Abstract
Although more than 2000 astronomical gamma-ray bursts (GRBs) have been detected, the precise progenitor responsible for these events is unknown. The temporal phenomenology observed in GRBs can significantly constrain the different models. Here we analyse the time histories of a sample of bright, long GRBs, searching for the ones exhibiting relatively long (more than 5per cent of the total burst duration) ‘quiescent times’, defined as the intervals between adjacent episodes of emission during which the gamma-ray count rate drops to the background level. We find a quantitative relation between the duration of an emission episode and the quiescent time elapsed since the previous episode. We suggest here that the mechanism responsible for the extraction and the dissipation of energy has to take place in a metastable configuration, such that the longer the accumulation period, the higher the stored energy available for the next emission episode.
1 Introduction
The study of gamma-ray bursts (GRBs) has undergone a revolution since the first fading sources at X-ray (Costa et al. 1997), optical (van Paradijs et al. 1997) and radio (Frail et al. 1997) wavelengths were discovered, making them the most powerful photon-emitters known in the Universe. Although much attention has been devoted to the late afterglow emission since then, the prompt gamma-ray emission still has to be understood. Many issues remain unsolved, regarding the nature of the central engine, the different scenarios giving rise to this prompt emission, and the radiation mechanisms.
The data collected by the Burst and Transient Source Experiment (BATSE) have provided us with an unprecedented wealth of information. None the less, GRBs are so complicated and diverse in the time domain that, at first sight, their behaviour obeys no simple rule.
One of the main issues that has remained largely unexplained is what determines the characteristic durations of the bursts, which typically range between 10−2 and 103s.1 Observationally (Kouveliotou et al. 1993) the short (≲2s) and long (≳2s) bursts appear to represent two distinct subclasses. An early proposal made by Katz & Canel (1996) to explain the bimodal distribution of durations was that accretion-induced collapse of a white dwarf into a neutron star plus debris might be a candidate for the long bursts, while neutron star-neutron star mergers could provide the short ones. However, it is at present unclear which, if any, of these progenitors is responsible for the bulk of GRBs.
Besides this apparent bimodality, GRB temporal profiles are enormously varied. Many bursts have a highly variable temporal profile with a variability time-scale that is significantly shorter than the overall duration, while in a minority of them there is only one peak, with no substructure. Furthermore, the time histories of long GRBs often show multiple episodes of emission, separated by background intervals, or ‘quiescent times’, of variable durations. In other words, it seems that the emission can turn off to a very low level and then turn on again. This observed property can provide an interesting clue to the nature of GRBs. At present, it is unclear if these separated emission episodes are consequences of the same physical process (e.g. internal or external shocks), and if the time separation is due to some intrinsic property of the central source or of its environment.
The purpose of this paper is to determine the properties of quiescent times in observations of long GRBs. In a forthcoming paper (Ramirez-Ruiz, Merloni & Rees 2000, hereafter Paper II) we study, within the framework of the internal-external shock model, the various possible mechanisms that can give rise to quiescent times in the observed gamma-ray light curves.
2 Observations
2.1 Procedure
A visual inspection of the BATSE catalogue of multi-peaked time histories reveals that in some of them the count rate drops to the background level in between two adjacent episodes of higher emission intensity. Our aim is to characterize and measure these episodes of quiescence.
In an earlier report, Koshut et al. (1995) found that about 3per cent of the bursts show signs of precursor activity, with a peak intensity lower than the main burst, separated from the remaining emission by a background interval that is at least as long as the rest of the burst. BATSE burst 2156, shown in the upper panel of Fig. 1, falls into this category. However, the above definition singles out a data set with rather extreme properties. Several time profiles show periods of quiescence without having precursor activity. See, as an example, BATSE burst 3067, which is shown in the lower panel of Fig. 1. For this reason, in order to study the periods of quiet emission, we adopted more general selection criteria. Here, we allowed multiple pairs of successive events separated by a quiescent time within a single burst, and we did not impose requirements on the relative intensities or on the time interval separating any two emission episodes. The periods of emission occurring before and after the quiescent time are therefore referred to as the ‘pre-quiet’ and ‘after-quiet’ times, respectively.
