Cosmic-ray muon flux at Canfranc Underground Laboratory

Residual flux and angular distribution of high-energy cosmic muons have been measured in two underground locations at the Canfranc Underground Laboratory (LSC) using a dedicated Muon Monitor. The instrument consists of three layers of fast scintillation detector modules operating as 352 independent pixels. The monitor has flux-defining area of 1 m${}^{2}$, covers all azimuth angles, and zenith angles up to $80^\circ$. The measured integrated muon flux is $(5.26 \pm 0.21) \times 10^{-3}$ m${}^{-2}$s${}^{-1}$ in the Hall A of the LAB2400 and $(4.29 \pm 0.17) \times 10^{-3}$ m${}^{-2}$s${}^{-1}$ in LAB2500. The angular dependence is consistent with the known profile and rock density of the surrounding mountains. In particular, there is a clear maximum in the flux coming from the direction of the Rioseta valley.


Introduction
Reduction of the intense particle flux induced by cosmic rays is one of the main reasons to locate low-background laboratories underground. Consequently, the residual muon intensity is a key parameter in site selection and evaluation. While the processes of creation of particle showers and their transport through the atmosphere and through the layers of rock and sediments are relatively well understood, the detailed numerical data on the geological structures above and around the laboratory are seldom available with the desired accuracy. In the end, a direct measurement is the best way to determine precisely the actual muon flux at the given underground location. For a comprehensive review of the deep underground laboratories and their scientific projects see the contributions to the focus issue of the European Physical Journal Plus 127(2012) [1,2,3,4,5,6,7,8,9,10,11]. Several dedicated measurements of cosmic muons in underground laboratories are described in [12,13,14,15,16,17,18,19,20].
The Canfranc Underground Laboratory (LSC) [21] is located under the Mount Tobazo (1980 m) in the Aragonese Pyrenees. The laboratory caverns have been excavated between the vacant train tunnel and the modern road tunnel joining Spain and France. Both tunnels are used as access routes to the laboratory area. The coordinates of the LSC are known with accuracy of ±5 cm. The exact po-sition of the Muon Monitor in the LAB2400 was: floor altitude 1204.479 m above the sea level, the longitude 0°31' 44.85570" W, and the latitude 42°46' 28.99971" N. In the LAB2500 the corresponding values were: 1206.470 m, 0°31' 45.26066" W, 42°46' 31.04089" N. Fig. 1 shows the cross section of the mountain range along the railway tunnel, following the SSE−NNW direction. Mount Tobazo, situated directly over the Hall A of LAB2400 (distance = 0 m), is the highest point. The valley of the Rioseta river, at minus 750 meters from Hall A, has the lowest elevation. These elevation changes in the profile of the mountain range surrounding LSC result in significant variations of the slant depth for different projection angle, as shown in Fig. 2. The projection angle alpha, defined in Fig. 1., is analogue to the zenith angle with the azimuth plane fixed to the SSE-NNW direction. The data for the plots in Fig. 1 and Fig. 2 were extracted from the April 2018 release of the dataset from the Advanced Land Observing Satellite (ALOS) [22].

Experimental setup
The measurements were performed with a Muon Monitor (MM) assembled especially for that purpose. It consisted of an array of 352 individual scintillator pixels arranged in 3 layers, as shown in Fig. 3. The active volume of one   scintillator pixel was 122 × 122 × 30 mm 3 . The key building block of the MM setup was a SC16 module housing 16 individual scintillators/pixels in one sturdy steel box, 120 mm thick, 500 × 500 mm 2 at the base. The top and bottom layers of the MM were made of 9 SC16 elements each. The flux-defining middle layer was made of 4 SC16 units and had the active area of 0.95 m 2 . The maximum detectable zenith angle for this configuration was approximately 80°.
The SC16 detectors were originally designed and constructed for the EMMA experiment [23] in the Pyhäsalmi mine in Finland. The time resolution of a SC16 is around 1.5 ns and the muon detection efficiency is 98% [23]. To reduce the sensitivity to gamma rays, the energy threshold was set at around 2 MeV. To generate a valid trigger, at least one pixel in each layer had to register an event with energy above 2 MeV. A typical trigger rate was around 20 triple-layer coincidences per hour. Throughout the acquisition period all detector pixels remained active and the electronics operated in a stable way. As a result, the overall data quality is very good. In the Hall A the data were recorded from September 2013 till October 2015. The effective acquisition time was 584 days. In LAB2500 the measurements took place from October 2015 till March 2018 with the effective acquisition time of 569 days. The exact position of the MM at both locations is shown in Fig. 4.
Additional information about the experimental setup is provided in [13]. For the description of the electronics, see [24,25]. The full details concerning the experimental setup, detectors, electronics, data acquisition, and data analysis will be described in a dedicated instrumental paper.

