Regions of Excessive Flux of PeV Cosmic Rays

📝 Abstract

An analysis of arrival directions of extensive air showers generated by cosmic rays in the PeV energy range and registered with the EAS MSU and EAS-1000 Prototype arrays reveals a considerable number of regions of excessive flux of cosmic rays. We present results of comparative analysis of regions found in the two data sets, estimate probabilities of their appearance, and discuss correlation of their locations with coordinates of possible astrophysical sources of PeV cosmic rays.

💡 Analysis

An analysis of arrival directions of extensive air showers generated by cosmic rays in the PeV energy range and registered with the EAS MSU and EAS-1000 Prototype arrays reveals a considerable number of regions of excessive flux of cosmic rays. We present results of comparative analysis of regions found in the two data sets, estimate probabilities of their appearance, and discuss correlation of their locations with coordinates of possible astrophysical sources of PeV cosmic rays.

📄 Content

The problem of the origin of cosmic rays (CRs) in the PeV energy range remains open for many years now. Attempts to find coincidences between arrival directions of CRs and their possible astrophysical sources is one of the routes of investigations on the subject. In the paper, we continue the earlier investigation [1] and present some of the results of a comparative analysis of arrival directions of extensive air showers (EAS) registered with the EAS MSU array in [1984][1985][1986][1987][1988][1989][1990] and with the EAS-1000 Prototype (“PRO-1000”) array in 1997-1999.

We selected 513 602 showers of the EAS MSU data set and 1 342 340 showers of the PRO-1000 data set for the purposes of the investigation. Showers registered with the two arrays have different number of charged particles N e in a typical event. For the EAS MSU array, the median value of N e is of the order of 1.6 × 10 5 , while that for the PRO-1000 array equals 3.7 × 10 4 . All selected EAS have zenith angles θ < 45.7 • .

The investigation is based on the method of Alexandreas et al. [2], which has been used by different research groups for the analysis of arrival directions of CRs. The idea of the method is the following. Every shower in the experimental data set obtains arrival time of another shower randomly. After this, new equatorial coordinates (α, δ) are calculated for the “mixed” data set thus providing a “mixed” map of arrival directions. The mixed map has the same distribution in δ as the original map. Both maps are divided into sufficiently small “basic” cells thus providing a way for comparison.

Mixed maps must be created multiple times in order to minimize the dependence of the result on the pseudo-random choice of arrival times. Finally, one calculates the mean of the mixed maps thus obtaining a “background” map. The underlying idea of the method is that this background map has most of the properties of an isotropic background, and presents the distribution of arrival directions of cosmic rays that would be registered with the array in case there is no anisotropy. Thus, deviations of the real map from the background one may be assigned to a kind of anisotropy of arrival directions of EAS registered at the array.

In our earlier analysis of arrival directions of EAS registered with PRO-1000, basic cells had the size 1 • × 1 • , and the number of cycles of “mixing” varied from 100 to 200 [1]. In the present investigation, we reduced the size of basic cells down to 0.5 • × 0.5 • in order to improve accuracy of locating the regions of excessive flux (REFs). This led to a slower rate of convergence of mixing. We thus had to perform a greater number of cycles of mixing. The difference in the number of EAS in basic cells of two consecutive maps is ≤ 0.02 after 800 cycles for the EAS MSU data set, and after approximately 900 cycles for the PRO-1000 data set. Thus we have chosen to run 1000 cycles of mixing for both data sets.

Regions of excessive flux (REFs) of CRs were searched for in the following way. Adjacent basic strips in δ (each 0.5 • wide) were joined into strips with width ∆δ = 3 • . . . 30 • with step equal to 0.5 • . Each wide strip was then divided into adjacent cells of width ∆α. After this, we calculated the number of EAS inside each of these cells for both experimental (N real ) and “background” (N bg ) maps. For each pair of cells, we then calculated the value of significance S = (N real -N bg )/ N bg . A cell was considered to be a region of excessive flux if S > 3.

Rather unexpectedly, maps obtained after 1000 cycles of mixing with different random seeds in different runs lead to selection of slightly different sets of REFs. Due to this, we performed three 1000-cycle runs for the EAS MSU data set and two 1000-cycle runs for the PRO-1000 data set. Only those REFs found in all runs were selected for the following analysis.

The method of Alexandreas et al. [2] does not put any requirements on the shape or size of regions in experimental and background maps to be compared. In what follows, we only consider so called “regular” regions. These are regions that have approximately the same area at different δ and fixed ∆δ, and have the shape of a square at δ = 0 • . To accomplish this, we used the standard formula ∆α = ∆δ/ cos δ, where δ is the mean value of δ for the current strip, and ∆α is rounded to the nearest half-integer number.

The method of Alexandreas et al. does not provide a direct answer to the question about the probability of appearance of a REF. To solve the problem, we introduced a simple model based on the binomial distribution. In the model, the number of trials equals the number of showers N in the data set under consideration, and an estimation of success (for a fixed region) equals p = N bg /N , where N bg is the number of showers in the region of the background map. The assumption is based on the fact that N bg may be considered as an expected number of showers in the region. Obviously, the probab

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