms is (are ?)
An additional question is to understand which
radiative processes are responsible for the emission
and the shape of the spectrum. In order to model
the phenomenology of GRBs (lightcurves, spectrum,
spectral evolution) both questions (energy extraction
mechanism and dominant radiative process) cannot
be considered independently.
spectrum cannot be computed without estimating
the physical conditions in the emitting region.
at work in GRBs.
Indeed the radiated
In this contribution we focus on the identification
of the dominant radiative process in the prompt
emission from GRBs assuming that it is produced
∗Institut Universitaire de France
†Present: CEA Saclay, DSM/IRFU/Service d’Astrophysique –
91191 Gif-sur-Yvette, France
by shock-accelerated electrons in internal shocks oc-
curing above the photospheric radius of the outflow.
It assumes that the magnetization of the outflow at
large distance of the central source is weak (σ < 1),
otherwise shock waves would not propagate within
the outflow. It also assumes that the photospheric
emission is weak and hidden by the non-thermal
radiation from internal shocks.
efficiency of the latter, it implies either that the
outflow is ejected from the innermost region of the
central engine (r0 ≤ 106cm) or that the outflow
is initially highly magnetized (σ > 10) and that
the acceleration is due to an efficient conversion of
the magnetic energy into kinetic energy below the
photosphere [Daigne and Mochkovitch 2002].
Due to the low
In such a situation, the two main radiative pro-
cesses that may be responsible to build the optically
thin non-thermal spectrum are synchrotron radiation
or inverse Compton scatterings. This is discussed in
Sect. 2. Then we present in Sect. 3 some results ob-
tained from a model of the internal shock phase that
includes a detailed treatment of the dynamics and the
radiation. Sect.4 is the conclusion.
2. What is the dominant radiative
process during the prompt GRB
emission ?
There are mainly two possibilities for the origin of
the soft γ-rays observed in GRBs : either they are
directly emitted by synchrotron radiation from highly
relativistic electrons or they are produced by inverse
Compton scatterings of soft synchrotron photons by
relativistic electrons (SSC). Observations seem now
to favor the synchrotron scenario. Indeed, in the SSC
case, the final shape of the spectrum is mainly deter-
mined by the value of the parameter YTh ∼ ǫe/ǫB,
where ǫB (resp.ǫe) is the fraction of the internal
energy available in the shocked region which is
transfered in the magnetic field (resp. the accelerated
electrons). Depending on the value of YTh∼ ǫe/ǫB, it
eConf C091122

