Performance Overview          Gamma-Hadron Separation

Detector Performance

            The simulation for HAWC is an extension of the Milagro simulation [ ] software package. CORSIKA [ ] is used to simulate gamma-ray and hadron induced atmospheric showers. A custom detector simulation using GEANT4 [ ] is used to propagate the secondary shower particles that reach the detector elevation through the HAWC detector. Cherenkov light production is simulated and individual Cherenkov photons are tracked through the detector. Detailed optical modeling of the water (absorption and scattering), reflection and absorption at surfaces, and the PMT response are included. The simulation has been thoroughly tested through comparison with Milagro data. The Milagro electronics utilize the TOT method for pulse amplitude estimation. The response of this system is simulated by generating a pulse waveform for every detected photon.  These simulated pulses are then digitized and converted to amplitude and timing measurements for use by the reconstruction software.
            In this section, we describe how the sensitivity of the HAWC detector is determined. We describe the detector simulation and show that the sensitivity of HAWC is ~15 times that of Milagro. We describe in detail the performance of the HAWC detector with 900 5m-diameter water tanks each instrumented with a single 8” PMT as the standard HAWC design. We then show how the sensitivity of HAWC would improve with the expansion of the detector coverage or the increase in the number of PMTs in each tank. Details of the sensitivity estimation can be found on the HAWC web site: http://umdgrb.umd.edu/hawc/Proposal.
Although we are able to dead reckon the rate of hadronic background events in Milagro to within ~40% of the flux as measured by high altitude balloon experiments [ ], [ ], we do not depend on dead reckoning to estimate the background rates in HAWC. Instead, gamma-ray and background rates are scaled from measured values in Milagro by comparing the predictions of the HAWC and Milagro simulations. In this way we not only remove potential systematic errors internal to the simulation from the air shower modeling, optical model, and detection efficiency, but also remove systematic errors in the measurement of gamma-ray fluxes and hadronic backgrounds provided by other experiments.

Detector Optimization

            The depth and spacing of the PMTs was optimized for gamma-ray sensitivity from 1-100 TeV. The detector must act as an effective calorimeter in order for the background rejection methods to work properly, so the PMTs need to be sufficiently deep that electro-magnetic (EM) particles are unable to pass close to the photo-cathode and produce large pulses that are not proportional to the deposited energy. We have found that this requires at least 3.5m of water (~9 radiation lengths).  However, if the PMTs are too deep, the sensitivity (PEs/GeV) is significantly reduced. At the selected depth of 4m (water above the photo-cathode), HAWC detects ~20 PEs/GeV for EM particles and ~30 PEs for through-going muons. The optimal radius of the tanks is determined by the Cherenkov angle in water. The illumination of EM particles is found to be roughly uniform over an area with a radius of 0.75 x depth. This dictates that for a tank of depth 4m, a radius of ~<3m is optimal. There is no scientific advantage to making the tanks smaller, but additional sensitivity to low energy showers can be achieved by increasing the photo-cathode density by placing more PMTs in each tank. This is discussed in detail at the end of this section.

