Dumb-bell-shaped equilibrium figures for fiducial contact-binary asteroids and EKBOs

Abstract

In this work, we investigate the equilibrium figures of a dumb-bell-shaped sequence with which we are still not well acquainted. Studies have shown that these elongated and nonconvex figures may realistically replace the classic "Roche binary approximation" for modeling putative peanut-shaped or contact binary asteroids. The best-fit dumb-bell shapes, combined with the known rotational period of the objects, provide estimates of the bulk density of these objects. This new class of mathematical figures has been successfully tested on the observed light curves of three noteworthy small bodies: main-belt asteroid 216 Kleopatra, Trojan asteroid 624 Hektor and Edgeworth-Kuiper-belt object 2001 QG 298 . Using the direct observations of Kleopatra and Hektor obtained with high spatial resolutiontechniques and fitting the size of the dumb-bell-shaped solutions, we derived new physical characteristics in terms of equivalent radius, 62.5 ± 5 km and 92 ± 5 km, respectively, and bulk density, 4.4 ± 0.4 gcm -3 and 2.43 ± 0.35 gcm -3 , respectively. In particular, the growing inadequacy of the radar shape model for interpreting any type of observations of Kleopatra (light curves, AO images, stellar occultations) in a satisfactory manner suggests that Kleopatra is more likely to be a dumb-bell-shaped object than a "dog-bone."

The Complex Rotational Light Curve of (385446) Manwë–Thorondor, a Multicomponent Eclipsing System in the Kuiper Belt

“…At maximum brightness viewed perpendicular to its spin axis, Manwë then has a surface area equivalent to a single sphere with diameter d M = d A [2(1+(d B /d A ) 2 )] 1/2 = 1.838d A and a volume equivalent to a sphere of diameter d MVOL = d A [2 (1+(d B /d A ) 3 )] 1/3 = 1.465d A = 0.797d M . With this shape, we are able to produce a light curve differing by less than 10% from the one generated by Descamps (2015) for the case W = 0.32, assuming the same scattering law.…”

“…For simplicity and to speed our computations, we approximate each lobe of the barbell shape calculated by Descamps by a pair of contacting spheres, A and B, with diameters d A and d B , aligned with the long axis of the barbell. To set their relative scale, we refer to the shape parameters a and b (the half the length of the barbell and its maximum crosssectional radius, respectively) given by Table 1 of Descamps (2015). Scaled to the radius of a sphere with the same volume as the barbell, a = 2.284 and b = 0.694.…”

“…Shape models for Manwë used for the multi-component light curve calculations presented in this paper. The barbell model (grey-shaded figure, with long axis, 2a, and maximum perpendicular radius, b) is the shape calculated byDescamps (2015) for a strengthless body with normalized rotational velocity [3p/rG]1/2/P = 0.31. To simplify our light curve calculations, we represent each lobe of this figure by a pair of contacting spheres (orange shading) with respective diameters dA = 2b and dB = a -2b.…”

A Possible Dynamically Cold Classical Contact Binary: (126719) 2002 CC249

“…This U/V shaped rotational lightcurve results from shadowing and viewing geometry effects from a contact binary viewed nearly equator-on (Hartmann & Cruikshank 1978;Wijesinghe & Tedesco 1979;Weidenschilling 1980). The U/V shape of a rotational lightcurve for a contact binary asteroid based on viewing geometry and phase angle effects has been further modeled in detail by several authors Lacerda & Jewitt 2007;Gnat & Sari 2010;Descamps 2015). The U-shape for the maximum and V-shape for the minimum peak of a lightcurve is apparent for contact binary asteroids viewed near equator on and at low phase angles, for which the latter occurs for all TNOs.…”

Stability of binaries. Part 1: Rigid binaries

“…While the first Darwin problem dealt with binaries whose secondary was much smaller than the primary, the second Darwin problem addressed binaries with congruent members. Leone et al (1985) attempted to extend the latter analysis to fluid binaries with unequal members through their so-called ''Roche binary approximation"; see also Descamps (2015). Within this approximation, the members orbit at a Keplerian value and the equilibrium shape of each member is found after neglecting the triaxial shape of its companion.…”