Mass composition of cosmic rays determined by muon fraction with $\varepsilon_{thr.}\geq$ 1 GeV in air showers with energy greater than 5 EeV

Astrophysics of cosmic rays of highest energies above 1 EeV is an important area of research for gaining knowledge about evolution and processes occurring in the Universe Ginzburg (1970, 1999); Gelmini et al. (2007); Bhattacharjee and Sigl (2000); Halzen and Hooper (2002).

Recent observations made by telescopes find interesting structures — some bubbles Li et al. (2019), which are possibly sources of intergalactic cosmic rays with energies greater than 5 EeV along with other active astronomical objects: supernova remnants, compact jets of active galactic nuclei Mannheim et al. (2000), clusters of galaxies Kang et al. (1996), radio galaxies Rachen and Biermann (1993), and gamma ray bursts Waxman (1995). In the past it has been assumed that protons dominate in this region Berezinsky and Zatsepin (1969), while at energies less than 0.1 EeV, galactic cosmic rays consist of a mix of nuclei Stanev et al. (1993).

At the same time, the astrophysical aspect of cosmic rays of highest energies is still a little studied area. There is no reliable information about the nature of the origin of cosmic rays of highest energies. In particular, sources and their location in the Universe are not known well enough. The mechanism of generation, acceleration and propagation of particles has not been reliably established. It is unknown how particles interact during their propagation in outer space with magnetic fields and cosmic microwave background Berezinsky and Zatsepin (1969); Becker (2008); Ahlers et al. (2010); Kotera et al. (2010); Gelmini et al. (2008).

At the largest experiments for the study of air showers, recently, interesting data have been obtained on cosmic rays in the energy region above 1 EeV: the cosmic ray spectrum Aab et al. (2017); Abbasi et al. (2016), the mass composition Knurenko and Petrov (2019); Hanlon et al. (2018); Berezhko et al. (2012); Kampert and Unger (2012); Knurenko and Petrov (2015); Thoudam et al. (2016); Aab et al. (2014); Abbasi et al. (2015), and the anisotropy of the arrival of particles with highest energies Knurenko et al. (2009); Ivanov (2008); Abreu et al. (2012) . Verification of the obtained data is still small and further research in these areas is required.

The following results have been obtained in the energy range 1-10 EeV: according to the Pierre Auger Observatory — mass composition is mainly protons Aab et al. (2014); according to the Telescope Array experiment — mass composition is a mixture of protons and helium nuclei Abbasi et al. (2015). The flux of cosmic rays according to the Yakutsk experiment data: in the energy range 10-100 PeV — a mix of light and heavy nuclei; in the energy range 0.1-10 EeV — a mix of protons and helium nuclei Knurenko and Petrov (2019); Berezhko et al. (2012).

The results obtained indirectly largely depend on the equipment and methods of the experiment, the atmospheric conditions, methods for processing the experimental data, hadronic interaction models, and other factors. Therefore, to verify the results obtained earlier, it is important to obtain mass composition using a different technique and a different component of air shower, e.g. muons. Muons are measured at the Yakutsk array almost the entire year. The technique does not depend on weather conditions, as in the case of Cherenkov light at the Yakutsk array or fluorescence light at the Auger and TA arrays. The total time of optical measurements, for comparison, at the Yakutsk is only $\sim$ 10$\%$ of the total time of charged particles measurements.

It is known that the muon component is sensitive to the mass composition of the primary particles that produces air shower Knurenko and Petrov (2018), as was shown by calculations using the QGSJETII-04 model Ostapchenko (2011) for the primary proton and iron nucleus. First of all, this refers to the relative content of muons, i.e. the ratio of the muon flux density to the charged shower component at a distance of 600 m from the shower axis $\rho_{\mu}/\rho_{\mu+e}$. This parameter is used at the Yakutsk experiment to analyze the mass composition of cosmic rays of highest energies. According to calculations, a joint analysis of the muon content with the longitudinal development of air shower at fixed energy and in the case of vertical shower can provide a reliable estimate of the mass composition of cosmic rays. It even can separate the primary particles by atomic weight Atrashkevich et al. (1981), i.e. to distinguish air showers produced by gamma rays, protons, and iron nuclei Knurenko et al. (2009). We performed such analysis for the Yakutsk array data and estimated Cherenkov light, total charged and muon components Knurenko and Petrov (2018). The data for this work consist of air showers with energies above 5 EeV and zenith angles $\theta\leq 60^{\circ}$. In the region of these energies, “dip” and “bump” type irregularities are formed in the spectrum of cosmic rays Aab et al. (2017); Abbasi et al. (2016), which has been interpreted as the interaction of galactic protons with the cosmic microwave background of the Universe Rachen and Biermann (1993); Berezinsky et al. (2004). This hypothesis can be confirmed only by having information about the mass composition of cosmic rays in the energy range 5-50 EeV. In this work, for this purpose, an analysis of the relative muon content in showers of highest energies was carried out.

