Influence of clouds on the parameters of images measured by IACT at very high energies

At first, we analyse the results of simulations of γ-ray and proton-induced showers for their fixed primary energies. We show the average number of Cherenkov photons, produced in the atmosphere within layers with a thickness of 10 ${\rm g}\;{\rm c}{{{\rm m}}^{-2}}$, versus the atmospheric depth for energies 5, 10 TeV of primary γ-rays and 10, 20 TeV of primary protons (see figure 1). All longitudinal distributions for proton-induced showers are multiplied by a factor of 10 for better visibility. In the same figure, we also plot the longitudinal distribution of Cherenkov photons as seen by the camera with FOV limited to 8$^{{}^\circ }$. Four vertical lines (thin solid) correspond to the clouds at altitudes of 10, 7, 6, and 5 km a.s.l. We show that most of the light is produced below 10 km for all simulated energies. Note that, when the cameraʼs FOV is limited, the shower maximum is higher in the atmosphere for both types of simulated primary particles. Below the shower maximum, the amount of Cherenkov light in the camera with 8° FOV is a factor of $\sim$2 lower in comparison to all Cherenkov light produced in the cascades. This results in a significant reduction of the light density on the ground. The shower maximums, for the investigated energy range of primary particles, lay between 5 and 10 km above the sea level. Therefore, the presence of clouds below this height should strongly effect the Cherenkov light arriving to the telescope.

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In general, densities of Cherenkov light on the ground and heights of Cherenkov photon production are correlated [12]. Therefore, the decrease of the Cherenkov photon density, due to the presence of clouds, should depend on the impact parameter of the shower for the fixed cloud transmission and altitude. In order to check this effect quantitatively, we show how the fully opaque clouds can reduce the average Cherenkov light density for different energies of primary particles, 5 TeV γ-ray showers (a), and 20 TeV proton showers (b) (see figure 2). Two cases are considered, i.e. the case of camera with unlimited FOV (black lines) and limited FOV to 8$^{{}^\circ }$ (grey lines). The figures show the ratio between the absorbed and not absorbed Cherenkov photon densities (the density fraction) as a function of the impact parameter of the shower. As expected, this ratio increases with the altitude of the fully opaque cloud.

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The impact parameter of the shower is defined as the distance between the shower axis and the telescope axis. Most of the Cherenkov photons produced very high in the atmosphere hit the ground close to the shower axis. Therefore, the presence of clouds significantly reduces the expected Cherenkov photon densities at very small impact parameters. Note, that all Cherenkov photon density distributions (figure 2) have the local minimum at the impact parameter R = 0 m, except in the case of a γ-ray with the cloud at 3 km a.s.l.. The second local minimum in these curves (at the impact parameter of $\sim$110 m, i.e. the so called the hump position) are related to the shower maximum. For larger impact parameters, the fraction of unabsorbed photons slowly decreases with the impact parameter. For the cloud at the altitude of 10 km, the loss of the light due to the total absorption in the cloud is only $\sim$10%. Therefore, we expect relatively small changes in the image parameters of showers for the case of high altitude clouds. The limited camera FOV strongly influences the density fraction of proton- and γ-ray initiated showers for impact parameters larger than the hump position. The density fraction of the Cherenkov light within an 8$^{{}^\circ }$ camera FOV falls with the impact parameter significantly faster than in the case of the detector with an unlimited FOV.

We have performed simulations of γ-ray- and proton initiated showers in order to investigate the images of the Cherenkov light produced by these showers in the presence of clouds. One thousand γ-ray induced showers, with a primary energy equal to 2 TeV, and also one thousand proton initiated showers, with an energy equal to 10 TeV, have been used in our analysis. Simulations were done for the clear sky conditions and for the fully opaque clouds at the altitude of 7, 6, and 5 km a.s.l.. The average angular distributions of the Cherenkov light on the telescope have been obtained for the telescope placed at a distance of 152.5 m from the shower core (see figure 3). We show that the images with the presence of clouds are shifted outwards of the camera center (defined by x = 0 and y = 0). For lower cloud altitude, the shift of the image is clearly larger. As expected, these images also contain less Cherenkov photons in comparison to the clear sky simulations (see different ranges of z-axes in figure 3).

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Two Hillas parameters called LENGTH and WIDTH (describing the image shape) are defined as the standard deviations of profiles of 2D Cherenkov light angular distribution [2]. The LENGTH and the WIDTH give the values along the long and short axes of the image, respectively. The DIST parameter (describing the position of the image) is the distance between the image center of gravity and the camera center (or the position of the source on the camera plane in cases of wobble observations) [2]. The camera FOV of 8$^{{}^\circ }$ corresponds to the limitation of the x axis to 4$^{{}^\circ }$.

