The IceCube detector is located at the geographic South Pole, containing 86 strings deployed in glacial ice. High-energy neutrinos interact with protons and produce leptons that emit Cherenkov light. Digital Optical Modules (DOMs) deployed into the ice then detect these photons.

The entire detector consists of 4800 DOMs in 80 strings with a 125 m horizontal spacing and 17 m vertical spacing between strings . A more compact group of strings that contains 360 additional DOMs is located at the bottom of the detector and is called DeepCore . Altogether, IceCube is operating with 86 strings containing 5160 DOMs. Before IceCube was completed in December 2010, it was operating in smaller detector configurations.

For the detector configuration with 40 and 59 strings (IC40 and IC59) a Moon shadow analysis was done in . This work makes use of the data taken from detector configurations with 79 and 86 strings (IC79 and IC86-I). Moreover, the second year (IC86-II) in which the detector was operating in its final configurations has been analyzed. A data selection for the IC40 and IC59 detector configuration is described in . At the South Pole Moon and Sun filters are enabled if the celestial body is at least 15∘ above the horizon . The Moon reaches this threshold for at least 6 days each month.

The Sun, on the other hand, reaches this threshold for three consecutive months during the Antarctic summer, from mid November though mid February each year. To reconstruct the trajectory of a charged particle travelling through the detector, the Multi-Photo-Electron (MPE) fit is used. The MPE fit takes into account all photons that reach a DOM.

Compared with the Single Photo-Electron (SPE) fit, which only uses the arrival time of the first photon in each DOM, the MPE fit yields a slightly better angular resolution in high-energy range, indicated by simulation studies .

Reconstruction quality cuts optimize the statistical significance because events with high uncertainty in the reconstruction are excluded in this analysis where two cut variables are used: The angular uncertainty in the muon reconstruction (σi) and the reduced log-likelihood (rlogL).

Both variables are used for standard selection cuts in neutrino analyses . Poisson statistics are assumed resulting in a proportionality of the statistical significance S to the fraction of events passing the cuts η and the resulting median angular resolution Ψmed after cuts: S∝ηΨmed.

In both detector configurations (IC79 and IC86) the quality cuts are σ< 0.71∘ and rlogL < 8.1.

The 1-D analysis compares one on-source region and eight off-source regions. The on-source region is a window of ±5∘ around the expected position of the Moon and Sun. With an offset of ±5∘, ±10∘, ±15∘ and ±20∘ the off-source regions are defined. In each bin (i) the relative deficit is computed by: ΔNi〈N〉=Nion-〈Nioff〉〈Nioff〉, with Non/off as all events in on-source/off-source regions. The uncertainty is given by σΔN/〈N〉=Nion〈Nioff〉1Nion+18⋅〈Nioff〉.

In , the Moon is described as a point-source sink that reduces the muon sample by ΦπRM2 events. The same approach can be used in this analysis, the radius of the Moon and Sun is given given by RM/S≈ 0.26∘.

Following further, the point spread function (PSF) can be described by a two-dimensional Gaussian. Assuming that the PSF is azimuthally symmetric, the relative deficit can be fit with a Gaussian function that depends only on the radial distance Ψ , f(Ψ)=-ΦπRM/S2σ2⋅e-Ψ2/2σ2. Thus, the relative deficit can be described as ΔN=-RM/S22σ2e-Ψi2/2σ2.

Approximately 30 % of all events pass the quality cuts each year and are included in Moon and Sun shadow analyses. Results can be found in Table  and Fig. .

The statistical significance S is computed by the difference between the χLine2 of a line and the χgaussian2 of a Gaussian that are fitted to data: Δχ2Δdof=χgaussian2-χLine2dof. Here, dof are the degrees of freedom. The difference Δdof is given by 1. Thus, the p value is computed via Δχ2 and results in the significance S: S=2⋅erf-1(1-p). Here, erf-1 is the Inverse Error Function and p the p value.

A smaller time binning of these results can be found in Table . The results show a constant angular resolution σ with error bars for each celestial body.

Both celestial bodies are observed with high statistical significance (>12σ). These significances are higher for both detector configurations (IC79 and IC86) as compared to IC40. A statistical significance of more than 12σ was also observed in IC59 .

The Moon shadow shows a steady amplitude of the fitted Gaussian where all values are within the statistical uncertainties and there is no statistically significant variation of the depth of the solar shadow at this point.

However, detailed information is not possible at this point and more studies are necessary to indicate a possible influence of the solar magnetic field. Additionally, there is a big difference between the Tibet AS-Gamma Experiment and Sun shadow analysis of the IceCube detector. The Tibet AS-Gamma Experiment could observe the Sun shadow the entire year but IceCube's observation time is shorter with approximately 90 days during the antarctic summer. Figure  shows the predicted and measured number of Sun spots by NASA and the median times corresponding to IceCube Sun shadow observations with different detector configurations.

Comparing the relative deficit maps in and Fig. , the anticorrelation between the number of Sun spots and the amplitude of the cosmic-ray Sun shadow is clearly visible. The Tibet AS-Gamma experiment observed the Sun shadow with a maximum of 170 Sun spots in the year 2000.

IceCube's Sun shadow observation period is during relatively lower Sun activity as seen in Fig. , where a maximum of 100 Sun spots is seen in IC86-I (2012). Furthermore, Fig.  illustrates that the number of Sun spots vary in a short time frame.

The shadowing effect of the Moon and Sun of cosmic-rays in the TeV range is observed with high statistical significance (>12σ). Data were taken from IC79 and two years of the final configuration IC86, during periods between June 2010 and May 2013 in which these celestial bodies were well above the horizon. Under the assumption that the sample of the IC40 and IC59 configuration are similar, the angular resolution is slightly improved.

In , an angular resolution of (0.71±0.07)∘ and (0.63±0.04)∘ are observed. For the Moon in IC79 and IC86 an average angular resolution of (0.46±0.05)∘ is measured. Additionally, the angular resolution of the three year period is constant within the statistical uncertainties.

The depth of the shadow is illustrated as the amplitude of the fitted Gaussian, which could be of big interest in future studies. An almost stable amplitude of the Moon shadow of 0.12±0.02 is shown in Table .

Further studies of upcoming years (IC86-III and IC86-IV) are necessary to investigate an influence of the solar magnetic field. In particular, it will be necessary to analyse each month separately in order to investigate the correlation between the magnetic field strength during that period and the depth of the shadow. In , the Tibet AS-Gamma experiment simulated particles influenced by different source surface (SS) models with different radii. For IceCube, it is also necessary to compute the expected Moon and Sun shadow within these models. Two-dimensional analyses are useful to make the shadows visible. A binned smoothing method and an unbinned analysis are options for this purpose.

An unbinned analysis was performed in for the IC40 and IC59 configuration.