1. Capability of Extended Air Shower Arrays for Gamma-Ray Astronomy
Andrew Smith for the HAWC Collaboration:
Los Alamos National Lab (Brenda Dingus, Gus Sinnis), Univ. of Maryland (Jordan Goodman, Andrew Smith, David Berley, Greg Sullivan, Buckley Hopper), Univ. of Utah (David Kieda, Stephan LeBohec, Miguel Mostafa), UC Irvine (Gaurang Yodh), Michigan State Univ. (Jim Linnemann),
Penn. State Univ. (Ty DeYoung), Univ. of New Hampshire (Jim Ryan), NASA/GSFC (Julie McEnery), UNAM (Magda Gonzalez),
INAOE (Alberto Carramiñana), BUAP (Humberto Salazar)
© A. Simmonet
Figure 3 Plotted in the 4 panels are the distribution of the energy reaching the observation level for a range of primary energies. The distributions are all roughly log-normal independent of both the primary gamma-ray energy and the depth of the observation with the single exception of the highest energy showers.
Abstract:
Current efforts in ground-based VHE gamma-ray astronomy use two methods: Atmospheric Cherenkov Telescopes (ACTs) and Extended Air Shower (EAS) Arrays. While ACTs typically have greater sensitivity to gamma-ray point sources and lower energy thresholds, EAS arrays have an enormous advantage in exposure to the sky due to their large fields of view and high duty cycle. The lower sensitivity of EAS detectors is largely due to the fact that they sample only the particles in the longitudinal tail of the shower that reach the ground level, whereas ACTs are able to observe the shower development high in the atmosphere. An examination of the intrinsic capabilities and limitations of EAS arrays as instruments for gamma-ray astronomy is presented. The angular and energy resolution and effective area of an optimized detector is shown as well as an analysis of gamma/hadron separation. The capabilities of the optimized detector are compared and contrasted to those of the recently proposed HAWC detector.
Gamma/Hadron Separation and Detector Size
In general, increasing the size of a detector will increase the collection area and thus the sensitivity. As both signal and background are increased, the relative sensitivity is expected to scale like (area)0.5. In simulations of EAS detectors however, we have found that the effectiveness of the gamma/hadron cuts improves drastically with detector size, because the lateral shower tails are more thoroughly sampled. Figure 6 illustrates this effect using simulations of the HAWC detector.
Intrinsic Angular Resolution
Typical detection elevations for EAS arrays are well below the shower maximum and often only a small fraction of the initial shower energy is available at the ground level.
We have estimated the optimal angular resolution achievable by an EAS array by simulating EAS showers with Corsika. The momentum of the particles that reach the observation level is combined in a vector sum. The direction of the resulting vector is compared to the direction of the primary to estimate the angular resolution for a given shower.
It should be noted that achieving this angular resolution depends on the detection of all the particles that reach the observation level and their momentum. While such a detector is impractical, a coarse calorimeter such as HAWC can obtain results not far from optimal.
Studies have shown that the angular resolution is strongly dependent on the shower energy reaching the observation level (Eground), so we have chosen to parameterize it as such. Eground depends on both the primary energy and the atmospheric depth. We can define an intrinsic threshold at Eground ~10 GeV. Below 10 GeV accurate reconstruction of the shower angle is difficult.
For high-energy showers, an angular resolution of ~0.1o is possible.
HAWC can reach at least ~0.2o angular resolution. (The angle reconstruction software for HAWC was adopted directly from Milagro and has not been optimized for the HAWC geometry. Further studies will likely lead to improved angle reconstruction for HAWC, particularly at high energy.)
Primary Energy
Mean log10(Egnd/E)
Sigma log10(Egnd/E)
Sigma/Mean 75
-1.862
0.476
0.256
150
-1.616
0.399
0.247
300
-1.407
0.339
0.241
600
-1.217
0.302
0.249
1200
-1.051
0.264
0.251
2400
-0.905
0.238
0.263
4800
-0.770
0.221
0.288
9600
-0.658
0.196
0.297
19200
-0.552
0.181
0.328
38400
-0.493
0.135
0.274
Figure 6 The sensitivity of the HAWC detector plotted vs the edge dimension. We simulated a 300m x 300m version of HAWC with the PMTs arranged in a 60x60 grid. The sensitivity as a function of detector size scales roughly linearly when no gamma/hadron cut is applied (cxpe0.0), but the sensitivity gain from gamma/hadron cut improves dramatically with detector size.
Table 1 The mean and the sigma for fits of Eground/Eprimary are shown for a variety of primary gamma-ray energies. While the fraction of energy reaching the ground level (Mean) and the width of the distribution (Sigma) are both a function of the primary energy, the ratio of the sigma and the mean is almost constant at ~25% over nearly 3 decades in energy.
The 25% solution - A simple accurate parameterization of energy fluctuations.
Table 1 shows the results of the fits of the log(Eground/E) distributions for 10 different gamma-ray energies. The mean and the sigma of the distribution are found to vary with energy, but the ratio of the two are roughly constant over 3 decades in energy with a value of ~0.25. This simple parameterization can describe all longitudinal shower fluctuations as only a function of the fraction of energy reaching the ground level, independently of the atmospheric depth (not demonstrated here) or the primary gamma-ray energy. For typical values of Eground of 20%,10% and 5% we get an error in the measurement of the primary energy of +32%/-24%, +70%/-44% and +300%/-70% respectively. The errors are log-normal, and thus asymmetric.