If the additional absorption by clouds is taken into account, then the image parameters change in comparison to images obtained in the clear sky simulations (see figure 3). Influence of the limited camera FOV on the image parameters depend on the altitude of the fully opaque cloud. The impact of the limited camera FOV is stronger for the lower altitude of the fully opaque clouds.

To obtain the distributions of the DIST, LENGTH and WIDTH parameters, we simulated the primary particles (γ-rays, protons) with the spectra as described in the Monte Carlo section. The angular distributions of the Cherenkov light, obtained from the MC simulations, have been cleaned. Signals recorded by pixels of the camera include photoelectrons created by both Cherenkov light and NSB photons. Photoelectrons produced by light of the NSB are randomly distributed over all pixels of the camera. Therefore, those photoelectrons should be subtracted before calculating the parameters of shower image. The cleaning procedure of the image is used for this purpose. The results of our simulations also contain photons of the NSB, which are distributed over the whole 2D angular distribution of Cherenkov light. In this paper, the image parameters are calculated after applying the cleaning image procedure, which neglects pixels when the signal is smaller than the chosen level. In our study, we checked three levels of the cleaning: 30, 45, and 60 photons. Distributions of the Hillas parameters are interpolated in the range of the shower-impact parameter between 22.5 m and 322.5 m. Note that very high energy γ-ray initiated showers, close to the telescope axis, create the images, which are usually very difficult to separate from hadron initiated showers since their images form very broad ellipses. Therefore, we limit the impact parameter of the analyzed showers to values greater than 22.5 m. On the other hand, for the very large impact parameters, the Cherenkov photon density can be too low to trigger the telescope. Therefore, the upper limit on the impact parameter has been fixed to 322.5 m, which is about 200 m farther from the shower axis than the hump position (see figure 2).

We show dependencies of the DIST, LENGTH and WIDTH [2] on the transparency of the cloud at the level 6 km a.s.l. (see figure 4). Both, γ-ray and proton-induced showers are shown for the images with the SIZE above 2000 photons. In our study, photons are not converted to photoelectrons, so the SIZE is given in photons. The distributions of DIST parameter of the γ-ray and proton initiated showers become wider for lower cloud transmission (see figures 4(a), (d)). The images of showers are significantly shifted towards larger values in the case of fully opaque clouds. This is due to the fact, that these images do not contain photons created above the cloud altitude, where the Cherenkov angle is small and the angular distribution of charged particles in the shower is narrow.

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The LENGTH distribution for primary γ-rays, which reflects the angular distribution of the charged particle along the shower core (figure 4(b)), is shifted towards lower values for the fully opaque clouds. The LENGTH distributions, obtained for higher cloud transparencies, show a different tendency. The scale of the shift towards larger values increases with decreasing transmission of the cloud for both γ-ray and proton initiated showers (see figures 4(b), (e)). This feature can be explained by the fact that, for the cloud with lower transparency, images are less concentrated and therefore the LENGTH parameter is larger.

The WIDTH distributions reflect the angular distributions of the charged particles in the direction perpendicular to the shower axis. Our simulations show that in the case of more opaque clouds, the WIDTH distributions are wider for both simulated primary particles (see figures 4(c), (f)). The WIDTH distributions are shifted towards larger values for the clouds with transmission of 0.2 and 0, in the case of the proton initiated showers and for the transmission equal to 0 in the case of γ-ray initiated showers. Those very opaque clouds at relatively low altitude create images much wider than those created under clear sky conditions. The changes of the image parameters described above can be noticed in all simulated cloud altitudes. However, in the case of the cloud at 10 km, the differences between clear sky and all investigated transparencies are very small. The presence of clouds influences the γ-ray and proton images in a similar way. Therefore, it is clear that the selection of γ-ray showers is possible at very high energies.

In this section we analyse the possibility of selecting of γ-ray initiated showers from the background of proton initiated showers in the presence of clouds by using the Hillas parameters describing the image shape only. Those Hillas parameters, which describe the image orientation, cannot be used in our study because proton initiated showers were simulated from the direction of the γ-ray source. The γ/hadron separation method, based on simply statical cuts in WIDTH and LENGTH, does not take into account the effect of correlation of those parameters with the image SIZE. Other variables, so called scaled WIDTH (WIDTH_S) and scaled LENGTH (LENGTH_S), have been proposed as better indicators of the γ-ray initiated showers, since they are independent on the image SIZE (for definition see [20]). The scaling factors are calculated from simulated γ-ray images only. They are applied to the calculations of the WIDTH$_{S}$ and LENGTH_S for the images of γ-ray and proton initiated showers. As a result, the WIDTH_S and LENGTH_S distributions of the γ-ray initiated showers are Gaussian distributions with mean equal to 0 and dispersion equal to 1. Both main statistical parameters describing WIDTH_S and LENGTH_S distributions for proton images have larger values, than for γ-ray images. The WIDTH and the LENGTH are always positive, and they are measured in degrees, while the WIDTH_S and the LENGTH_S can also be negative, and they do not have units. The parameters WIDTH_S and LENGTH_S allow us to optimize the cut limits independent of the SIZE parameter.

