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Identification of Patterns in Cosmic-Ray Arrival Directions

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Identification of Patterns in Cosmic-Ray Arrival Directions Identification of Patterns in Cosmic-Ray Arrival Directions using Dynamic Graph Convolutional Neural Networks T. Bister, M. Erdmann, J. Glombitza, N. Langner, J. Schulte, M. Wirtz RWTH Aachen University, III. Physikalisches Institut A, Otto-Blumenthal-Str., 52056 Aachen, Germany Abstract We present a new approach for the identification of ultra-high energy cosmic rays from sources using dynamic graph convolutional neural networks. These networks are designed to handle sparsely arranged objects and to exploit their short- and long-range correlations. Our method searches for patterns in the arrival directions of cosmic rays, which are expected to result from coherent deflections in cosmic magnetic fields. The network discriminates astrophysical scenarios with source signatures from those with only isotropically distributed cosmic rays and allows for the identification of cosmic rays that belong to a deflection pattern. We use simulated astrophysical scenarios where the source density is the only free parameter to show how density limits can be derived. We apply this method to a public data set from the AGASA Observatory. Keywords: ultra-high energy cosmic rays, sources, magnetic fields, neural networks 1. Introduction of particles with energies above 39 EeV with star- burst galaxies exhibits an increasing significance, The quest for sources of ultra-high energy cosmic currently at the 4.5σ level [11, 12]. rays has entered a new phase. On the one hand, For nuclei with charge Z, deflections in cosmic the experimental results of recent years have sharp- magnetic fields of several degrees per charge unit ened the boundary conditions for this search; on the are estimated [13, 14, 15, 16, 17, 18, 19, 20], with other hand, current developments in data analysis the strongest deflection expected in the magnetic technologies are opening up new perspectives. field of our Galaxy [21, 22, 23, 24, 25]. The dif- The measurements relevant to source searches ferent rigidities of the nuclei may lead to patterns include first the sharp drop in the energy spec- in the arrival directions which can be used to dis- trum above 50 EeV [1, 2, 3, 4]. Second, measure- tinguish cosmic rays of a single source or of a con- ments of the slant depth of air showers in the at- catenated source cluster from isotropically arriving mosphere indicate a mixed composition of protons particles [26, 27]. and heavier nuclei [5, 6, 7]. Both these observa- In the field of data analysis, new technologies tions increase the probability of astrophysical sce- around machine learning are the driving force of narios in which the sources are some megaparsecs much lot of the progress. Deep-learning meth- away and accelerate nuclei to a maximum rigidity ods [28] in particular have gained considerable at- (=energy/charge) [8]. The third relevant observa- tention in astroparticle physics [29, 30, 31, 32, 33, tion is the discovery of a large-scale dipole signal 34, 35, 36, 37, 38, 39]. arXiv:2003.13038v1 [astro-ph.HE] 29 Mar 2020 above 8 EeV energy which shows - with a signifi- Recently, we introduced a fit method which con- cance of more than five standard deviations - that tracts patterns in the arrival directions induced by the arrival directions of cosmic rays are not en- the Galactic magnetic field to determine most prob- tirely isotropic [9, 10]. Also, there is an indication able extragalactic source directions [40]. In this of an intermediate-scale anisotropy: the correlation fit, several thousand parameters are determined si- multaneously (source directions, particle charges), Email address: [email protected] which was realized by using the backpropagation (M. Erdmann) method developed for neural network training [41]. Preprint submitted to Astroparticle Physics March 31, 2020 In this paper we present a new method for source Later, in an advanced simulation, we use an as- identification that directly uses pattern recognition trophysical scenario that depends only on one free in cosmic-ray arrival directions. A similar approach parameter, the density of sources. Here, all cos- using convolutional neural networks was developed mic rays originate from these sources, with only a in parallel [39]. Here, we use the concept of so-called few closer sources contributing several cosmic rays dynamic graph convolutional neural networks [42] which form a pattern in the arrival distributions. which have already been successfully adapted and This results in a few signal patterns distributed applied to challenges in particle physics [43, 44]. across the whole sky, each with particles from a In contrast to our fit method [40], here we do common source, while most particles appear to have not use an explicit model of the Galactic magnetic isotropic arrival directions. field, but instead train the network with typical Finally, we present the AGASA Observatory