An autocorrelation function (ACF) analysis was performed on 17 gamma-ray bursts with known redshift, using data from the GRBM on board Beppo-SAX. When corrected from the cosmic time dilation effect, the ACFs show a bimodal distribution at about half-maximum, in agreement with a previous study based on BATSE and Konus burst data. Although the results show more dispersion, the separation between the two classes is highly significant

Borgonovo, L.

Frontera, F.

Guidorzi, C.

Montanari, E.

Soffitta, P.

English

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DOI 10.1393/ncc/i2005-10038-0IL NUOVO CIMENTO Vol. 28 C, N. 3 Maggio-Giugno 2005Autocorrelation analysis of GRBM–Beppo-SAX burst data(∗)L. Borgonovo(1), F. Frontera(2), C. Guidorzi(2), E. Montanari(2) andP. Soffitta(3)(1) Stockholm Observatory, AlbaNova - SE-106 91, Stockholm, Sweden(2) Dipartimento di Fisica, Universita` di Ferrara - 44100 Ferrara, Italy(3) Istituto di Astrofisica Spaziale e Fisica Cosmica, CNR - 90146, Palermo, Italy(ricevuto il 23 Maggio 2005; pubblicato online il 16 Settembre 2005)Summary. — An autocorrelation function (ACF) analysis was performed on 17gamma-ray bursts with known redshift, using data from the GRBM on board Beppo-SAX. When corrected from the cosmic time dilation effect, the ACFs show a bimodaldistribution at about half-maximum, in agreement with a previous study based onBATSE and Konus burst data. Although the results show more dispersion, theseparation between the two classes is highly significant.PACS 98.70.Rz – γ-ray sources; γ-ray bursts.PACS 01.30.Cc – Conference proceedings.1. – IntroductionThe study of time scales is essential for the physical understanding of any astronomicalphenomena. For gamma-ray bursts (GRBs) though, no characteristic time has beenclearly identified, aside from the time duration of the events in the observed energy band.Individual power density spectra (PDS) are in general very diverse, but the average PDSof many bursts showed a power-law behaviour over two frequency decades, suggesting theabsence of any preferred time scale [1]. However, since long bursts are at cosmologicaldistances, it is likely that some temporal features might be blurred by time dilationeffects. In a recent analysis of 16 long GRBs with known redshift z, that were detectedby the BATSE and Konus experiments, it was shown that when corrected for cosmic timedilation the autocorrelation function (ACF) exhibits a clear bimodal distribution [2].Taking as a measure the half-width at half-maximum, there is a highly significant gapbetween a narrow and a broad width class, the separation in standard deviations being> 7σ. The average widths (relative dispersions) are 1.6 s (32%) and 7.5 s (4%) for thenarrow and broad classes, respectively. The results in [2] were based on a small numberof observations, and therefore need to be confirmed by a larger statistical sample. In thispaper we present preliminary results of an extension of that work using GRB data from(∗) Paper presented at the “4th Workshop on Gamma-Ray Burst in the Afterglow Era”, Rome,October 18-22, 2004.c© Societa` Italiana di Fisica 275276 L. BORGONOVO, F. FRONTERA, C. GUIDORZI, ETC.