Limit on an Isotropic Diffuse Gamma-Ray Population with HAWC
Data from 105 days from the High Altitude Water Cherenkov Observatory (HAWC) have been used to place a new limit on an isotropic diffuse gamma-ray population above 10 TeV. High-energy isotropic diffuse gamma-ray emission is produced by unresolved extragalactic objects such as active galactic nuclei, with potential contributions from interactions of high-energy cosmic rays with the inter-Galactic medium, or dark matter annihilation. Isotropic diffuse gamma-ray emission has been observed up to nearly 1 TeV. Above this energy, only upper limits have been reported. Observations or limits of the isotropic photon population above these energies are very sensitive to local astrophysical particle production. Of particular note, we expect a photon population to accompany the TeV-PeV astrophysical neutrino detection seen in the IceCube instrument. Observations or limits of a photon population above this energy can point to the origin of these neutrinos, indicating whether they are within the gamma-ray horizon or not. HAWC, with superior sensitivity to gamma rays between 100 GeV and 100 TeV, continuously observes the overhead sky and will measure or constrain isotropic emission above 1 TeV. We present a limit above 10 TeV based on the background rejection achieved in a 105-day observation of the Crab Nebula with HAWC. The limit will improve substantially with additional data and study.
Isotropic Diffuse Gamma-Ray Emission in HAWC
\FullConferenceThe 34th International Cosmic Ray Conference,
30 July- 6 August, 2015
The Hague, The Netherlands
Isotropic diffuse gamma-ray emission can arise from a number of mechanisms including unresolved sources, dark matter, or more exotic phenomena. Of particular interest are gamma-rays produced in conjunction with the TeV-PeV neutrino population reported by the IceCube collaboration  which may occur in astrophysical pion production or in dark matter annihilation . Charged pion production should be accompanied by neutral pion production and these neutral pions will decay into gamma rays. If the IceCube neutrinos are from pion decay, gamma rays should be produced with a similar spectrum and flux as the neutrinos . Gamma rays above 1 TeV that originate outside the galaxy are heavily attenuated by the Extra-Galactic Background Light (EBL). This situation creates a testable hypothesis: A photon flux at the level of the IceCube measurement suggest that the neutrinos are produced locally, within or near our own galaxy . An absence of photons would suggest the neutrinos are produced beyond the gamma-ray horizon . For this reason, diffuse gamma-ray observations are particularly interesting if they reach sensitivity below the level of the IceCube astrophysical neutrino detection.
Electrons and positrons produce similar air showers to gamma rays and appear very similar in a ground array. Cosmic-ray electrons can be accelerated by a nearby pulsar or supernova remnant, but the electrons are isotropized by the intervening magnetic field. Electrons have been observed up to 1 TeV by H.E.S.S. . The spectrum appears to be falling very rapidly, near . The cosmic-ray electron/positron spectrum is interesting in its own right; models suggest that the cosmic-ray electron spectrum may flatten if a nearby source is bright enough . It may also constitute a background to photon observation if the spectrum hardens.
The High Altitude Water Cherenkov Observatory (HAWC) is a water-Cherenkov air shower array operating near Sierra Negra in Mexico. A key feature of the high-energy sensitivity of the HAWC instrument is its ability to distinguish electromagnetic air showers from hadronic showers. The 300 4.5-meter deep Water Cherenkov Detectors (WCDs) that make up the instrument are designed for identifying the penetrating particles characteristic of hadronic air showers. HAWC maintains this ability across its entire 20,000 area.
HAWC is designed to observe localized sources of TeV photons. When observing a localized source, the hadron background is measured from data by interpolating between “off source” observations. When looking for an isotropic population, the hadron background must be determined a priori from simulation. HAWC’s ability to distinguish hadronic showers from electromagnetic showers is critical. In Section 2 we present some studies of the photon/hadron rejection by looking at the 10 TeV signal from the Crab Nebula. The hadron rejection is so good that we can improve upon existing isotropic photon limits at 10 TeV without a dedicated isotropic photon analysis. In Section 3, we show the computation of this limit. A number of analysis improvements stand to improve our sensitivity by a factor of 100. Section 4 discusses these prospects.
HAWC cannot easily distinguish between high-energy electrons, positrons and photons. To the extent that air showers from electrons, positrons and photons behave the same, our limits are actually a limit on the combined flux of photons, electrons and positrons. For this analysis, we frame the discussion in terms of gamma rays because we have not yet considered any differences in the air showers generated by electrons or positrons. The prospects for detecting the TeV electron/positron population are discussed elsewhere in these proceedings .
2 Crab Studies
As the strongest steady TeV source in the sky, the Crab Nebula serves as an important benchmark and calibration source for TeV instruments, including HAWC. The Crab is detected in HAWC data (in the 250-tank configuration) at 38 standard deviations in 150 days of observation  and is being used to verify the pointing, stability and energy response of the HAWC instrument. We also use the Crab to evaluate the effectiveness of our photon/hadron discrimination.
Figure 1 exhibits one photon identification variable, a goodness-of-fit measure of the HAWC core reconstruction, described in . It provides excellent separation of photons and hadrons, especially at the high energies we are using for this isotropic photon analysis. The figure corresponds to a photon energy of more than 10 TeV. Photons characteristically have a much lower (i.e. better) goodness-of-fit than cosmic rays, allowing us to distinguish the two.