Page 2

2
2009 Fermi Symposium, Washington, D.C., Nov. 2-5
Figure 1: Steepening of the synchrotron spectrum
due to inverse Compton scatterings in
Klein-Nishina regime (from Daigne et al. [2010]).
Using a detailed radiative code, we compute the
synchrotron spectrum for a fixed value wm = 100 of the
parameter measuring the importance of Klein-Nishina
corrections and for a an increasing value of the parameter
YTh measuring the importance of inverse Compton
scatterings (see text). The low-energy photon index is
steepening from −3/2 for low YTh to ∼ −1 for high YTh
(bottom panel). The inverse Compton process remains
energetically sub-dominant as indicated by the inserted
table in the top panel.
is expected that either the synchrotron component at
low energy is dominant (YTh< 1), leading to a bright
prompt optical emission which is not observed, or
that the dominant component is the second inverse
Compton peak (YTh > 1), due to second scatterings
(third and other scatterings are suppressed by Klein-
Nishina effects). This predicts a strong component
that does not seem to be detected by Fermi-LAT
[Piran et al. 2009, Boˇ snjak et al. 2009]. In addition,
the peak energy of the soft γ-ray component is highly
sensitive to the physical conditions in the emitting
region in the SSC scenario, as the typical energy of
inverse Compton photons in Thomson regime is pro-
portional to BΓ4
m, where B is the magnetic field and
Γm the typical Lorentz factor of shock-accelerated
electrons. This leads to a spectral evolution in pulses
in GRB lightcurves which is too rapid compared
to observations [Daigne and Mochkovitch 1998].
the synchrotron scenario, these two problems do not
appear : the spectral evolution is slower and there
is no bright component expected in the Fermi-LAT
range as even the first inverse Compton scatterings
occur in Klein-Nishina regime. Indeed high electron
Lorentz factors are needed to produce synchrotron
In
Figure 2: The low-energy index α of the
fast-cooling synchrotron spectrum (from
Daigne et al. [2010]). Using radiative calculations
including only synchrotron radiation and inverse
Compton scatterings (assuming Γc ≪ Γm), the
low-energy photon index α is plotted as a function of wm
and YTh. For high values of these two parameters it
becomes as steep as −1. Lines of constant ratio of the
luminosity radiated in the inverse Compton component
over the luminosity radiated in the synchrotron
component are also plotted and show that inverse
Compton scatterings are usually energetically
sub-dominant. Note that this ratio should be even lower
when including γγ annihilation.
photons in the soft γ-ray range and therefore, the
parameter wm = Γmhν′
synchrotron frequency of electrons at Γm, is large
(Klein-Nishina corrections become important for
wm> 1).
m/mec2, where ν′
mis the
There is however a well known problem in the syn-
chrotron scenario, related to the low-energy photon in-
dex measured in GRB spectra [Ghisellini et al. 2000].
To reproduce both the high variability and the huge
luminosity in GRB lightcurves, it is necessary that the
relativistic electrons are radiatively efficient, i.e. that
their radiative timescale is shorter than the dynamical
timescale. When only synchrotron radiation is consid-
ered, this condition is equivalent to Γc< Γm, where
Γc is defined as the Lorentz factor of electrons hav-
ing a synchrotron time scale equal to the dynamical
timescale. In this fast-cooling regime, the low-energy
photon index below the peak of νFνis α = −3/2 [see
e.g. Sari et al. 1998], in contradiction with measured
values which are centered around −1 [Preece et al.
2000].
eConf C091122

Page 3

2009 Fermi Symposium, Washington, D.C., Nov. 2-5
3
Figure 3: An example of internal shock dynamics (from Daigne and Mochkovitch [1998]). Left: evolution of the
Lorentz factor distribution within the outflow in Lagrangian coordinates. The initial conditions (relativistic ejection by
the central engine) are described in the text. The formation of two shocks appears clearly. The first ones disappears
rapidly as it reaches the front edge and the second shock crosses the whole ejecta. Right: the physical conditions in the
shocked region are plotted as a function of the observer time tobs/(1 + z) = t − R/c : Lorentz factor Γ∗, comoving
density ρ∗ and specific internal energy density ǫ∗. In addition, the evolution of the magnetic field B′and the electron
Lorentz factor Γm is also indicated for a given set of microphysics parameters.
A typical GRB spectrum is well fitted by a phe-
nomenological function introduced by Band et al.
[1993].Assuming a high-energy photon index
β = −2.3, it is easy to calculate that it is necessary
to remove only ∼ 20% of the energy radiated in the
synchrotron component to move α from −3/2 to
−1. This means that in principle, a sub-dominant
process should be enough to solve the problem. It is
tempting to suggest that inverse Compton scatterings
in Klein-Nishina regime play this role [Derishev et al.
2001].Indeed, Klein-Nishina limitations are more
important for the scatterings of high-energy pho-
tons and therefore the probability to be scattered
increases when the photon energy decreases, leading
to a steepening of the synchrotron spectrum.
Thomson regime (wm < 1), all photons have equal
probability to be scattered and the synchrotron
shape is unaffected.This effect is illustrated in
Fig. 1. The spectra shown in this figure have been
computed using a radiative code developed for the
purpose of GRB studies [Boˇ snjak et al. 2009], that
solves simultaneously the time-evolution of electrons
and photons.For clarity, the calculations done
in Fig. 1 include only synchrotron radiation and
inverse Compton scatterings. Figure 2 illustrates the
evolution of the low-energy photon index α in the
parameter space YTh(importance of inverse Compton
scatterings) versus wm (importance of Klein-Nishina
corrections). These numerical results agree well with
the simplified semi-analytical model developped by
In
Nakar et al. [2009]. It appears then that there is a
large region of the parameter space that allows steep
slopes ranging from −3/2 to −1. Lines of constant
ratio Lic/Lsynare also plotted in Fig. 2 and show that
inverse Compton scatterings remain sub-dominant in
most situations.
These results, which will be discussed in more de-
tails in a paper to be submitted [Daigne et al. 2010],
offer a nice possibility to reconcile synchrotron radi-
ation with GRB observed spectra. However, to go
further and check if the conditions necessary for steep
slopes can indeed be reached in GRBs, one needs to
make some assumptions regarding the physical mech-
anism responsible for the extraction of the energy in
the prompt GRB phase. This is done in the next sec-
tion in the framework of the internal shock model.
3. The expected emission from internal
shocks
We have developped a detailed model of the
emission from internal shocks.
the shock waves is followed using the model by
Daigne and Mochkovitch [1998]. It allows to compute
the evolution of the physical conditions in shocked
regions within the outflow. We use then a standard
parametrization to evaluate the magnetic field and
The dynamics of
eConf C091122