Fig. 1 shows the location of observation stations at the Yakutsk array. The array consists of 120 scintillation detectors with a threshold of 10 MeV and a receiving area of 2 m². Each station has two scintillation detectors and one Cherenkov detector with a photocathode receiving area of 176 cm² or 530 cm² Artamonov et al. (1994).

Subfigure (Fig. 1) shows the central part of the array in close-up. Over an area of $\sim$ 0.8 km², registration station for charged particles, air shower Cherenkov light (integrated and differential detectors), muon telescopes, cameras obscura and radio antennas are located Egorov et al. (2018); Knurenko et al. (2017a). The distances between the stations are 50, 100, 250 and 500 m. The central area is filled with a small Cherenkov array with its own independent trigger that detects air shower events in the energy range from 2 PeV to 1 EeV using the trigger from the detectors of Cherenkov light Knurenko et al. (1998).

The Yakutsk experiment in various configurations has been operating since 1970, continuously registering ultra-high energy air shower events. In the 70s of the last century, registering air showers on an area of 3.5 km². From 1974 to 1994 — over an area of $\sim$ 20 km². From 1994 to 2004, registration was carried out over an area of $\sim$ 18 km², and after 2004, the area decreased to the current $\sim$ 13 km². The Yakutsk experiment differs from other large experiments by its hybrid measurements: the charged and muon components, Cherenkov and radio emission from air showers. The system of observation stations selects shower events in ground-based scintillation detectors using a single “500” trigger (the trigger uses detectors with 500 m spacing) — matching scheme C6 = C2 + C3. This scheme is a coincidence of two local triggers: C2 and C3. C2 — coincidence of signals from two scintillation detectors for 4 $\mu s$ in the observation station; C3 — coincidence of three or more stations within 40 $\mu s$ located in a triangle. Satisfying these two conditions is called the “C6” trigger. From the air shower events selected in this way, a primary database of the Yakutsk experiment was created. After a preliminary analysis of the data, a set of showers was used to find the parameters of individual air showers: arrival direction, coordinates of the core, power of the shower — total number of charged particles $N_{s}$, and the classification parameter $\rho_{\mu+e}$ — density of the flux of charged particles at distances of 600 m from the shower axis.

We used the lateral distribution function (LDF) of charged particles perpendicular to the axis of the shower to locate the core:

where $R_{0}$ is the Moliere radius in meters, $b_{s}$ is the slope characteristic of the lateral development function (LDF) of charged particles, which depends on the classification parameter $\rho_{\mu+e}$ and the zenith angle $\theta$, according to formula (2):

This expression was obtained empirically from measurements of showers with different energies and different zenith angles Glushkov et al. (1993).

In the table 1 as an example, a part of the data is shown — 2009-2015. Table 1 shows the observation time, statistics of recorded air showers, the percentage of analyzed showers, the number of showers with registered muons and Cherenkov light, the observation time of the Cherenkov component and the number of showers with energies above 10 EeV. N — total number of registered air shower events, $N_{muon}$ — number of air shower events with registered muon component, and $N_{ch}$ — number of air shower events with registered Cherenkov component.

Currently, the Yakutsk array has an area of $\sim$ 13 km² and is medium in size, between compact arrays with an area of s $\leq$ 1 km² and giant arrays with s $\geq$ 1000 km² Abraham et al. (2004); Abu-Zayyad et al. (2012). The array with such area is able to efficiently detect showers in energy range from 1 PeV to 100 EeV, and it allows us to study both galactic and metagalactic cosmic rays.

The registration of muons with a threshold of $\varepsilon_{thr.}\geq$ 1 GeV at the Yakutsk experiment was started in 1974 by three observation points with an area of 16 m² each. Two points were located at a distance of 500 m and one at a distance of 300 m from the array center. Later, in 1994, three more stations were built, each with an area of 20 m². Two points were located at a distance of 800 m and one point at a distance of 500 m from the array center. In 1998, another station for registering muons with $\varepsilon_{thr.}\geq$ 0.5 GeV and an area of 190 m² was added to the existing stations. It is located at a distance of 150 m from the array center Artamonov et al. (1994); Ivanov et al. (2010).

As part of the Small Cherenkov Array, there are three muon telescopes with $\varepsilon_{thr.}\geq$ 1 GeV. The scheme of the telescope is shown in Fig. 2. The muon telescope consists of two scintillation detectors, ground and underground, located one above the other with 1 and 2 m² area respectively.

