KASCADE-Grande Limits on the Isotropic Diffuse Gamma-Ray Flux between 100 TeV and 1 EeV

High-energy gamma-rays represent a very small but also very important fraction of primary cosmic rays. Their importance derives from the fact that they, unlike the charged particles which constitute the bulk of cosmic ray primaries, are not deflected by interstellar magnetic fields. Hence, their direction of incidence on Earth points back to their origin. Also for the case of non-observation of gamma-rays in a certain energy range, upper limits on the flux provide important information.

In addition, investigations of the Galactic and extragalactic diffuse gamma-ray emission are potentially able to give information about the source and propagation of Galactic cosmic rays. The measured flux of diffuse gamma-rays and its spectrum thus would provide new insights into the acceleration of cosmic rays. High-energy diffuse gamma-rays are the sum of contributions from several components. One is the cascading products from the collision of cosmic rays with interstellar gas and dust in the disk of the Galaxy (Berezinsky et al. 1993). In this case, the predicted integral intensity is concentrated in the Galactic plane. The other is due to electromagnetic cascades induced by the interaction of ultra-high-energy cosmic rays with the cosmic microwave background radiation (Halzen et al. 1990) and the unresolved point sources in extragalactic astronomical objects (Sigl et al. 1994). In these cases, this results in an isotropic flux of secondary photons. Therefore, measurements of the diffuse isotropic gamma-ray flux might provide information on the ultra-high-energy cosmic ray components. Moreover, this flux would represent a background for experiments searching for the gamma-ray enhancement from the direction of the Galactic disk.

Up to energies well into the GeV region gamma-rays are best observed from quite a number of satellites which have been active during recent decades (Ackermann et al. 2015). But with their limited detector size, typically well below 1 m², they run out of statistics at higher energies, due to the steep decrease of intensity of all types of primary cosmic ray particles. Therefore, only ground-based experiments are capable of extending observations to higher energies.

Gamma-ray astronomy in the upper GeV and TeV regions has seen a dramatic development over the last decade. This was possible due to the development of the Imaging Atmospheric Cherenkov (IAC) technique (Abramowski et al. 2014). Here, the primary particle is not observed directly, but indirectly via the large number of secondary particles produced by its interactions in the Earth's atmosphere. Most of these are relativistic electrons which emit Cherenkov light since they move faster than the speed of light in air. It has been possible, using this technique, to identify gamma-rays from astronomical objects up to about 100 TeV.

Extending these measurements to higher energies is again hampered by poor statistics. IAC telescopes have an effective acceptance area of several times ${10}^{4}$ m². But their field of view is small, below 5°, and they can only take data in dark and clear nights, which limits their observations to 10%–15% of real time even at the most suitable observation sites. Non-imaging Cherenkov light measurements, like the Tunka-133 experiment (Prosin et al. 2014), provide coverage of larger areas, but are still hampered by the requirement of clear, moonless nights. Therefore, air-shower detectors which measure the charged particles produced by the high-energy primary in the atmosphere have been employed to search for cosmic gamma-rays above 100 TeV. Their angular acceptance is well above 60° and they can take data around the clock.

Extensive air showers are mainly characterized by the total electron number and the total muon number. In general, muons are produced by the decay of charged kaons or pions, which in hadronic showers are produced in nucleus–nucleus interactions, whereas in photon-generated showers only by photoproduction processes. The ratio between the cross sections of photoproduction and nucleus–nucleus interaction processes is very small, on the order of $\sim {10}^{-3}$. Therefore, the usual strategy for searching for primary gamma-rays in extensive air showers is to discriminate gamma-ray primaries from the hadronic background by identifying muon-poor or even muon-less extensive air showers.

This paper presents upper limits on the relative intensity of the gamma-ray component of cosmic rays from the measurements by the KASCADE and KASCADE-Grande experiments. In particular, the results of the original KASCADE experiment are updated by including eight years' more data since the publication in Schatz et al. (2003). For the present results of KASCADE-Grande, nearly five times more data sets of the gamma-ray simulations are used, compared to that for the initial result in Kang et al. (2015a), although the same method of analysis is applied.

