On the Source Contribution to the Galactic Diffuse Gamma Rays above 398 TeV Detected by the Tibet ASγ Experiment

Potential contribution from gamma-ray sources to the Galactic diffuse gamma rays observed above 100 TeV (sub-PeV energy range) by the Tibet ASγ experiment is an important key to interpreting recent multimessenger observations. This paper reveals a surprising fact: none of the 23 Tibet ASγ diffuse gamma-ray events above 398 TeV within the Galactic latitudinal range of ∣b∣ < 10° come from the 43 sub-PeV gamma-ray sources reported in the 1LHAASO catalog, which proves that these sources are not the origins of the Tibet ASγ diffuse gamma-ray events. No positional overlap between the Tibet ASγ diffuse gamma-ray events and the sub-PeV LHAASO sources currently supports the diffusive nature of the Tibet ASγ diffuse gamma-ray events, although their potential origin in the gamma-ray sources yet unresolved in the sub-PeV energy range cannot be ruled out.


INTRODUCTION
The Tibet ASγ experiment has performed the first detection of Galactic diffuse gamma rays above 100 TeV (sub-PeV range) well concentrated on the Galactic Plane (Amenomori et al. 2021).The hadronic origin of the Tibet ASγ diffuse gamma rays is supported by the observation of Galactic neutrinos by IceCube (IceCube Collaboration et al. 2023); the energy spectrum of the Tibet ASγ diffuse gamma rays converted into the neutrino flux assuming the hadronic interaction smoothly connects at ≃ 60 TeV with the all-sky Galactic-neutrino flux scaled by the intensity of the diffuse emission template proposed by Ackermann et al. (2012) in the field of view of the Tibet ASγ experiment.However, it is controversial whether they have a totally diffusive nature or include some contributions from yet-unresolved, dim gamma-ray sources.Fang & Murase (2021) suggest that some very energetic sources such as hypernova remnants could largely contribute to the Tibet ASγ diffuse gamma-ray events.Vecchiotti et al. (2022) also demonstrate that the Tibet ASγ diffuse gamma-ray events can be explained with the truly diffuse emission plus the emission from unresolved pulsar-wind nebulae too dim to be detected, the latter of which could make a significant contribution.
The possible pictures above can be tested experimentally with the LHAASO observatory which is now steadily operating and surveying gamma rays from the northern sky in the sub-PeV energy range with a sensitivity one order of magnitude better than the other existing gamma-ray observatories (Cao et al. 2021a,b).Considering the excellent sensitivity of LHAASO, one can naturally expect their detection of many gamma-ray sources that the Tibet ASγ experiment could not detect in the directions the Tibet ASγ diffuse gamma-ray events come from.Furthermore, the LHAASO collaboration recently reported their first catalog (1LHAASO catalog) of gamma-ray sources detected in 1 TeV < E < 25 TeV and/or E > 25 TeV, and 43 out of the sources found in the latter energy range are also detected above 100 TeV with more than 4 σ levels (Cao et al. 2023).The detection of the sub-PeV gamma-ray sources gives us a good opportunity to consider whether these sources contribute to the Tibet ASγ diffuse gamma-ray events.

Tibet ASγ Galactic diffuse gamma-ray emission events
This study focuses on the 23 gamma-ray-like diffuse events above 398 TeV detected by the Tibet ASγ experiment in the Galactic latitudinal range of |b| < 10 • , as reported in Amenomori et al. (2021); hereafter let us simply call these events the Tibet ASγ Galactic diffuse gamma-ray emission (T-GDE) events.These events are found in the data taken by the observatory during a live time of 719 days from February 2014 to May 2017.The Tibet ASγ experiment consists of a surface air shower array covering a geometrical area of 65 700 m 2 and an underground muon detector array with a 3400 m 2 area.The latter counts the number of muons in air showers, leading to powerful discrimination of primary gamma rays and cosmic rays.Amenomori et al. (2021) found the T-GDE events after the event selection with the tight muon cut which realizes the cosmic-ray survival ratio of 10 −6 and the gamma-ray survival ratio of 30% above 398 TeV.Note that the 23 events include 2.73 background cosmic-ray events and four gamma-ray-like events detected within 4 • from the center of the Cygnus Cocoon; see Amenomori et al. (2021).

