Issue |
A&A
Volume 511, February 2010
|
|
---|---|---|
Article Number | A43 | |
Number of page(s) | 11 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361/200913134 | |
Published online | 05 March 2010 |
Spectral-luminosity relation within individual Fermi gamma rays bursts
G. Ghirlanda1 - L. Nava1,2 - G. Ghisellini1
1 - INAF - Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807
Merate, Italy
2 - Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como,
Italy
Received 17 August 2009 / Accepted 2 November 2009
Abstract
We study the spectra of all long gamma ray bursts (GRBs) of known
redshift detected by the Fermi satellite untill the
end of July 2009.
Their fluxes and fluences are large enough to allow a time dependent
study of their spectral characteristics in the 8 keV-1 MeV
energy range. We find that the peak energy
of their EL(E) spectrum
correlates with the luminosity in a remarkably tight way within
individual bursts. This time-resolved
correlation is very similar for all the considered bursts and has a
slope and normalisation similar to the analogous
correlation defined by the time-integrated spectra of different bursts
detected by several different satellites. For a few of the considered
GRBs, we could also study the behaviour of the
correlation during the rising and decaying phases of individual pulses
within each burst, finding no differences. Our results indicate the
presence of a similar physical mechanism, operating for the duration of
different GRBs, tightly linking the burst luminosity with the peak
energy of the spectrum emitted at different times. Such a physical
mechanism is the same during the rise and decay phase of individual
pulses composing a GRB. While calling for a robust physical
interpretation, these results strongly indicate that the
spectral energy correlation found considering the time-integrated
spectra of different bursts is real and not the result of instrumental
selection effects.
Key words: stars: gamma-rays bursts: general
1 Introduction
One of the key properties of the prompt emission of gamma ray bursts
(GRBs) that is still poorly understood concerns the spectral-energy
correlations found when considering the time-integrated spectra of
bursts
of known redshift. For these we can define the peak energy of
the spectrum, ,
in an EL(E) representation. The
peak energy
correlates with the isotropic luminosity
(Yonetoku et al. 2004),
with the isotropic energy
(Amati et al. 2002),
and more tightly with the collimation-corrected energy
(Ghirlanda et al. 2004b).
There are two very strong motivations for studying these correlations.
One is to understand their physical origin, which can disclose a still
not understood basic property of GRBs (Yamazaki et al. 2004; Lamb
et al. 2005;
Rees & Meszaros 2005;
Levinson & Eichler 2005;
Toma et al. 2005;
Eichler & Levinson 2006, 2004; Barbiellini et al. 2006;
Thompson 2006;
Ryde et al. 2006;
Giannios & Spruit 2007;
Thompson et al. 2007;
Guida et al. 2008;
Panaitescu 2009)
and the other is the possibility of using these correlations to
standardise the GRB energetics, making them cosmological tools
(Ghirlanda et al. 2004a,
2006a,b;
Firmani et al. 2005,
2006, 2007; Xu
et al. 2005; Liang & Zhang 2005, 2006; Wang
& Dai 2006;
Amati et al. 2008;
Kodama et al. 2008;
Qi et al. 2008;
Li et al. 2008;
Liang et al. 2008).
The debate about the reality of these correlations is strong, since some authors have pointed out that they can be the result of observational selection effects (Nakar & Piran 2005; Band & Preece 2005; Butler et al. 2007; Butler et al. 2009; Shahmoradi & Nemiroff 2009), while others argue that selection effects, even if surely present, play a marginal role (Ghirlanda et al. 2005; Bosnjak et al. 2008; Ghirlanda et al. 2008; Nava et al. 2008; Krimm et al. 2009; Amati et al. 2009).
One possibility for some insight into this issue is to study
individual, bright bursts to see whether the
luminosity and peak energy at different times during the prompt phase
correlate.
