Energy Reconstruction

The energy distribution of gamma-ray events from a source is the basis for the spectral analysis of that source. It is difficult to find an analytical function from which the energy of incoming gamma rays can be found given the Hillas parameters of the resulting images. A simple but effective, and computationally efficient, strategy for reconstructing the incident particle’s energy is to generate a large number of detailed Monte Carlo events and use those to decide the most likely energy of the incoming photon given the size and impact distance of its shower image. The first step in generating these tables is producing realistic simulations of particles with known energies.

5.5.3.1 Simulations

The Monte Carlo simulations made for VERITAS have two major components that are created by two completely separate software packages. The first component is the shower simulation, whereby simulated primary events are generated and propagated through a simulated atmosphere. The particle trajectory and interactions with the atmosphere are simulated, resulting in a shower of Cherenkov light. For the purposes of the sources studied in my analysis, the primary particles thrown are gamma rays. Millions of gamma rays are thrown to achieve high statistics, and the energies vary in a randomized manner, covering a range from 50 GeV to 250 TeV. The number of gamma rays thrown at each energy is proportional to the power law E−2, which roughly reflects the inverse power law spectrum of most VHE sources. The events are thrown at random locations within an area 750 m in radius from the center of the array, with uniform numerical density by area. To simulate the different observing conditions, events are thrown at various zenith angles and azimuth angles to simulate observing at different positions in the sky, and at different angular offsets from the pointing direction to simulate the different observing modes. The shower and atmospheric simulations are done using a package called COsmic Ray SImulations for KAscade (CORSIKA) (Heck et al., 1998), which is developed by the Karlsruhe Institute of Technology group and used by a wide range of projects outside of VERITAS. VERITAS uses a simulation package

called Groptics to handle the ray tracing of photons. Groptics traces the reflections of the photons on the telescope mirrors and generates a set of hit times and positions in the camera plane.

I used a software package called GrISUDet for simulation of the VERITAS detector optics and electronics. Different light levels of the NSB can be simulated by artificially changing the pedvar levels in the detector simulations. For a given set of shower simulations, the detector simulations can be run and processed with multiple different pedvar values, and those noise levels are used as another parameter in the lookup tables described below. The end result is a set of VBF files in the same format as the real data that can be analyzed using the software packages described previously in this section.

5.5.3.2 Lookup Tables

With the simulation data available, another program is run to populate a large multi- dimensional arrays of lookup tables (LTs) with information about the showers. Each LT is a wrapper class around a weighted two-dimensional histogram that stores information. The z-axis of the histogram stores the weighed mean and standard deviation for one of three lookup parameters: width, length, and energy. The independent axes of all table histograms are log₁₀(size[dc]) (range1.5–5.5 ) and impact distance (0–800 m). Note that because simulations are being used, the impact location is known and the impact distance is calculated exactly. The tables in a file are organized into bins of a parameter space that describes the observing conditions of an event. The dimensions of that space are zenith angle, azimuth angle, wobble offset, noise level, and the telescope ID for the image. Each set of observing conditions has three separate tables, each of which contains information for a particular lookup parameter. To populate the LTs, first the standard analysis is run on the raw data files through the image parameterization stage. The LT manager loops through each image and checks if it passes quality cuts. Note that the size cut is excluded because the histograms are binned in the log of size. Each event that passes cuts is appended to a vector of values for that size / impact distance bin. After all events have been processed, the mean and standard deviation

of each lookup parameter are calculated for each bin. The histogram’s bin content is set to the mean value, and its error is set to the standard deviation of values. Once fully populated, the tables are combined into a single ROOT file for use with real data. LTs corresponding to different atmospheric conditions, such as for summer and winter, or for different array epochs, are stored in separate files.

During shower reconstruction (stage 4), an LT can be used to look up expected values and standard deviations of its three parameters. These are used for calculating stereo parameters (explained in the next section) and for the standard method of energy reconstruction. For every image, the appropriate histograms are examined in order to find the parameter value based on the size and the core impact distance. The program performs a multi-dimensional interpolation between tables and bins to return a mean value and error. In the standard method of energy reconstruction, the energy used for an event is the average of the energies found for each telescope image. The uncertainty is found by taking the RMS of the energy values about the average.