Page 4

4
2009 Fermi Symposium, Washington, D.C., Nov. 2-5
Figure 4: Two examples of a synthetic single pulse burst (from Daigne et al. [2010], Boˇ snjak et al. [2009]).
Using the simulation presented in Fig 3, lightcurves (left) and spectra (right) are computed using two different sets of
microphysics parameters (see text) : ǫe = ǫB = 1/3 and ζ = 3 × 10−3(top) and ǫe = 1/3, ǫB = 5 × 10−3and
ζ = 2 × 10−3. In addition, the top panel above the lightcurves shows the evolution of wm, Γc/Γm and YTh in the
shocked region.
the distribution of relativistic electrons in these
regions : ǫeand ǫBas defined earlier. In addition we
assume that only a fraction ζ of the electrons are ac-
celerated. The radiation produced at a given instant
during the propagation of a shock wave is computed
in the comoving frame using our radiative code,
including the most relevant processes : synchrotron
radiationandself-absorption,
scatterings, γγ annihilation and adiabatic cooling.
Finally we compute the observed flux by integrating
these elementary contributions over equal-arrival
time surfaces. This allows to produce synthetic GRBs
with lightcurves in different channels and spectra
inverse Compton
in different time intervals, and to compare their
properties with observations.
Figure 3 shows the dynamics of internal shocks in
a simple example that leads to a single pulse burst.
It has to be considered as a building block for more
complex lightcurves. The central engine is ejecting
relativistic matter during 2 s, with a constant kinetic
energy flux˙E = 5 × 1053erg/s and a Lorentz factor
which increases from 100 at the beginning of the
ejection to 400 at the end. This ejection leads to the
propagation of internal shocks : the properties in the
shocked medium are also plotted in the same figure.
eConf C091122

