A reproducible method to determine the meteoroid mass index

Context. The determination of meteoroid mass indices is central to flux measurements and evolutionary studies of meteoroid populations. However, different authors use different approaches to fit observed data, making results difficult to reproduce and the resulting uncertainties difficult to justify. The real, physical, uncertainties are usually an order of magnitude higher than the reported values. Aims. We aim to develop a fully automated method that will measure meteoroid mass indices and associated uncertainty. We validate our method on large radar and optical datasets and compare results to obtain a best estimate of the true meteoroid mass index. Methods. Using MultiNest, a Bayesian inference tool that calculates the evidence and explores the parameter space, we search for the best fit of cumulative number vs. mass distributions in a four-dimensional space of variables ($a,b,X_1,X_2$). We explore biases in meteor echo distributions using optical meteor data as a calibration dataset to establish the systematic offset in measured mass index values. Results. Our best estimate for the average de-biased mass index for the sporadic meteoroid complex, as measured by radar appropriate to the mass range $10^{-3} > \mathrm{m} > 10^{-5}$ g, was $s=-2.10 \pm 0.08$. Optical data in the $10^{-1} > \mathrm{m} > 10^{-3}$ g range, with the shower meteors removed, produced $s=-2.08 \pm 0.08$. We find the mass index used by Grun et al. 1985 is substantially larger than we measure in the $10^{-4} < m < 10^{-1}$ g range.