Introduction

γ-ray bursts (GRBs) are a phenomenon in which gamma rays from the depths of the universe suddenly increase on a short-time scale; they are the most violent explosion phenomenon after the Big Bang. Theoretically, the prompt emission of the GRB is generated by the energy dissipation process inside the relativistic jet, whereas the multi-band afterglow emission is generated by the external shock caused by the collision between the relativistic jet and the external medium. Therefore, gamma bursts are used to study the emergence of compact celestial bodies (black holes with constant star mass and neutron stars), gravitational wave radiation, relativistic shock waves, extremely high-energy cosmic rays, high-energy neutrinos, and other extreme objects in astronomical laboratories for scientific phenomena and high-precision testing of basic physical principles; they are also important probes for early universe star formation and evolution, high-redshift galaxies, and high-redshift cosmology.

The first γ-ray burst (GRB) was discovered by the Vela U.S. military satellites in 1967 and was recognized early as being of extrasolar origin [1]. A bimodal structure (first reported in [2]) in the duration distribution of GRBs was detected by the Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma Ray Observatory (CGRO) [3], based on which GRBs are currently commonly classified as short (with a duration T₉₀ < 2 s, SGRBs) and long (with T₉₀ > 2 s, LGRBs) [4]. BATSE observations have also confirmed that GRBs have an isotropic angular distribution in the sky [3, 5-8]. GRB970508, with 0.835 < z ≤ 2.3, was placed at a cosmological distance of at least 2.9 Gpc, which was later corroborated by the first redshift measurement [9]. Subsequently, the progenitors of LGRBs were associated with supernovae (SNe) [10-14] related to the collapse of massive stars. The first direct detection of gravitational waves (GWs) by the Laser-Interferometer Gravitational-Wave Observatory, termed GW150914, was interpreted as a merger of two stellar-mass black holes (BHs) with masses and was, by itself, a discovery of prime importance [15]. It became especially interesting in light of the discovery of a weak transient source lasting 1 s in [16] and detected by Fermi/GBM [17] only 0.4 s after the GW150914 (termed GW150914-GBM). The highest-energy GRB photon ever recorded by Fermi-LAT thus far had been emitted by GRB 130427A in the early afterglow phase and had an energy of 95 GeV (128 GeV in the rest frame during a redshift z=0.34) [18]. While LAT-detected GRBs commonly exhibit photon energies of a few hundred MeV, higher energies are relatively rare. Although satellite experiments have provided a vast number of exciting results, they are limited by their effective areas and have difficulty detecting higher-energy photons in the prompt emissions of GRBs.

Recently, sub-TeV energy γ rays were successfully observed by the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) and High Energy Stereoscopic System (H.E.S.S.) telescopes approximately 1 min after the GRB 190114C burst and 10 h after the end of the prompt-emission phase of GRB 180720B [19, 20, 21]. These events were unique, as researchers were able to observe them for the first time in afterglow emission photons with sub-TeV energies. Soon thereafter, the H.E.S.S. collaboration announced the detection of photons with energies up to 4 TeV high from GRB 190829A between 4 h and 56 h after the trigger [22]. Additionally, MAGIC reported the detection of hundreds of GeV γ-ray emissions from GRB 201216C in the afterglow phase [23]. Along with GRB 160821B and GRB 201015A, from which over 100 GeV of emissions at the ≤ 3σ level have been reported [24, 25], six GRBs have been reported with VHE afterglow emissions. Imaging atmospheric Cherenkov telescopes (IACTs) have been making great progress in the observations of VHE emissions in the afterglow phase. However, it is challenging for IACTs to perform conduct prompt-phase observation. They have a narrow field of view (FoV) and need to slew because a GRB does not typically enter their FoV within the first seconds of the prompt phase occurring, even if they have larger effective areas (unless the GRB occurs in their FoV, which has a very small probability).

Traditional extended air shower (EAS) experiments, for example, the High-Altitude Water Cherenkov Observatory [26] and the Large High Altitude Air Shower Observatory [27], which have wide FoVs, high duty cycles, and large effective areas, have not yet detected GRBs. In general, the energy thresholds of the EAS experiments are also higher than those of the IACT experiments.

The detection of high-energy photons in the prompt phase of the GRB is conducive to understanding the acceleration mechanisms and energetics because it constrains the progenitors, jet feeding mechanism, and extragalactic background light (EBL)-induced absorption of high-energy photons, which limits the Lorentz invariance violation (LIV). Therefore, it is important to search for prompt VHE emissions from GRBs using ground-based instruments that can achieve excellent sensitivity and a low-energy threshold over a wide FoV. The high-altitude detection of astronomical radiation (HADAR) experiment is a new observation instrument that uses a large-dimensional refractive water lens as a light collector to observe Cherenkov light induced by VHE cosmic rays (CRs) and γ rays in the atmosphere. In 2016, a prototype experiment was conducted and was successfully operated at the Yangbajing Observatory (4300 m above sea level, 90.522° E, 30.102°N, 606 g/cm²) in Tibet, China. Cosmic rays were successfully detected. More detailed information is available in [28, 29].

