The basic question is can the information in the shower wavefront be used to improve the energy resolution of an array of gamma ray telescopes, such as the VERITAS array. We are motivated to ask this question by the observation that the timing structure near the core reflects the emission altitude of the photons. You can see this in figure 1 which shows a plot of the photon arrival times versus distance from the shower core for a 50 GeV gamma shower. The photons are color coded by their altitude of emission: Photons emmitted above 10,000m are colored blue, those emitted between 6000m and 10,000m are purple, and thoseemitted below 6000m are colored black. Figure 2 is a similar plot for 4 different 300 GeV gamma showers.
Our first question to anwser is: does knowledge of emission altitude
giveimproved energy resolution? To answer this we use a very simple
model. ASsumethe amount of light emmitted by the shower is proportional
to the energy. Alsoassume that the light is all emmitted at height h.
The amount of light measuredby the telescope is given by the parameter
"size". We assume that the lightmeasured will be proportional to the
(light emmitted)/square(distance to shower).The square of the distance
to the shower is equal to the square of the heightplus the square of
the distance along the ground from the shower core to thetelescope (the
impact parameter r) or: d**2 = r**2 + h**2. Putting these termstogether
we find that
Using the monte carlo generated gamma ray data base for the VERITAS array, wecan look the accuracy of this energy estimate. To limit ourselves to regionsnear the shower core, we select events with an impact parameter r < 40m. Wehave also selected events with energy greater than or eqaul to 300 GeV. (Thereis no good reason for this cuts other than a vague intuition that we expectbetter energy resolution for higher energy showers). Figure 3 shows a plot of size*(r**2+h**2) for all events with energy >= 300 GeV and r<40m. It also showssupperimposed the plots for selected energies. This plot hints that in fact, theenergy estimator does distiguish eneries. We found the mormalization constant(by a procedure described later) and calculate the difference between the actual energy and the estimated energy. Figure 4 shows a plot of these energyresidules and the results of a gaussian fit. The standard deviation is 54 GeV, resulting in and energy resolution of 18% for 300 GeV showers and better for the higer energy showers. From this plot we conclude that knowledge of theemission altitude can indeed lead to improved energy resolution.
It should be noted that this is an optimistic estimate because we have perfect timing information from the monte carlo. We have used the medianarrival times of all photons in the trigger. It does not include a realisticmodel of the time signature of the pulses, not does it include mirror timeaberations. Thus to proced we need a better model.
There is a memo with more details about this initial look at using the emisison altitude to calculate energy.
Our next big question is can we get the altitude of emission from the timingimformation? Consider again figure 1 and figure 2. It is only near the corethat the timing structure reflects the altitude of emission. Thus we will needto know the location of the shower core. Other work on the array and theparallax method (links to be added later) show that the array is capable oflocating the shoer core. Additionally, we will have to be able to calibrate thearrival time ve. altitude relation. Again, looking at figure 1 and figure 2,you note that near 100 m from the center, photons from all altitudes arrive ina very narrow time band. We hope that this information can be used to calibratethe timing. Clearly this is an important consideration that we need to look atcarefully. Finally, we need a procedure to relate the emission altitude to thearrival times. This is the subject of the next section.
For more information of the timing at 100m look at the folowingplots:
To stay near the shower core, we select events with impact parameter r lessthan 40 meters. For these events, we have made plots of the emission altitude vs time for each of the threetimes (cfd, peak, and mean) for both isocnronous and anisochronous mirrors.We did each case including noise and with no noise. We then fit emissionaltitude to a second order polynomial in time (there is no good reason for thischoice of fitting function other than it looks reasonable as a starting point).From the fit, we estimate emission altitude from time. Finanlly we calculatethe difference between the actual emission altitude and the estimated emissionaltitude. The following plots show these results.
Table 1 lists the standard deviations of the fits for each kind of time withnoise for the isochronous and anisochronous cases.
| cfd | peak | mean | |
| isochronous | 575 m | 679 m | 855 m |
| anisochronous | 862 m | 754 m | 874 m |
Based on these results we have decided to use cfd times as giving the bestestimate of emission altitude. Also, from here on we will alway include noise.
We plot emission altitude vs cfd times for this slightlylarger data
base, along with the 2nd order polynomial fit. To estimate theenergy,
we use the simple model discussed earlier, with:
Finally, we repeat the above procedure with the addition of making simple shapecuts on the gamma ray images. the shape cuts used are: alpha < 15,0.1 < length < 0.44, and width < .16. These were derived from previous work on theVERITAS data base. The following plots are similar to the last set, but withthe addition of this selection on the gamma ray image.
| |
no cuts | |
| isochronous | 74 GeV | 69 GeV |
| anisochronous | 86 GeV | 76 GeV |
Last updated: 24 Oct, 2005