We demonstrate the distributions of LENGTH_S and WIDTH_S for images of the γ-ray and proton initiated showers in the case of fully opaque clouds at different altitudes (see figures 5(a), (b)). These distributions are made for images with the SIZE above 2000 photons. It is easy to find out that the number of images with the SIZE above 2000 photons drop for the clouds at lower altitude. These considered parameters still allow clear separation of the γ-ray induced showers in the presence of clouds. Note also that the distributions of WIDTH_S allow better separation than distributions of LENGTH_S. The γ/hadron separation applied in our work is based on the cuts in the WIDTH_S and LENGTH_S. To demonstrate the selection efficiency we used the quality factor. This factor is related to the significance of the measurement (the ratio of the γ-ray signal and the dispersion of the Poisson-like hadronic background) [31]. The quality factor is defined as,

$$\begin{eqnarray*}&&{{Q}_{{\rm F}}}\equiv \frac{N_{\gamma }^{{\rm c}}/N_{\gamma }^{{\rm all}}}{\sqrt{N_{{\rm p}}^{{\rm c}}/N_{{\rm p}}^{{\rm all}}}},\end{eqnarray*}$$

where $N_{\gamma }^{{\rm all}}$,$N_{{\rm p}}^{{\rm all}}$ are the total numbers of events for chosen SIZE cut and $N_{\gamma }^{{\rm c}}$, $N_{{\rm p}}^{{\rm c}}$ are the numbers of events surviving the γ/hadron procedure. The lower limits on WIDTH_S and LENGTH_S were set to the value –2. The upper limits were optimized in the way to get the maximum value of ${{Q}_{{\rm F}}}$ for each investigated cleaning level, the altitude of the cloud, and its transmission. The quality factor versus cloud transparency for the SIZE above 2000 photons and cleaning level of 45 photons are shown in figure 6(a). Black and grey lines correspond to different scaling parameters used to calculate WIDTH_S and LENGTH_S. The scaling parameters, computed from the simulated γ-ray initiated images in the presence of clouds, were used to get ${{Q}_{{\rm F}}}$ (see black lines). The simulations of γ-ray initiated showers in the case of clear sky conditions were used to calculate the scaling parameters. They are applied in the optimization of the quality factors (see grey lines). The γ-ray selection method is working much better in the case of scaling made with the simulation of the real atmospheric conditions. For the cloud at 10 km a.s.l., the clear sky simulations can be used if the transparency of the cloud is larger than 0.4. However, for the cloud at lower altitudes, a suitable scaling should be used when analyzing data. In this case, the quality factor increases with the transmission for the altitudes equal to 7, 6, and 5 km a.s.l. In contrast, for 10 km, ${{Q}_{{\rm F}}}$ almost does not depend on the cloud transparency.

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We also show the quality factors for images with SIZE above 10000 photons applying the image cleaning levels of 30 photons and 60 photons, respectively (see the black and grey curves in figure 6(b)). ${{Q}_{{\rm F}}}$ values are higher for the cleaning image on the level of 30 photons. It means that the presented lower cleaning level is sufficient to efficiently select γ-ray events. With the higher cleaning level, we observe the degradation of the quality factor, since fewer events survive the SIZE cut.

It has been shown in [13] that a part of produced Cherenkov light, which is scattered by aerosols, is able to reach the ground. Clouds provide additional aerosols in the atmosphere. Therefore, a higher level of NSB is required. This reduces the γ/hadron separation efficiency. To confirm this, we performed additional simulations with different NSB. Figure 6(c) shows the quality factors for different NSB levels. We assumed that, the NSB depends only on the cloud transmission and it linearly decreases with the transparency of the cloud. For the fully opaque cloud, we applied NSB larger by a factor 2.5 than in the case of clear sky simulations. These calculations were obtained for the SIZE above 10 000 and the cleaning level of 45 and 30 photons, respectively (see black and grey lines in figure 6(c)). We show that the higher NSB leads to significant degradation of the quality factors when the cloud transmission is below 0.6, in the case of cleaning on the level 30 photons. For higher transparencies, a much smaller reduction of separation efficiency is expected. Using the higher cleaning level (45 photons), ${{Q}_{{\rm F}}}$ value significantly improves for all investigated transparencies and altitudes of clouds. We conclude that the effect of the higher NSB level, due to the presence of clouds, can be partially compensated by using the higher level of image cleaning in the data analysis.