Earlier measurements of this kind have claimed that about 1 in 1000 cosmic ray particles are gamma-rays at energies around PeV (Nikolsky et al. 1987). More recent experiments (Aglietta et al. 1996; Chantell et al. 1997) were unable to confirm these results and yielded only upper limits of order 10⁻⁴ for the gamma-ray fraction at energies from $5.7\times {10}^{14}$ eV to $5.5\times {10}^{16}$ eV. Recently, a re-analysis of the Moscow State data (Kalmykov et al. 2013) claimed observation of detected gamma-rays at an energy of around 100 PeV, a claim which is still under discussion (Fomin et al. 2017). We have therefore considered it worthwhile to search the full measurements taken by the cosmic ray experiments KASCADE and its extension KASCADE-Grande for events induced by primary gamma-rays. For the present analysis we have chosen the traditional method following Helene (1983) in order to compare our results directly with those of earlier studies.

2.1. The KASCADE Experiment

The KArlsruhe Shower Core and Array DEtector (KASCADE) was located at the Karlsruhe Institute of Technology, Germany ($8\buildrel{\circ}\over{.} 4$ E, $49\buildrel{\circ}\over{.} 1$ N) at 110 m above sea level, corresponding to an average vertical atmospheric depth of 1022 g cm⁻². It operated up to the end of 2012 and all components have been dismantled. The experiment measured the electromagnetic, muonic, and hadronic components of extensive air showers with three major detector systems: a large field array, a muon tracking detector system, and a central detector. A detailed description of the KASCADE experiment can be found in Antoni et al. (2003).

In this analysis, data from the 200 × 200 m² scintillation detector array are used. The 252 detector stations are uniformly spaced on a square grid of 13 m separation. They are organized in 16 electronically independent clusters with 16 stations in the 12 outer clusters and 15 in the four inner clusters (see Figure 1). The stations in the inner and outer clusters contain four and two liquid scintillation detectors, respectively, covering a total area of 490 m². In addition, plastic scintillators are mounted below an absorber of 10 cm of lead and 4 cm of iron in the 192 stations of the outer clusters (622 m² total area). The absorber corresponds to 20 electromagnetic radiation lengths, representing a threshold for vertical muons of 230 MeV. This configuration allows measurement of the electromagnetic and muonic components of extensive air showers.

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Applying an iterative shower reconstruction procedure, the numbers of electrons and muons¹⁹ in a shower are determined basically by maximizing a likelihood function describing the measurements using the Nishimura–Kamata–Greisen (NKG) formula (Greisen 1956; Kamata & Nishimura 1958), assuming a Moliere radius of 89 m. Detector signals are corrected for contributions of other particles, e.g., the signal of the electromagnetic detectors for contributions from muons, secondary gamma-rays, and hadrons (Antoni et al. 2001). The directions of the incoming primary particles are determined without assuming a fixed geometrical shape of the shower front by evaluating the arrival times of the first particle in each detector and the total particle number per station.

In this analysis, to remove from the data set poorly reconstructed showers and to obtain the precise muon number measurement, the following cuts were applied: all of the 16 clusters should be working, shower core positions have to lie inside a circular area of 91 m radius around the center of the KASCADE array to avoid large reconstruction errors at the edges of the detector field, and zenith angles are required to be $\theta \lt 20^\circ$, where the angular resolution of KASCADE is better than 055 for electron numbers lg(N_e) > 4. The data set was recorded between 1996 October and 2010 May, which corresponds to an effective time of about 4223.6 days. About 1.0 × 10⁸ events remain for the analysis after the cuts.

