1 COSMIC RAY ANISOTROPY STUDY BY MEANS OF DETECTION OF MUON BUNDLES

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COSMIC RAY ANISOTROPY STUDY BY MEANS OF

DETECTION OF MUON BUNDLES

G. Trinchero

, M.B. Amelchakov

, A.G. Bogdanov2, A. Chiavassa2,

, A.N. Dmitrieva2,

G. Mannocchi1, S.S. Khokhlov2, R.P. Kokoulin2, K.G. Kompaniets2, A.A. Petrukhin2,

V.V. Shutenko2, I.A. Shulzhenko2, I.I. Yashin2, E.A. Yurina2

ABSTRACT

In this work, we use muon bundles which are formed in extensive air showers and

detected at the ground level as a tool for searching anisotropy of high energy cosmic rays. Such

choice is explained by the penetrating ability of muons which allows them to retain the direction

of primary particles with a good accuracy. In 2012-2022, we performed long-term muon bundle

detection with the coordinate-tracking detector DECOR, which is a part of the Experimental

complex NEVOD (MEPhI, Moscow). To search for the cosmic rays anisotropy, the muon

bundles arriving at zenith angles in the range from 15 to 75 in the local coordinate system are

used. During the entire period of data taking, about 14 million of such events have been

accumulated. In this paper, we describe some methods developed in the Experimental complex

NEVOD and implemented in our research, including: the method for compensating the influence

of meteorological conditions on the intensity of muon bundles at the Earth’s surface, the method

for accounting the design features of the detector and the inhomogeneity of the detection

efficiency for different directions, as well as the method for estimating primary energies of

cosmic rays. Here we present the results of the search for the dipole anisotropy of cosmic rays

with energies in the PeV region and also compare them with the results obtained at the other

scientific facilities.

1. INTRODUCTION

Cosmic ray (CR) anisotropy is usually defined as the relative deviation from the assumed

isotropic flux. Study of CR anisotropy on the Earth’s surface is a very complicated problem

which holds a lot of puzzles. The phenomenon of cosmic ray anisotropy is associated with the

distribution of the CR sources on the celestial sphere, as well as with the interaction of CR with

matter and fields in the interstellar space. The so-called small scale anisotropy (SSA) is

associated with local sources. Thus, on the celestial sphere the perturbation of the CR flux has a

local character. To observe the SSA, it is necessary that the particles emitted from the source had

rather high energy to retain the direction during their passing through the scattered magnetic

Osservatorio Astrofisico di Torino – INAF, Italy

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409 Russia

Dipartimento di Fisica dell’ Università degli Studi di Torino, 10125 Torino, Italy

Sezione di Torino dell’ Istituto Nazionale di Fisica Nucleare – INFN, 10125 Torino, Italy

fields in the Galaxy. Typical interstellar magnetic field in the (Malcolm

2011). For example, the proton with energy of 1 PeV has a gyroradius of about 3 light years in

the Galaxy. It corresponds to the distances to the stars closest to the Sun (4 - 5 light years). To

observe SSA from more distant objects, the energy of the emitted charged particles must be

much higher.

An uneven distribution of CR sources and magnetic fields in the Galaxy create conditions

for CR diffusion which, in its turn, could cause the large scale anisotropy (LSA). Since the Solar

system is on the periphery of our Galaxy, we should expect an excess of CR from the central part

of the Galaxy. But also the Sun is located at the inner edge of the Orion Spur (Reid & Zheng

2020) which could be the other reason of LSA. Existing models of CR diffusion from the center

of the Galaxy predict that the amplitude of the dipole anisotropy depends on the rigidity of

primary particles as ~ R1/3 (Berezinsky 1990).

The other reason of LSA is Compton-Getting effect (Compton & Getting 1935). It occurs

when the detector moves relative to the flux of cosmic rays. In this case, the anisotropy can be

expressed by the formula (Gleeson & Axford 1968):

    

. (1)

where  is the absolute value of the power-law index of the CR differential energy spectrum, w is

the detector velocity relative to the cosmic ray flux, v is the particle velocity.

Since the detector is located on the Earth’s surface, it is possible to consider the orbital

speed of the Earth (~ 30 km/s) around the Sun and the peculiar motion of the Sun (~ 20 km/s)

with respect to the so-called local standard of rest (Schönrich et al. 2010). In these cases the

calculated amplitude of anisotropy is of about 10-4. A circular rotation speed of the Sun around

the center of the Galaxy is 240 ± 8 km/s (Reid et al 2014), and the amplitude of anisotropy

should be by an order of magnitude greater (~ 10-3), but only for the extragalactic flux of CRs

with energy higher than 1000 PeV.

In ground-based installations, the components of extensive air showers (EAS) are used as

tools to study anisotropy. The EAS components appear as a result of the development of nuclear-

electromagnetic cascades in the atmosphere. Therefore, a change in the state of the atmosphere

affects the development of cascades. To correct data for the atmospheric effect in the analysis,

the East-West method (Bonino et al 2011) is used in most experiments. The total counting rates

of events observed in either the Eastern or the Western half of the field of view of installations

can be varied due to different factors during a sidereal day that may complicate the search for

anisotropy. The East-West method is aimed at reconstructing the equatorial component of a

genuine large scale pattern of anisotropy by using only the difference of the counting rates from

the Eastern and Western hemispheres.

