A&A 487, 503-508 (2008)
X. W. Liu1,2,3 - X. F. Wu1,2,3,4 - T. Lu1,2,3
1 - Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, PR China
2 - National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, PR China
3 - Joint Center for Particle Nuclear Physics and Cosmology of Purple Mountain Observatory - Nanjing University, Nanjing 210008, PR China
4 - Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125, USA
Received 3 October 2007 / Accepted 15 May 2008
Aims. The high-redshift (z=4.048) gamma-ray burst GRB 060206 showed unusual behavior, with a significant rebrightening by a factor of 4 at about 3000 s after the burst. We argue that this rebrightening implies that the central engine became active again after the main burst produced by the first ejecta, then drove another more collimated jet-like ejecta with a larger viewing angle. The two ejecta both interacted with the ambient medium, giving rise to forward shocks that propagated into the ambient medium and reverse shocks that penetrated into the ejecta. The total emission was a combination of the emissions from the reverse- and forward- shocked regions. We discuss how this combined emission accounts for the observed rebrightening.
Methods. We apply numerical models to calculate the light curves from the shocked regions, which include a forward shock originating in the first ejecta and a forward-reverse shock for the second ejecta.
Results. We find evidence that the central engine became active again 2000 s after the main burst. The combined emission produced by interactions of these two ejecta with the ambient medium can describe the properties of the afterglow of this burst. We argue that the rapid rise in brightness at 3000 s in the afterglow is due to the off-axis emission from the second ejecta. The precession of the torus or accretion disk of the central engine is a natural explanation for the departure of the second ejecta from the line of sight.
Key words: gamma rays: bursts - gamma rays: theory - gamma rays: observations
- began to observe this burst 58 s after the BAT trigger time. At the same time, -UVOT started the on-target monitoring and detected the optical afterglow (Boyd et al. 2006). A number of ground-based telescopes performed follow up observations. The 2-m robotic Liverpool Telescope began to observe it at t=309 s and carried out multicolor r'i'z' photometry. In the R-band the light-curve exhibited three obvious bumps in the first 75 min including a steep rise ( at s) (Monfardini et al. 2006). About 48.1 min later after the trigger time, the Rapid Telescopes for Optical Response (RAPTOR) system at Los Alamos National Laboratory began to take optical images. The obtained light curve confirmed the rebrightening from to a peak value . The subsequent decline to at t=80 min was followed by a secondary rebrightening by around t=90 min ( et al. 2006). The MDM telescope observed a smooth break at days with another bump at s. The overall X-ray light curve has a similar shape as the optical light curve (Stanek et al. 2007).
One of the most remarkable features of this burst is that the optical light curve had a significant rebrightening and exhibited small ``bumps'' and ``wiggles''. Similar bumps and wiggles have also been seen in a number of optical afterglows (Stanek et al. 2007). GRB 970508 had an optical afterglow light curve rather similar to that of GRB 060206 (Galama et al. 1998). The optical light curve of another recent burst, GRB 060210, also displayed a rebrightening at time s and a shallow decay in the early epoch. The above ``unusual'' behavior, which is not predicted by the standard fireball model, may be more the norm than the exception (Stanek et al. 2007).
Possible scenarios for the remarkable rebrightening in GRB 060206 at 3000 s are a renewed energy injection (Rees & Mészáros 1998; Kumar & Piran 2000; Sari & Mészáros 2000) and a density-jump in the circum-burst medium (Dai & Lu 2002). However, as discussed by Monfardini et al. (2006), the X-ray band frequency is above the cooling frequency at s, so the flux does not depend on the ambient density (Freedman & Waxman 2001). Nakar & Granot (2007) showed that even a sharp and large increase in the ambient medium density cannot produce a significant rebrightening as seen in the afterglow. So the rebrightening cannot be due to a density jump in the ambient medium. If the rebrightening is caused by energy injection, a huge impulsive energy injection at 3000 s was required, where E0 is the blast wave energy before the rebrightening.
In this paper, we present an alternative scenario. The central engine of this burst become active again after the initial burst and ejects another more collimated jet with a larger viewing angle. This jet and the initial jet sweep up the interstellar medium (ISM). The multi-wavelength emission predicted by this model can reproduce both the observed X-ray and optical data. The observational results are presented in Sect. 2. We describe the scenario in Sect. 3 and fit the remarkable optical rebrightening of GRB 060206 in Sect. 4. Finally, we summarize our results and discuss their implications in Sect. 5.
Multi-epoch spectral energy distribution (SED) analysis revealed either an SED evolution or an additional unresolved activity (or both) during the early time interval from s to s based on the i' and z' photometric data (Monfardini et al. 2006). At a later time, the infrared to X-ray fluxes (after a significant rebrightening) can be fitted by a single power law with a spectral index . However, a broken power law with and cannot be ruled out.