2.2. The KASCADE-Grande Experiment

An essential part of the present analysis is the Monte Carlo simulation of the shower development and the response of the experiment. Showers initiated by primary photons, protons, He, CNO, Si, and iron nuclei were simulated in order to estimate the mean energies of gamma-rays and cosmic rays, respectively. However, the optimization of the selection of primary gamma candidates is based on the comparison of measured events with simulations of primary gamma-rays, only.

For the simulation of the physical processes in the air shower development the CORSIKA 6.9 (Heck et al. 1998) program was used. To determine the signals in the individual detectors, all secondary particles at the ground level were passed through a complete detector simulation program using the GEANT 3 (Brun et al. 1987) package. The predicted observables at ground level, such as e.g., the number of electrons, muons and photons were then compared to the measurements. The FLUKA 2002.4 (Fassò et al. 2005) model was used for hadronic interactions at low primary energies (E < 200 GeV). High-energy interactions were treated with a different model, in our case with QGSJET-II-02 (Ostapchenko 2006). The same number of showers was generated for each particle type. The simulations covered the energy range of ${10}^{14}\mbox{--}{10}^{18}$ eV and the zenith angle interval 0°–60°. The zenith angle distribution followed that of an isotropic flux, where the mean values after considering threshold effects were 127 and 20° for KASCADE and KASCADE-Grande, respectively. The azimuth distribution was flat and uniform over 360° for both arrays. The simulations were performed with an ${E}^{-2}$ spectral index for photons and cosmic rays as well. In total, around 2.5 million events were generated for cosmic rays and also for gamma-rays.

3.1. Estimation of Cosmic Ray Energy

3.2. Efficiency

To calculate the upper limits of the gamma-ray component of the cosmic ray flux the efficiencies of the experiment have to be known. The trigger and reconstruction efficiency of both experiments is shown in Figure 2. The efficiency is defined by the ratio of the number of reconstructed events in the area compared to the number of simulated events falling in this area, where binomial statistical errors are used. An efficiency greater than one is possible, due to the fact that, from the core uncertainty, eventually more events are reconstructed inside the area than simulated.

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For the KASCADE experiment, the trigger and reconstruction efficiency as a function of the shower size, i.e., the number of electrons, is demonstrated in the upper graph of Figure 2. The detector array reaches full efficiency on the detection of showers for electron numbers lg(${N}_{e})\gt 4$ for air showers induced by gamma-rays, protons, and iron primary particles, which approximately corresponds to a primary energy of $2.5\times {10}^{14}$ eV for gamma-rays and $3.3\times {10}^{14}$ eV for charged cosmic rays.

The trigger and reconstruction efficiency of KASCADE-Grande as a function of the shower size, i.e., the number of charged particles, is demonstrated in the lower graph of Figure 2. Full efficiency is reached at the number of charged particles of around 10⁶ for air showers induced by protons and iron primary particles, which corresponds to a primary energy of about 10¹⁶ eV. However, for showers induced by photon primaries, full efficiency is reached at a higher number of charged particles due to the missing muon trigger at large distances. The limit at high energies is due to the restricted area of the Grande array.

4.1. Gamma–Hadron Discrimination

Since gamma-ray-induced air showers are notable for their lack of muons compared to hadronic showers, we select a data sample enriched in gamma showers by rejecting showers containing muons. Simulations of hadronic air showers underlie large systematic uncertainties due to being above the interaction energies of accelerators and the unknown elemental composition. Therefore, our selection concept is based on using the comparison of the measured events with simulated gamma-ray-induced showers.

