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.
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.
-------------------------- METHODOLOGICAL INFORMATION --------------------------
1. Description of methods used for collection/generation of data: 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.
2. Methods for processing the data: 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.
3. Instrument- or software-specific information needed to interpret the data: Appropriate software is included in directory.
4. Standards and calibration information, if appropriate: none
5. Environmental/experimental conditions: all calculations were run on the NASA discover cluster
6. Describe any quality-assurance procedures performed on the data: Aside from tests summarized in the papers described in item 1, test calculations are summarized in the Appendix of each paper and compared to an appropriate benchmark.
7. People involved with sample collection, processing, analysis and/or submission: Scott Kenyon and Ben Bromley and --------------------- DATA & FILE OVERVIEW ---------------------
Files summarized in items 1-8 are binary output files from n-body simulations as described in Kenyon & Bromley, "A Pluto-Charon Sonata: Dynamical Limits on fate Masses of the Small Satellites" (2019, Astronomical Journal). Files described in item 9 are ascii txt. The C programs in items 10, 11, and 12 provide different ways to access the binary output. Each C program describes the architecture of the binary files.
1. pcs2-0mmm-nnn[a-z] files: heavy satellites, mmm = 100 x mass factor for all satellites, nnn = number of Symplectic steps per PC orbit, a-z = version
2. pcs2-1mmm-nnn[a-z] files: light satellites, mmm = 100 x mass factor for all satellites, nnn = number of Symplectic steps per PC orbit, a-z = version
3. pcs2-2mmm-nnn[a-z] files: light satellites with 2x nominal mass of Styx & Kerberos, mmm = 100 x mass factor for all satellites, nnn = number of Symplectic steps per PC orbit, a-z = version
4. pcs2-3mmm: heavy satellites, 40 Symplectic steps per PC orbit, mmm = 100 x mass factor for Nix only
5. pcs2-4mmm: heavy satellites, 40 Symplectic steps per PC orbit, mmm = 100 x mass factor for Kerberos only
6. pcs2-5mmm: heavy satellites, 40 Symplectic steps per PC orbit, mmm = 100 x mass factor for Hydra only
7. pcs2-6mmm light satellites, 40 Symplectic steps per PC orbit, mmm = 100 x mass factor for Nix only
8. pcs2-7mmm: light satellites, 40 Symplectic steps per PC orbit, mmm = 100 x mass factor for Hydra only
9. pcs2-n000.dat: summary of lifetimes for binary files in each archive 10. lifetime.c: summarizes lifetime and mass factor for binary file usage example: "lifetime pcs2-6110"
11. summary.c: generates basic summary of timesteps in a binary file usage example: "summary pcs1-0013d"
12. extrxyz.c: extracts (x,y,z) for N satellites and outputs (x,y,z) usage example: "extr6d pcs1-6110 6" will output (x,y,z) for SNKH 3. Additional related data collected that was not included in the current data package: There are other binary output files not included in this archive. 4. Are there multiple versions of the dataset? no