-15 -10 -5 0 5 10 15 2000.20.40.60.81ACF-15 -10 -5 0 5 10 15 20τ [s]00.20.40.60.81ACFa) b)Fig. 1. – a) Observed autocorrelation functions of 17 GRBM bursts. b) Local ACFs where thetime dilation effect has been corrected, with τ ′ = τ/(1 + z). Although not as clearly as withBATSE data, two width classes are noticeable at half-maximum. The gap separation representsa 3.1σ deviation with a chance probability p < 0.0008.the Gamma Ray Burst Monitor (GRBM) on the Beppo-SAX satellite. The drawbackof mixing data from different instruments is that this in itself might introduce moredispersion, that could in fact outweigh the benefits of an increased sample. For thisreason we will consider separately the GRBM burst sample and evaluate its suitabilityfor our ACF analysis.2. – Data and methodsThe ACF width shows a dependency with the energy band [3] and, like the pulsestructure, it broadens at lower energies. We use the lower energy channel data of theGRBM that, being in the 40–700 keV energy range, roughly matches the BATSE (50–320 keV) and Konus (50–200 keV) ranges of the previous ACF study [2]. Note that sincethe ACF is a quadratic function of the number of counts, and there are more counts atlower energies, it is more important the agreement between the lower-end energy limits.The standard high resolution 7.8125 ms data was binned up into a time resolution of62.5 ms to improve the signal-to-noise ratio (S/N). This has no significant consequencefor the measurement of the time scales that concerned us here, and reduces some noiseartifacts in the ACF. In addition, it better matches the standard BATSE 64 ms temporalresolution for later comparison. In one case (GRB990510), because the on-board logicwas not triggered by the burst, only 1 s data are available. A total of 17 GRBs wereincluded in our sample. The light curves were corrected for dead-time and backgroundsubtracted.To derive the ACF from the GRB light curves we followed the methods described in [2].From a uniformly sampled count history with ∆T time resolution and N time bins, letmi be the total observed counts at bin i. Also let bi be the corresponding backgroundlevel and ci = mi − bi the net counts. The discrete ACF as a function of the time lagτ = k∆T is(1) A(τ) =N−1∑i=0cici+kA0, k = 1, . . . , N − 1and A(0) = 1 for k = 0. Here the periodic boundary conditions (ci = ci+N ) are assumed.AUTOCORRELATION ANALYSIS OF GRBM–BEPPO-SAX BURST DATA 277Table I. – Sample of 17 GRBs detected by GRBM with known redshift. The first six columnsgive the burst name, the measured redshift z and the corresponding reference, the width class(n: narrow, b: broad), the ACF half-width at half-maximum τ0, and the corresponding widthcorrected for time dilation τ ′0 = τ0/(1 + z). The last two columns give, when available forcomparison, the width estimation done based on BATSE data τB0 [2], and the relative difference∆τ0/τ¯0 with respect to the average value τ¯0.GRB z Ref. Class τ0(s) τ′0(s) τB0 (s) ∆τ0/τ¯0(%)970228 0.695 [4] n 1.20 0.71970508 0.835 [5] n 3.92 2.14 2.70 37.1971214 3.418 [6] n 8.65 1.96 8.02 8.4980326 1.2 [7] n 2.44 1.11980329 3± 1 [8] n 6.14 1.53 5.96 3.0980425 0.0085 [9] b 8.88 8.81 7.62 15.2990123 1.6 [10] b 17.43 6.70 19.81 −12.8990506 1.3066 [11] n 3.51 1.52 3.83 −8.6990510 1.619 [12] n 3.28 1.25 2.54 25.5990705 0.86 [13] b 14.28 7.67990712 0.434 [14] n 4.08 2.84991216 1.02 [15] n 3.33 1.65 3.80 −13.2000210 0.846 [16] n 1.91 1.04000214 0.47 [17] n 2.53 1.72010222 1.477 [18] n 5.42 2.19010921 0.45 [19] b 9.81 6.77011121 0.362 [20] b 10.91 8.01The normalisation constant A0 is defined as(2) A0 =N−1∑i=0(c2i −mi).The normalisation makes the ACF of each burst fluence independent. The term miin eq. (2) subtracts the contribution of the uncorrelated noise assuming that it followsPoisson statistics.3. – Results and discussionIn fig. 1a we show the observed ACFs of all our GRB sample, and in fig. 1b thelocal ACFs where the cosmic time dilation effect has been removed, with τ ′ = τ/(1 + z)being the corrected time lag. Though not as evident as when using BATSE data, stilltwo classes given by the local width at half-maximum can be recognised. We focus onthe central part of the ACF. In some bursts where the light curve presents a few wellseparated pulses of similar