The upper graph of Figure 3 shows the distribution of the electron versus truncated muon number lg(${N}_{\mu ,\mathrm{tr}})$ − lg(N_e) for measured showers by KASCADE with simulated gamma-ray-induced showers. The graph indicates the whole experimental data set, as well as the distribution of the simulated gamma-ray events. Here ${N}_{\mu ,\mathrm{tr}}$ denotes the number of muons in the distance range of 40–200 m from the shower core. The electron number N_e is corrected to a zenith angle of 127 using an attenuation length of ${{\rm{\Lambda }}}_{{N}_{e}}=158$ g cm⁻² (Antoni et al. 2003). In Figure 3, showers without any detected muons are plotted with lg $({N}_{\mu ,\mathrm{tr}})=1.5$ to be visible on the logarithmic axis.²¹ The distribution of the shower size for gamma-ray-induced showers motivates the following cuts to select the muon-poor showers: lg(${N}_{\mu ,\mathrm{tr}})\lt 2$ for lg(${N}_{e})\lt 5.15$ and lg(${N}_{\mu ,\mathrm{tr}})\lt 1.4\,\cdot$ lg(${N}_{e})\,-5.21$ for lg(${N}_{e})\gt 5.15$. This selection of the muon-poor showers, i.e., gamma-ray candidates, is indicated by straight lines in Figure 3 (top).

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For KASCADE-Grande, the distribution of the observed number of muons lg(${N}_{\mu }$) versus the charged particles lg(N_ch) is shown in the lower graph of Figure 3, where there was never any detection of zero muons.²² The simulated gamma-ray showers are superimposed as well. Attenuation of the shower size through the atmosphere is corrected to a zenith angle of 20° using the method of constant intensity cut (Apel et al. 2012). The selection of muon-poor showers is indicated by the straight line in Figure 3 (bottom): lg(${N}_{\mu })\lt 3.2$ for lg(${N}_{\mathrm{ch}})\lt 6.2$ and lg(${N}_{\mu })\lt 1.64\,\cdot$ lg(${N}_{\mathrm{ch}})-6.95$ for lg(${N}_{\mathrm{ch}})\gt 6.2$.

The stringent selection cuts are motivated by the simulated gamma-rays and their optimization was investigated by changing the slope of the selection line. The cut values were found and optimized by Monte Carlo simulations in order to maximize the purity/efficiency ratio of gamma-ray-induced events. The events below the straight line were taken into consideration for further analysis. They amount to 1056 out of a total of 17 millions events in the case of KASCADE-Grande and to 12,087 out of 100 millions in the case of KASCADE. In the region below this line the events are expected to be mainly due to primary gammas because air showers induced by heavy nuclei show a larger muon-to-electron ratio. We therefore use a conservative method of searching for gamma-ray-induced showers in which the expected background is not subtracted from the event number below the selection lines shown in Figure 3.

4.2. Upper Limit of ${I}_{\gamma }/{I}_{\mathrm{CR}}$

There is no excess of events consistent with a gamma-ray signal seen in the data. Hence, we assume that all events below the selection line are primary gamma-rays and set upper limits on the gamma-ray fraction of the cosmic rays.

To determine an upper limit on the fraction of the gamma-ray with respect to the cosmic ray integral flux, ${I}_{\gamma }/{I}_{\mathrm{CR}}$, we use the equation given by Chantell et al. (1997):

$$\begin{eqnarray}&&\displaystyle \frac{{I}_{\gamma }}{{I}_{\mathrm{CR}}}\lt \displaystyle \frac{{N}_{90}}{{N}_{\mathrm{tot}}{\epsilon }_{\gamma }}{\left(\displaystyle \frac{{E}_{\mathrm{CR}}}{{E}_{\gamma }}\right)}^{-\beta +1}.\end{eqnarray} \tag{ 1 }$$