In our scenario illustrated in Fig. 1, the accretion-powered GRB
central engine firstly generates a jet (denoted by Jet A) along
LOS, which produces the observed prompt -ray emission. The
interaction between Jet A and the ambient medium is responsible
for the first part of the afterglow until the large rebrightening. A
period later, the central engine ejects the second jet
(denoted by Jet B) at a larger viewing angle preventing
-ray detection. By assuming that the isotropic energy of
Jet B is, however, significantly higher than that of Jet A, the
off-axis afterglow emission from Jet B produces significant
rebrightening at lower energies. The two jets should also not
intersect, and therefore collide, with each other.
|Figure 1: Schematic two jets scenario for GRB 060206.|
|Open with DEXTER|
Pre-large rebrightening. Emission from the forward shock,
driven by Jet A, interacts with the ambient medium to produce an
afterglow for up to 3000 s; during this time, the temporal decay
indices of the two small bumps are similar to the values predicted
by the standard fireball model. There is no signature of reverse
shock emission, which possibly ceases at very early times.
Alternatively, the reverse shock emission could be suppressed by the
magnetization of the ejecta (Zhang & Kobayashi 2005) and many other
physical processes (Kobayashi 2000; Nakar & Piran 2004; Kobayashi
et al. 2007; Jin et al. 2007). We consider that the cold Jet Awith a total isotropic kinetic energy
erg propagates into the ambient
medium with a constant density n1. A forward shock emerges and
energizes the surrounding materials by converting the bulk kinetic
energy of the jet into the internal energy of the shocked materials.
This internal energy is assumed to be shared by electrons and
magnetic fields with energy equipartition factors
respectively. If the shock is adiabatic, the
synchrotron emission produced by slow cooling electrons is expected
to have a peak flux
For GRB 060206, no early flux peaks were detected in the optical and X-ray bands, even at s. It is reasonable to believe that the flux peak time was less than . A lower limit to the peak flux can be obtained accordingly, by extrapolating the R-band flux of the first post-bump back to 200 s. Since the optical flux peak was at time and a cooling break in the X-ray afterglow was not observed, the orderof the frequencies, after the flux peak, was , where is the cooling frequency and is the typical X-ray frequency. The redshift of GRB 060206 is known, so the isotropic energy of its first jet is erg. The energy equipartition factors of magnetic fields and electrons, according to Eqs. (2) and (3), can be constrained if the number density of the ambient medium is known. The spectral analysis revealed a high number density in the environment of GRB 060206 (Fynbo et al. 2006). Given a rational value of n1=50 , it can be proven that and . Our subsequent numerical results are consistent with this constraint. We calculate the forward shock synchrotron emission from Jet A that reproduces the first post-bump segment of the R-band light curve of temporal index , which implies an electron energy spectral index .
Large rebrightening. The large rebrightening is due to the
off-axis emission from the second beamed jet. The off-axis effects
can generate a fast rise light curve, and the gamma-ray emission,
from internal shocks in the second jet, would not trigger
-BAT due to the large viewing angle and the
initially large Lorentz factor when the condition
is fulfilled, where is the initial bulk Lorentz factor of Jet B. The half opening angle
of Jet B can be estimated by the measured jet break time
s (e.g., Frail et al. 2001)
When Jet A/B sweeps up the ambient medium, a pair of shocks could be generated, including a forward shock propagating into the medium and a reverse shock penetrating into the ejecta. However, as analyzed above, the reverse shock driven by Jet A can be ignored for the afterglow phase of interest, whereas it may be necessary to consider the contribution of the reverse shock to the afterglow emissions for Jet B. We would therefore describe the dynamics of the two jets in different ways.
of the forward shock driven by Jet A with an
initial Lorentz factor
equation (Huang et al. 2000)
With respect to Jet A,
the consideration of Jet B is more complicated
because of the involvement of the reverse shock. The system is
divided into four regions by the two shocks and the
contact discontinuity surface: the unshocked medium, the
shocked medium, the shocked ejecta, and the unshocked
ejecta, which is denoted by 1-4, respectively. Since the
and energy density e are
continuous along the contact discontinuity, we have
eB2=eB3 (Sari & Piran
1995). The hydrodynamics of the forward-reverse shock
pairs are determined by (Huang et al. 2000; Yan et al. 2007)
It is accepted in general that the synchrotron radiation of the
shocked electrons produces the observed X-ray and optical afterglow
emissions. In a detailed calculation, we consider, as often assumed,
that the electrons without energy losses are accelerated by the
shocks in a way described by a power law distribution
Using the derived electron distribution,
we can calculate the synchrotron emissivity to be (Rybicki &
We also take into account the synchrotron self-absorption effect, which implies that a correction should be applied to spectra below the synchrotron self-absorption frequency as performed by Wu et al. (2003) and Zou et al. (2005).
