This page represents work in progress on looking at the energy resolution ofthe VERITAS array. The basic idea is to use the wavefront timing information todetermine the altitude of maximum Cherenkov emission. Our Compton symposiumpaper of wavefront timing suggests a correlation between structure inthe Cherenkov wavefront and the altitude of emission of the photons. Thecorrelation is strongest near the shower center, and least at the well knownannulus. In the VERITAS array, we will be able to determine the location of theshower core, thus we can use the timing information to estimate the altitude ofmaximum emission. With this information we should be able to improve on ourenergy resolution. Motivated by the spectral work of Carter-Lewis and Mohanty,we have constructed an energy estimator. In our case the estimator is based onrather simple geometric arguments. Our energy estimator is given by:

e_est = constant * ( b**2 + h**2) * size

where b is the impact parameter (which will be determined by the array), h isthe mean emission altitude (which will be determined by the timing) and size isthe amount of light in the image (the same as our cuurent size parameter).

The following are a series of plots exploring these ideas. The monte carlo dataset used is the gamma ray data set at an altitude of 1300 m. The triggercondition was 15 pe's on three or more pmt's. All plots are selected for smallimpact parameters (b<40m) and for indident energy greater than 300 GeV. In somecases additional shape cuts have been made, either an alhpa cut (alpha < 15)alone, or what I call "simple shape cuts" which are given by: alpha less than 15,length between 0.1 and 0.44, and width is less than 0.16.

The first set of plots is of the energy estimator, e_est, given above forvarious cuts. These plots use an un-normalized e_est (i.e. the constant = 1) Next is a series of plots showing the distribution of differencesbetween the energy estimated by e_est (normalized as described below) and the actual value of the energy fromthe monte carlo. To findthe normalizing constant in the above equation, I plotted size*(b**b+h**2)/(monte carlo energy) and fitted this to a gaussian. The meanof the gaussian is the value of the normalization constant.

Figure 1: This is a plot of the unnormalized e_est(that is the constant = 1) with no image shape cuts. Superimposed on this plotare the distributions os e_est for events selected by monte carlo energies of400, 600, 800 and 1000 GeV.
Figure 2: The same as figure 1, but with analph cut of alpa <15.
Figure 3: The same as figure 1 but with simpleshape cuts as described above.
Figure 4: Energy residuals energy, e_est -energy, for no image shape cuts.
Figure 5: The same as figure 4, but with simple image shape cuts

The standard deviation of the gaussian fit to the energy residuals in figure5 suggests that with this simple geometric energy estimator, theuncertainty in our energy estimation is on the order of 54 GeV.

The next series of plots looks at emmision altitude as a function of medianarrival time. The plots are for monte carlo events selected for small impactparameter (b<40 m) and energy greater 300 GeV.

Figure 6: This plot shows therelation between emission altitude and median time. Note that this is the timespread only due to the arrival times of the photons. The mirror time aberationsare not included.
Figure 7: This plot shows a 2nd order polynomial fit to theemission altitude as a function of median time.
Figure 8: This plot shows thedistribution of e_est using emission altitude (in black, this isthe same as the black curve in figure 1), and the energy estimate using median timeto estimate the emission altitude (in red).

I am working on energy residual plots using the median time in the energyestimator.

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Last updated: 24 Oct, 2005