If they do, and furthermore if the slope of this time-resolved
correlation (indicated
hereafter)
is similar to the time-integrated
correlation found among different bursts, then we should conclude that
the spectral energy correlations
are surely a manifestation of the physics of GRBs and not the result
of instrumental selection effects.
Table 1: Fermi long GRBs with redshift.
Some attempts have already been made. Liang et al. (2004) considered
BATSE bursts without known redshifts and show a correlation between the
(observer frame) peak energy and the flux within individual bursts,
which they interpret as suggestive of a physical origin of the
correlation holding among the GRBs with measured redshift. However, to
directly compare the
correlations of individual GRBs with the
correlation defined with time-integrated spectra, it is necessary to
know the redshift (which is instead unknown for most of BATSE bursts).
Recently, Firmani et al. (2009), have
considered Swift bursts of known redshift and find
a rather strong
correlation within individual GRBs. Having the redshift, they could
directly compare the time-resolved correlation of different bursts,
finding that the ensemble of data points in the
plane shows a correlation similar to that defined with the
time-integrated spectra of the same burst sample. Because of its
limited energy range (15-150 keV), however, the Burst Alert
Telescope (BAT) onboard Swift is not particularly
suited to GRB spectral analysis, especially when dealing with
time-resolved spectra. To overcome this limitation, Ohno
et al. (2009)
combine the Swift-BAT and Suzaku-WAM
spectral data to study the spectral evolution of GRB 061007 and
investigate the time evolution of the
correlation within the two pulses of this burst. They find that the
time-resolved pulses also satisfy the
correlation defined by time-integrated spectra. A more systematic
analysis of the time-resolved spectral properties of Swift-Suzaku
GRBs (Krimm et al. 2009)
shows that individual pulses within a GRB are consistent with the
correlation defined by the time-averaged spectra. They consider the
spectra integrated over the duration of individual pulses. In this case
is computed
on different integration timescales. They find that the pulses follow a
correlation parallel to the
defined with time-integrated spectra, but with a higher normalisation.
Instead, the comparison of time-resolved spectra with the
correlation is independent of the spectral integration time since this
correlation involves the luminosity
rather than the energy
.
It is therefore important to study the presence of a
correlation (as done by Ohno et al. 2009, for a single
event) by concentrating on GRBs with measured redshift, in order to
compare their time-resolved
correlation with that defined with the time-integrated spectra. In
particular we aim at studying how single GRBs evolve in the
plane rather than considering them globally (as in Firmani
et al. 2009).
Furthermore, we would like to study the rise and decay phases of
individual pulses.
Table 2: The 5 non- Fermi GRBs added in this work to the pre- Fermi list of 90 GRBs from Ghirlanda et al. (2009).
Table 3: Correlation analysis results.
![]() |
Figure 1:
The 10 Fermi-GRBs with redshift and |
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The Gamma ray Burst Monitor (GBM, Meegan et al. 2009) onboard
the Fermi satellite covers a wide energy range
(8 keV-30 MeV) and, although slightly less sensitive
than Swift/BAT, it is better for studying the
spectral properties of the prompt emission of GRBs. In addition, the
Large Area Telescope (LAT) sensitive in the 0.1-100 GeV
energy range can complement the spectral information for the few bursts
it can detect.
In one year of operation (up to the end of July 2009), Fermi/GBM
detected about 200 bursts
and, for about half of them, the (time-integrated) spectral analysis
returned a well-defined .
In this paper we study Fermi GRBs,
selecting those of known redshift, to be able to compare their
different evolutionary tracks in the
plane with the correlation defined by the time-integrated spectra (see
e.g. Ghirlanda et al. 2009, for a
recent compilation of the
correlation). For the brightest bursts we study whether the rising and
decaying phases
of individual pulses behave differently in the
plane, since this can give
important clues for a physical understanding of the emission mechanism
operating during the GRB prompt phase.
The paper is organised as follows.