and deflection patterns resulting from these field mod- its public data set of ultra-high energy cosmic rays. els [45, 46, 47, 48, 49, 50]. The scope of our method is to search for the exis- 2.1. Simplified cosmic-ray scenario with a single tence of patterns in cosmic-ray arrival directions: if source such patterns are detected by the network, we clas- In order to keep the results unambigous and sify which individual particles originate from a com- clean, this first simulation setup is simplified yet mon source and which can be attributed to isotropic fairly in agreement with the measurements de- arrival directions. For this classification we analyze scribed in section 1. variables autonomously formed by the network. During the training process we generate up to If no pattern is found, we derive a lower limit 300.000 simulation sets on-the-fly with the following on the density of cosmic-ray sources using astro- general setup. The predominant part of all NCRs physical simulations with the source density as their events, called background, is positioned isotropi- only free parameter. We exploit public data of the cally on the sky. We then add a certain fraction AGASA Observatory to demonstrate the applica- fS = NS=NCRs of NS signal cosmic rays which tion to real cosmic-ray measurements. mimic a pattern arising from deflections in the This work is structured as follows. First, we Galactic magnetic field (GMF). Current models of present astrophysical benchmark simulations used the GMF consist of a superposition of a regular for training and performance estimation as well as field part which deflects particles coherently and the public dataset of the AGASA Observatory. We a turbulent field part which results in blurring and then introduce the functionality of dynamic graph widening of the incoming particle beam. The mag- convolutional neural networks. We describe the nitude of the magnetic field influence depends on search for the existence of anisotropic patterns, the the cosmic-ray rigidity subsequent identification of cosmic rays and the de- termination of source density limits. Finally, we E R = ; (1) apply our methods to the data measured by the Z AGASA Observatory. We complete the work with our conclusions. the ratio of its energy and charge. To prevent over- training of the network which could learn specific patterns in fixed directions of the sky we do not 2. Cosmic rays: simulations and measure- use one fixed field parametrization. Instead, we ments use a random value for the orientation of the sig- In this section we first present the simulated data nal pattern and adopt the field magnitude of both we use for training the network and evaluating its regular and turbulent fields from [46, 48] in the fol- performance. lowing way: we account for the turbulent field by For an in-depth understanding of the network, we a Fisher [51] distribution with a rigidity-dependent start with simplified simulations in which a single width of source generates a few cosmic rays that exhibit typ- T σturb(R) = rad ; (2) ical signal patterns in the arrival directions due to R = EV the deflection in cosmic magnetic fields. As back- ground we further add isotropically arriving cosmic where we choose T position-dependently based on rays. typical scattering obtained in [46, 48]. During the 2 training we fix T = 2:8 which corresponds to half 60◦ the maximum of the expected turbulent deflection in [46, 48] and more than double the mean value. 30◦ It was tested that training with a fixed value T for 90◦ 0◦ -90◦ all training sets is beneficial for the network per- 0◦ formance even when evaluating with varying values of T . -30◦ The coherent deflection angle δcoh is described by -60 D ◦ δcoh(R) = rad ; (3) R = EV 19.6 19.8 20.0 20.2 20.4 log10(Energy / eV) with a varying deflection power D which is deter- mined position-dependently based on typical deflec- Figure 1: Example of simulated arrival directions used for tions from [46]. For the training it is taken from network training: the pattern induced by a magnetic field with a coherent deflection power D = 7:2 is situated at a Gaussian distribution based on deflections again ◦ ◦ D Galactic longitude l ≈ 16 and Galactic latitude b ≈ 45 . from [46]. Additionally, a lower cut on ensures The source of this signal pattern is indicated by the star that the coherent deflection mostly remains larger symbol. It has a signal fraction of fS = 5:5%, thus NS = 55 than the turbulent one. signal cosmic rays are contained in this arrival pattern. The The cosmic-ray energies follow the parameterized remaining 945 events are isotropically distributed. measured energy spectrum given in [52] which con- tains a broken power law with a smooth transition function above the ankle. The energy threshold of fixed number of signal cosmic rays. In the follow- 40 EeV is oriented on the data used for the recent ing we extend this simplified approach to constrain first indication of intermediate-scale anisotropy in actual physics quantities using the network.
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