Hillas

Hillas parameters are a set of image-shape descriptors used in imaging atmospheric Cherenkov telescopes (IACTs) to characterize the Cherenkov light image produced by an extensive air shower. They were introduced by A. M. Hillas in 1985 to enable the extraction of gamma-ray signals from a background of cosmic-ray–induced showers.

The analysis treats the camera image as an ellipse, derived from the second moments of the light distribution. Key parameters include SIZE (total light collected), LENGTH (extent along the major axis of the ellipse), WIDTH (extent along the minor axis), and DISTANCE (the distance from the image centroid to the camera center). The orientation is given by the major axis angle, often described by ALPHA, the angle between the major axis and the line from the image centroid to the camera center. Additional parameters such as the orientation angle and asymmetry along the major axis can also be computed to capture head-tail information of the shower image.

Applications in gamma-ray astronomy include discriminating gamma-ray–like images from hadronic backgrounds, since gamma-ray showers tend to produce compact, elongated images aligned toward the source direction. When multiple telescopes observe the same event, the major axes intersect to help determine the incoming direction, and the SIZE parameter aids in estimating the gamma-ray energy after calibration.

Hillas parameters remain foundational in IACT data analysis, providing a robust, model-independent description of shower images. They are complemented by more advanced methods and likelihood analyses in modern experiments but continue to influence gamma-ray reconstruction and background rejection.