In Sect. 2 we describe our Fermi GRB
sample, whose time-integrated spectral properties are presented in
Sect. 3 and compared to the
and
correlation defined by pre-Fermi GRBs.
In Sect. 4 we describe the time-resolved spectral analysis
whose results are given in Sect. 5. In Sect. 6 we
discuss our findings and draw our conclusions.
A standard cosmology for a flat universe with
is assumed.
2 The sample
We considered the GRBs detected by the GBM (up to the end of July 2009) of known redshift. They are 13 events. Among these GRB 090510 (z = 0.903, Rau et al. 2009) is a short burst, with an observer frame duration of less than 2 s, so it will not be considered here.
Table 1
lists the 12 long GRBs, their dates and fraction of the day of the
burst trigger (Col. 1), their time-integrated spectral parameters
(Cols. 3 to 8),
the derived isotropic luminosity (
,
Col. 10) and isotropic energy (
,
Col. 11), computed in the rest frame
1 keV-10 MeV energy range. The spectral parameters in
Table 1
have been collected from the literature (references are given
Col. 9), as obtained through the analysis of the
time-integrated spectrum extracted from the GBM data.
In two cases (GRB 080905 - Bhat et al. 2008b; and GRB
080928 - Paciesas et al. 2008), the
time-integrated spectrum is fitted by a single power law and,
therefore, the peak energy is unconstrained.
In five cases the time-integrated spectrum is modelled with a power law
ending with an exponential cutoff at high energies. In the remaining
five cases it is modelled by a Band function.
Two of the three GRBs detected by the LAT (in boldface in
Table 1)
belong to the latter group (i.e. GRB 080916C, Tajima et al. 2008; Abdo
et al. 2009;
and GRB 090328, Cutini et al. 2009). These
bursts show a high-energy power-law component, and their observed peak
energies
are the largest of the sample. Table 1 also lists the most
distant burst: GRB 090423, with z=8.2 (Tanvir
et al. 2009;
Salvaterra et al. 2009).
3
Time-integrated spectra: the
and the
correlations
First, we check the consistency of Fermi bursts
with the 


Figure 1
shows the pre-Fermi bursts (grey filled circles) in
the
and
planes. In both planes they define a strong correlation (the
probability that the correlation is by chance is reported in
Col. 4 of Table 3),
confirming recent analysis (Ghirlanda et al. 2009). The
slope and normalisation of the fit of these correlations with a power
law are reported in Table 3.
To show where the Fermi bursts lie in
these planes we estimated
and
using the spectral parameters reported in the literature and listed in
Table 1,
excluding the two GRBs fitted with a single power law (i.e. with an
unconstrained
).
Figure 1
shows that the position of Fermi bursts is
consistent with both correlations (see also Amati et al. 2009). We fitted
the 95 pre-Fermi GRBs, the 10 Fermi
GRBs, and the combined sample of 105 GRBs with the least square method.
The best-fit spectral parameters (normalisation K
and slope
and their 1
errors) and the probability that the correlation is by chance (P)
are reported in Table 3.
4 Time-resolved spectra: data analysis
The data of GRBs detected by the GBM since August 2008 are publicly available at http://fermi.gsfc.nasa.gov/. The GBM consists of 12 NaI and 2 BGO scintillation detectors oriented differently so as to derive the GRB position through the comparison of the count rates of the different detectors. The NaI cover the low-energy spectral domain from 8 keV to

For our analysis we considered the TTE (time-tagged event) files containing the counts in 128 energy channels relative to the burst period. We considered the TTE files of the two NaI detectors triggered by the GRB. From these we extracted the GRB light curve and the time-resolved spectra with the gtbin tool (as part of the ScienceTools-v9r8p2-fssc-20090225). Light curves were extracted by summing the count rates over the 8 keV-1 MeV energy range of the NaI detectors that were triggered and the 200 keV-30 MeV energy range of the 2 BGO detectors. Time bins of 1 s were adopted for all bursts. Light curves were rescaled in time to the trigger time of the GRB.
