научная статья по теме SIMULATIONS OF ULTRA-HIGH-ENERGY COSMIC RAYS PROPAGATION Физика

Текст научной статьи на тему «SIMULATIONS OF ULTRA-HIGH-ENERGY COSMIC RAYS PROPAGATION»

SIMULATIONS OF ULTRA-HIGH-ENERGY COSMIC RAYS

PROPAGATION

O. E. Kalashev'1*, E. Kidoh**

" Institute for Nuclear Research, Russian Academy of Sciences 117312. Moscow, Russia

b Institute for Cosmic Ray Research. University of Tokyo Iiashiwa, Chiba, Japan

Received November 8, 2014

We compare two techniques for simulation of the propagation of ultra-high-energy cosmic rays (UHECR) in intergalactic space: the Monte Carlo approach and a method based on solving transport equations in one dimension. For the former, we adopt the publicly available tool CRPropa and for the latter we use the code TransportCR, which has been developed by the first author and used in a number of applications, and is made available online with publishing this paper. While the CRPropa code is more universal, the transport equation solver has the advantage of a roughly 100 times higher calculation speed. We conclude that the methods give practically identical results for proton or neutron primaries if some accuracy improvements are introduced to the CRPropa code.

DOI: 10.7868/S0044451015050055

1. INTRODUCTION

Identification of the origin of ultra-high-energy cosmic rays is one of the main problems of modern astrophysics. Although the existence of particles with the energy E > 101B eV has been confirmed by several experiments, their possible sources, propagation mechanism, and even their nature are still subjects of intense research. Noticeable progress has been achieved during the last decade by the new-generation experiments. A suppression of the cosmic-ray flux above E « 4-1019 eV has been observed by HiRcs, Telescope Array fl], and Pierre Auger Observatories [2,3]. Depending on the assumed ultra-high-energy cosmic rays (UHECR) composition, this may indicate either the observation of the GZK effect [4, 5] or a natural cut-off in the energy of cosmic-ray sources. The measurements of the position of the shower maximum and its fluctuations by the Pierre Auger experiment suggest a significant fraction of heavy nuclei above 101B eV [G]. However, both composition and energy spectrum studies by HiRcs [7] and Telescope Array [8] show consistency with the pure

* E-mail: kalashevflinr.ac.ru

**E-mail: ekido'fflicrr.u-tokyo.ac.jp

proton or light-element composition in the same energy range.

Ultra-high-energy protons and nuclei cannot be kept by the galactic magnetic field and therefore freely-escape the galaxy. Currently, there are no known sources within the Milky Way that could possibly accelerate protons or nuclei to ultra-high energies, and it is therefore assumed that the particles should have extragalactic origin. During their propagation through intergalactic space, UHECRs rapidly lose energy in interactions with the intergalactic photon background. Understanding the UHECR attenuation process is crucial for making model predictions and interpreting experimental results.

Many studies on propagation of ultra-high-energy nucleons and nuclei exist in the literature, including analytic solutions of the transport equations, which can be found for some specific situations, such as the propagation of nucleons near the GZK cutoff (see, e. g., [9 12]) or using the continuous energy loss (CEL) approximation (see, e.g., [13 15]). Due to the small inelasticity, the CEL approximation works well for pair production by protons and nuclei. But for pion production on a photon background, due to its large inelasticity and stochastic nature, the CEL approximation predicts a sharper pile-up right below the

GZK cutoff compared to exact solutions [16]. Numerical solutions for nucleons solve the transport equations either directly [10 20] or through Monte Carlo simulation [21 25]. In Ref. [26] (see also references therein), a universal approach to the simulation of cosmic ray propagation is discussed based on the adjoint cascade theory. The photodisintogration of ultra-high-energy nuclei was first discussed in [27] and later in [19,20,22,24,25,28,29].

Unfortunately most of the numerical codes mentioned above are not public. The mutual checks between different propagation codes show a consistency level of about 10%. Due to the growing experimental statistics, improving the simulation accuracy becomes crucial. In this paper, we focus on predictions of the spectra from proton sources. We describe in detail our transport-equation-solving code, which has already been used in a number of works [19], although has not been publicly available until now. We compare our tool with the actively developed Monte Carlo code CRPropa [25], which is publicly available and used in the Pierre Auger Collaboration analysis [30]. While the former code benefits exceedingly high calculation speed, the latter is more universal and easy customizable. In Sec. 2, we discuss the simulation techniques on which the codes are based. In Sec. 3, we compare the results of proton propagation simulations and suggest improvements to CRPropa. Finally, we make a conclusion.