Results and discussion
The integrated muon flux measured in the Hall A of the LAB2400 is (5.26 ± 0.21) × 10 −3 m −2 s −1 . The corresponding value for the LAB2500 is (4.29 ± 0.17) × 10 −3 m −2 s −1 . Because of the long duration of the measurements, needed to extract the angular distributions, the statistical fluctuations of the integrated fluxes are negligible (∼ 0.2%). The dominant uncertainty, estimated at ±4%, is due to the systematics. It reflects the uncertainty in the correction for the events caused by electromagnetic contamination from secondary showers, dispersion in pixel efficiencies, and alignment accuracy.
The angular distributions of the muon flux displayed as a function of the azimuth and zenith angle are shown in Fig. 5. A two-step approach was needed to obtain continuous distributions from the coarsely sampled data extracted from 352 pixels. First, the angular phase-space was determined for each three-pixel combination. Next, the registered coincidence was randomly allocated to one of the directions from the accessible phase-space for the given pixel sequence. The result is a smooth distribution with no detectable artefacts or remanences of the original pixelization. As expected, for both locations the maximum flux is observed from the direction of the Rioseta valley, around the zenith angle of θ = 40°and the azimuth angle of φ = 150°.

Consistency check
By combining the efficiency-corrected angular distribution of the muon flux from Fig. 5 with the satellite data on the shape of the terrain shown in Fig. 2, one can correlate the flux arriving from the given direction with the slant depth along that path. The outcome is plotted in Fig. 6. To obtain a similar result without muon tracking would require a series of measurements at multiple locations of different depth.
As a consistency check we have fitted both formulae to the data points from Fig. 6. The slant depth, expressed in meters of water equivalent (m.w.e.) in (1) and (2), was converted into meters of rock by dividing it by a free parameter representing rock density. The best fit with (1) yielded the average density of 2.67 g/cm 3 (dashed curve) Fig. 6. Muon intensity as a function of slant depth. The blue circles were measured at LAB2400 and the red squares, at LAB2500. The error bars represent 5% uncertainty in the projected thickness determination from the satellite data and the 4% systematic error of the measured intensity. The best fit using (1) yielded the average rock density of 2.67 g/cm 3 (dashed curve), while (2) yielded 2.73 g/cm 3 (dotted curve). and 2.73 g/cm 3 (dotted curve) with (2). Both values are within 1% from the expected density of limestone (2.7 g/cm 3 ) that is the dominant component of the rock in the vicinity of LSC. This agreement confirms the consistency between the measured muon flux and the known geology and shape of the mountain above the LSC. The main reason for the relatively large horizontal error bars in Fig. 6 is the limited angular resolution of the MM.

Summary and conclusions
The residual flux and angular distribution of high-energy cosmic muons in the Canfranc Underground Laboratory (LSC) have been measured. The integrated muon flux is (5.26 ± 0.21) × 10 −3 m −2 s −1 for LAB2400 (Hall A) and (4.29±0.17)×10 −3 m −2 s −1 for LAB2500. These results supersede the preliminary values published earlier [13]. For each site the data were collected over the period of nearly 600 days. The measurements were done with the Muon Monitor assembled especially for that purpose. The obtained angular dependence is consistent with the known mountain profile and rock density. In particular, there is a clear maximum in the flux from the direction of the Rioseta valley. As a result, the integrated muon flux is larger than what one would expect from the thickness of the overburden directly above the site. Consequently, some of the older evaluations have underestimated the integrated muon flux at LSC by up to a factor of two.

Acknowledgments
We gratefully acknowledge the help and support from the directorate and staff of the Canfranc Underground Laboratory during the design, planning, construction and data acquisition phases of this project. This work has been supported in part by the Council of Oulu Region, the European Union Regional Development Fund, and by the grant of the Ministry of Education and Science of the Russian Federation number 3.3008.2017.