Efficiency characterization of the V-shape asteroid family detection method

Abstract

Following the break up of a parent body, the Yarkovsky effect causes asteroid family members to spread in orbital semimajor axis with a rate often inversely proportional to their diameter. This size dependent semimajor axis drift causes family members to form structures in the semimajor axis vs inverse diameter plane that have the shape of the letter V. The V-shape method consists in finding the borders of such V-shapes of unknown center and opening. Although successfully employed to find some very old families in the inner main asteroid belt, the V-shape searching method is very sensitive to many parameters. In this work, we first created and evolved a synthetic asteroid family over billions of years. Then, by adding uncertainties to semimajor axis and diameter of the evolved synthetic family components, we randomly generated additional 99 similar, but not perfectly V-shaped, family clones. We chose a fairly low initial velocity dispersion of 20 m/s for our family. Thus, we can more easily relate the spreading in semimajor axis with the family's age (slope of the evolving V). A synthetic background with an initially randomly distributed components was also created and evolved for 100 Myr. Thus, by setting different levels of ratio of the synthetic family and background asteroids, we derived a detection efficiency map for the V-shape method and determined how sensitive the results can be based on signal-to-noise levels. We also determined optimal parameter values for the method's efficiency. We found that, families older than ≈3 Gyr are likely undetectable, with a method efficiency of 50% or less, whereas younger families (0.5-2.5 Gyr) are more easily detected by the method, with an efficiency of ≳80%.

Asteroid Families: properties, recent advances and future opportunities

“…In light of these results, Delbó et al (2017Delbó et al ( , 2019 seem to be lucky to detect the ancient families. As stated by Deienno et al (2021), this is still a work in progress, even though promising. Other steps will include adding statistical analysis and other debiasing techniques to fully characterise the V-shape methods' efficiency.…”

“…The offset is established as a delta in 1/D and named as a w (Delbó et al, 2017). Deienno et al (2021) summarizes the two techniques saying that the dC/dK-method searches for (K ± ∆K)|a p − a p,c | and the a w -method searches for (K|a p − a p,c | ± a w ).…”

“…Both categories have been tested on synthetic families (Walsh et al, 2013;Bolin et al, 2017;Deienno et al, 2021) and they have also been used to try to detect primordial families. Walsh et al (2013) were the first to use the Vshape based family identification finding the new Polana family, about 2 Gyr old group, and the Eulalia family, about 0.8 − 1 Gyr old group, both within the Nysa-Polana complex.…”

“…However, the V-shape family identification method is also very sensitive to many parameters involved in the search, and additional verifications are needed to fully quantify the robustness of the method. Deienno et al (2021) have done a comprehensive study to characterise the efficiency of the V-shape method in detecting asteroid families. They worked using a synthetic population of asteroid families and background asteroids, letting those families evolve over billions of years, setting different levels of ratio of the synthetic family and background asteroids to derive a detection efficiency map for the V-shape method.…”

Astrocladistics of the Jovian Trojan Swarms

“…Milani 1993;Beauge & Roig 2001;Nesvorný et al 2015). Another family identification method, uses the size dependent drift pattern due to the Yarkovsky effect (Bottke et al 2006) to identify ancestral dynamic families in main-belt Asteroids (Walsh et al 2013;Bolin et al 2017Bolin et al , 2018Deienno et al 2020). The technique, while useful in the Main belt, has reduced usefulness in the Trojans.…”