However, the bottleneck in wide-FoV Cherenkov technology is caused by the high rate of night-sky background (NSB) noise from random stars overwhelming the Cherenkov light signal from a GRB. Consequently, images of air showers recorded by telescopes are indistinguishable, and the fitting of a Hillas ellipse with the fired photomultiplier tubes (PMTs) on the camera, a critical step in event reconstruction, cannot be precisely performed. In this study, we propose a novel method that considers the spatial properties of GRBs and the temporal characteristics of Cherenkov radiation to reject NSB noise.

The remainder of this paper is organized as follows. Section 2 describes the HADAR experiment in detail. Section 3 presents a novel trigger method for wide-view IACT experiments, and Sect. 4 includes the results of the novel trigger method. Section 5 presents the conclusions of the study.

Imaging Atmospheric Cherenkov Technique and the HADAR Experiment

trigger algorithm

GRB jets are usually unresolved and are viewed as point sources by instruments that are observational rather than intrinsic. This is because of their intrinsically small size, especially at early times, and their cosmological distances, which result in very small angular sizes [33]. Therefore, the GRB signal exhibits spatial characteristics. The main high-rate noise is NSB noise, which is emitted from random stars because IACTs can only make observations on clear and moonless nights. In contrast, NSB is isotropic and has no spatial characteristics.

Generally, H.E.S.S. or MAGIC telescopes are equipped with a large optical reflecting dish. These telescopes must rotate with the gamma source when they make scientific observations because they have a narrow FoV. However, owing to the small FoV, the night sky background noise received by the mirror is significantly lesser. After a simple cut on pixels (e.g., image cleaning), a clearer Cherenkov image caused by CR or γ rays can be obtained on the camera. However, this trigger method cannot be directly applied to experiments with a wide FoV, such as the HADAR. Because HADAR telescopes have a wide FoV, this introduces a significant amount of NSB noise. The challenge for the HADAR experiment is determining how to reject the high rate of NSB noise from random stars. For high-energy events, the effect of the NSB noise can be ignored because high-energy events generate many Cherenkov photons. The signal is not overwhelmed by the noise. However, low-energy events do not generate as many photons as high-energy events. It is difficult to distinguish which PMTs have been triggered by noise, and which have been triggered by Cherenkov photons. Clear images cannot be obtained. Therefore, to make better scientific observations using HADAR, we improved the trigger method.

As shown in Fig. 1, on a clear and moonless night, a GRB appeared at δ(i,j) on the celestial sphere, which was in the FoV of the HADAR experiment. High-energy γ rays from the GRB entered and interacted with the Earth's atmosphere. They produced a large number of electron–positron pairs with enormous velocities. When electron–positron pairs travel faster than light in the Earth's atmosphere, their passage causes a brief flash of light: Cherenkov light. The photons from the Cherenkov radiation were collected by the lens and focused on by the camera (this was the signal of interest). Simultaneously, the photons from the random stars also entered the lens and were recorded by the camera (this was the main noise). At low energy, the crucial signals from the GRB were submerged by NSB noise.

Figure 1Full-screen View

(Color online) Mapping the location where there was a GRB on a celestial sphere with a fired PMT on the camera. δ(i,j) denotes the position of the GRB on the celestial sphere. δ′ (i′,j′) is the area where the signal is stronger and concentrated in the camera (circled by the red ellipse).

The trigger algorithm used by HADAR was as follows: (1) one PMT was fired if ≥ 9 photoelectrons were collected by the PMT within the time window; (2) if the number of adjacent triggered PMTs on the camera was n ≥ 3, a telescope was considered to be triggered; (3) an event was recorded if ≥ 2 telescopes were triggered in a time window of 20 ns (to reconstruct the event); (4) a 10 × 10 PMT matrix was selected from the camera with adjacent triggered PMTs as the center. Subsequently, all fired PMTs in the matrix were used to fit the Hillas ellipse (a key step for event reconstruction). The area enclosed by the ellipse is denoted as δ′ (i′,j′). Other PMTs outside the matrix were masked to reduce the trigger rate of the NSB noise. As previously mentioned, GRBs have distinct spatial properties. Therefore, to perform detection even at low energies, a map between δ (i,j), the position of the GRB on the celestial sphere, and δ′ (i′,j′), where the signals were large and concentrated on the camera, could be constructed as follows: $f(\delta (i\mathrm{,}j))={\delta }^{\text{'}}(i^{\text{'}}\mathrm{,}{j}^{\text{'}})$. This implies that a limited number of PMTs were selected from one direction.

