The Compton Gamma Ray Observatory (CGRO) observed many

types of data and one of them is the time-tagged photon events (TTE data). We use the Bayesian block analysis, using Bayesian statistics, analyses the TTE data. Our results; calculations of duration (T100), count rates (burst photon numbers in different channels) and count peaks (in 64, 16 and 4 ms). We present the duration, the peak duration and the distance between peaks distributions. Principal Component Analysis (PCA) has been also applied. The PCA shows interesting results, such as channel 4 (highest energy channel) probably is very important

Balázs, L. G.

Horváth, I.

Norris, J. P.

Scargle, J. D.

English

arXiv

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2005-10043-3IL NUOVO CIMENTO Vol. 28 C, N. 3 Maggio-Giugno 2005Preliminary results of the analysis of the BATSE TTE data(∗)I. Horva´th(1), J. P. Norris(2), J. D. Scargle(3) and L. G. Bala´zs(4)(1) Department of Physics, Bolyai Military University - H-1456 Budapest, POB 12, Hungary(2) GLAST Science Support Center, Code 661, NASA Goddard Space Flight CenterGreenbelt, MD 20771, USA(3) Space Science Division, MS 245-3, NASA Ames Research CenterMoffett Field, CA 94035-1000, USA(4) Konkoly Observatory - H-1525 Budapest, POB 67, Hungary(ricevuto il 23 Maggio 2005; pubblicato online il 9 Settembre 2005)Summary. — The Compton Gamma Ray Observatory (CGRO) observed manytypes of data and one of them is the time-tagged photon events (TTE data). Weuse the Bayesian block analysis, using Bayesian statistics, analyses the TTE data.Our results; calculations of duration (T100), count rates (burst photon numbers indifferent channels) and count peaks (in 64, 16 and 4ms). We present the duration,the peak duration and the distance between peaks distributions. Principal Com-ponent Analysis (PCA) has been also applied. The PCA shows interesting results,such as channel 4 (highest energy channel) probably is very important.PACS 98.70.Rz – γ-ray sources; γ-ray bursts.PACS 98.80.-k – Cosmology.PACS 01.30.Cc – Conference proceedings.1. – IntroductionThe CGRO/BATSE observed many types of data about gamma-ray bursts (GRBs),and their statistical analyses gave several useful results. For example, the logN-LogSanalyses [5, 2] gave useful information about the spatial distribution of GRBs. Thestudy of the time behavior of the spectra [7, 8] led to the better understanding of thetime dependence of GRBs. In this paper the time-tagged photon events (TTE) will bestudied. The TTE data recorded the arrival time (within a two microsecond bin), energy(within four discriminator channels) and detector of each photon. The Bayesian blockanalysis, using Bayesian statistics, analyses the TTE data and the output is the most(∗) Paper presented at the “4th Workshop on Gamma-Ray Burst in the Afterglow Era”, Rome,October 18-22, 2004.c© Societa` Italiana di Fisica 291292 I. HORVA´TH, J. P. NORRIS, J. D. SCARGLE and L. G. BALA´ZS 0 10 20 30 40 50 60-2.5 -2 -1.5 -1 -0.5  0  0.5N    log  T100  Fig. 1. – The duration distribution of the analyzed 273 bursts (solid line) and the durationdistribution of the 174 one-peak bursts (dashed line).probable segmentation of the observation into time intervals during which the photonarrival rate is perceptibly constant.In the BATSE database there are 532 burst TTE (time tagged event) data. The TTEdata contains the detection time as many as 32 768 photons with a 2 microsecond timeresolution in four energy channels. Many cases there were more than 32 768 photonsduring the burst time or there were bursts photons before the starting time of TTE. Weused the 273 bursts TTE data, which were complete (covered the whole burst).2. – The Bayesian block analysisThe Bayesian block (BB) analysis has been already developed in the literature foranalyzing different data types [4, 10, 9, 6]. It is a method to find optimal changepoints(times at which the count rate is modeled as abruptly changing). The marginal posteriorprobability of the model is:(1) L(Mi,D) =∫P (D/ΘiMi)P (Θi/Mi)dΘi,where Mi refers to the parameters specifying the changepoint locations, and all otherparameters—specifying the photon rates—represented by Θi are marginalized as indi-cated by the integration in the equation. The explicit form of this posterior for a blockof data depends on only two sufficient statistics, namely the number of photons in theblock, and the length (in time) of the block. The algorithm in [3] yields