To check the impact of the limited camera FOV on quality, we have considered only a part of the angular distributions of Cherenkov light on the ground, limited to 4$^{{}^\circ }$ in x-axis (corresponding to the full camera FOV of 8$^{{}^\circ }$). We have repeated all calculations starting from the computation of the standard Hillas parameters. We show the comparison of the results obtained for the camera with limited FOV (grey lines) and results presented above (black lines), see figures 7(a), (b). Both plots are obtained with the cleaning level of 30 and the SIZE above 10 000 photons. Surprisingly, the quality factors for a camera with limited FOV (figure 7(a)) are slightly better for almost all investigated transmissions and altitudes of the cloud. To explain this fact, we demonstrate the fraction of the γ-ray images, which survives the selection procedure as a function of the cloud transparency (figure 7(b)). It is clear, that more γ-ray events are recognized for the camera with unlimited FOV (black lines) than for the camera with limited FOV (grey lines). We have checked and the same tendency is observed for the fraction of protons which survive cuts. The differences between cameras with unlimited and limited FOV are greater for the proton initiated showers than for the γ-ray initiated showers. Consequently, we obtain a larger quality factor for the camera with limited FOV. It proves that the γ/hadron separation, based on the optimization of the WIDTH_S and LENGTH_S cuts, is possible at the very high energies in the presence of clouds, even in case of the camera with FOV limited to 8$^{{}^\circ }$. The smaller fraction of images survive the selection criteria for the camera with fixed size because for some events a part of the image is not recorded. This results in a smaller SIZE value. Also the Hillas parameters can change. Both effects are important in optimizing the γ/hadron separation. On one hand, a part of events do not survive SIZE cut. On the other hand, the leakaged images of γ-ray initiated showers are more similar to images of the proton showers. The impact of the camera edge, on the fraction of identified γ-rays with SIZE above 10 000 photons is demonstrated in figure 7(b). The fraction of identified γ-ray events for the camera with limited FOV is approximately 8% lower than for the camera with unlimited FOV in the case of the clear sky simulations.

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There are two types of the observations with the Cherenkov telescopes. In the first (so called mono mode), the single IACT is detecting one image of the EAS. In the second (so called stereo mode), a system of telescopes records at least two images of the same shower. The stereo mode has advantages in respect to the mono mode of the observations, since showers are better reconstructed in stereo mode [32].

Using at least two recorded images allows us to replace WIDTH_S and LENGTH_S parameters by mean-scaled WIDTH and mean-scaled LENGTH [33]. As a result, more efficient hadron rejection is obtained in the stereo mode. All images of the same shower can be changed due to cloudiness. The efficiency of the γ/hadron separation, based on the WIDTH_S and the LENGTH_S, declines in the presence of clouds. Therefore, we expect similar worsening of the γ/hadron separation also for the observations with the system of Cherenkov telescopes due to cloudiness.

The reconstructed shower direction depends on the direction of the major axis of the image for observations with a single telescope. In the stereo mode, the intersection of the directions, defined by the major axes of the images recorded in each camera, determines the shower direction. Therefore, the direction of the shower is more accurate with the stereo mode of the observation. The presence of clouds does not influence the determination of the major axis (or axes) of the image recorded by a camera with an unlimited FOV for very high energies. Therefore, the capability of the γ-ray selection, based on the parameters describing the orientation of the image, should be similar for the case of clear sky observation and observation with the cloudiness.

In the case of mono observations at very high energies, the reconstructed energy increases with both the SIZE parameter and DIST parameter. In the presence of clouds the image SIZE decreases but the DIST parameter can increase. First effect causes a bias in the reconstructed energy towards lower values. This bias can be only partially compensated for by the second effect. We have shown that the shift in the DIST distributions of the γ-ray showers is significant for clouds with low transmission only.

The position of the shower core is better determined with stereo observations. For this reason, the primary energy of the γ-ray is more accurately estimated than for the single IACT. In the presence of clouds, the shower reconstruction becomes worse also with the stereo mode of the observations. For this reason, the reconstructed energy is biased towards lower values [15]. Reconstruction of the primary energy of the γ-ray is based on the MC results for a particular single telescope or system of IACTs. The MC simulations have to take into account the presence of clouds in order to avoid a bias in the reconstructed energy.