N_tot is the total number of events and N₉₀ is the 90% C.L. upper limit on the number of detected events, which is estimated by means of the statistical method from Helene (1983). Using the gamma simulations, we estimate the efficiency for gamma-ray detection and reconstruction, ${\epsilon }_{\gamma }$, after applying the selection cuts. E_CR and ${E}_{\gamma }$ are the mean energies of cosmic rays and gamma-rays, respectively, which produce the same shower size. β is the spectral index of the integral flux of cosmic rays: β = 2.7 for $E\lt 4\times {10}^{15}$ eV and β = 3.0 for $E\gt 4\,\times {10}^{15}$ eV. This means that, to calculate the energy we weight the simulated energy spectra of gamma-ray and cosmic ray showers to ${E}^{-2.7}$ below and ${E}^{-3}$ above the knee, assuming the latter is located at 4 × 10¹⁵ eV, as indicated by the measurements of Antoni et al. (2005). The mean energies of cosmic rays and gamma-rays are then calculated bin by bin. Gamma-ray primaries produce larger showers than cosmic ray primaries at the same energy. For this reason, to convert fixed shower size to fixed energy of gamma-ray primary, different factors in the equation have to be taken into account with the assumption that both components have the same spectral index.

Contributions to the systematic uncertainties are mainly due to the quality of discrimination of gamma-rays from cosmic rays (i.e., the statistics of the gamma-ray simulations), the estimation of the cosmic ray energy (i.e., the weighting of the energy spectral index and unknown composition), and the uncertainty in the validity of the hadronic interaction models.

The results of the search for diffuse ultra-high-energy gamma-rays for different threshold values of N_ch are summarized in Tables 1 and 2 for both experiments. Detailed systematic uncertainties on the upper limit of ${I}_{\gamma }/{I}_{\mathrm{CR}}$ are determined and also listed in the tables. We considered here the uncertainties on the energy reconstruction of the cosmic rays and gamma-rays as well as on the slope of the cosmic ray spectrum and the efficiency of the cut. The uncertainties of the estimation of the cosmic ray and gamma-ray energies are estimated to be about 20% (Antoni et al. 2005; Apel et al. 2011) and 10%, respectively. Other sources of systematic uncertainties, like variation of hadronic interaction models or the unknown chemical composition as well as the uncertainties in the slope of the all-particle energy spectrum, are included in these numbers. The error on the efficiency for the gamma-ray detection is evaluated to be smaller than 20%. Thus, the resulting uncertainty is less than 25% in the flux limits, except for the three highest-energy bins of KASCADE, since there the number of events at 90% C.L. is estimated from zero observed events.

Table 1.  Results of the Search for Diffuse Ultra-high-energy Gamma-Rays at Different Threshold Values of lg(N_e) Using KASCADE Data

lg(Ne)	Ntot	N90	${\epsilon }_{\gamma }$	ECR	${E}_{\gamma }$	${I}_{\gamma }/{I}_{\mathrm{CR}}$	${I}_{\gamma }$
>4	$1.02\times {10}^{8}$	11653.5	0.33	333	248	$\lt (2.1\pm 0.5)\times {10}^{-4}$	$\lt 4.02\times {10}^{-13}$
>4.5	$2.19\times {10}^{7}$	583.3	0.27	783	605	$\lt (6.3\pm 1.5)\times {10}^{-5}$	$\lt 2.67\times {10}^{-14}$
>5	$3.92\times {10}^{6}$	19.0	0.18	1994	1502	$\lt (1.7\pm 0.6)\times {10}^{-5}$	$\lt 1.46\times {10}^{-15}$
>5.5	$5.76\times {10}^{5}$	2.3	0.20	5247	3673	$\lt (1.1\pm 0.8)\times {10}^{-5}$	$\lt 1.73\times {10}^{-16}$
>6	$6.75\times {10}^{4}$	2.3	0.44	14618	8603	$\lt (3.1\pm 2.4)\times {10}^{-5}$	$\lt 8.77\times {10}^{-17}$
>6.5	$6.66\times {10}^{3}$	2.3	0.94	44952	18610	$\lt (8.1\pm 5.8)\times {10}^{-5}$	$\lt 4.47\times {10}^{-17}$

Note. The median cosmic ray energy, E_CR, and the median gamma-ray energy, ${E}_{\gamma }$, are given in the fifth and sixth columns, respectively, in units of TeV. The quantities N₉₀ and ${\epsilon }_{\gamma }$ are defined in the text. ${I}_{\gamma }/{I}_{\mathrm{CR}}$ is the 90% upper confidence limit on the integral gamma-ray fraction with systematic uncertainties, and ${I}_{\gamma }$ is the 90% upper confidence limit on the integral γ-ray flux, in units of photons cm⁻² s⁻¹ sr⁻¹.

