Amplification of the Signal-to-Noise Ratio in Cosmic Ray Maps Using the Mexican Hat Wavelet Family

TL;DR

This paper investigates how different wavelet-based smoothing techniques, including Gaussian and Mexican Hat wavelets, can enhance the signal-to-noise ratio in cosmic ray maps, aiding in source detection.

Contribution

It introduces a comparative analysis of smoothing kernels on cosmic ray maps, extending to a virtual observatory setup with realistic acceptance laws.

Findings

Mexican Hat wavelets improve signal-to-noise ratio more effectively than Gaussian smoothing.

Optimal wavelet order depends on background noise patterns.

Analysis applicable to full-sky and partial-sky observatories.

Abstract

In this work we analyze the effect of smoothing maps containing arrival directions of cosmic rays with a gaussian kernel and kernels of the mexican hat wavelets of orders 1, 2 and 3. The analysis is performed by calculating the amplification of the signal-to-noise ratio for several background patterns (noise) and different number of events coming from a simulated source (signal) for an ideal detector capable of observing the full sky with uniform coverage. We extend this analysis for a virtual observatory with two sites, one in the northern hemisphere, the other in the southern, considering an acceptance law.