2. DIPOLE ANISOTROPY SEARCH

Isotropy means that some object or phenomenon has the same physical properties in all

directions. In its turn, the term “anisotropy” is used to describe situations where properties vary

systematically, dependent on direction. In case of dipole anisotropy the resulting CR flux would

be described by the formula:

    





, (2)

where I0 is the isotropic flux,  is the unit vector of observation direction, 





is the dipole vector.

The flux I has the maximum value when the observation vector and the anisotropy dipole have

the same direction. Consequently, the amplitude of anisotropy of the cosmic ray flux for selected

angle of view () relative to the dipole direction can be expressed as

    

, (3)

where d is the module of 





,  is the angle between vectors 





and .

Determination of the dipole anisotropy parameters is not a completely trivial task. The

problem is related to the spherical shape of the Earth. The installation located on its surface

cannot observe the entire celestial sphere. In the 2nd equatorial coordinate system (Sadler et al.

1974) the formula (3) transforms to the following form:



   , (4)

where 0 (right ascension) and 0 (declination) are the coordinates of dipole anisotropy vector, 

and  define the direction of detection. In formula (4), the measured value of the relative

deviation is associated with three unknown parameters (d, 0, 0). To simplify the analysis we

can use the projection of the anisotropy vector onto the plane. In this case, the most convenient

plane is the equatorial one. Usually, the equatorial plane is used in order to provide the

possibility of comparing the results obtained at the installations located in the southern and

northern hemispheres. In the 2nd equatorial system, the projection on the equatorial plane is

equivalent to projection onto the right ascension axis. To obtain the result, it is necessary to

integrate formula (4) over the declination (). In this case, the dipole anisotropy vector

declination (0) remains undefined, as well as the absolute value of the vector itself. The only

parameter determined from direct measurements is 0 which is called the anisotropy phase.

Attempts to study the anisotropy are made with almost all installations for detecting EAS

components in a wide range of primary energies from TeV to EeV. The anisotropy amplitude in

the projection on the right ascension axis varies in the range from 10-4 to 10-3. The region of

primary energies near 200 TeV is of particular interest. Data from the ARGO-ABJ (Bartoli et al

2012), Tibet-AS (Amenomori et al 2017), LHAASO-KM2A (Gao et al 2021) and IceCube

(Aartsen et al 2016) facilities, which use different types of detectors and measure different EAS

components, indicate that in this region a sharp change of the anisotropy dipole occurs in the

observed direction and the anisotropy amplitude reaches its minimum. This phenomenon occurs

just below the first “knee” in the energy spectrum, and its cause is still unclear. The data of other

installations, such as KASCADE-Grande (Chiavassa et al 2019), IceTop (Aartsen et al 2016), do

not cover this region, but confirm the trends in the energy dependences of the anisotropy

amplitude and phase.

In this paper, we present a method of anisotropy search based on muon bundle detection,

as well as a method of atmospheric effect correction. In contrast to other experiments, we use the

local muon density measured in the detector for primary energy estimating.

3. EXPERIMENTAL SETUP

To investigate cosmic rays in a wide range of primary energies, the Experimental

complex NEVOD (Petrukhin 2015) has been constructed in MEPhI (Moscow, Russia) at the

ground surface, about 164 m above the sea level. The complex includes several scientific

installations for EAS components investigations (Yashin et al 2021). One of them is the

coordinate-tracking detector DECOR (Barbashina et al. 2000). It includes 8 supermodules (SM)

with a total area of about 70 m2 which are arranged around the 2000 m3 water tank of the

Cherenkov water detector NEVOD, as shown in Figures 1 and 2. Two supermodules are

installed in each of two short galleries of the laboratory building (SMs 0, 1, 6, 7) and four

supermodules (SMs 2, 3, 4, 5) are located in the long one. The main DECOR features are the

vertical deployment of detecting planes and good spatial and angular resolutions (~ 1 cm and ~

1) for inclined muon tracks. Each supermodule represents an eight-layer system of plastic

streamer tubes with a resistive coating of the cathode. The planes are suspended at a distance of

6 cm from each other. Each layer is equipped with aluminum strips forming two-coordinate

readout system (vertical and horizontal).

The muon bundle is a group of several genetically related muons with quasi-parallel

tracks. Muon bundles are generated close to the air-shower core and can reach the detector in a

wide range of zenith angles. Moreover, muon bundles retain the direction of primary particle

with a good accuracy. Therefore they can be used to study CR anisotropy.

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1COSMICRAYANISOTROPYSTUDYBYMEANSOFDETECTIONOFMUONBUNDLESG.Trinchero1,M.B.Amelchakov2,A.G.Bogdanov2,A.Chiavassa2,3,4,A.N.Dmitrieva2,G.Mannocchi1,S.S.Khokhlov2,R.P.Kokoulin2,K.G.Kompaniets2,A.A.Petrukhin2,V.V.Shutenko2,I.A.Shulzhenko2,I.I.Yashin2,E.A.Yurina2ABSTRACTInthiswork,weusemuonbundleswhicharef...

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