2.2.
Positions of the T-GDE events and the sub-PeV LHAASO sources Vecchiotti et al. (2022) propose that ≃ 50% of the diffuse gamma-ray flux above 398 TeV measured by the Tibet ASγ experiment could be the contributions from gamma-ray sources unresolved by the Tibet ASγ experiment.This means that ∼ 50% of the T-GDE events come from unresolved sources.If the 1LHAASO catalog sources detected above 100 TeV (hereafter simply called sub-PeV LHAASO sources) are the origins of the T-GDE events, about 10 sources should overlap the T-GDE events under the picture proposed by Vecchiotti et al. (2022).Is that the case?
Figure 1 shows the incoming directions of the T-GDE events (red points) and the positions and extensions of the sub-PeV LHAASO sources (blue circles; Cao et al. 2023).Assuming a two-dimensional Gaussian morphology, the extensions of 95% containment radii are calculated from the published extensions of the 39% containment radii (Cao et al. 2023).For point-like sources, the 95% upper limits on the extensions are shown.Surprisingly, no T-GDE events have their arrival directions within the extensions of the sub-PeV LHAASO sources.This means that none of the sub-PeV LHAASO sources is the origin of the T-GDE events.

Statistical consistency of the observations by the Tibet ASγ experiment and LHAASO
One may think of the accidental positional overlap of the T-GDE events with the sub-PeV LHAASO sources.The sum of the extensions (in terms of 95% containment radii) of the sub-PeV LHAASO sources located in the area of interest shown in Figure 1 covers ≃ 3.7% of the area of interest, and the expected number of the T-GDE events that accidentally overlap the sub-PeV LHAASO sources is estimated to be ≃ 0.037 × 23 = 0.86.Therefore, it is natural to see no accidental overlap between the T-GDE events and the sub-PeV LHAASO sources, as observed.
In the Tibet ASγ diffuse-gamma-ray analysis performed by Amenomori et al. (2021), they masked the gamma-ray sources listed in the TeVCat catalog as of 2021.Twenty out of the 43 sub-PeV LHAASO sources are associated with the TeVCat catalog sources masked in the analysis of Amenomori et al. (2021), while the remaining 22 sources are not; hereafter such sources are called newly-reported sub-PeV LHAASO sources, listed in Table 1.The statistical consistency of the non-detection of gamma-ray events by the Tibet ASγ experiment from these sources should be studied.The number of gamma-ray events n above 398 TeV from each of the newly-reported sub-PeV LHAASO sources can be estimated as (1) Here  2023)) in the Galactic coordinates.The extensions of the sub-PeV LHAASO sources have 95% containment radii assuming a two-dimensional Gaussian morphology.For point-like sources, the 95% upper limits on the extensions are shown.The green dashed circle with a 6 • radius encloses the Cygnus region centered at (l, b) = (79.• 62, 0. • 96), the position of HAWCJ2030 + 409 (Abeysekara et al. 2021).Note that some of the sub-PeV LHAASO sources have |b| > 10 • and thus are not shown in the plot.
(719 days) of the dataset used in the Tibet ASγ data analysis.The results of the n's for the newly-reported sub-PeV LHAASO sources are shown in Figure 2 as a function of declination δ.Since the newly-reported sub-PeV LHAASO sources with δ < −10 • or δ > 70 • do not culminate in θ < 40 • at the site of the Tibet ASγ experiment (30.• 102N), they have n = 0 and are not shown in the figure.The sum of the n's of the newly-reported sub-PeV LHAASO sources is 1.2, so the non-detection of gamma-ray events by the Tibet ASγ experiment from the newly-reported sub-PeV LHAASO sources is statistically consistent.Therefore, our result currently supports the diffusive nature of the T-GDE events, although the potential origin of the T-GDE events in the gamma-ray sources yet unresolved in the sub-PeV energy range cannot be ruled out.

