Meteor statistics I: The distribution of instrumental magnitudes

TL;DR

This paper proposes modeling meteor magnitude distributions with an exGaussian distribution, which better fits observed data and allows extraction of key parameters for flux estimation and extrapolation.

Contribution

It introduces the exGaussian distribution as a superior model for meteor magnitudes, improving parameter estimation over previous models.

Findings

ExGaussian fits meteor magnitude data better than other distributions.

Parameters from the fit enable conversion of observed rates to fluxes.

The model applies to both optical and radar meteor data.

Abstract

The distribution of meteor magnitudes is known to follow an exponential distribution, where the base of this distribution is called the population index. The distribution of observed magnitudes preserves this behavior, but is truncated by the detection threshold. If both the population index and detection threshold can be determined, observed meteor rates can be converted to fluxes and extrapolated to any desired brightness or size. We argue that the distribution of observed or instrumental meteor magnitudes is best modeled as an exponentially modified Gaussian (exGaussian) distribution. This is for three reasons: first, an exGaussian distribution is the natural result of random variations in detection threshold and/or post-detection measurement errors in magnitude. Second, an exGaussian distribution provides a better fit to the magnitude distribution than all other competing distributions in the literature; we demonstrate this using both a set of faint optical meteor magnitudes and a set of radar meteor echo amplitudes. Finally, the population index, mean detection threshold, and random variation/error terms are easily extracted from the best-fit parameters of an exGaussian distribution.