The efficacy of the hadron rejection is shown most convincingly with real data from the instrument. Figure 2 shows the region around the Crab in 105 days of data with HAWC in its 250-WCD configuration (HAWC-250). For the treatment here, we look at the largest, highest-energy events in HAWC, events which have at least 85% of the available PMTs seeing light. This cut restricts the energy of photon events to roughly 10 TeV. Data are shown with a 0.45 top hat smoothing, counting how many events occur within a 0.45-radius circle around the points shown. The left panel of Figure 2 shows data with more than 85% of the available PMTs seeing light. The right panel shows the same region of the sky with a strong cut on the core fit goodness-of-fit. The background is suppressed by about 10 with 25% efficiency for photons. At these extreme cut levels (very large, very gamma-like events), events are very rare. We record 12 events (in the 0.45 bin) from the direction of the Crab Nebula in 105 days. Using events recorded more than 1 from the Crab, we estimate 0.810.05 background events.
Figure 3 shows how the Crab excess depends on background rejection. We show measured and predicted event passing rates as a function of the remaining background. The shape agrees well between data and simulation. Because it is time consuming to simulate a full 100 days of experimental data, the background estimate becomes statistically limited at a weaker cut than data. Given the agreement at less-tight levels, we are confident that 25% gamma-ray efficiency with only background contamination is achievable, even at this early stage in the analysis. Stronger rejection, and a more pure photon sample, appears possible with harder cuts.
3 Isotropic Gamma-Ray Limit
The strength of the photon/hadron rejection allows us to set a simple, robust limit on an isotropic diffuse gamma-ray flux. Under no circumstances can an isotropic gamma-ray population overproduce the observed off-Crab events. Furthermore, we have a bright gamma-ray source of known flux to normalize our observations.
Consider , the point-source differential flux of the Crab at some energy. Assume we measure events from the Crab in some sample of time. Let us assume the isotropic diffuse emission has the same spectral shape and is given by at the same energy as we measure the Crab. Since the isotropic flux is normalized per unit solid angle, a small patch of sky with solid angle will produce as many photons as a point source with a flux . If, in the experiment, we record no more than events in an sized bin, and as long as we are looking near enough to the Crab that the instrument response is flat, then we can say that the isotropic population of photons can be no higher than:
From the Crab observation in Figure 2, we recorded 12 total events at the Crab location, with a background of 0.810.05 in a round bin. There will be some photons from the Crab outside our bin. The bin size was chosen to maximize the statistical significance of the Crab detection and, for a Gaussian-distributed point spread function, that optimum includes only about 70% of the photons. Given the systematic uncertainties introduced by trying to account for these lost events, at this early stage in the analysis, we conservatively perform the limit calculation with the assumption that the total number of Crab events is 11.2.
At 90% confidence, we expect the true mean signal to background ratio on the Crab to be larger than =8.4. Using the H.E.S.S. fit of the differential flux of the Crab , we obtain the limit 8.0 at 17 TeV. Using the HAWC-measured Crab flux yields a similar limit. As we are still evaluating the HAWC systematic errors, we choose to anchor the analysis on a published Crab flux for this study.
The HAWC limit is shown in Figure 4 along with a number of isotropic measurements, limits and models for photons and other particle species. We quote a HAWC limit from 11-23 TeV, the simulated energy range expected from the Crab for the cuts in this analysis.
4 Discussion and Prospects
The limit presented here is very conservative and essentially comes “for free” from the HAWC observation of the Crab Nebula. It is not representative of what is possible with HAWC, and a number of improvements are possible:
HAWC data have the potential to constrain higher-energy photons, but we restrict the range of the claimed limit to the energy range over which the Crab is detected in this analysis. As the modeling of the instrument is better understood, this limit will be extended to lower and higher energies. The sensitivity of HAWC at 100 TeV should be at least an order of magnitude better than at 10 TeV.
We make no attempt to ascribe the observed off-Crab events to hadronic cosmic-rays. This assumption is robust, but very conservative. A stronger limit is possible if some fraction of the remaining background can be demonstrated, through simulation, to be cosmic-ray background. As we understand HAWC better, this will be possible and will improve the sensitivity substantially. Note that we must have some understanding of the background a priori in order to make a positive detection. The analysis presented here can only yield an upper limit.
We choose a photon/hadron separation cut that results in a convincing Crab detection with an excellent signal to background ratio. As we acquire more data, we will be able to cut harder and further enhance the purity of our sample. Figure 3 suggests that more pure gamma-ray samples are possible. This stands to further improve the results.
The first HAWC limit improves upon the current best limit in the 11-23 TeV range by the GRAPES-3 instrument. Ultimately, we expect to achieve a limit below the level of the IceCube diffuse neutrino flux at 10-100 TeV. HAWC is able to distinguish muons in an air shower across essentially all of its 20,000 m area, more than a factor of 10 larger than CASA-MIA or GRAPES-3.
The limit presented here is formed using the background around the Crab Nebula. Strictly speaking, this limit does not apply to any area of the sky except the immediate vicinity of the Crab. Extending this analysis to the rest of the sky is underway.
Nevertheless, the present limit is the strongest in its energy range. With all the improvements discussed here, future observations will provide a new unique constraint on the combined electron/positron/photon flux. Above 100 TeV, our observations may be able, in the near future, to constrain the origin of the IceCube astrophysical neutrino population.
We acknowledge the support from: the US National Science Foundation (NSF); the US Department of Energy Office of High-Energy Physics; the Laboratory Directed Research and Development (LDRD) program of Los Alamos National Laboratory; Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico (grants 260378, 55155, 105666, 122331, 132197, 167281, 167733); Red de Física de Altas Energías, Mexico; DGAPA-UNAM (grants IG100414-3, IN108713, IN121309, IN115409, IN111315); VIEP-BUAP (grant 161-EXC-2011); the University of Wisconsin Alumni Research Foundation; the Institute of Geophysics, Planetary Physics, and Signatures at Los Alamos National Laboratory; the Luc Binette Foundation UNAM Postdoctoral Fellowship program.
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