We discuss a new set of ~ 500 numerical n-body calculations designed to constrain the masses and bulk densities of Styx, Nix, Kerberos, and Hydra. Comparisons of different techniques for deriving the semimajor axis and eccentricity of the four satellites favor methods relying on the theory of Lee & Peale (2006), where satellite orbits are derived in the context of the restricted three body problem (Pluto, Charon, and one massless satellite). In each simulation, we adopt the nominal satellite masses derived in Kenyon & Bromley (2019b), multiply the mass of at least one satellite by a numerical factor f >= 1, and establish whether the system ejects at least one satellite on a time scale <= 4.5~Gyr. When the total system mass is large (f >> 1), ejections of Kerberos are more common. Systems with lower satellite masses (f ~ 1) usually eject Styx. In these calculations, Styx often signals an ejection by moving to higher orbital inclination long before ejection; Kerberos rarely signals in a useful way. The n-body results suggest that Styx and Kerberos are more likely to have bulk densities comparable with water ice, rho_SK <= 2 g/cm^3, than with rock. A strong upper limit on the total system mass, M_SNKH <= 9.5 x 10^19 g, also places robust constraints on the average bulk density of the four satellites, rho_SNKH <= 1.4 g/cm^3. These limits support models where the satellites grow out of icy material ejected during a major impact on Pluto or Charon.
The data were generated by computer simulations using the C++ code "Orchestra", a proprietary hybrid code that follows the dynamical evolution of solids and gas orbiting a central object. Algorithms in the code are described in the following papers (author names abbreviated to B for Bromley, K for Kenyon, and L for Jane X Luu along with a year for publication date, AJ = Astronomical Journal, ApJ = Astrophysical Journal, S=Supplement): KL1998, AJ 115:2136; KL1999, AJ 118:1101; KB2001,AJ 121:538; KB2002,AJ 123:1757; KB2004, AJ 127:513; BK2006, AJ 131:2737; KB2006, AJ 131:1837; KB2008, ApJS 179:451; KB2010, ApJS 188:242; BK2011, ApJ 731:101; KB2012, AJ 143:63; KB2014, AJ 147:8. Initial conditions for these simulations described in the published paper.
Various C and fortran programs are used to analyze the data for the calculations. Several C programs needed to extract information from the computer generated binary output files are included with the dataset. The C programs include basic summaries of the structure of the data files and the usage to extract data from each binary file.
We consider a scenario where the small satellites of Pluto and Charon grew within a disk of debris from an impact between Charon and a trans-Neptunian Object (TNO). After Charon’s orbital motion boosts the debris into a disk-like structure, rapid orbital damping of meter-size or smaller objects is essential to prevent the subsequent re-accretion or dynamical ejection by the binary. From analytical estimates and simulations of disk evolution, we estimate an impactor radius of 30–100 km; smaller (larger) radii apply to an oblique (direct) impact. Although collisions between large TNOs and Charon are unlikely today, they were relatively common within the first 0.1–1 Gyr of the solar system. Compared to models where the small satellites agglomerate in the debris left over by the giant impact that produced the Pluto-Charon binary planet, satellite formation from a later impact on Charon avoids the destabilizing resonances that sweep past the satellites during the early orbital expansion of the binary.