2. CALCULATION OF OBSERVABLE SPECTRA

Calculations of the observable UHECR spectra for given production scenarios involve simulation of sources and attenuation effects such as interactions of cosmic rays with inter galactic media and their deflection by-galactic and intergalactic magnetic fields. The interaction rate calculation accuracy depends on our knowledge of the infrared intergalactic photon background and its evolution, while particle trajectory calculations rely on the models of intergalactic and galactic magnetic fields. Neither of the above factors is currently known sufficiently well to make definitive predictions. On the other hand, identifying UHECR sources would help constrain the properties of intragalactic media, which especially applies to magnetic field estimates. Our present knowledge of the intergalactic magnetic field (IGMF) is very poor. The theoretical and observational constraints on the mean IGMF strength B

and the correlation length Lcor are summarized in review [31]:

10-17 G < D < 10-fi G, (1)

Lcor > 1 pc. (2)

The simulation assuming the magnetic field growth in a magnetohydrodynamical amplication process driven by structure formation out of a magnetic seed field present at high redshift [32], suggests the present IGMF strength B < 10-12 G (see also Ref. [33]). It can be shown (see, e.g., Ref. [34]) that the effect of magnetic fields on the average energy spectrum of protons with energies E > 1018 eV is negligible for the IGMF strengths B < 10-10 G (assuming Lcor < 1 Mpc) if the average distance between the UHECR sources does not exceed the GZK radius. If these conditions are realized, the computation of the averaged fluxes can be done by solving the coupled Boltzmann equations for UHECR transport in one spatial dimension or using one-dimensional Monte Carlo simulation (the first method is usually much faster). In the limit of strong magnetic fields, when it is important to follow particle trajectories, e.g., for calculating the images of discrete sources of UHECR, only the full 3D Monte Carlo simulation can give reliable results. Our code [19] uses the formalism of transport equations, while the CRPropa [25] implements either ID or 3D Monte Carlo simulations. Below, we describe the CRPropa code only briefly and pay more attention to the transport equation solution.

2.1. CRPropa

CRPropa [25] is a Monte Carlo simulation tool aimed at studying the propagation of neutrons, protons, and nuclei in the intergalactic medium. It provides a one-dimensional (ID) and a three-dimensional (3D) modes. In the 3D mode, the magnetic field and source distributions can be defined on a 3D grid. This allows performing simulations in the source scenarios with a highly structured magnetic field configuration. In the ID mode, magnetic fields can be specified as functions of the distance to the observer, but their effects are restricted to energy losses of electrons and positrons due to synchrotron radiation within electromagnetic cascades. Furthermore, in the ID mode, it is possible to specify the cosmological source evolution as well as the redshift scaling of the background light intensity. All important interactions with the cosmic infrared (IRB) and microwave (CMB) background light

are included, namely, production of electron positron pairs, photopion production, and neutron decay. Additionally, CRPropa allows tracking and propagating secondary 7-rays, e+e- pairs, and neutrinos. The code also contains a module solving one-dimensional transport equations for electromagnetic cascades initiated by electrons, positrons, or photons, taking pair production and inverse Compton scattering and synchrotron radiation of electrons into account. For more details 011 the code, we refer the reader to the Ref. [25].

2.2. Transport code

The code developed in [19] simulates attenuation of protons, neutrons, nuclei, photons, and stable lep-tons by solving the transport equation in one dimension taking all standard dominant processes into account. Ultra-high-energy particles lose their energy in interactions with the electromagnetic background, which consists of CMB, IRB, and radio components (the last effects the electromagnetic cascade development only at ultra-high energies). For IRB backgrounds, several models are implemented [35 40]. For highest-energy protons, neutrons, and nuclei, the main attenuation process is photopion production. Below the photopion production threshold, photodisintogration (for nuclei only) and pair production provide the attenua-

tion mechanism. Although the attenuation of nuclei is implemented in the code (we use photodisintegration rates derived in [41]), a reliable description of the propagation of heavy nuclei can be achieved only for energies E > 101B eV (assuming B < 10-10 G) because deflections in magnetic fields cannot be precisely-described within the ID transport equation formalism. Below, we focus 011 proton and neutron propagation simulations. With the photopion production by protons

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