Relationship between Radar Cross Section and Optical Magnitude based on Radar and Optical Simultaneous Observations of Faint Meteors

TL;DR

This study establishes a quantitative relationship between radar cross section and optical magnitude for faint meteors through simultaneous observations, enabling the derivation of a luminosity function for interplanetary dust detection.

Contribution

It introduces a new transformation function linking radar cross sections to optical magnitudes, enhancing understanding of faint meteor detection and dust size distribution.

Findings

A linear relationship between radar cross section and optical magnitude was identified.

Derived a luminosity function with a population index of 3.52.

Demonstrated MU radar's capability to detect interplanetary dust of various masses.

Abstract

Radar and optical simultaneous observations of meteors are important to understand the size distribution of the interplanetary dust. However, faint meteors detected by high power large aperture radar observations, which are typically as faint as 10 mag. in optical, have not been detected until recently in optical observations, mainly due to insufficient sensitivity of the optical observations. In this paper, two radar and optical simultaneous observations were organized. The first observation was carried out in 2009 to 2010 using Middle and Upper Atmosphere Radar (MU radar) and an image-intensified CCD camera. The second observation was carried out in 2018 using the MU radar and a mosaic CMOS camera, Tomo-e Gozen, mounted on the 1.05-m Kiso Schmidt Telescope. In total, 331 simultaneous meteors were detected. The relationship between radar cross sections and optical V-band magnitudes was well approximated by a linear function. A transformation function from the radar cross section to the V-band magnitude was derived for sporadic meteors. The transformation function was applied to about 150,000 meteors detected by the MU radar in 2009--2015, large part of which are sporadic, and a luminosity function was derived in the magnitude range of $-1.5$ to $9.5$ mag. The luminosity function was well approximated by a single power-law function with the population index of $r = 3.52{\pm}0.12$. The present observation indicates that the MU radar has capability to detect interplanetary dust of $10^{-5}$ to $10^{0}$ g in mass as meteors.