The construction and analysis of a whole-sky map using underground muons

A sample of 16 million underground muons has been collected between January, 1989, and June, 1993, at a depth of 2090 m.w.e. in the SOUDAN 2 detector. This data-set has been passed through standard event reconstruction programs to give a sample of 14 million muons after run and event cuts. The trajectories of all muons in this data-set have been projected back onto the celestial sphere.
Software has been developed to compute the apparent motions of the Sun and Moon as viewed from the surface of the Earth. The errors on the coordinates computed by these programs are well understood. The programs have been used to search the data-set for evidence of the cosmic ray shadow cast by the stopping of primaries in the Sun and Moon. This procedure was used to test the assumption that the detector alignment is known to ~ 0.25° and that the resolution is ~ 1°. The observed distribution of events was found to be consistent with this hypothesis. However the test performed lacked sufficient power to reject strongly the alternative hypothesis, that no shadow had been observed. A 95% lower limit of 0.46° was set on the single-muon resolution.
A procedure has been developed to construct and analyse a map of the underground muon flux across the entire celestial sphere. A whole-sky background calculation has been developed and it has been verified that the background computed for the observed data-set is an acceptable description of the distribution of event coordinates. By a monte-carlo procedure, it has been demonstrated that the statistical properties of the analysis method are understood and agree with the distribution computed analytically. It has been shown that there is no evidence for drift or bias in the background computed.
The procedure has been applied to the data-set, asymmetrically divided into two subsets of 10.6 and 3.3 million muons respectively. A search for anomalous muon excess in the larger data-set found the largest deviation to be an excess within 1.9° degrees of Active Galactic Nucleus 3C 273. The significance of the excess was estimated to be ~ 10% and the significance of it's proximity to 3C 273 to be ~ 2%. A 1.7 s.d. excess was found in the identical position in the smaller data set. The number of excess events for both data-sets, scaled by their relative exposures, were consistent at the level of 1 s.d. The overall level of confidence is conservatively estimated to be better than 99%.
On the assumption that this excess does represent a real flux of muons, due to primary cosmic rays from 3C 273, the region in excess was examined in greater detail. A maximum likelihood fit was used to extract confidence limits for the strength, coordinates, and r.m.s. width of the excess. It was found that association with 3C 273 should be rejected, with a confidence of 95%, unless the r.m.s. source width was permitted to increase from the a priori value of 1° to 2.4°. With this modification excess coordinates were estimated to be ⍺ = (188.2 +2.1 [above] -2.8)°, δ = (2.2 +2.3 [above] –2.1)°.
The background subtracted distributions of a selection of event parameters were examined and found to be consistent with the background expectation. On the assumption that the flux has the same spectral index as the background, the underground muon flux was estimated to be 10.3 +11.3 [above] -9.2 x 10⁻¹² cm⁻²s⁻¹. Such a flux is not consistent with the observed ɣ-ray flux from 3C 273, and can only be explained by unconventional physics.

Keywords: whole-sky map
map
muons
underground muons
astronomy
statistical