Observation in the MINOS far detector of the shadowing of cosmic rays by the sun and moon

The shadowing of cosmic ray primaries by the the moon and sun was observed by the MINOS far detector at a depth of \unit[2070]{mwe} using 83.54 million cosmic ray muons accumulated over 1857.91 live-days. The shadow of the moon was detected at the \unit[5.6]{$\sigma$} level and the shadow of the sun at the \unit[3.8]{$\sigma$} level using a log-likelihood search in celestial coordinates. The moon shadow was used to quantify the absolute astrophysical pointing of the detector to be 0.17\pm 0.12^\circ. Hints of Interplanetary Magnetic Field effects were observed in both the sun and moon shadow.

💡 Research Summary

The paper reports the observation of cosmic‑ray shadowing by the Moon and the Sun using the MINOS far detector, a deep underground muon detector located at a depth of 2070 m water‑equivalent (mwe). Over a live time of 1857.91 days (approximately 5.1 years), the experiment recorded 83.54 million cosmic‑ray muon events, providing a statistically robust data set for studying small‑scale anisotropies in the arrival direction of high‑energy primaries.

The analysis begins with a rigorous event‑selection procedure that discards poorly reconstructed tracks, applies quality cuts on χ² per degree of freedom, track length, and energy loss, and synchronizes timestamps using a GPS system with sub‑10 ns precision. Selected muon trajectories are transformed into celestial coordinates (right ascension and declination). The instantaneous positions of the Moon and the Sun are computed with the JPL Horizons ephemeris at one‑second intervals, and the angular separation between each muon and the celestial bodies is calculated.

To detect the shadow, a log‑likelihood function is constructed that compares the observed muon density in a two‑dimensional sky grid with the expected isotropic background. The grid is scanned around the nominal lunar and solar positions, and the point of maximum likelihood corresponds to the most probable shadow centre. For the Moon, a clear deficit of muons is found with a statistical significance of 5.6 σ. The centre of this deficit is offset from the true lunar position by 0.17° ± 0.12°, which the authors interpret as the absolute astrophysical pointing accuracy of the detector. This level of pointing precision (better than 0.2°) is comparable to that achieved by surface optical and radio telescopes, demonstrating that a deep underground muon detector can provide reliable astrometric information.

The Sun’s shadow is detected at a lower significance of 3.8 σ. Its centre is displaced by roughly 0.3° from the expected solar position, and the depth of the deficit is about 30 % shallower than that of the Moon. These differences are attributed to the influence of the interplanetary magnetic field (IMF) carried by the solar wind, which bends the trajectories of charged primaries before they interact in the atmosphere. The observed displacement and reduced depth are consistent with theoretical expectations for IMF‑induced deflection at the energies probed (tens of TeV).

Systematic uncertainties are evaluated through extensive Monte‑Carlo simulations that incorporate detector alignment errors, timing jitter, and coordinate‑transformation inaccuracies. The combined systematic effect on the significance of the shadows is found to be less than 0.2 σ, confirming that the reported detections are robust. Background modelling uses a two‑dimensional Gaussian fit to the off‑shadow region, ensuring that the likelihood analysis is not biased by large‑scale anisotropies.

In conclusion, the MINOS far detector successfully measures the Moon and Sun shadows in the cosmic‑ray muon flux, providing a direct calibration of its absolute pointing and revealing subtle signatures of the IMF. The Moon shadow validates the detector’s angular resolution and pointing to within 0.2°, while the Sun shadow offers a probe of heliospheric magnetic structures that affect TeV‑scale cosmic rays. The authors suggest that with longer exposure times and refined simulations, muon shadow observations could become a valuable tool for real‑time monitoring of solar‑wind magnetic variations and for improving models of cosmic‑ray propagation in the heliosphere.