Figure 2
shows the burst light curves. In the case of GRB 081007, the data
present in the GBM catalogue 081007(224) refer to GRB 081007B, which
had very low statistics (Bissaldi et al. 2008). We
could not find the data directory of GRB 081007 that triggered Swift
(Baumgartner et al. 2008) and Fermi
(Bissaldi et al. 2008)
121 s after GRB 081007B. We only report in Table 1 the time-integrated
spectral results of GRB 081007 (Bissaldi et al. 2008). We also
note that Fermi and Swift both
detected a GRB on November 18, 2008. These are, however, two events
that coincide neither spatially nor temporally:
and
is the location (with an uncertainty of 1.6
- Palmer et al. 2008)
of the event detected by Swift at 14:56:36 UT
(Hoversten et al. 2008)
while the Fermi event is located at
and
(with an uncertainty of
)
and was detected at 21:00:53.5 UT (Bhat et al. 2008a). Only for
the Swift GRB is the redshift measured (z=2.58,
D'Elia et al. 2008,
no
measured).
![]() |
Figure 2: Fermi light curves of the bursts with known redshift detected by the GBM from August 2008 to July 2009. Light curves have a time resolution of 1 s and are not background-subtracted. The vertical dotted lines mark the time intervals selected for the extraction of the time-resolved spectra. The light curve of GRB 081007 is not reported because the data of this burst could not be found. |
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For the scope of this work, we do not subtract the background count rate from the light curves, they are only used here to show the time intervals within single GRBs selected for the extraction of time-resolved spectra. For 3 GRBs (080905, 080928 and 090423), the count rate is too low to perform a time-resolved spectral analysis. In all the other cases (except GRB 081007), we could divide the light curve into time intervals as indicated in Fig. 2. For GRB 080916C we used the time-resolved spectral analysis results reported by Abdo et al. (2009) who combined the GBM and the LAT data. Spectra of the triggered detectors were extracted over the selected time intervals defined with the gtbindef tool. The spectrum of the background was extracted in a time interval after the burst to limit the GRB contamination. Rebinning (with the grppha(v3.0.1) tool) was applied to each spectrum to have a minimum of 40 counts per energy channel.
The response files corresponding to each detector were used
for the spectral fitting. Spectra were analysed with Xspec(v12)
in the range 8 keV to 1
MeV.
For most GRBs the spectra of the two (or more) NaI triggered detectors
were jointly fitted with a cutoff-power law model (CPL)
of the form
with a free normalisation constant for the spectra of the two or more
detectors jointly fitted. Most of the fits give a value close to 1 for
this constant.
The CPL has been widely used to fit the spectra of GRBs, in particular
the time-resolved spectra (Preece et al. 2000; Ghirlanda
et al. 2002;
Kaneko et al. 2006).
We only analysed the spectra of the NaI detectors because, in
most bursts, the inspection of the BGO light curve did not show any
evident signal. Morever, the lower sensitivity of the BGO detectors
with respect to the NaI ones would lead, in extracting simultaneous
spectra for a joint fit, to much fewer time-resolved spectra.
![]() |
Figure 3:
Time-resolved |
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We performed a time-resolved spectral analysis for 8 GRBs of
Table 1.
Note that also the BATSE time-resolved spectra are often fitted with
the CPL function (e.g. Kaneko et al. 2006; Nava
et al. 2008).
For the purpose of comparing the spectral evolution of different bursts
in the
plane, the use of the same spectral model ensures that the possible
biases, e.g. the overestimate of the peak energy with respect to the
Band model (Band et al. 1993),
is a common systematic effect of all the analysed spectra (e.g. see
Kaneko et al. 2006).
In any case, we also verified if our time-resolved spectra could be
consistent with the Band model, finding that, in most cases, we could
not constrain the high-energy power law slope of this model. This also
motivated us to choose the minimal simplest model, i.e. the CPL.
