The Flux Distribution and Sky Density of 25th Magnitude Main Belt Asteroids

Abstract

Digital tracking enables telescopes to detect asteroids several times fainter than conventional techniques. We describe our optimized methodology to acquire, process, and interpret digital tracking observations, and we apply it to probe the apparent magnitude distribution of main belt asteroids fainter than any previously detected from the ground. All-night integrations with the Dark Energy Camera (DECam) yield 95% completeness at R magnitude 25.0 and useful sensitivity to R = 25.6 mag when we use an analytical detection model to correct flux overestimation bias. In a single DECam field observed over two nights, we detect a total of 3234 distinct asteroids, of which 3123 are confirmed on both nights. At opposition from the Sun, we find a sky density of 697 ± 15 asteroids per square degree brighter than R = 25.0 mag, and 1031 ± 23 brighter than R = 25.6 mag. We agree with published results for the sky density and apparent magnitude distribution of asteroids brighter than R = 23 mag. For a power law defined by dN/dR ∝ 10 αR , we find marginally acceptable fits with a constant slope α =0.28 ± 0.02 from R = 20 to 25.6 mag. Better fits are obtained for a broken power law with α = 0.218 ± 0.026 for R = 20–23.5 mag, steepening to α = 0.340 ± 0.025 for R = 23.5–25.6 mag. The constant or steepening power law indicates that asteroids fainter than R = 23.5 mag are abundant, contrary to some previous claims but consistent with theory.

Hubble Asteroid Hunter

“…In our case, we do not have enough observations around this magnitude value to confirm this feature. Heinze et al (2019) performed main belt observations from the Blanco Telescope at Cerro Tololo Inter-American Observatory, reporting a non-constant population power-law slope. In this latter work, the apparent R-band population distribution shows a transition around R = 19-20, with a shallower slope for fainter magnitudes, which is in good agreement with our benchmark (Gladman et al 2009).This shallower slope is maintained up to two fainter magnitudes than Gladman et al (2009), which reinforces the results from our work showing a constant slope maintained up to H ≈ 19-20 mag.…”

NEOMOD: A New Orbital Distribution Model for Near-Earth Objects

“…The differential absolute magnitude distribution is denoted by ( ) ( ) dn H n H dH = . Given that the magnitude distribution is not seen to wildly vary across the main belt (Heinze et al 2019), and craters on the main-belt asteroids follow a common size distribution (Bottke et al 2020), we use a similar setup for different main-belt sources. Specifically, the magnitude distribution produced by source j is set to be ( )…”

“…32 The magnitude distribution in the extended magnitude range 15 < H < 28 is discussed in Sections 8 and 10. Heinze et al (2019) estimated the slope of the absolute magnitude distribution for main-belt asteroids. They found γ ; 0.22 for H = 20-23.5 and γ ; 0.34 for H = 23.5-25.6.…”

Hubble Asteroid Hunter: Identifying asteroid trails in Hubble Space Telescope images

“…In our case we do not have enough observations around this magnitude value to confirm this feature. Heinze et al (2019) performed Main Belt observations from the Blanco Telescope at Cerro Tololo Inter-American Observatory reporting a non-constant population power law slope. In this work, the apparent R-band population distribution shows a transition around R = 19-20, with a shallower slope for fainter magnitudes in good agreement with our benchmark (Gladman et al 2009) and maintained up to two fainter magnitudes than it, thus reinforcing the results from our work showing a constant slope maintained up to H ≈ 19 − 20 mag.…”