Table 1: The main parameters adopted in our calculations.
Using the model described above with parameter values as listed in Table 1, we describe numerically the R-band afterglow data of GRB 060206 in Fig. 2. As can be seen, the first post-bump in the light curve can be reproduced well using the forward shock emission from Jet A. Both the forward- and reverse-shock light curves of Jet Bare also presented in Fig. 2. The large rebrightening can be attributed mainly to the forward shock emission from Jet B because the off-axis effect suppresses the peak flux of the reverse-shock emission, which usually peaks at a few hundred seconds from its beginning. For Jet A, we observe that the values of , , and n1 are consistent with our analysis in Sect. 3. For Jet B, we adopt typical values of 0.1 for and 0.01 for since there is no observational constraint on the shock parameters. The shock parameters for different jets and/or for different shocked regions may be different as found for the two-component jets model (Jin et al. 2007) and the forward-reverse shock model (Fan et al. 2002). The off-axis effect alone cannot explain the fast rise in the large rebrightening. In addition, the zero time effect can steepen the rise further (Zhang et al. 2006; Liang et al. 2006). We find that the time delay between the two jets is s, which agrees with the rising segment, the subsequent normal decay phase, and the break in the light curve at late times.
It should be noted that the parameters (, , ) for Jet A, (, , , , , , ) for Jet B and the number density of the ambient medium n1 are not exclusively determined. The jet break time for Jet A is hidden by the dominating emission of Jet B, while the isotropic kinetic energy of Jet B cannot be measured because its gamma-ray emission cannot trigger the detector. The most appropriate method for determining the parameter values depends upon the following ingredients: (1) we fit the observational R-band data of the first post-bump segment to constrain the values of and combined with the known isotropic gamma-ray energy of Jet A, (2) typical values of , and are used for Jet B, (3) the off-axis angle cannot be too large, otherwise an abnormally large isotropic energy for Jet B is required, (4) the condition of should be satisfied to avoid the detection of gamma-ray emission from Jet B, and (5) to simplify the calculation, we assume that the path of Jet A does not intersect with that of Jet B, which requires that .
|Figure 2: R-band light curve of GRB 060206. ``FE'' and ``RE'' represent the forward shock emission and the reverse shock emission, respectively. The dotted line represents the contribution from Jet A. The thick, dashed line and the thin, dashed line correspond to the emissions from the forward shock and the reverse shock of Jet B, respectively. The dash-dotted lines represent the emission from Jet B taking into account the zero-time effect. The thick, solid line includes the contribution from both Jet A and Jet B. R-band data are taken from Monfardini et al. (2006), Stanek et al. (2007) and et al. (2006).|
|Open with DEXTER|
The isotropic energy of the second jet is more than one order of magnitude higher than the first jet in our scenario. The collimation-corrected energy of Jet Bis 4.3 times larger than Jet A, which is larger than the energy required to explain the big rebrightening in the energy injection model as mentioned in Sect. 1. The precise mechanism that triggers the central engine again remains unknown. One possibility is that a mass of debris falls back onto the central compact object, generating another more energetic jet. Since our scenario can reproduce well the observations of the large bump in GRB 060206, as a conservative extrapolation, we propose that GRB 970508 and GRB 060210, which display remarkable rebrightening, may have in addition a precessing torus or accretion disk.
A further consequences of our scenario is that the jet break is determined by the off-axis second jet rather than the first one, which produces the main burst. In this case, we cannot measure the isotropic energy of the second jet directly and must fit the afterglow data to obtain an estimation. When a large bump appears in GRB afterglows, we are therefore unlikely to be able to derive the jet opening angle, using the break time and isotropic gamma-ray energy release, because these two quantities originate in two different jets (Stanek et al. 2007).
Finally, several models could be applied to explain afterglow light curves exhibiting rebrightening. These include variable external density profiles (Lazzati et al. 2002), refreshed shocks (Granot et al. 2003; Bj rnsson et al. 2004), and angular dependence of the energy profile on the jet structure (Nakar et al. 2003), each of which can play a role. Peculiar behavior in light curves caused by the precession of the central engine was discussed by Reynoso et al. (2006), although more observations are required to identify its true nature.
We would like to thank the anonymous referee's constructive comments and suggestions which improved our paper significantly. X.W. Liu thanks D.M. Wei for his encouragement to accomplish this work. We thank Y.F. Huang, Y.W. Yu, Y. Li and L. Shao for helpful discussions. This work was supported by the National Natural Science Foundation of China (grants 10473023, 10503012, 10621303, and 10633040). XFW gratefully acknowledges Re'em Sari during his visit to Caltech, also thanks the supports of China Postdoctoral Science Foundation, K.C. Wong Education Foundation (Hong Kong), and Postdoctoral Research Award of Jiangsu Province.