The intrinsic limitations of EAS detectors are in general small compared to the amplitude of shower fluctuations, so the fluctuations in the atmosphere will dominate the energy resolution of any practical detector.
(GeV)
Optimal Angular Resolution
HAWC (<30o)
Figure 1 Intrinsic angular resolution of an ideal EAS detector (blue) compared to the angular resolution of the proposed HAWC detector plotted as a function of the energy reaching the observation level. The HAWC angular resolution is computed with a full detector simulation and event reconstruction.
Intrinsic
Threshold
HAWC and Potential Future Detectors
The HAWC collaboration has submitted a proposal to the NSF for the construction of a high altitude water Cherenkov EAS gamma-ray observatory (See poster by B. Dingus). The HAWC instrument is ~22,500m2 with an intrinsic threshold of ~ 1 TeV. The sensitivity of HAWC is shown in figure 7.
While HAWC represents a substantial improvement over the current Milagro experiment, with additional funding substantial improvements are possible over the proposed HAWC design. Potential improvements include:
Increase Altitude: Move from 4300m to 4800m - 1.5x lower threshold
Increase photocathode density: 3-4 PMTs/cell - ~1.5x lower threshold
Increase size: Sensitivity ~ (Area)0.8 up to 300mx300m, not (Area)0.5, due to improved gamma/hadron separation.
Sensitivity of potential future detectors:
HAWC 300x300 is assumed to be a 300mx300m detector with 4x the area of HAWC. We also assume that the PMT density is increased. The sensitivity curve is conservatively estimated at ~5x below the curve for HAWC with a lower threshold. We estimate the cost of this instrument to be ~$30M.
HAWC 1000x1000 is assumed to be a 1000m x 1000m extrapolation of HAWC 300x300. The sensitivity for low energy showers is assumed to increase by ~√10 times (background limited) and at high energies by 10 times (signal limited). We estimate the cost of this detector at ~$300M.
Effective Area Below the Intrinsic Threshold
The same shower fluctuations that limit the energy resolution have the benefit that they increase the effective area of EAS detectors at low energies.
Figure 4 The longitudinal shape of EAS showers of different energies. The slope of the curves is the same for all energies past shower maximum: ~1.65x decrease /radiation length.
Cascade profiles all have the same slope past shower max
Energy Reaching Observation Level
In order to evaluate the angular resolution as a function of primary gamma-ray energy I compute the fraction of energy that reaches the observation level (in this case 4300m a.s.l.). Figure 2 shows the median energy reaching the observation level vs primary gamma-ray energy.
Intrinsic
Threshold
Figure 2 Energy reaching 4300m elevation as a primary gamma-ray energy. A range of zenith angles are shown. The ‘Intrinsic Threshold’ as defined in the previous section ranges from ~200 GeV to 1 TeV.
Figure 7 Differential sensitivity per quarter decade. The lines depict the 5 sigma detection flux level with at least 25 gamma rays. Data for GLAST,VERITAS, Whipple and the 1km2 ACT courtesy of S. Fegan. For the 1km2 ACT array, the 4 lines refer to 4 different background models.
Figure 4 shows the average cascade longitudinal profile as described by approximation B [2]. Note that showers of all energies have the same shape after shower maximum. So, for all energies, if a primary gamma-ray penetrates one radiation length deeper than average, the result will be a ~1.65x increase in the energy observable at ground level. This provides the possibility that showers with energies below the nominal energy threshold can be detected. We can compute the number of radiation lengths (N) that a gamma ray with energy (E), below the nominal threshold energy (Ethr), will need to penetrate beyond the average depth in order to be detected.
The probability the a VHE gamma ray will penetrate N radiation lengths before interacting is
Conclusion
The sensitivity of EAS detectors is easily understood in terms of cascade physics.
Angular resolution approaching 0.1o is achievable.
EAS arrays can be characterized by an intrinsic threshold at which they are ~100% efficient. This threshold is roughly 1 TeV for HAWC and is limited to be above GeV for the highest altitude detectors.
The energy resolution of EAS arrays, while good at high energies, is limited by longitudinal fluctuations in the cascade.
EAS detectors have a power law shaped effective area curve below the intrinsic threshold. This is a consequence of fluctuations in the development of showers.
Beyond HAWC, potentially large sensitivity increases still exist.
Intrinsic Energy Resolution:
The energy resolution for an EAS detector is intrinsically limited by longitudinal fluctuations in the development of the electro-magnetic cascade. The early development is of particular importance as fluctuations in the depth of the initial interaction of the primary gamma ray translate directly into fluctuations in the depth of the shower maximum and the decay profile of the tail.
We choose to parameterize the energy resolution of an EAS detector as the sum in quadrature of 2 components, the intrinsic detector measurement resolution combined with longitudinal shower fluctuations.
Figure 3 shows the distribution of shower energy at the ground level for 4 different ranges in primary gamma-ray energy. The distributions are log-normal.
Combining the 2 expressions gives
P(E) ~ (E/Ethr)2.6
Characteristic threshold
Power Law: A~E2.6
Eff Area ≈ Detector Area
Figure 5 Effective area of the proposed HAWC detector. The blue curve shows the HAWC effective area derived from the detector simulation. The black lines show the effective area can be well described as a power law at low energies and as constant at high energies.
References:
[1] Corsika Air Shower Simulation Program.
[2] Rossi, B., & Greisen, K. 1941, Reviews of Modern Physics, 13, 240.