intensity the ACF shows strong secondary features, while inmost cases these secondary peaks are negligible. Our measurements are summarised intable I. Note that although GRB980329 redshift is only known to be in the z = 2.0–3.9range [8], in any case its ACF would lie within the other narrow width bursts. In fig. 1bwe used an average value of z = 3.We obtained a mean value of τ ′(n)0 = (1.6 ± 0.2) s and τ ′(b)0 = (7.6 ± 0.5) s, and asample standard deviation of σ(n) = 0.7 s and σ(b) = 1.2 s for the narrow and broad278 L. BORGONOVO, F. FRONTERA, C. GUIDORZI, ETC.sets, respectively. The gap separation between the two sets represents a 3.1σ deviation.The probability p of a random occurrence of such a gap was estimated using a MonteCarlo simulation, assuming that there are no characteristic time scales. I was found thatp < 0.0008. The results are fully consistent with [2], as expected if width errors are largerbut stochastic, since only 6 GRBs in this paper were not considered before. The mainobserved difference is the larger dispersion of the second class (∼ 16%), while the firsthas about the same spread (∼ 43%).Table I shows in its last two columns a comparison of the ACFs widths of burstsdetected by both GRBM and BATSE. The widths are not systematically broader in thefirst case (positive differences), therefore the discrepancies can not only be attributed tothe different energy range. A better S/N and a more uniform directional response in theBATSE case, our reference instrument, might also be significant factors. The averagepercentile width difference at half-maximum is ∼ 15%. Therefore the dispersion incre-ment in each class width can be explained taken into account the qualitative differenceof the GRBM data.4. – ConclusionsIn this comparative study we found that the ACFs and their derived measurementsbased on GRBM data are consistent with the previous analysis using BATSE/Konusdata. The observed dispersion is larger, but mean values of the characteristic time scalesfor each width class are equal to within the estimated uncertainties. Consequently, atleast for this analysis, we can assume that the errors introduced by the instrument weremainly stochastic. Furthermore, despite the increased spread we were still able to identifytwo separated classes with a very high confidence level (p < 0.0008).∗ ∗ ∗REFERENCES[1] Beloborodov A. M., Stern B. E. and Svensson R., ApJ, 535 (2000) 158.[2] Borgonovo L., A&A, 418 (2004) 487.[3] Fenimore E. E., int’t Zand J. J. M., Norris J. P., Bonnell J. T. and NemiroffR. J., ApJ, 448 (1995) L101.[4] Djorgovski S. G., Kulkarni S. R., Bloom J. S. and Frail D. A., GCN Report, 289(1999) .[5] Metzger M. R. et al., Nature, 387 (1997) 878.[6] Kulkarni S. R. et al., Nature, 393 (1998) 35.[7] Jimenez R., Band D. and Piran T., ApJ, 561 (2001) 171.[8] Lamb D. Q., Castander F. J. and Reichart D. E., A&AS, 138 (1999) 479.[9] Tinney C. et al., IAU Circular, 6896 (1998) .[10] Kulkarni S. R. et al., Nature, 398 (1999) 389.[11] Bloom J. S., Berger E., Kulkarni S. R., Djorgovski S. G. and Frail D. A., AJ,125 (2003) 999.[12] Beuermann K. et al., A&A, 352 (1999) L26.[13] Amati L. et al., Science, 290 (2000) 953.[14] Le Floc’h E. et al., ApJL, 581 (2002) L81.[15] Vreeswijk P. M. et al., GCN Report, 496 (1999) .[16] Piro L. et al., ApJ, 577 (2002) 680.[17] Antonelli L. A. et al., ApJL, 545 (2000) L39.[18] Jha S. et al., ApJL, 554 (2001) L155.[19] Djorgovski S. G. et al., GCN Report, 1108 (2001) .[20] Garnavich P. M. et al., ApJ, 582 (2003) 924.

Autocorrelation analysis of GRBM–Beppo-SAX burst data

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Autocorrelation analysis of GRBM–Beppo-SAX burst data

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