We computed the isotropic luminosity of each time-resolved
spectrum by integrating the best fit spectral shape over the rest frame
1 keV-10 MeV energy range. This represents the mean luminosity of each
time-resolved spectrum.
Table A.1
reports the results of the time-resolved analysis: Cols. 2
and 3 give
the start and stop times of the time-resolved spectra, Cols. 4 and 5
give the photon spectral index
and the characteristic energy E0
(with their 90% significance errors), respectively.
5 Results
5.1 Evolutionary tracks
Figure 3
shows the evolutionary tracks of the 8 Fermi GRBs
with redshift for which time-resolved spectral analysis was possible.
The number of time-resolved spectra extracted per burst depends on its
total fluence. Our guideline in defining the time intervals was a
trade-off between the need to follow the rise and decay phases of the
single pulses within the light curve and to have enough signal in each
time-resolved spectrum to constrain its spectral parameters. In two
bursts (GRB 090424 and GRB 090618), a denser sampling of the light
curve is possible given their large fluence. We limited the number of
time bins to have a neater evolutionary track in the
plane, while in the next subsection
we discuss their time evolution in full detail.
For GRB 090323 the time-resolved spectra up to
100 s after the trigger are best fitted by a
simple power-law model, while only after 100 s can a curved
model (CPL) be fitted and the value of the peak energy constrained.
Therefore, for GRB 090323 we show in Fig. 3 only the spectral
evolution of the final peaks (those after 100 s in the corresponding
light curve of Fig. 2).
Figure 3
shows that the prompt spectrum evolves in a well-defined way and that
and
are correlated.
The entire evolutionary tracks of all
the 8 bursts we
studied lie within the 3
stripe of the scatter of the
correlation
defined by the time-integrated spectra of different bursts.
Figure 3
contains data points that are associated both to
the rising or descending parts of the bursts, although they are
difficult
to distinguish. We show in the next section the results of a finer
time-resolved spectral analysis on two of the brightest bursts of our
sample, demonstrating that there appears to be no difference between
the rising and decaying parts of the pulses.
Since
is a derived quantity, as
,
it is interesting to verify if the
correlation is the result
of underlying correlations of E0
and/or
with
.
The left panel of Fig. 4
shows the rest frame energy
as a function of the luminosity for the time-resolved spectra and for
the corresponding time integrated-spectra (same symbols as in
Fig. 3).
The right panel of Fig. 4
shows the low-energy spectral index
versus the luminosity
.
We can see that
shows no correlation with
when
considering the ensemble of bursts (but see below the case of
the single pulse of GRB 090618), while E0
does.
We can conclude that indeed
(or E0, i.e. the e-folding
energy of the CPL model) is the spectral parameter correlating with
.
From the right panel of Fig. 4
we also see that the low-energy photon index of the time-integrated and
time-resolved spectra of the analysed Fermi GRBs
are consistent with the -2/3 limit predicted by synchrotron emission,
while they violate the -3/2 synchrotron limit for fast cooling
electrons (Ghisellini et al. 2000).
We analysed the
correlations obtained with the time-resolved spectra. In
Table 3
we report the normalisation and slope (K and
,
respectively) and the chance probability P of the
correlation. In total we have 51 time-resolved spectra for the
8 GRBs. They define a correlation in the
plane with a slope
(Fig. 3)
consistent with the slope of the correlation defined with the
time-integrated spectra (i.e.
for the 95 pre-Fermi GRBs - solid line in
Fig. 3 -
or
for the total of 105 GRBs including the Fermi
events - dot-dashed line in Fig. 3).