Event Reconstruction

          In HAWC, as in Milagro, the primary source of PMT noise is secondary gamma rays, electrons and muons from low-energy hadronic cosmic ray showers. Uncorrelated noise rates set the limit for the trigger threshold. In Milagro, the noise rate is ~20 kHz in the top layer and ~50kHz in the bottom layer. The rate from dark noise and ambient radioactivity is only ~2kHz. We have simulated EAS showers from primary hadrons with energies as low as 5 GeV in Milagro and HAWC. Despite the higher elevation the single PMT hit rate for HAWC will be approximately equal to the top layer of Milagro, ~20kHz. This relatively low noise rate is due to the optical isolation of the tanks in HAWC, compared with the open design of Milagro. A single particle in HAWC will only illuminate a single PMT, where in Milagro many PMTs can be hit. The total non-correlated hit rate for the entire detector will be ~20MHz, or ~1 PMT hit/50ns. We anticipate triggering on showers that produce >~30 PMTs hit within a 50ns window and anticipate no difficulty achieving this threshold. We estimate the trigger rate in this regime to be ~5-10kHz, about 3-6 times the trigger rate of Milagro. However, the absence of the second layer reduces the average event multiplicity by about a factor of ~2, so the data rate in HAWC will only be ~1.5-3 times Milagro, or 7.5-15 Mbytes/s (uncompressed). This rate will be easily accommodated with the upgraded VME TDC based DAQ.
            To reconstruct the direction of atmospheric showers in HAWC we first determine the shower core by fitting the distribution of pulse amplitudes to a standard lateral distribution profile. After the core is located, the PMT hit times are adjusted to account for the curvature of the shower front. Typically, the shower front curvature correction is ~0.5o-1.0o, so misidentification of the core position leads to degraded angular resolution. The corrected PMT hit times are then fit to a plane to determine the incoming shower angle. The width of the distribution of timing residuals ranges from ~1-3ns depending on the pulse amplitude. Figure 20(a) shows the effective area of HAWC and Figure 20(b) shows the angular resolution of HAWC. We find that the angular resolution of HAWC reaches a minimum of ~0.25o above 5 TeV. One would expect that the angular resolution would improve as the energy rises. The flattening is a consequence of systematic errors in the parameterization of the curvature correction as a function of energy. The curvature correction used here was optimized for Milagro and has not been re-optimized for HAWC. As we improve the reconstruction algorithms we expect the angular resolution to improve, however, for estimation of sensitivity, we conservatively characterize the angular resolution as depicted in Figure 20.
            Notice that HAWC has a substantial effective area well below the nominal threshold. This is a phenomenon that is not unique to HAWC, but common to all EAS gamma-ray detectors. The longitudinal shower profiles of electromagnetic showers of different energies have the same shape after shower maximum. In this regime, the energies of the particles in the shower have dropped below the critical energy (the energy where the cross-section for pair production and Compton scattering are equal) and the number of EM particles in the shower begins to diminish. Past shower maximum, the total energy carried by high energy particles is reduced by a factor of ~1.65 for each radiation length. Therefore, if a primary gamma ray penetrates one radiation length deeper than average prior to its first interaction, the result will be a ~1.65x increase in the energy observable at ground level. Thus showers with energies below the nominal energy threshold can be detected when the primary gamma-ray penetrates deeply into the atmosphere before interacting. In order to be detectable below the nominal threshold energy Ethr, a gamma-ray of energy E must penetrate additional radiation lengths N before interacting, and N is simply N = ln(E/Ethr)/ln 1.65. The probability P that the gamma ray will penetrate N radiation lengths before interacting is P=exp((-9/7)N).  Combining the two expressions gives P(E) ~ (E/Ethr)2.6  Thus the effective area below the effective threshold should scale like a power-law with index 2.6 which is indeed reproduced by the detailed Monte Carlo simulation seen in Figure 20 (a) for both HAWC and Milagro.

Hadron Rejection

            Hadronic showers are identified through the pattern of energy deposition in the detector. While gamma-ray induced showers have compact cores with smoothly falling lateral density, hadronic showers typically deposit large amounts of energy in distinct clumps far from the shower core.  This is due not only to the presence of hadrons and muons in hadronic showers, but also clumps of EM energy far from the core caused by high PT hadronic interactions in the development of the atmospheric shower. As a simple gamma/hadron discriminator, we have extended the compactness parameter, C, developed for Milagro .  Here C is defined as the total number of PMTs hit divided by the largest pulse amplitude that is more than 40 m from the reconstructed core position. Gamma ray induced showers have only small hits far from the core and therefore have large values of C. Hadron induced showers with muons and hadrons and multiple clumps of EM energy have low values for C. Figure 21 shows Compactness distribution for gamma ray and hadron triggers for three different energies. The background rejection capability of HAWC improves with increasing energy. Figure 20(c) shows the efficiency for protons passing the gamma-hadron cut for HAWC when the gamma-ray efficiency is fixed at 50%. At similar energies, HAWC can reject hadronic backgrounds ~10x better than Milagro.
            Figure 22 illustrates the hadron rejection capacity of HAWC. The top four panels show typical gamma-ray induced events and the bottom four panels show proton events. The hit amplitudes in the array are indicated by the color scale.  The large black circle indicates the position of the fit core and the radius of the circle defines the exclusion region for the compactness cut. All of the proton events have large hits outside the shower core where none of the gamma-ray events do. At high energies there are many independent hits outside the shower core that would lead to the redundant rejection of the proton events. All of the simulated proton events shown here would not pass the gamma-ray cut (C>6-8).  Note that the area enclosed by the circle around the shower core is roughly the same as the area of the calorimetric layer of the Milagro detector, so this core exclusion method can not be applied to Milagro.
            It is important to point out that despite simulating hundreds of millions of atmospheric showers, the available statistics in our current simulated data set at high energies are insufficient to reliably predict the background rejection (i.e. no simulated proton events with energies above ~50 TeV survive the cut criteria). HAWC may be capable of rejecting nearly all-hadronic background above 10-20 TeV, but at this time we are unable to simulate enough high-energy background events to demonstrate this. The gamma/hadron capability shown here should be regarded as conservative. Further study will likely reveal substantial improvement.