Positional correlation between the T-GDE events and gamma-ray sources other than the sub-PeV LHAASO sources
This study checks overlaps between the T-GDE events and existing gamma-ray sources other than the sub-PeV LHAASO sources to study the potential source origin of the T-GDE events.First, the positional correlation between the T-GDE events and the total 47 1LHAASO catalog sources detected only below 100 TeV is studied.The circular region with a radius of 0.5 • centered at each of the 47 1LHAASO catalog sources is considered and the T-GDE events within these circular regions are seached.The radius of the circular regions is the same as that employed for the masked regions in the Tibet ASγ diffuse-gamma-ray analysis (Amenomori et al. 2021).As a result, it is found that only one T-GDE event named TASG-D01-025 with the arrival direction of (α J2000 , δ J2000 ) = (286.96• , 7.96 • ) (see the Supplemental Material of Amenomori et al. (2021)) is within the circular region of 1LHAASO J1907+0826 which is detected only in 1 TeV < E < 25 TeV by the LHAASO Water Cherenkov Detector Array.The fact of the one overlap is statistically consistent with an expected accidental overlap (0.19 events).
Furthermore, overlaps between the T-GDE events and the gamma-ray sources listed in the latest TeVCat catalog (Wakely & Horan 2008) are checked.Out of the total 273 sources listed in the latest TeVCat catalog1 , there are 92 sources in the sky region displayed in Figure 1 after removing extragalactic sources.Note that the 92 TeVCat catalog sources include the sources masked in the Tibet ASγ diffuse-gamma-ray analysis (Amenomori et al. 2021), while they do not include the 1LHAASO catalog sources.The circular region with a radius of 0.5 • centered at each of the 92 TeVCat catalog sources is considered and the T-GDE events within these circular regions are searched.As a result, there is no overlap between the T-GDE events and the TeVCat catalog sources, and it is statistically consistent with an expected accidental overlap (0.38 events).The results presented in this section further support the diffusive nature of the T-GDE events.

CONCLUSION
Our study shows that the 43 1LHAASO catalog sources detected above 100 TeV (sub-PeV LHAASO sources) are not the origins of the 23 T-GDE events above 398 TeV from the fact that no T-GDE events have their arrival directions within the extensions of the sources.The number of accidental overlaps between the T-GDE events and the sub-PeV LHAASO sources is estimated to be 0.86, and the expected number of gamma-ray events from the 22 newly-reported sub-PeV LHAASO sources is 1.2, both ensuring the statistical consistency of no overlap between the T-GDE events and the sub-PeV LHAASO sources.No overlap between the T-GDE events and the sub-PeV LHAASO sources currently supports the diffusive nature of the T-GDE events, although the potential origin of the T-GDE events in the gamma-ray sources yet unresolved in the sub-PeV energy range cannot be ruled out.This work is supported in part by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science in Japan, the joint research program of the Institute for Cosmic Ray Research (ICRR), the University of Tokyo, and the use of the computer system of ICRR.This work is also supported by the National Natural Science Foundation of China under Grants No. 12227804, and the Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, CAS.Note-δ, declination of the source; n, the expected number of gamma-ray events that would be observed by the Tibet ASγ experiment from the source during the live time, calculated from Equation (1).The sources outside the field of view of the Tibet ASγ experiment have n = 0; see the main text.

Figure 1 .
Figure 1.Incoming directions of the Galactic diffuse gamma-ray events above 398 TeV observed by the Tibet ASγ experiment (red points) and the positions and extensions of the sub-PeV LHAASO sources: the gamma-ray sources detected by LHAASO above 100 TeV (blue circles; Cao et al. (2023)) in the Galactic coordinates.The extensions of the sub-PeV LHAASO sources have 95% containment radii assuming a two-dimensional Gaussian morphology.For point-like sources, the 95% upper limits on the extensions are shown.The green dashed circle with a 6 • radius encloses the Cygnus region centered at (l, b) = (79.• 62, 0. • 96), the position of HAWCJ2030 + 409(Abeysekara et al. 2021).Note that some of the sub-PeV LHAASO sources have |b| > 10 • and thus are not shown in the plot.

Figure 2 .
Figure2.Expected number of gamma-ray events above 398 TeV that would be observed by the Tibet ASγ experiment from the 22 newly-reported sub-PeV LHAASO sources.For more details, see the main text.

Table 1 .
List of the newly-reported sub-PeV LHAASO sources