Page 5

2009 Fermi Symposium, Washington, D.C., Nov. 2-5
5
Note that some of these properties evolve strongly
(see for instance the magnetic field). This leads to
some spectral evolution in the radiated pulse, as
shown in Fig 4 where the lightcurve and the spectrum
of the emitted GRB are plotted for two different sets
of microphysics parameters (high or low ǫB).
These two examples show several interesting fea-
tures. The dominant component in the spectrum is
the synchrotron component that peaks in the soft γ-
ray range (Fermi-GBM). The evolution of the physical
conditions in the shocked region leads to a decrease of
the peak energy of this component with time. The
expected spectral evolution is therefore reproduced,
at least qualitatively : hard-to-soft evolution in the
pulse, the pulse peaks earlier at higher energy, the
width of the pulse increases at low energy, etc. In ad-
dition to the peak energy, the low-energy index is also
evolving (due to the fact that wmdecreases with time).
For the low ǫBcase (high YTh), as expected from the
previous section, it is steeper than −3/2 for most of
the pulse (∼ −1.2 → −1.1 for this example). Due to
the high values of wm, the additional inverse Compton
component is initially limited by Klein-Nishina effects
and is very weak. However, this limitation is reduced
at later times and in the case with a low ǫB (high
YTh), this leads to the delayed emergence of a well
identified additional component in the spectrum at
high-energy (Fermi-LAT range). Such a variable ad-
ditional component at high-energy, delayed compared
to the GBM lightcurves, is observed in a good fraction
of LAT bursts (see e.g. Abdo et al. [2009]). Note that
there is also a weaker precursor in the GeV range in
the second example. This is due to the assumed shape
of the initial distribution of the Lorentz factor in the
outflow (see Fig. 3) that leads to an internal shock
which is only mild initially and become more violent
later. This precursor disappears in simulations done
assuming a steeper variation of the Lorentz factor in
the initial ejecta. On the other hand, the delayed GeV
emission at the end of the pulse is a generic feature
as it is directly related to a propagation effect (espe-
cially the decrease of the magnetic field with distance).
All these calculations are done assuming constant mi-
crophysics parameters during the shock propagation,
which is not necessarily the case. Then depending on
the evolution of these parameters it could either am-
plify or reduce the behaviour presented in these two
examples.
4. Discussion and conclusion
We have presented a detailed model of the emission
from internal shocks propagating within a relativistic
outflow and applied it to the prompt emission from
GRBs. In this framework, recent observations, in-
cluding the detection of a few GRBs by Fermi-LAT,
strongly favor the situation where the dominant radia-
tive process is synchrotron radiation. We show that
inverse Compton scatterings in Klein Nishina regime
should occur and can steepen the low-energy photon
index of the synchrotron component from −3/2 to −1,
which is in better agreement with observations. In
addition, we show that the model has the capacity
to reproduce the spectral evolution observed in pulses
in the soft γ-ray range (GBM) and predict, for low
values of ǫBthe presence of a variable additional com-
ponent in the GeV range which emerges with a delay
due to an initial limitation of inverse Compton scat-
terings by the Klein-Nishina effect. This scenario of-
fers a possible explanation to several features observed
in the lightcurve of the bursts detected by Fermi. It
also puts interesting constraints on the microphysics
parameters and therefore on the physics of shock ac-
celeration.
References
R. Sari and T. Piran, ApJ 485, 270 (1997).
M. J. Rees and P. M´ esz´ aros, ApJL 430, L93 (1994).
M.Lyutikov andR.Blandford
ph/0312347.
F. Daigne and R. Mochkovitch, MNRAS 336, 1271
(2002).
F. Daigne et al., to be submitted in A&A (2010).
T. Piran, R. Sari, and Y. Zou, MNRAS 393, 1107
(2009).
ˇZ. Boˇ snjak, F. Daigne, and G. Dubus, A&A 498, 677
(2009).
F. Daigne and R. Mochkovitch, MNRAS 296, 275
(1998).
G. Ghisellini, A. Celotti, and D. Lazzati, MNRAS
313, L1 (2000).
R. Sari, T. Piran, and R. Narayan, ApJL 497, L17+
(1998).
R. D. Preece, M. S. Briggs, R. S. Mallozzi, G. N.
Pendleton, W. S. Paciesas, and D. L. Band, ApJS
126, 19 (2000).
D. Band,J. Matteson,
D. Palmer, B. Teegarden, T. Cline, M. Briggs,
W. Paciesas, G. Pendleton, et al., ApJ 413, 281
(1993).
E. V. Derishev, V. V. Kocharovsky, and V. V.
Kocharovsky, A&A 372, 1071 (2001).
E. Nakar, S. Ando, and R. Sari, ApJ 703, 675 (2009).
A. A. Abdo et al., Science 323, 1688 (2009).
(2003),astro-
L. Ford, B. Schaefer,
eConf C091122