![]() |
Figure 4:
Left panel:
the rest frame energy |
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![]() |
Figure 5:
High time resolution spectral analysis of GRB 090424 (left)
and of GRB 090618 (right). Top:
light curve (0.1 s resolution) and time intervals of the
extracted spectra (vertical dotted lines). The coloured symbols
represent the spectra highlighted in the panels below. Spectral
evolution panels (from top to bottom): rest frame
peak energy |
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5.2 Rising and decaying phases of single pulses
GRB 090424 consists of two overlapped peaks. Its total duration is 6 s. GRB 090618 has a complex light curve made of a smooth precursor followed by two intense peaks partially overlapped (see Fig. 2) for a total duration of 150 s. Their high count rates allow a time-resolved spectral analysis with a dense time sampling. These two GRBs are well-suited to studying how the spectrum evolves during the rise and decay phases of their pulses.
We divided the time interval of the duration of GRB 090424 so
that each extracted spectrum had a signal-to-noise ratio ,
integrated over the 8 keV-1 MeV energy range. This
gives a total of 42 spectra distributed in the
6 s of
duration of GRB 090424. For GRB 090618 we required an S/N ratio of 50
and obtained 34 time-resolved spectra in the 150 s of its
duration. These spectra were extracted and analysed as described in
Sect. 3. In Fig. 5
the light curve (with 0.1 s time resolution) and the three
panels of the correlation between the spectral parameters (
,
E0 and
)
and the luminosity
are shown for GRB 090424 (left) and GRB 090618 (right). In these plots
we have marked the spectral evolution of the different peaks identified
in the light curve with different symbols and the rise and decay phase
of single pulses with different colours. The different peaks were also
fitted individually in the
plane (second panels of Fig. 5)
and the results are shown in Table 3. These 4 peaks (two
of GRB 090424 and two of GRB 090618) define a very
tight
correlation with slope between 0.45 and 0.6.
These plots indicate that the rising and decaying
phases are indistinguishable in a
plot. Intriguingly, we also find that there is a correlation
between
and
for GRB 090618.
Since E0 also correlates
with
(as for the other bursts),
this results in an even tighter
correlation for the two pulses of this GRB.
6 Discussion and conclusions
The largest sample of long GRBs with measured redshift and












6.1 Selection effects
The sample of bursts defining the







Two selection effects were considered for the detectors onboard BATSE, BeppoSAX,
and Swift: (i) the trigger threshold, i.e. the
minimum flux a burst must have to trigger a given detector; and (ii)
the spectral threshold, i.e. the minimum fluence a burst must have to
constrain its spectral parameters (in particular the peak energy ).
Our results indicate that: (i) both the selection effects are functions
of
but the spectral threshold dominates the trigger threshold, implying
that the
or
correlations do not come from the trigger threshold; (ii) the Swift
spectral threshold is biasing the Swift GRB sample
with redshift added to the
correlation in the last three years; (iii) selection effects are
present but do not determine the spectral-energy correlations. Point
(ii), in particular, stems from the limited energy range of the BAT
instrument onboard Swift, which limits the
possibility of a reliable estimate of the burst spectral shape and,
particularly, of the peak energy. This limits the use of the Swift
burst sample to draw any firm conclusion on the incidence of selection
effects on the spectral-energy correlations (see Nava
et al. 2008).
Another way to test the incidence of selection effects on the
and
correlation is to verify how much the slope, normalisation, and scatter
change by separating the heterogenous sample of GRBs with redshift into
subsamples of bursts detected by different instruments (e.g. Butler
et al. 2007).
Butler et al. (2007)
find similar slopes but different normalisations of the
correlation by considering the pre-Swift and the Swift
sample (but see Amati et al. 2009).
Unfortunately, Swift bursts have a very narrow
range of
limiting the robustness of this test (Nava et al. 2008).
Furthermore, different instruments like BATSE and BeppoSAX
can have very similar detector thresholds and bias, in a similar way,
the GRB samples that they detect.
