The influence of the Sun and Moon on the observation of very high energy gamma-ray sources using EAS arrays

Very high energy (VHE, E$>$0.1 TeV) gamma-rays, located at the highest energy band of the cosmic electromagnetic radiation, are a powerful probe for astrophysics and fundamental physics under extreme conditions. Thanks to the advancements in ground-based gamma-ray detectors, our knowledge about the VHE gamma-ray universe has made impressive progress over the past two decades. The successful operation of the second generation Imaging Atmospheric Cherenkov Telescopes (IACTs), such as H.E.S.S. (Jung 2001), MAGIC (Baixeras 2003), and VERITAS (Weekes et al. 2002), has significantly increased the number of detected VHE gamma-ray sources from about 10 to over 200 since 2004. Due to the limitation of this technique which adopt optical detectors, the observation can only be implemented during the clear and moonless night. Therefore, the influence of the Sun and Moon and their light on the very high energy gamma-ray sources are ignored for a long time.

Recently, the sensitivity of another ground-based detector technique EAS arrays has greatly improved thanks to the successful operation of the new generation arrays, such as HAWC and LHAASO. The HAWC (DeYoung & HAWC Collaboration 2012; Springer 2016) and LHAASO (He & the LHAASO Collaboration 2018) observatories has detected 65 and 90 VHE sources(Albert et al. 2020; Cao et al. 2023), respectively. Since the EAS arrays adopt particle detectors, they have a large field of view which cover 1/7 of the whole sky at each moment, and they are usually operated with nearly full duty cycle regardless of the day and the night. In such a situation, some of the gamma-ray sources may be very close to the line of sight of the Sun or Moon during observation which would lead to the underestimation of the sources flux. Therefore, the influence of the Sun and the Moon on the very high energy gamma-ray sources near the line of sight should be carefully studied and some strategy is needed to guide the data analysis to avoid the underestimation of the gamma-ray emission.

When a gamma-ray sources is very close to the line of sight of the Sun or the Moon, the measurement of the gamma-ray emission may be affected due to four factors. Firstly, when a source is blocked by the Sun or the Moon, the gamma-rays from the source will not reach the earth. Secondly, when a source is close to the line of sight of the Sun, the gamma-rays from the source will suffer the $\gamma-\gamma$ absorption by the sunlight during their propagation to the earth. The quantitative absorption should depend on the energy of the gamma-rays and also depend on the space angle between source and the Sun. The extinction of the VHE gamma-ray by sunlight has been noticed in a brief paper (Loeb 2022) when studying the TeV gamma-ray background, however, no detailed results are presented and the quantitative impact on gamma-rays from a specific source is not estimated. Thirdly, the Sun and Moon will produce a shadow on the cosmic ray background, which will lead to a deficit source that cancel the gamma-ray signals. These shadows have been well measured by EAS arrays with high significance and were adopted to calibrate detectors and perform physics measurements (Ambrosio et al. 1998, 2003; Aielli et al. 2011; Bartoli et al. 2011, 2017; Aartsen et al. 2021). Fourthly, the Sun could also produce gamma-ray emission due to interaction of cosmic ray with the solar atmosphere. The solar gamma-rays have been well detected and studied using Fermi-LAT data at GeV band (Abdo et al. 2011; Ng et al. 2016; Linden et al. 2018; Tang et al. 2018). The emission at VHE band have been studied by several literature (Albert et al. 2018; Bartoli et al. 2019; Li et al. 2024) and a positive signal was also reported by HAWC collaboration recently (Albert et al. 2023).

In this paper, we will study the influence of the Sun and Moon on the very high energy gamma-ray sources near the line of sight. Especially, the absorption of very high energy gamma-ray by sunlight will quantitative calculated for the first time. Then, we will explore some strategy on data analysis to avoid affection of the Sun and Moon on the measurement of the gamma-ray emission from the sources. The paper is organized as follows: the known VHE gamma-ray sources that may be very close to the Sun and Moon are explored in Section 2. The absorption of very high energy gamma-ray by sunlight is calculated in Section 3 including method and results. Some strategy to avoid the affection of the Sun and Moon are presented in Section 4. Section 5 is the summary.

Due to the Earth’s orbit around the Sun, the position of the Sun in the celestial coordinates varies annually. Figure 1 shows the track of the Sun in the in celestial coordinates. The declination of the Sun can vary from -23.6^∘ to 23.6^∘. The track is about same every year. Due to the Moon’s orbit around the Earth, the position of the Moon in the celestial coordinates varies with a duration of 29.53 days. Besides this monthly variation, the varying range of the declination also vary with a duration of 18.61 year. The maximum (minimum) declination can change from 18.2^∘ (-18.2^∘) to 28.7^∘ (-28.7^∘). The track of the Moon in the celestial coordinates during the 18.61 year is also shows in Figure 1. It is worth to note that both the Sun and Moon are extended source in the sky with a radius about 0.26^∘.

Up to now, about 300 VHE gamma-ray sources have been detected according to TeVCat ¹¹1http://tevcat.uchicago.edu/. All these sources are also presented in the Figure 1. According to the Figure 1, it is clear that some sources can be blocked by the Sun or Moon and some sources would be very close to the Sun or Moon during some period. Table 1 list the 20 known VHE sources that with the closest space angle less than 2^∘ from the Sun or Moon. The right ascension (R.A.) and declination (Dec) of the sources and their closest space angle to Sun and Moon are presented in the table 1. These sources include both Galactic and extra-galactic sources. Obviously, these sources should be with careful treatment when measure their gamma-ray emission using the EAS array data. The impact of the Sun and the Moon will be studied later.

