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.
Using a suite of numerical calculations, we consider the long-term evolution of
circumbinary debris from the Pluto--Charon giant impact. Initially, these solids
have large eccentricity and pericenters near Charon's orbit. On time scales of
100--1000 yr, dynamical interactions with Pluto and Charon lead to the ejection
of most solids from the system. As the dynamics moves particles away from the
barycenter, collisional damping reduces the orbital eccentricity of many particles.
These solids populate a circumbinary disk in the Pluto-Charon orbital plane; a large
fraction of this material lies within a `satellite zone' that encompasses the orbits
of Styx, Nix, Kerberos, and Hydra. Compared to the narrow rings generated from the
debris of a collision between a trans-Neptunian object (TNO) and Charon,
disks produced after the giant impact are much more extended and may be a less promising option for producing small circumbinary satellites.
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-sized or smaller objects is essential to prevent the subsequent reaccretion 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.