Energy Resolution

            The energy resolution of EAS arrays is in general poorer than that of IACTs. IACTs are able to directly sample the entire shower as it develops in the atmosphere, so the detected light at the surface is approximately proportional to the energy of the shower. For EAS arrays with nearly 100% coverage of the ground, such as Milagro and HAWC, the total energy carried by the particles reaching the ground level can be accurately estimated (as indicated by the red line in Figure 23), but because only the longitudinal tail of the shower is sampled, fluctuations in the depth of the development of the shower can lead to large fluctuations in the energy reaching detector elevation and thus the measured energy.  The energy resolution of EAS detectors does however improve with detector elevation. The energy resolution of HAWC is log-normal and ranges from ~100% at 1 TeV (.5 TeV-2 TeV 1s error), the nominal threshold of HAWC, to ~30% at 100 TeV. Although HAWC has substantial effective area below 1 TeV, in this regime positive fluctuations in the depth of the shower maximum are required for detection. Such showers are indistinguishable from threshold events. For further information on the energy resolution of EAS showers see [ ].
            HAWC will be vastly superior to Milagro for the measurement of gamma-ray spectra both due to improved sensitivity and energy resolution. Also, with Milagro, we have found that the gamma/hadron separation variable is highly energy dependent, which introduces systematic uncertainties into the energy analysis. In Milagro, low energy showers required the core to be on the pond in order to be detected, but then the background rejection is limited. HAWC spectral analyses will not have this problem, as the event energies are almost completely independent of the gamma/hadron cut level because of the much larger detector.

Sky Survey Sensitivity

            Because the sensitivity of the detector is strongly dependent on the zenith angle of the source being studied, we compute the sensitivity by estimating of the number of signal and background events collected during a single transit of the source from horizon to horizon. As a reference source, the Crab is selected. The differential spectrum of the Crab is assumed to be (2.8 x 10-11) E-2.62 particles/s/cm2/TeV [ ], but since the results are normalized to the Milagro measurements, the sensitivity is nearly independent of the assumed source spectrum. The source Declination is selected so that the source passes 15o from zenith as it transits so that a more or less typical sensitivity is estimated. HAWC is ~15% more sensitive to sources that pass through zenith and ~20% less sensitive for sources that transit 25o from zenith. The peak sensitivity of HAWC is at ~2 TeV, where we will detect the crab at ~75 sigma/sqrt(year), which is ~15 times more sensitive than Milagro. For 1 year of observing, HAWC will have a 5s detection threshold of 60-70mCrab with basic cuts.
            For Milagro we have developed a likelihood analysis methodology that weights each event by the ratio of the probability that it is a gamma ray to the probability that it is a proton [ ]. This results in a ~60% improvement in sensitivity compared to making a simple cut on the value of the compactness parameter. We have applied the same technique to the simulated HAWC data where a similar sensitivity increase is predicted. For HAWC, we predict ~6s detection for a crab-like source from a single transit and ~120s for a year of observing. For a 1 year survey of the overhead sky, HAWC will have a 5s point source detection threshold of ~40 mCrab.  In 4 years, HAWC will survey the viewable sky to the level of ~20 mCrab. As stated above, the sensitivity depends on zenith angle, but is not substantially reduced for transit zenith angles <30 deg. As seen in Figure 24, the HAWC detector deployed at latitude 19oN will survey 44% of the entire sky (4p sr) with a sensitivity <50mCrab and 64% of the sky with sensitivity <80mCrab in one year of operation. Table 3 shows the predicted event rates and sensitivity for various cuts in HAWC compared to Milagro (for point sources with a Crab-like energy spectrum).

Table 3 Comparison of the survey sensitivity of Milagro and HAWC for a Crab-like source transiting 15o from zenith. The signal and background events are in an angular bin optimized for the detector point spread function. We show the results for various trigger  thresholds. The peak sensitivity of HAWC comes between 2 and 10 TeV.
            HAWC’s modular design will allow us to operate the detector early in the second year of construction. With the deployment of the first 100 tanks, HAWC will have a total area nearly the size of Milagro and with the higher elevation HAWC will have ~2x the Milagro’s sensitivity. With the expansion of HAWC, the sensitivity will rapidly rise until completion. When the detector is competed in the 4th year, we will have collected data with equivalent sensitivity to one year of operation of the full detector.

