A Pluto–Charon Sonata: Dynamical Limits on the Masses of the Small Satellites

Abstract

During 2005-2012, images from Hubble Space Telescope (HST) revealed four moons orbiting Pluto-Charon (Weaver et al. 2006;Showalter et al. 2011Showalter et al. , 2012. Although their orbits and geometric shapes are well-known, the 2σ uncertainties in the masses of the two largest satellites -Nix and Hydra -are comparable to their HST masses (Brozović et al. 2015;Showalter & Hamilton 2015;Weaver et al. 2016). Remarkably, gravitational n-body computer calculations of the long-term system stability on 0.1-1 Gyr time scales place much tighter constraints on the masses of Nix and Hydra, with upper limits ∼ 10% larger than the HST mass. Constraints on the mass density using size measurements from New Horizons suggest Nix and Hydra formed in icier material than Pluto and Charon.Subject headings: planets and satellites: dynamical evolution and stabilityplanets and satellites: individual (Pluto)

A Pluto--Charon Concerto II. Formation of a Circumbinary Disk of Debris After the Giant Impact

“…Charon has mass m C = 1.586 × 10 24 g, radius R C = 606 km, and mean density ρ C = 1.702 g cm −3 . Combined with analyses of HST observations (Brozović et al 2015;Showalter & Hamilton 2015), detailed n-body calculations (Kenyon & Bromley 2019b) provide limits on the mass of Nix (m N 4.5 × 10 19 g) and Hydra (m H 4.8 × 10 19 g; see also Youdin, Kratter & Kenyon 2012). Although constraints on the masses of Styx (m S ) and Kerberos (m K ) are more elusive, plausible estimates are m S ≈ 6 × 10 17 g and m K ≈ 10 18 g. Thus, the total mass in satellites is m sat ≈ 10 20 g. These satellites orbit within a 'satellite zone,' a ≈ 33-66 R P , defined as a region that encompasses the orbits of the four satellites (e.g., Kenyon & Bromley 2019a;Bromley & Kenyon 2020).…”

“…For each combination of a and e of the central binary, we choose two values for the initial inclination, ı 0 = 0.025 and 0.25. The first choice allows for maximum collisional damping throughout the evolution; the second choice provides limits on the ability of collisions to evolve a thick disk into the thin disk required for the growth of satellites (Kenyon & Bromley 2014b;Walsh & Levison 2015).…”

“…For a time step ∆t, the coagulation code derives the changes in the e and ı of each mass bin from collisions and orbital interactions with all other mass bins. Collision rates are derived from the particle-in-a-box algorithm (e.g., Kenyon & Bromley 2002, 2004. For each mass bin k in annulus i, the collision rate with solids in mass bin l in annulus j depends on the number density of particles (n ik and n jl ), the collision cross-section, the relative velocity, and the overlap of orbits (see sec.…”

“…For each mass bin k in annulus i, the collision rate with solids in mass bin l in annulus j depends on the number density of particles (n ik and n jl ), the collision cross-section, the relative velocity, and the overlap of orbits (see sec. 2 of Kenyon & Bromley 2008). When i = j, the overlap is 1; otherwise, the overlap is approximately the ratio of the volume of annulus j that lies within the volume of annulus i.…”

“…Several analyses explain how small satellites on circumbinary orbits become unstable as the central binary expands from a period of 1-2 d to the current 6.4 d (e.g., Ward & Canup 2006;Lithwick & Wu 2008;Youdin et al 2012;Cheng et al 2014b;Bromley & Kenyon 2015b;Woo & Lee 2018). Kenyon & Bromley (2014b) and Walsh & Levison (2015) consider how collisional damping converts eccentric circumbinary orbits into the more circular orbits required for the growth of solids into 5-20 km satellites. Bromley & Kenyon (2015b) demonstrate how a swarm of cm-sized pebbles could stabilize satellite orbits throughout the tidal evolution of the central binary.…”