Meteor statistics I: The distribution of instrumental magnitudes

TL;DR

This work demonstrates that instrumental meteor magnitudes are best modeled by an exponentially modified Gaussian (exGaussian) distribution, arising naturally from normal fluctuations in detection threshold and post-detection measurement errors. By fitting exGaussian models to faint CAMO optical data and CMOR radar amplitudes, the authors extract physically meaningful parameters: the population index $r$, the mean detection threshold, and a combined error term, with $r$ typically around $2.7$–$2.9$ and related mass indices $s$ near $2.0$–$2.2$. They compare exGaussian to competing models (Gumbel, Gamma, EGP, GL4) and find exGaussian to provide the best balance of interpretability and fit quality, while remaining robust to overdense contamination in radar data. The study confirms that exGaussian fitting yields reliable estimates of detection thresholds, enabling accurate flux calculations and cross-network comparisons, and it highlights the practical availability of exGaussian implementations (e.g., in SciPy). Overall, the paper establishes exGaussian as a principled, interpretable framework for modeling meteor magnitude distributions and extracting key observational parameters.

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.

Figures (10)

• Figure 1: The probability distribution function (PDF) of each distribution discussed in sec. \ref{['sec:dists']}, plotted on both a linear (top) and log (bottom) scale. We hold $\mu$ and $\delta$ fixed across all examples, but present several choices of shape parameter in each case.
• Figure 2: Peak apparent magnitude vs. apparent angular motion (in pixels per frame) for meteors detected by camera 01G. Points are color-coded by point density to help the reader identify the most populated areas (in yellow). The dashed white line follows eq. \ref{['eq:dmag']} with ${u_0 = 10}$ ppf.
• Figure 3: The PDF in each family that best fits the distribution of motion-adjusted magnitudes from one EMCCD camera (black points). The lower panel zooms in on the peak of the distribution.
• Figure 4: The azimuth and elevation angle of echoes recorded by CMOR for solar longitudes between $116^\circ$ and $118^\circ$. Points are color-coded by solar longitude within this range. Radial gridlines correspond to $20^\circ$ increments in zenith angle. In the top panel, we show all data. At center, we plot only cluster members identified by DBSCAN. At bottom, we plot the data that remains after we remove the clusters.
• Figure 5: The distribution of solar longitudes in our data set. All data appear in yellow; anomalous events and two major meteor showers have been excluded from the data set shown in gray.