Time profiles observed with BATSE (at energies >20keV) that contain periods of quiet emission. Upper panel: BATSE burst 2156 has a very strong main burst after a long quiet emission period. Lower panel: BATSE burst 3067 has a very strong main burst before the count rate drops to the background level.
For the purpose of our analysis, we have used all 94 bursts from the 4B BATSE catalogue longer than 5s (90 > 5s) and brighter than 5photonss−1cm−2 (BATSE peak photon flux in the 256-ms time-scale). We have used the BATSE 64-ms four-channel data (i.e. from 25 to ∼800keV). A background model was created for each energy channel by fitting user-defined background intervals with a second-degree polynomial and interpolating this fit across the source interval. We subtracted the background model from the observed count rates in each energy channel. This then gave us the total source count rates as a function of time. In order to be selected, a burst must have at least one quiescent period in its time history. The selection was accomplished by calculating the total number of counts, over the entire energy range, recorded in a temporal window sliding along the time axis. The width of the window was set to 5per cent of the duration of the burst. Thus the width of the window varied from burst to burst, allowing us to avoid bias against quiescent times with duration less than some arbitrary window width. We define a drop to the background level whenever the number of net counts in a window is smaller than the 2σ level in the corresponding background counts window. We have used this absolute test, rather than a relative limit (e.g. a fixed fraction of the highest number of counts in any given window), to try to avoid the possibility of the existence of source emission below our detection level, during any time interval in any burst.
We found that ∼15per cent of the analysed long and bright bursts contain at least one quiescent interval in their time history (of duration ≳0.05T90) and ∼25per cent of these have more than one. Fig. 2 illustrates the distribution of durations for, respectively, all bursts in the sample (dotted line), the subset of those that contain at least one quiescent period (dashed line), and the bursts with two or more quiet emission intervals (solid line).
Distribution of GRB durations. The dotted line is the distribution of all bright bursts that were longer than 5s and brighter than 5photonss−1cm−2, the dashed one represents the bursts that show at least one quiescent time, and the solid one the bursts with two or more quiescent intervals.
Fig. 2 shows that the distribution of durations for the subset of bursts that contained quiet emission periods is consistent with the sample distribution. We find no significant evidence that the presence of quiescent times is preferentially found in longer or shorter bursts within our sample. Some limitations are necessarily inherent in our approach and data selection: the conclusions that we reach are based on measurements of a subset of the bursts detected with BATSE; we analyse relatively bright bursts with durations greater than ∼5s, recorded with 64-ms temporal resolution and four-channel spectral resolution. Analysis of quiescent times in shorter bursts will be more difficult owing to the fact that few short bursts are brighter than 5photonss−1cm−2. The selection of a high-brightness sample is appropriate in order to avoid the systematic effects that might change the observed time histories with different statistics. The time histories of dim events would be more randomized by fluctuations than the time histories of bright bursts. Using other GRB samples with a high signal-to-noise ratio (≳3photonss−1cm−2) gives similar results.
2.2 Results: correlations between emission properties
We have searched for correlations between the temporal properties of the different emission periods. Any correlation will provide strong constraints on various burst models. In particular, we have investigated the dependence of the duration of the quiescence period on the after-quiet and the pre-quiet burst durations. It is worth stressing that, by comparing time intervals within each burst, we eliminate the distance dependence (or time dilation effects) that would arise if we compared, for example, the total number of counts of an emission episode with the duration of the quiescent period. We find no evidence for a correlation between quiescent times and pre-quiet burst times, as seen in Fig. 3(a). However, a strong one-to-one correspondence seems to exist between quiescent times and after-quiet burst durations, at about the 4σ confidence level (linear correlation coefficient s ∼ 0.89). Stated otherwise, we have found that, in our time history sample, the longer the quiescent time the longer the duration of the following emission period, as shown in Fig. 3(b).
Correlations between the temporal properties of the different emission periods. In panel (a) we plot the duration of an emission episode (pre-quiet burst time) against the duration of the following quiescent time. No clear correlation is found in this case. In panel (b) we plot the duration of an emission episode (after-quiet burst time) against the duration of the previous quiescent time. There is a clear trend: the longer the quiescent time, the longer the duration of the following emission period.
