A reproducible method to determine the meteoroid mass index

Abstract

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 > m > 10 −5 g, was s = −2.10 ± 0.08. Optical data in the 10 −1 > m > 10 −3 g range, with the shower meteors removed, produced s = −2.08 ± 0.08. We find the mass index used by Grün et al. (1985) is substantially larger than we measure in the 10 −4 < m < 10 −1 g range.

Meteoroids at the Moon: Orbital Properties, Surface Vaporization, and Impact Ejecta Production

“…Grun et al () provided an excellent compilation of available measurements at that date and for size ranges treated in this manuscript reported α = 5.05. Shallower size indexes were reported from the latest meteor radar and optical measurements at Earth that suggest α = 4.51 ± 0.21 (Blaauw et al, ) and α = 4.30 ± 0.28 (Pokorný & Brown, ). An excellent measurement of SFD from low Earth orbit was performed by the LDEF spacecraft (Love & Brownlee, ) , which recorded impact cratering statistics for 5.7 years.…”

“…One source of discrepancy might be a different size range observed by LDEF and radar and optical meteor systems. Data in Cremonese et al () show a very steep distribution for meteoroids with D > 200 μm and no impacts from particles with D > 400 μm, whereas radars and optical systems observe meteors show more complete data sets for D > 400 μm (see, e.g., Pokorný & Brown, ).…”

“…Cremonese et al (2012) used hydrocode modeling of the cratering process to derive from LDEF data a complex SFD which can be approximated with two power laws; = 8.8 for meteoroids with D > 200 m and = 2.8 for D < 200 m. One source of discrepancy might be a different size range observed by LDEF and radar and optical meteor systems. Data in Cremonese et al (2012) show a very steep distribution for meteoroids with D > 200 m and no impacts from particles with D > 400 m, whereas radars and optical systems observe meteors show more complete data sets for D > 400 m (see, e.g., Pokorný & Brown, 2016).…”

A new method for measuring the meteor mass index: application to the 2018 Draconid meteor shower outburst

“…A similar approach is used in other fields as well, although ways of estimating the value x min differ (Corral & González 2019). Pokornỳ & Brown (2016) suggested fitting two parameters x min , x max which describe the range of magnitudes, radar echo amplitudes (or equivalently masses) for which the linear approximation is valid. They argue that the addition of the upper boundary x max is necessary as small number statistics may skew the power law at larger amplitudes/masses.…”

“…Blaauw et al 2011a). We note that Pokornỳ & Brown (2016) used the same data set, but their algorithm fitted a line to the histogram on the part after the inflection point, slightly reducing the value of the mass index to s = 2.09. Due to the large number of data points, the estimate of the mass index of sporadic meteors can be accurately estimated, but often in practice, only tens of shower meteors are available.…”