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

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.

💡 Research Summary

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This paper investigates how different smoothing kernels affect the signal‑to‑noise ratio (SNR) of cosmic‑ray arrival‑direction maps, with the ultimate goal of improving the detection of faint point‑like sources. The authors compare a simple Gaussian kernel with members of the Mexican Hat Wavelet Family (MHWF) of orders 1, 2, and 3. The MHWF is generated by repeatedly applying the Laplacian operator to a two‑dimensional Gaussian; each higher order emphasizes higher‑frequency features while suppressing low‑frequency background fluctuations.

The study uses Monte‑Carlo simulations. A synthetic source is placed at Galactic coordinates (l, b) = (320°, 30°) with an angular radius of 2°. Two source intensities are examined: 200 events (10 % brighter than the surrounding background) and a weaker case with 50 events. Four background models are considered: (i) isotropic (white‑noise) distribution, (ii) a dipole excess toward the Galactic centre (7 % amplitude), (iii) a dipole offset at (266.5°, −29°) with 0.5 % amplitude, and (iv) a set of ten additional sources of various sizes (σ = 0.5°–30°) and amplitudes (0.5 %–100 %). Each background contains 800 000 events, providing a realistic statistical environment.

Two detector configurations are simulated. The first is an ideal, full‑sky instrument with uniform exposure. The second mimics a realistic observatory consisting of two sites (one in the Northern hemisphere at 38° N, 102° W, the other in the Southern hemisphere at 36° S, 65° W). The northern site has seven times the collecting area of the southern one, and both follow a zenith‑angle acceptance proportional to sin θ cos θ for 0° ≤ θ ≤ 60°.

For each combination of source strength, background pattern, and detector exposure, the maps are convolved with the Gaussian and each MHWF kernel over a range of scales (σ). The amplification factor λ is defined as

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