Upgrade Paths

            The modular design of the HAWC detector allows multiple upgrade paths. To increase the sensitivity at the highest energies, the detector coverage could be extended through the deployment of additional tanks, or the re-deployment of the existing tanks over a larger area. The low energy sensitivity could be increased through the installation additional PMTs in each tank or in a central detector core to increase the efficiency for detection of low energy shower particles thereby lowering the energy threshold.  Upon completion of the deployment of the 900 PMTs in 900 tanks detector (the scope of this proposal), if full (matching) funding is available from our Mexican colleagues or if we gain additional collaborators with additional funding or equipment, we will then pursue an upgrade of the detector based on state of the science at that time. Furthermore, such an upgrade can be conducted concurrently with ongoing operation of the detector. Below we discuss the sensitivity gain expected from these two potential upgrade paths.
            One might anticipate that for background limited observations, the sensitivity of a detector would scale like (Area)0.5 since both the signal and background increase with expansion of the detector coverage. For HAWC, this is not the case because, despite the large size of the HAWC detector, the lateral extent of atmospheric showers on the ground is still larger. Doubling the size of the detector would not only double the collection area, but also provide more complete containment of each detected shower. This improves both the gamma-hadron separation and angular resolution. Studies indicate that the sensitivity of HAWC roughly scales like ~(Area)0.8. At the highest energies, E>20 TeV, the sensitivity of HAWC is limited more by the paucity of signal events than by background fluctuations. In this regime, the sensitivity scales directly with the collection area, so large gains can be realized with the expansion of the detector.
            The photo-cathode density of HAWC is about 1/3 that of Milagro. HAWC detects ~1PE/60MeV of EM energy absorbed compared to ~1PE/20MeV in Milagro.  As a result, many shower particles that reach the surface are not detected. By increasing the number of PMTs in each tank from 1 to 3 the photo-cathode density of HAWC would be roughly that of Milagro, and will substantially increase the sensitivity of HAWC at energies below 1 TeV. This upgrade yields a ~3x increased effective area at low energies and a reduced energy threshold as illustrated in Figure 25.
            With the additional PMTs, we also anticipate improved gamma-hadron separation. This will be possible because the pulse amplitude measurements will be more precise and redundant. For example, with hits in each of the 3 PMTs in a tank, we will be able to track the trajectory of through-going muons and develop cuts that can distinguish muon-like (radiates like a line source) hits from EM-like (radiates like a diffuse EM-shower). This will increase our muon rejection efficiency, which is the key to hadron rejection at the lowest energies. We cannot do this with a single PMT. Studies of gamma-hadron separation and angular resolution gained from increasing the number of PMTs in HAWC indicate substantial improvement at all energies, however the most compelling improvement is in the sensitivity at low energies where a ~3x increase in effective area and a 1.4x lower energy threshold are realized. This upgrade would make the detector >2 times as sensitive to low-energy high-redshift gamma-ray sources such as GRBs and distant AGN. HAWC in this regime will have >100 times the effective area of Milagro and, depending of the VHE flux of GRBs, could be an effective GRB detector. If this is the case, HAWC will not only be able to make coordinated GRB observations with GLAST and other GRB satellites, but it will be able to self trigger and notify the community of VHE GRBs within seconds of their occurrence.

HAWC Construction

	Year 1	Year 2	Year 3	Year 4	Year 5	TOTAL
# of Tanks	100	300	600	900
Time to observe Crab with 5 s	1 month	1 week	3days	4 hours
TANKS						4,679
Tank Purchase	482	824	1,236	1,273
Water Filtration System	49	18	18	18	20
Water Distribution System	50	50	22	22
Cabling & Lightening Protection	42	56	84	98
Tank Installation	38	58	112	112
INSTRUMENTATION						1012
Refurbish PMTs	61	30
DAQ System	35	72
Front End Electronics Upgrade		27	54	80	107
Spare PMTs					25
Trigger	15	22	29	58	36
Scaler System	14	28	8	6
High Voltage	39	39
Calibration	78	78	22	22	22
Cooling	19
COMPUTING						286
Online Computing	51	25
Offline Computing	21	42	42	42	63
SITE INFRASTRUCTURE						1,396
Site Preparation	431	56	56	56	56
Water Supply	52	444
Support Buildings	74	25
Milagro Trailer Upgrade	55	18
Shipping	29	29	15
TOTAL EQUIPMENT COST	1,636	1,940	1,697	1,787	305	7,349
MEXICAN EQUIp. CONTRIBUTION	300	400	400	300	100	1,500
US EQUIPMENT CONTRIBUTION	1,336	1,540	1,297	1,487	205	5,877
US LABOR + Subcontracts	585	523	436	160		1,704
TOTAL REQUEST TO NSF	1,921	2,063	1,733	1,647	205	7,581
Table 4 – HAWC construction budget and deployment strategy. This table shows our proposed plan for the deployment of tanks and the funding profile (in k$) required to meet that schedule.

Last modified: October 19, 2007 11:20:19.