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Table 2.  Results of the Search for Diffuse Ultra-high-energy Gamma-Rays at Different Threshold Values of N_ch Using KASCADE-Grande Data

lg(Nch)	Ntot	N90	${\epsilon }_{\gamma }$	ECR	${E}_{\gamma }$	${I}_{\gamma }/{I}_{\mathrm{CR}}$	${I}_{\gamma }$ (×10−17)
>6.5	6.19 × 106	358	0.71	3.21 × 104	1.38 × 104	$\lt (1.88\pm 0.44)\times {10}^{-5}$	<1.19
>7	85537	351	∼1.0	8.72 × 104	3.29 × 104	$\lt (6.79\pm 1.58)\times {10}^{-4}$	<8.51
>7.5	9640	214	∼1.0	2.21 × 105	8.30 × 104	$\lt (2.08\pm 0.49)\times {10}^{-3}$	<8.64
>8	1239	122	∼1.0	5.31 × 105	1.98 × 105	$\lt (1.03\pm 0.26)\times {10}^{-2}$	<8.32
>8.5	165	78	∼1.0	1.13 × 105	2.92 × 105	$\lt (2.48\pm 0.68)\times {10}^{-2}$	<3.89

Note. The mean cosmic ray energy, E_CR, and the mean gamma-ray energy, ${E}_{\gamma }$, are given in the unit of TeV. ${I}_{\gamma }/{I}_{\mathrm{CR}}$ is the 90% upper confidence limit on the integral gamma-ray fraction with systematic uncertainties, and ${I}_{\gamma }$ is the 90% upper confidence limit on the integral gamma-ray flux in units of photons cm⁻² s⁻¹ sr⁻¹.

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To determine upper limits to the integral flux of gamma-rays at fixed gamma-ray energies, we use measurements of the all-particle primary energy spectra reported in Antoni et al. (2005) and Apel et al. (2011). The limits on the gamma-ray flux ${I}_{\gamma }$ are also listed in Tables 1 and 2. To obtain the integral flux of gamma-rays, we multiplied the reconstructed all-particle energy spectrum by the fraction of gamma-rays relative to cosmic rays $({I}_{\gamma }/{I}_{\mathrm{CR}})$.

Figure 4 displays the measurements on the gamma-ray fraction as a function of the energy, including this work, for the energy range from 10¹⁴ eV up to 10¹⁸ eV. The upper limits of the fraction of gamma-rays at $1.5\times {10}^{15}$ eV and $3.7\times {10}^{15}$ eV are obtained to be $1.7\times {10}^{-5}$ and $1.1\times {10}^{-5}$, respectively. These are the lowest upper limits to date. In addition, since around 10¹⁷ eV (Figure 4) not many experiments have reported results, the limits obtained by KASCADE-Grande are of heightened interest. It should be noted that all values in Figure 4 are upper limits, except that from MSU (Fomin et al. 2013, 2014). This positive signal, however, is in conflict with the limits presented here. Also, a further reanalysis of the MSU data does not confirm the positive signal (Fomin et al. 2017).

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Figure 5 shows the comparison of integral flux of gamma-rays with previous experiments (Aglietta et al. 1996; Chantell et al. 1997). Compared with the earlier obtained limits by KASCADE in 2003 (Schatz et al. 2003) there are some differences, in particular at lower energies. This is accounted for by a more detailed investigation using more parameters (i.e., the lateral slope and the smoothness of the electromagnetic component), which affected mainly the lower energies. In this work we focused on higher energies by applying the same method to the KASCADE and KASCADE-Grande data, where those additional parameters for selecting muon-poor events are not effective. The MSU collaboration (Fomin et al. 2014, 2017) recently presented upper limits on the diffuse gamma-ray flux for primary energies around 10–100 PeV obtained from a reanalysis of their old measurements. They are compatible with the presented KASCADE-Grande limits.