Lochner (1992) studied the relation between successive emission episodes in multiple-episode bursts observed with the Pioneer Venus Orbiter (PVO) GRB detector. Unlike the work presented here, his data set was only a collection of multiple-event bursts and did not result from a systematic search throughout the entire PVO data base. Lochner (1992) reported a strong correlation (s ∼ 0.73) between the duration of an event and the duration of the subsequent event.
In a study of precursor activity (Koshut et al. 1995), a similar trend was found. However, in the analysis of Koshut et al., such a correlation is simply a consequence of the definition of precursor activity, since the authors required that the two sub-bursts be separated by a background interval at least as long as the remaining emission episode.
Furthermore, Lochner (1992) also reported a moderate correlation between the hardness of an event and the hardness of the following event. We found no evidence for such a property in our sample.
The existence of a correlation between the duration of the quiescent time and the total energy of the after-quiet burst would of course reveal very interesting properties of GRB sources. However, to characterize the total energy of a burst, we would need information about the distance of the event.2 Without this information, looking for any correlation between the total number of counts (and hence energy) of the afterquiet emission and the duration of the quiet period in different events will be misleading.
None the less, one could expect a correlation between the duration of an emission episode and the total energy radiated. If this were the case, the correlation between times that we found should simply reflect a correlation between the burst strength and the time elapsed since the previous emission episode. It will then be indicative of an accumulation of fuel, similar to what is observed in the galactic superluminal jet source GRS 1915+105 (Belloni et al. 1997). On the other hand, a correlation between the burst strength and the time until the next burst, indicative of a relaxation oscillator behaviour, is ruled out by the observations.
3 Discussion
Here we present a few simple considerations that can be drawn from the hypothesis that the gaps in the gamma-ray light curves of GRBs are a consequence of a central engine which actually becomes dormant for a period of time comparable to the duration of the gaps. To disprove this hypothesis clearly requires a thorough scrutiny of all the alternative possibilities. These possibilities will be addressed in detail in Paper II. In particular, in the framework of the internal shock model, we show that there are realistic assumptions that produce a long quiescent interval in the light curve of a GRB, without having to postulate that the central source itself turns off for a comparably long time.
All the bursts analysed here are long and structured. Clearly in these cases the central engine has to be active for a period extremely long compared with the typical dynamical time-scale (∼milliseconds) for stellar-mass compact objects. Thus the central engine has to evolve into a configuration that is stable enough to survive the violent gravitational instabilities associated with the merging/collapse of compact objects, while still keeping enough binding energy to power the burst. A thick torus (or an advective, optically thick accretion disc) accreting at a rate of 0.01 to 10M⊙yr−1 (Popham, Woosley & Fryer 1999, hereafter PWF) is a key ingredient for achieving this. The system also needs to be highly unstable to produce the extremely varied light curves that we observe (Stern 1999), and this requirement is even stronger for the bursts exhibiting quiescent times.
Of the two more popular mechanisms that have been proposed to explain the energy release of GRBs (neutrino annihilation and conversion of Poynting flux into a magnetized wind), the first seems unable to produce the longer, more energetic and variable bursts (PWF; Rees 1999). As PWF have shown, the efficiency of such a process is highly variable and extremely sensitive to the accretion rate: higher accretion rates lead to higher efficiencies. They conclude that neutrino annihilation in hyper-accreting black hole systems can explain bursts of energy up to 1052erg.
The other popular scenario, the conversion of Poynting flux into a magnetized wind, requires, in order to liberate the observed amount of energy, a magnetic field ≳1015G (Rees 1999, and references therein). Such a high field is not unphysical: first, because it is about two orders of magnitude smaller than the virial limit; secondly, because it has possibly been observed in some peculiar neutron stars (the so-called ‘magnetars’; see e.g. Duncan & Thompson 1992, Kouveliotou et al. 1998, and references therein).
A neutron torus, with its huge amount of differential rotation, is a natural site for the onset of a dynamo process that winds up the field to the required intensity (Kluźniak & Ruderman 1998), provided that a fluid element is able to complete a sufficient number of orbits around the hole. This number, in turn, depends on the viscosity inside the disk, N ∼ α−1, where α is the standard Shakura-Sunyaev viscosity.