Muon telescopes, in addition, record the spatio-temporal image of signals Knurenko et al. (2013); Knurenko et al. (2017b). Examples of registration of pulses from the passage of charged particles and muons in an individual shower are shown in Fig. 3.

In Fig. 3a, the signal sweep consists of several peaks separated by the time of the particles arrival at the detector, and in aggregate corresponds to the total signal from electrons, gamma rays, and muons. The concrete cuts off the electromagnetic component of the shower, and the underground scintillation detector measures only the response from muons. Muon component has narrower signal with single-pulse structure (Fig. 3b). Comparing both figures we can say that the contribution of electrons and gamma rays to the signal is small, because the signal of the underground detector is very close in amplitude to the surface detector signal. At the zenith angle $\theta\geq$45^∘, the air shower disk at the ground level mainly contains muons, which are distributed in time from 0 to 3 $\mu s$ Knurenko et al. (2013); Knurenko et al. (2017b).

Fig. 4 shows lateral distributions of charged particles (circles) and muons (squares) of an individual shower with energy $E_{0}$ = 20.9 EeV and zenith angle $\theta$ = 44.8^∘. Muon LDF is measured relative to the air shower axis and given as a function of muon density divided by detector area $\rho_{\mu}(R)$ = n/s$\cdot\cos{\theta}$, where n — number of muons and s — area of the detector.

Air shower event from 5.01.2018 is not an ordinary one, because of its inclination ($\theta$ = 44.8 ^∘) and low measured muons compared to total charged particles. It may happen in the case of $X_{max}$ of air shower is at or below the sea level. In this case, it is initial stage of air shower development in the atmosphere and formula (8) for energy estimation is not applicable. It’s better to use formula (6), since electron-photon component of the shower is at the maximum of development and its energy almost equal to air shower energy. It is possible that this shower has been produced by primary gamma ray of ultra-high energy with the depth of maximum near the sea level. Depth of maximum $X_{max}$ estimation results in 953$\pm$55 g$\cdot$cm^-2 Knurenko and Petrov (2018).

The dotted line (Fig. 4) shows the data approximation for charged particles using function (1). Dashed approximation line is for muons. The dashed horizontal lines indicate the flux density of charged particles and muons for distances R = 300 and 600 m from the shower axis, which are used as classification parameters at the Yakutsk experiment. The classification parameter for showers with energies below 0.5 EeV, we use $\rho_{\mu+e}$ (R = 300), and for energies greater than 0.5 EeV we use $\rho_{\mu+e}$ (R=600). In this work we use only $\rho_{\mu+e}$ (R=600). This parameter correlates with air shower energy and is used for the fast estimation of shower energy and the selection of showers for a particular physical tests.

The muon component measured at the Yakutsk array made it possible to obtain information on the lateral distribution, relative content, and spatio-temporal distribution of muons in the air shower disk with energies of 5-50 EeV. Thanks to the long-term (over 40 years) measurements of muons at the array, it was possible to create a database for further study of the characteristics of muons in showers of highest energies. It turned out that the lateral distribution of muons is more flatter compared to the lateral distribution of charged particles (Fig. 4). Such feature of the radial development of muon component and electron-photon component of the shower at sea level, is associated with the nature of the primary particle interaction with the nuclei of air atoms and with the longitudinal development of air shower — the depth of shower development maximum $X_{max}$Knurenko et al. (1998); Egorov et al. (2018); Knurenko et al. (2017a).

It was used in the present work for an independent estimation of the mass composition of cosmic rays in the region of highest energies. For this purpose, the parameter $\rho_{\mu}/\rho_{\mu+e}$ was chosen, which was measured with good accuracy on the array and is sensitive to the mass of the primary particle producing the air shower. From the measurements, the dependence $\rho_{\mu}/\rho_{\mu+e}$ on the zenith angle and shower energy was established. The dependence made possible to normalize all selected showers to the same conditions for the development of muons in the atmosphere and use these data to estimate the mass composition of cosmic rays.

Fig. 10 shows the experimental energy-normalized distribution of the parameter $\rho_{\mu}/\rho_{\mu+e}$ as a function of the number of muons in the average shower at a fixed energy. QGSJETII-04 simulations for different primary particles are also plotted there. It can be seen from Fig. 10 that the distribution has several maxima, and these maxima relate to particles with different atomic weights. A quantitative comparison of the experimental data with the calculations showed: a) the group of showers with energies of 5-10 EeV is presumably produced by protons p and He helium nuclei, which is 40-50$\%$ of the total number of showers in the sample; b) (1-2)$\%$ of showers are possibly produced by primary gamma rays $\gamma$; c) other showers are produced by nuclei of heavier chemical elements, e.g. CNO and iron nuclei Fe.

We wish to thank all of the staff of the Yakutsk Array for the opportunity to use experimental data and useful discussion during the article preparation.