It is known that that VHE gamma-rays emitted from distant astronomical sources would be absorbed by low energy background photons through photon-photon interaction. These absorption leads to opacity of the universe to the VHE gamma-rays. The absorption of gamma-rays at a specific energy $E$ is mainly due to the low energy photons with wavelength around $\lambda\sim$ 1.5($E$/1TeV) $\mu m$. The gamma-ray opacity above 100 TeV is mainly due to the absorption f Cosmic Microwave Background (CMB) (Hauser & Dwek 2001). The gamma-ray opacity bellow 100 TeV is mainly due to the absorption of Extragalactic background light (EBL) in the intergalactic space (Finke et al. 2010; Saldana-Lopez et al. 2021). The interstellar radiation fields (ISRF) within our Galaxy would also absorb the gamma-rays bellow 100 TeV with a visible fraction for some cases (Moskalenko et al. 2006). Before a cosmic VHE gamma-ray photon reaches the Earth, it should also pass through the sunlight. Therefore, the gamma-ray should suffer the $\gamma-\gamma$ absorption by the sunlight. The density of sunlight dependent on the distance to the Sun $r$, which is in inverse proportion to $R_{\bigodot}^{2}$. The absorption should dependent on the space angle between a gamma-ray source and the Sun. In the following, the Crab Nebula will be taken as an example to estimate the absorption by sunlight.

Based on the calculations from the previous section, it is evident that the absorption of gamma-rays by sunlight is extremely minimal and can be disregarded during most observation periods. The Moon primarily reflects sunlight and has a much lower brightness compared to the Sun, resulting in an even smaller absorption of gamma-rays by moonlight, which can be directly ignored. However, when the angle between the direction of the gamma-ray source and the directions of the Sun and Moon is less than $0.25^{\circ}$, the gamma-rays will be completely blocked by the Sun and Moon, and cannot be ignored during this time period. Therefore, it is necessary to exclude this data during the analysis.

Additionally, when the angle between the direction of the gamma-ray source and the directions of the Sun and Moon is small, the Sun and Moon directly block the cosmic ray background, creating a missing negative source. This shadow can counteract the gamma-ray signal, and its impact depends on the ratio of the number of gamma-ray signals to the background. For previous arrays like ARGO-YBJ, which lacked the ability to distinguish between gamma-ray and cosmic ray background, the gamma-ray signals only accounted for a small portion of the backgrounds. For example, in observations of the brightest gamma-ray source, the Crab Nebula, the gamma-ray signals were only about 1% of the backgrounds (Bartoli et al. 2015), leading to a significant counteracting effect from the shadow on the gamma-ray signals.

For the LHAASO array, due to its excellent ability to distinguish between gamma-rays and cosmic ray backgrounds, the proportion of gamma-rays to backgrounds has significantly increased. For example, in observations of the Crab Nebula, the ratio of gamma-ray signals to backgrounds for the LHAASO-WCDA array is 20% at 1 TeV, 80% at 6 TeV(Aharonian et al. 2021a), and for the LHAASO-KM2A array, the corresponding ratios are 12% at 10 TeV, 260% at 25 TeV, and 4100% at 100 TeV(Aharonian et al. 2021b). However, considering the current detection sensitivity of LHAASO is at 1% of the Crab flux level, the impact at energies bellow 100 TeV cannot be ignored.

Fig.7 shows the counteracting effect of Sun or Moon shadow on the gamma-ray signals at different space angles. In this example, we assume the detector angular resolution to be 0.5^∘ and the number of deficit shadow events to be three times that of the gamma-ray signals. This situation is similar to the observation of LHAASO-KM2A on a gamma-ray source with a flux around 10% Crab unit at 10 TeV. It is clear that the gamma-ray signals will be completely counteracted by the shadow when they are very close the direction of Sun or Moon. The counteracting effect decreases as the increasing of the space angle. To ensure safety, we recommend removing data when the space angle between the gamma-ray source and the directions of the Sun and Moon is less than 3 times the angular resolution plus $0.25^{\circ}$. For example, the observation time of the EAS array for Crab is approximately 7 hours per day, and only during a few days the space angle between Crab and Sun or Moon is less than 2^∘ in one year. The data from this period of observation can be excluded for data analysis, thus eliminating its impact. Since the angle between the source and the directions of the Sun and Moon varies periodically, this portion of the data accounts for a very small percentage, generally less than 1% of the total observation time in one year, and therefore does not significantly affect the observation of the source.

Table 1 lists known gamma-ray sources with a minimum angle less than $2^{\circ}$ between the source and the Sun or Moon. When measuring their radiation using EAS arrays such as LHAASO and HAWC, special attention should be paid to excluding data when the space angle between the source and the Sun or Moon is small.

With significant advancements in ground-based extensive air shower arrays, numerous very high-energy (VHE) gamma-ray sources have been discovered and are being continuously monitored by LHAASO and HAWC, regardless of day or night. With investigating the celestial coordinates of the Sun and Moon, we identified 20 sources that can come close to the line of sight of the Sun or Moon during some certain periods. We have conducted the first estimation of sunlight absorption on very high-energy gamma-rays. The absorption primarily affects gamma-rays with energies ranging from 0.1 TeV to 100 TeV, with maximum absorption occurring around 0.9 TeV. The absorption is contingent on the spatial angle between the Sun and the sources; however, the overall absorption is minimal, with a maximum of less than 1.2%. The primary influence is the obstruction of the Sun and Moon on gamma-rays, and their shadow on the cosmic ray background. The impact is also contingent on the detector’s angular resolution. To mitigate its effects, we recommend excluding data when the angle between the gamma-ray source and the directions of the Sun and Moon is less than a certain value taking into account the experiment angular resolution.