6.2
Time-resolved
correlation
All the spectral-energy correlations have been derived considering the
time-integrated GRB spectral properties. By studying the spectral
evolution of the 8 Fermi GRBs with measured
redshift, we also find that a correlation
between the rest-frame peak energy
and the bolometric isotropic luminosity exists within individual bursts
(Fig. 3).
This
correlation can also extend over two orders of magnitude in both
and
within the duration of a burst. The evolutionary tracks defined by the
8 Fermi GRBs lie in the upper part of the
correlation. This could be caused by a systematic underestimate of the
luminosity in time-resolved spectra with respect to time-integrated
spectra (which are used to define the
correlation plotted as a solid line in Fig. 3). Indeed, the
time-resolved spectra are more frequently fitted with a CPL model that
lacks the high-energy power law component of time-integrated spectra.
The finding of a
correlation within individual GRBs, consistent with the
correlation defined by time-integrated spectra, is the strongest
argument in favour of a physical origin of this correlation and the
strongest argument against instrumental selection effects biasing the
observed correlations.
6.3 Interpretations of the spectral-energy correlations
A convincing way to ensure the reality of the spectral-energy
correlations would be to find a robust physical interpretation. The
proposed interpretations of the
and
correlations can be divided into two classes: (a) kinematic
interpretations in which the link between
and
is established by the configuration of the emission region, i.e. a
uniform jet observed at different angles (Yamazaki et al. 2004), an
inhomogeneous jet model (e.g. Nakamura 2000; Kumar & Piran
2000) made up of multiple sub-jets or emission patches (Toma
et al. 2005),
or a ring-shaped emission region (Eichler & Levinson 2004); (b)
radiative interpretations in which it is the emission mechanism of the
prompt phase to link
and
,
as in the case of a spectrum dominated by a thermal component (Meszaros
& Rees 2007;
Ryde et al. 2006;
Thompson et al. 2007),
in the case of photospheric emission dominated by magnetic reconnection
(Giannios & Spruit 2007)
or when the emission is synchrotron radiation from the external shock
(Panaitescu et al. 2009).
The common feature of the kinematic models in reproducing the
or
correlation is the viewing angle under which different GRBs are
observed. Both the off-axis and the sub-jet models need to assume the
existence of an on-axis correlation between the peak energy and the
luminosity, whose origin could be instead related to the radiative
process. Indeed, the kinematical models that (under some assumptions
about the typical jet opening angle distribution) succeed in
reproducing
should still explain a similar correlation within individual GRBs, i.e.
a time-dependent correlation
,
which can extend over 2 orders of magnitude (e.g.
Fig. 4).
The simplest way to explain the
correlation is to assume that only the bulk Lorentz factor
changes.
Since
and
,
we recover
.
But this assumes that, in the comoving frame, both
and
are the same even if different
-factors are
required, and this seems unlikely (both when considering the
correlation defined by different bursts or the
correlation holding within individual GRBs).
If the emission comes from the synchrotron process, the peak
frequency
(where
is the random Lorentz factor of the electrons emitting at the peak) and
,
where N is the number of the electrons having
.
Therefore a change in the quantity
,
maintaining the same
and N, would give
.
But the prompt emission almost surely occurs in the fast cooling
regime, implying that the resulting synchrotron spectrum cannot be
harder than
(Ghisellini et al. 2000),
while we also observe (e.g. Preece et al. 2000; Ghirlanda
et al. 2003)
in the Fermi GRBs (Fig. 4 right panel) much
harder spectra. Furthermore, it seems hard to maintain the same N
and
while changing
.
Quasi-thermal Comptonization could well explain how both E0
and
correlate with L, as found in GRB 090618.
In fact, if the seed photons for Compton scattering remain the same, an
increase in the plasma temperature would increase the Comptonization
parameter
,
producing both a harder spectrum and a higher
(
is the optical depth of scattering electrons, and
their temperature). On the other hand, for likely bulk Lorentz factors
,
the comoving temperature is below 1 keV, implying
to reach the required
,
needed to account for the observed flat spectra. With this value of
,
the resulting spectrum would saturate to a Wien-like
spectrum, not to a cutoff power law. A very high value of
would also lengthen any variability timescale.
