On the properties of the RHESSI intermediate-duration gamma-ray bursts

arXiv:1109.3037v1 [astro-ph.HE] 14 Sep 2011 On the properties of the RHESSI intermediate-duration gamma-ray bursts Jakub ˇRípa∗, Péter Veres† and Attila Mészáros∗ ∗Charles University, Faculty of Mathematics and Physics, Astronomical Institute, V Holešoviˇckách 2, 180 00 Prague 8, Czech Republic †Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest, Hungary Abstract. The intermediate-duration gamma-ray bursts (GRBs) identified in the data of the RHESSI satellite are investigated with respect to their spectral lags, peak count rates, redshifts, supernova observations, and star formation rates of their host galaxies. Standard statistical tests like Kolmogorov-Smirnov and Student t-test are used. It is discussed whether these bursts belong to the group of so-called short or long GRBs, or if they significantly differ from both groups. Keywords: gamma-ray astrophysics, gamma-ray bursts PACS: 01.30.Cc, 95.85.Pw, 98.70.Rz METHODS In paper [1] we identified a group of intermediate-duration GRBs (here Figure 1, left panel), significant at ∼3σ level, by the Maximum Likelihood (ML) ratio test and bivariate fitting of log-normal functions on the hardness ratio-duration plane. Here we focus on the other properties of these bursts and employ the same sample, i.e., the data obtained from the RHESSI satellite between February 14, 2002 and April 25, 2008. The number of the GRBs belonging to the group of, by the highest probability, short, intermediate, and long bursts is 40, 24, 363, respectively. We evaluated spectral lags, similarly to [2, 3], by fitting of the peak of the cross-correlation function (CCF) of the background-subtracted count light-curves at two channels 400 −1500keV and 25 −120keV (see an example in Figure 1, right panel). Then we applied Kolmogorov-Smirnov (K-S) and Student t-test to find whether the group of intermediate-duration GRBs is more similar to the group of short or long bursts. In some cases the evaluation of the lag was impossible, because of the high noise level of the CCF. Therefore the sample of the lags is smaller than the overall number of the RHESSI bursts. Results are shown in Figure 2 and summarized in Table 1. Next we focused on the count peak rates. Figure 3 presents the peak count rates vs. T90 durations and the cumulative distributions of the all three identified groups. The K-S and t-test probabilities were calculated and results are presented in Table 2. RESULTS AND CONCLUSIONS The K-S test applied on the spectral lag distributions of the short- and intermediate-duration bursts gives the K-S probability 20.7 % and K-S distance 0.33. The tabular critical value of the K-S distance at the significance level α = 5 % and the given number of the elements (24 and 15) is 0.45. Therefore the null hypothesis that the lags of the short and intermediate bursts are drawn from the same distribution cannot be rejected at the 5 % significance level. On the other hand, the same test applied on the lags of the intermediate vs. long (and short vs. long) bursts gives the K-S probability 1.47 % (0.01 %) and the K-S distance 0.42 (0.49). The tabular critical value of the K-S distance at the 5 % significance level for the number of the intermediate and long bursts (15 and 98) is 0.38. Therefore the hypothesis that the lags of the intermediate and long bursts are drawn from the same distribution can be rejected at this 5 % significance level. Similarly, it can be rejected, at the 5 % significance level, that the lags of short and long bursts are drawn from the same distribution. The critical K-S distance is in this case 0.31. From the results of the K-S test applied on the peak count rates it follows that the distributions of the peak count rates are different over all three groups. The t-test is not persuasive for both cases; spectral lags and peak count rates. FIGURE 1. Left panel: The hardness ratio H vs. T90 duration plot with the best ML fit of three bivariate log-normal functions is shown. Different symbols correspond to different GRB groups identified in the article [1]. For each GRB the probability of belonging to either short-, intermediate-, or long-duration group is known. The crosses, full circles, and triangles mark GRBs belonging, by the highest probability, to the group of short-, intermediate-, or long-duration bursts, respectively. Right panel: An example of cross-correlation function of background-subtracted count light-curve (here very bright GRB 060306) at two different energy bands. The inset presents the fit of the CCF peak by the third order polynomial (thick solid curve). The maximum of the polynomial fit (dotted line) was taken as the true spectral lag. The boundaries of the fit are marked with dashed lines. TABLE 1. Left part: Results from the Kolmogorov-Smirnov test of equality of distributions of the spectral lags and Student t-test of equality of the mean lags for different GRB groups are presented. The K-S distance, and the K-S probability is mentioned. The null hypothesis that two s

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