The actual properties of the expected variability depend on the details of the configuration of the disc corona generated by the magnetic field, which is removed from the disc interior via turbulent flux buoyancy (Araya-Gòchez 1999). This is a very complicated (and almost unaddressed; but see Tout & Pringle 1996) issue, on which some insight can come from the observations.
The tentative correlation found between the duration of an emission episode in a multi-peaked burst and the duration of the preceding quiescent time hints at the following general scenario.
The system builds up its energy (via a magnetohydrodynamic instability-driven dynamo, for example) and reaches a near-critical or metastable state. Any local instability can, by definition, cause a rapid dissipation of all the stored energy through an avalanche of dissipation events. The system will tend to return to a more stable configuration, characterized by a certain threshold energy E0, or a sub-critical coronal magnetic field configuration. The source then becomes quiescent. If the lifetime of the accreting torus is long enough and depending on the rate at which the energy is actually extracted from the disc (or from the black hole) and deposited into the external magnetic field, the system can undergo another episode of strong emission. As we can assume E0 to be fixed by the geometry and by the physical parameters of the black hole-accretion disc system, the longer the quiescent time, the higher will be the stored energy above the threshold available for the next episode. Such a situation will give rise to the observed correlation.
This is a mechanism different from any relaxation oscillator, in which the threshold energy is an upper limit for the system. As soon as the system reaches such a limit it is forced to release energy: in this case, the larger the amount of energy released, the longer will be the time needed to reach the threshold again, and we would obtain a correlation between the burst time and the pre-quiet time, contrary to what is observed.
It is also important to note that the threshold energy E0 above which the system is in a metastable state is not directly related to the intensity of the seed magnetic field inside the neutron torus. It is instead most likely related to the intensity and the topological configuration of the amplified field which emerges from the torus.
Finally, we would like to point out the suggestive analogy with the microquasar GRS 1915 + 105, a galactic black hole candidate which exhibits a strikingly similar (even quantitatively) correlation between the duration of a quiescent time and that of the following burst (Belloni et al. 1997). This source is believed to accrete at a rate very close to (or maybe higher than) the Eddington limit, which is also the case for the configuration suggested for gamma-ray bursters discussed above.
4 Conclusions
The very existence of quiescent times in GRB light curves imposes severe restrictions on the emission models (see Fenimore & Ramirez-Ruiz 1999; Paper II) and, possibly, gives direct insight into the dynamical properties of the hidden central engine.
Apart from the energy requirements that any viable model has to fulfil, we envisage that the observed temporal structure will bring fundamental information to the understanding of GRB progenitors.
We have systematically analysed a sample of bright, long GRBs, searching for those exhibiting relatively long quiescent times (more than 5per cent of the total burst duration). These amount to ∼15per cent of the sample. We have found an interesting correlation between the duration of the quiescent interval and the duration of the following emission episode, while no correlation has been found between the quiescent time and the duration of the previous emission episode.
We suggest here that, in the hypothesis that the gaps in the observed light curves directly reflect a period of inactivity of the central source, the mechanism responsible for extracting and dissipating the energy in the high Lorentz factor ejecta has to develop a metastable configuration: that is, a configuration in which a local instability can abruptly drain the system of all the stored energy, probably via a cascade of correlated smaller scale events.
Acknowledgments
We thank M. Rees, P. Natarajan, P. Madau, A. Fabian and G. Morris for useful comments and suggestions. ER-R acknowledges support from CONACYT, SEP and the ORS foundation. AM thanks PPARC and the TMR network ‘Accretion onto black holes, compact stars and protostars’, funded by the European Commission under contract number ERBFMRX-CT98-0195, for support.
References
The definition of the burst duration is not unique. The BATSE team characterizes it using T90 (T50): the time needed to accumulate from 5 to 95per cent (from 25 to 75per cent) of the counts in the 50–300keV band (Meegan et al. 1996). For the purpose of our analysis, we used T90 as a measure of burst duration.
At the moment, there is only one BATSE event (7560) with periods of quiet emission in its light curve and for which a redshift measurement has been made (GRB 990510).