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Figure 5 also compares the exemplary results with theoretical curves using a specific IceCube neutrino excess model assuming proton–proton (pp) interactions and cutoff at 6 PeV (Ahlers & Murase 2014). The lines are the IceCube excess models originating from different distances of neutrino sources in the Galaxy, where these neutrinos are also responsible for primary gamma-rays. The secondary pions from the hadronic interactions of cosmic rays decay at the source and produce a flux of high-energy neutrinos as well as gamma-rays. The relative numbers of neutrinos and gamma-rays depend on the ratio of charged to neutral pions. The flux limits on the gamma-ray flux ${I}_{\gamma }$ of this work at $1.5\times {10}^{15}$ eV and $3.7\times {10}^{15}$ eV are lower than the theoretical prediction of the IceCube excess model coming from an 8.5 kpc source distance (dotted black line), which corresponds to the distance from the Galactic center. Therefore, this observation is not in contradiction to the statement that the IceCube excess is associated with extragalactic sources, e.g., gamma-ray bursts or active galactic nuclei. Moreover, there are other scenarios, e.g., the PeV dark matter decay model in the Galactic halo, suggested to explain the IceCube excess (Ahlers & Murase 2014), which can be additionally constrained by the results of this work, in a similar way as done by Kalashev & Troitsky (2015).

Using data sets measured by the KASCADE and KASCADE-Grande experiment over a period of 14 and 9 years, respectively, we determined the 90% upper confidence limits to the diffuse flux of ultra-high-energy gamma-rays for the energy range from 10¹⁴ eV to 10¹⁸ eV by selecting showers with low muon content.

The upper limit of the fraction of gamma-rays at $1.5\times {10}^{15}$ eV from the KASCADE measurement is estimated to be $1.7\times {10}^{-5}$, while it is $1.1\times {10}^{-5}$ at $3.7\times {10}^{15}$ eV. These are currently the lowest upper limits, which were used to set constraints on theoretical predictions, in particular on the distance of sources for the IceCube neutrino excess model (Ahlers & Murase 2014).

By means of the KASCADE-Grande measurements, the best upper limit to the fraction of the gamma-ray to the cosmic-ray flux is obtained: ${I}_{\gamma }/{I}_{\mathrm{CR}}\lt 1.88\times {10}^{-5}$ for 13.8 PeV. The stringent limits above 100 PeV might constrain a limit to the background rate of muon-poor showers in the search for the Galactic disk enhancement of cosmic rays.

The angular resolutions of KASCADE and KASCADE-Grande are sufficient over the whole energy range to search also for gamma-ray point sources, where a preliminary result was presented in Kang et al. (2015b). However, both analyses will profit from an analysis of combined KASCADE and KASCADE-Grande data, where a coherent shower reconstruction is currently under development. By then, also, an advanced analysis method has to be optimized to give the best results (see, e.g., discussions in Homola & Risse 2007) for such a wide energy range in the search for a diffuse gamma-ray flux.

The authors would like to thank the members of the engineering and technical staff of the KASCADE-Grande collaboration, who contributed to the success of the experiment. The KASCADE-Grande experiment is supported in Germany by the BMBF and by the "Helmholtz Alliance for Astroparticle Physics—HAP" funded by the Initiative and Networking Fund of the Helmholtz Association, by the MIUR and INAF of Italy, the Polish Ministry of Science and Higher Education, and the Romanian Authority for Scientific Research UEFISCDI (PNII-IDEI grants 271/2011 and 17/2011). J.C.A.V. acknowledges the partial support of CONACyT. Z.F. is supported by the Natural Sciences Foundation of China (Nos. 11405182).