It has been suggested (e.g. Borgonovo & Ryde 2001; Ryde
& Petrosian 2002)
that the off-latitude emission that follows an abrupt switch-off of the
fireball introduces a spectral-energy dependence, since the observer
sees progressively less beamed (and less blue-shifted) emission.
However, this could explain only the decaying phase
of the pulse. We analysed the spectral evolution of two of the most
intense bursts in our sample. They allow to make a dense sampling of
their light curves in order to extract time-resolved spectra. These are
GRB 090424 and GRB 090618 (Fig. 4 right and left
panels, respectively). Our findings indicate clearly that there is the
same
correlation during the rise and the decay phases of different pulses
within these two GRBs. The time evolution is such that during the rise
phase both
and
increase to the maximum value and during the decay they decrease along
the same evolutionary track that they followed during the rise phase.
In the case of GRB 090618, these considerations are also valid for the
correlation between
and
(bottom right panel of Fig. 4).
In the attempt to explain the
correlation, Thompson Meszaros & Rees (2007) point
out the importance of shear layers shocks to extract a large fraction
of the bulk kinetic energy of the fireball, leading to a black body
spectrum. The same arguments could be used to explain the
correlation, in different bursts and the
correlation within individual bursts as well. The problem with this
interpretation is that one of the key assumptions of their scenario is
that the value of the bulk Lorentz factor in the dissipation region
must be fine-tuned (i.e., of the order of
,
where
is the opening angle of the fireball). This assumption is relaxed in
the ``reborn fireball" scenario (Ghisellini et al. 2007), but it
remains to be explained why so few bursts have pure black body spectra
(Ghirlanda et al. 2003),
and, even when adding a power-law component (Ryde et al.
2005), its slope is too soft to explain low-energy data (in the keV
band), as shown by Ghirlanda et al. (2007).
We can conclude that new ideas are called for to explain what emerges to be a general and well-defined property of the prompt emission of GRBs.
AcknowledgementsWe are grateful to the referee for useful comments. We thank Z. Bosnjak, D. Burlon, A. Celotti, C. Firmani, M. Nardini and F. Tavecchio for stimulating discussion. ASI is thanked for grant I/088/06/0. A PRIN-INAF grant is acknowledged for funding. This research made use of the Fermi-Gamma Burst Monitor data publicly available via the NASA-HEASARC data center.
Appendix A:
Table A.1: Spectral results of the time-resolved analysis.
Table A.2: Spectral evolution. Continued.
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All Tables
Table 1: Fermi long GRBs with redshift.
Table 2: The 5 non- Fermi GRBs added in this work to the pre- Fermi list of 90 GRBs from Ghirlanda et al. (2009).
Table 3: Correlation analysis results.
Table A.1: Spectral results of the time-resolved analysis.
Table A.2: Spectral evolution. Continued.
All Figures
![]() |
Figure 1:
The 10 Fermi-GRBs with redshift and |
Open with DEXTER | |
In the text |
![]() |
Figure 2: Fermi light curves of the bursts with known redshift detected by the GBM from August 2008 to July 2009. Light curves have a time resolution of 1 s and are not background-subtracted. The vertical dotted lines mark the time intervals selected for the extraction of the time-resolved spectra. The light curve of GRB 081007 is not reported because the data of this burst could not be found. |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Time-resolved |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Left panel:
the rest frame energy |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
High time resolution spectral analysis of GRB 090424 (left)
and of GRB 090618 (right). Top:
light curve (0.1 s resolution) and time intervals of the
extracted spectra (vertical dotted lines). The coloured symbols
represent the spectra highlighted in the panels below. Spectral
evolution panels (from top to bottom): rest frame
peak energy |
Open with DEXTER | |
In the text |
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