Because the atmospheric index of refraction was very close to 1, the Cherenkov light almost kept pace with radiating charged particles. Near the edge of the "light pool", most of the light from the γ ray shower arrived within 2 ns. Thus, a very short temporal window was possible, allowing for suppression of the dominant NSB. The number of background photons is given as follows: $n_{\text{ph}}=BA\Omega \xi \tau \mathrm{,}$ (2) where B is 557m^-2sr^-1ns^-1, A is the mirror area (in this study, $A\approx 43{\text{ m}}^2$), Ω is the solid angle corresponding to each PMT ($\Omega \approx 1.6\times {10}^{-4}$ sr), ξ is the photocathode quantum efficiency, and τ is the integration time of ≈ 20 ns. The number of Cherenkov photons is given as follows: $N_{\text{ph}}=NA\xi \mathrm{,}$ (3) where N is the number of Cherenkov photons per m^-2 inside the solid angle Ω at a given distance from the shower axis. In the integration temporal window of τ=20 ns, the Cherenkov signal was fully recorded, while introducing as little noise as possible. This suggests the use of fast photomultiplier cameras in telescopes for this purpose.

Result

After applying the new trigger method, the NSB was suppressed and the angular resolution and effective area were significantly improved.

In Fig. 2, the black line represents the time distribution of all photons (including NSB and Cherenkov photons) received by all PMTs. The NSB overwhelmed the Cherenkov signals of interest. After selecting the area δ′ (i′,j′) with the strongest signal on the camera (blue line), the NSB was suppressed, and the Cherenkov signal was well preserved compared to the case that only included Cherenkov signals (red line).

Figure 2Full-screen View

(Color online) Time distribution of photons received by the PMT. The black line represents the time distribution of all photons (including the NSB and Cherenkov photons) received by all PMTs. The blue line represents the time distribution of photons, including a small number of NSB photons and most Cherenkov photons after selecting δ′ (i′,j′) on the camera. The red line represents the time distribution containing only the Cherenkov photons. To demonstrate this more clearly, the selection and Cherenkov distributions were both scaled by 10.

In addition, the angular resolution was improved and the effective area increased. Fitting a Hillas ellipse is a critical step for event reconstruction in IACTs. However, while applying all PMTs of one camera, it becomes a challenge to fit a Hillas ellipse with fired PMTs because many of them are fired by the NSB. This results in a significant difference between the reconstructed and real directions. Therefore, the angular resolution was > 1° at E< 200 GeV, as indicated by the black line in Fig. 3, when applying all PMTs of one camera. As the energy increased, the angular resolution gradually approached < 1°. This was because the Cherenkov signals became stronger and were no longer submerged by the NSB. The angular resolution improved considerably after selecting δ′ (i′,j′) on the camera, as indicated by the red line. After selection, the fired PMTs could be fitted by a qualified ellipse that contained the essential parameters for event reconstruction at low energy. Furthermore, the angular resolution of the high-energy event was also improved. In contrast to the blue line, which corresponds to the case with only Cherenkov photons, the red line indicates that the NSB has a certain influence on the event reconstruction.

Figure 3Full-screen View

(Color online) Angular resolution. Black line: application of all PMTs to the camera. Red line: after selection. Blue line: only Cherenkov photons

Figure 4 shows the effective area of the HADAR experiment. The simulated area was 800 × 800 m². The black line was the effective area before PMT selection. At E < 200 GeV, almost every event triggered the telescope array because the NSB was introduced heavily, resulting in many PMTs being fired. After PMT selection, because the NSB was suppressed and Cherenkov photons were lower in low energy, the probability of event triggering the telescope array became lower, which was almost the same as the case with only Cherenkov photons, as shown by the red and blue lines. Aside from the angular resolution, when E > 300 GeV, the effective area was almost the same in the three cases.

Figure 4Full-screen View

(Color online) Effective area. Black line: application of all PMTs to the camera. Red line: after selection. Blue line: only Cherenkov photons

Conclusion

Unlike the afterglow theory, which is relatively simple and well-tested by data, the GRB prompt-emission theory is much more complicated. Thus, more experimental data are required for prompt GRB emissions. The HADAR experiment provides an effective solution for detecting GRB prompt emissions on the ground. Unlike satellite experiments with small effective areas and traditional IACTs with narrow FoVs, the HADAR experiment has a large effective area and wide FoV. The wide FoV allows telescopes to cover a larger area of the celestial sphere and observe GRBs without slewing. However, a wide FoV introduces considerable noise from the NSB, making it difficult to observe low-energy events.

To solve this problem, the GRB's spatial properties and temporal structure of atmospheric Cherenkov radiation were fully utilized. At the coordinates δ′ (i′,j′), a stronger and concentrated signal on the camera was selected and mapped to δ (i,j), the position of the GRB on the celestial sphere. To fully record the Cherenkov signal while introducing as little noise as possible, a 20-ns integration temporal window was selected. After applying the new trigger method, the angular resolution of low-energy events significantly improved, and the angular resolution was < 1° at 10 GeV. Moreover, the trigger rate of the telescope array was significantly reduced at low energy because the NSB noise was suppressed. This method can be used in all the wide-FoV IACT experiments. As the angular resolution and effective area of HADAR have improved, HADAR’s capacity to observe GRBs increases the detection rate to at least one GRB per year. We hope that future experimental observations can confirm the progress of physics in the prompt phase and relevant parameters.