A Deep Search for Stable Venus Co-orbital Asteroids: Limits on the Population

A stable population of objects co-orbiting with Venus was recently hypothesized in order to explain the existence of Venus's co-orbital dust ring. We conducted a 5 day twilight survey for these objects with the Cerro-Tololo Inter-American Observatory (CTIO) 4 meter telescope covering about 35 unique square degrees to 21 mag in the $r$-band. Our survey provides the most stringent limit so far on the number of Venus co-orbital asteroids; it was capable of detecting $5\%$ of the entire population of those asteroids brighter than 21 magnitude. We estimate an upper limit on the number of co-orbital asteroids brighter than 21 magnitude (approximately 400-900 m in diameter depending on the asteroid albedo) to be $N=18^{+30}_{-14}$. Previous studies estimated the mass of the observed dust ring co-orbiting with Venus to be equivalent to an asteroid with a 2 km diameter ground to dust. Our survey estimates $<6$ asteroids larger than 2 km. This implies the following possibilities: that Venus co-orbitals are non-reflective at the observed phase angles, have a very low albedo ($<1\%$), or that the Venus co-orbital dust ring has a source other than asteroids co-orbiting Venus. We discuss this result, and as an aid to future searches, we provide predictions for the spatial, visual magnitude, and number density distributions of stable Venus co-orbitals based on the dynamics of the region and magnitude estimates for various asteroid types.