the optimalblock segmentation of the TTE data.3. – Calculation of the burst parametersOnce one has the BB representation of the burst, one can calculate the burst pa-rameters. First we have T100 rather than T90, since BBs show us the start and theend points of the burst. Second we need a background counts. Firstly we adjust theTTE data with cat64ms data. Secondly two 0,64 second long intervals were chosen. OnePRELIMINARY RESULTS OF THE ANALYSIS OF THE BATSE TTE DATA 293 0 10 20 30 40 50 60 70-3 -2.5 -2 -1.5 -1 -0.5  0  0.5N     log  t  Fig. 2. – The peak length distribution of the 431 well-defined peaks (solid line) and the distancedistribution between these peaks (dashed line).before the burst and one after the burst. In other words ten consecutive bins were cho-sen before the burst and also after the burst from the cat64ms data for calculating thebackground. Third we assume during the burst the background rate was constant. Afterthese one can calculate similar burst parameters then the BATSE catalog contains. Onecan calculate the counts in the four channels (like fluence) and also find the highest binin different timescales. This can be called peakcounts (like peakflux). This was donein three timescales 64ms, 16ms and 4ms. The natural definition of pulse width using ablock representation might be called T100 rather than T90. Figure 1 shows the durationdistribution of the 273 bursts and the duration distribution of the 174 one-peak bursts.For peaks one can calculate the peak width or length rather than FWHM. Figure 2 showsthe peak length and the distance between peaks distributions.4. – Principal Component Analysis (PCA)Using the logarithm of these 8 parameters one can make a PCA. The Principal Com-ponent Analysis can show us which parameters are important to characterize the bursts.Table I. – The eigenvalues of the principal component analysis of the 8 quantities of Gamma-Ray Bursts (T100, four count rates, three count peaks). The first three PCs are important andthe cumulative percentage is 96%, which means only three variables can explain 96% of the wholeinformation.Principal component Eigenvalues % of variance Comulative percentage1 5.299 66.23 66.232 1.723 21.54 87.773 0.676 8.45 96.224 0.119 1.50 97.715 0.070 0.88 98.66 0.066 0.82 99.47 0.027 0.34 99.748 0.011 0.24 100.0294 I. HORVA´TH, J. P. NORRIS, J. D. SCARGLE and L. G. BALA´ZSTable II. – The eigenvectors of the principal-component analysis of the 8 quantities of Gamma-Ray Bursts (T100, four count rates (Ch1-4), three count peaks (P64, P16, P4)).Eigenvectors lg T100 lg Ch1 lg Ch2 lg Ch3 lg Ch4 lg P64 lg P16 lg P41 0.54 0.88 0.92 0.93 0.7 0.91 0.8 0.752 0.8 0.29 0.27 0.26 0.12 −0.35 −0.58 −0.623 −0.07 −0.32 −0.21 0.16 0.7 −0.06 −0.04 −.05Table I shows the PCA eigenvalues and table II shows the eigenvectors. The first PC isthe sum of the all parameters. The second PC is mainly the difference between durationand peakcounts. The third PC is mostly channel 4 just itself.However our analysis use different timescale and only for the short bursts these resultsare a good agreement with [1]. This does not means short and long bursts are similar. Ourresult meaning is the same 2-3 parameters can describe the BATSE observed parametersfor all bursts. But the short and the long ones can be in different place in this 3D space.∗ ∗ ∗Thanks are due to the valuable discussions with Z. Bagoly, P. Me´sza´ros and G.Tusna´dy. This research was supported through OTKA grants T034549 and T48870.REFERENCES[1] Bagoly Z., Mesza´ros A., Horva´th I., Bala´zs L. G. andMsza´ros P., ApJ, 498 (1998)342.[2] Horva´th I., Me´sza´ros P. and Me´sza´ros A., ApJ, 470 (1996) 56.[3] Jackson B. et al., IEEE Signal Processing Letters, 12 (2004) 105.[4] Loredo T.J., Statistical Challenges in Modern Astronomy, edited by Feigelson andBabu (Springer, New York) 1992, p. 275.[5] Me´sza´ros A. and Me´sza´ros P., ApJ, 466 (1996) 29.[6] Norris J. P., Scargle J. D. and Bonnell J. T., Gamma-Ray Bursts in the AfterglowEra, Proceedings of the International workshop held in Rome, edited by Costa E.,Frontera F. and Hjorth J. (Springer, Berlin) 2001, p. 40.[7] Ryde F. et al., A&A, in press (2005) astro-ph/0411219.[8] Ryde F., A&A, 429 (2005) 869.[9] Scargle J. D., ApJ, 504 (1998) 405.[10] Sivia D. S., Data Analysis: A Bayesian Tutorial (Clarendon, Oxford) 1996.

Preliminary results of the analysis of the BATSE TTE data

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