Measurements of the time-dependent cosmic-ray Sun shadow with seven years of IceCube data: Comparison with the Solar cycle and magnetic field models

Observations of the time-dependent cosmic-ray Sun shadow have been proven as a valuable diagnostic for the assessment of solar magnetic field models. In this paper, seven years of IceCube data are compared to solar activity and solar magnetic field models. A quantitative comparison of solar magnetic field models with IceCube data on the event rate level is performed for the first time. Additionally, a first energy-dependent analysis is presented and compared to recent predictions. We use seven years of IceCube data for the moon and the Sun and compare them to simulations on data rate level. The simulations are performed for the geometrical shadow hypothesis for the moon and the Sun and for a cosmic-ray propagation model governed by the solar magnetic field for the case of the Sun. We find that a linearly decreasing relationship between Sun shadow strength and solar activity is preferred over a constant relationship at the $6.4\sigma$ level. We test two commonly used models of the coronal magnetic field, both combined with a Parker spiral, by modeling cosmic-ray propagation in the solar magnetic field. Both models predict a weakening of the shadow in times of high solar activity as it is also visible in the data. We find tensions with the data on the order of $3\sigma$ for both models, assuming only statistical uncertainties. The magnetic field model CSSS fits the data slightly better than the PFSS model. This is generally consistent with what is found previously by the Tibet $\mathrm{AS}\text{−}\gamma$ Experiment; a deviation of the data from the two models is, however, not significant at this point. Regarding the energy dependence of the Sun shadow, we find indications that the shadowing effect increases with energy during times of high solar activity, in agreement with theoretical predictions.

Figure 1

The IceCube Neutrino Observatory.

Figure 2

Comparison of moon declination $\delta$ and final moon shadow sample event rate. At the South Pole, the elevation of an object equals $-\delta$.

Figure 3

On- and off-source regions used for the data analysis. The black “x” marks the zero point of the relative coordinates, i.e., the center of the moon and Sun.

Figure 4

Energy distribution in a $\pm 3°$ declination band around the base declination ${\delta }_0=-21.3°$. The thick yellow, orange, and red lines indicate the median primary cosmic-ray energies studied in Section 5g.

Figure 5

Angular error distribution in a $\pm 3°$ declination band around the base declination ${\delta }_0=-21.3°$.

Figure 6

Boxcar-smoothed two-dimensional contour map of the moon shadow for the years IC79 to IC86-6 showing the computed center of gravity of the shadow as a white cross. The white circle indicates the seven-year mean of the weighted average of the angular moon radius.

Figure 7

Boxcar-smoothed two-dimensional contour map of the Sun shadow for the years IC79 to IC86-6 showing the computed center of gravity of the shadow as a white cross. The white circle indicates the weighted average of the angular Sun radius.

Figure 8

Comparison of measured relative deficit due to the moon shadow (black circles) and relative deficit expected from shadowing by the lunar disk (red squares).

Figure 9

Comparison of measured relative deficit due to the Sun shadow and relative deficit expected from shadowing by the solar disk.

Figure 10

Comparison of measured relative deficit due to the Sun shadow and average sunspot number as a tracer for solar activity.

Figure 11

Correlation of measured relative deficit due to the Sun shadow and average sunspot number. A correlation of the two quantities is found to be likely.

Figure 12

Normalized moon shadow deficit versus sunspot number.

Figure 13

Comparison of measured relative deficit due to the Sun shadow and relative deficit expected from different models of the solar magnetic field.

Figure 14

Relative deficit due to the Sun shadow normalized to the expectation from the solar disk as a function of the median energy of the subsamples. For better visualization, pairs of data points for a specific season where shifted along the abscissa. The inner (outer) gray band indicates the statistical uncertainty of the disk-prediction for the low-energy (high-energy) sample.