Resonant interactions and chaotic rotation of Pluto’s small moons

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Abstract

Four small moons—Styx, Nix, Kerberos and Hydra—follow near-circular, near-equatorial orbits around the central ‘binary planet’ comprising Pluto and its large moon, Charon. New observational details of the system have emerged following the discoveries of Kerberos and Styx. Here we report that Styx, Nix and Hydra are tied together by a three-body resonance, which is reminiscent of the Laplace resonance linking Jupiter’s moons Io, Europa and Ganymede. Perturbations by the other bodies, however, inject chaos into this otherwise stable configuration. Nix and Hydra have bright surfaces similar to that of Charon. Kerberos may be much darker, raising questions about how a heterogeneous satellite system might have formed. Nix and Hydra rotate chaotically, driven by the large torques of the Pluto–Charon binary.

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Figure 1: Example HST images of Pluto’s small moons.
Figure 2: Numerical integrations of the Styx–Nix–Hydra resonance.
Figure 3: Mass-dependence of the Laplace-like resonance.
Figure 4: Normalized light curves.
Figure 5: Numerical simulations of Nix’s rotation.

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Acknowledgements

M.R.S. acknowledges NASA’s Outer Planets Research Program for their support through grants NNX12AQ11G and NNX14AO40G. Support for HST programme GO-12436 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. D.P.H. acknowledges NASA Origins Research Program and grant NNX12AI80G.

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Affiliations

Authors

Contributions

M.R.S. performed all of the astrometry, photometry, orbit fitting and numerical modelling discussed here. D.P.H. was co-investigator on the Kerberos discovery and has participated in the dynamical interpretations of all the results.

Corresponding author

Correspondence to M. R. Showalter.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Variations in orbital elements by year.

Changes in mean motion (a), eccentricity (b) and inclination (c) are shown during 2010–2012 for Nix (red), Kerberos (green) and Hydra (blue). Vertical bars are ±1σ. Each individual point is a fit to a single year of data (compare with Extended Data Table 1). In a, Δn is the mean motion of each body minus its average during 2006–2012.

Extended Data Figure 2 The role of Kerberos in the Laplace-like resonance.

We have initiated an integration with Styx exactly in its resonance with Nix and Hydra, and then have allowed it to evolve for 10,000 years. The diagrams are for MK nominal (a), MK reduced by 1σ (b) and MK = 0 (c). The amplitude of the libration is stable when Kerberos is massless, but shows erratic variations otherwise.

Extended Data Figure 3 Spectral signatures of Kerberos.

We merge Pluto and Charon into a single central body and integrate Φ(t) for Styx in exact resonance. The fast Fourier transform (FFT) power spectrum for MK = 0 (light grey) obscures the same spectrum obtained when MK is nominal. Unobscured spikes are caused by Kerberos. a, The impulses of Kerberos passing each moon create a signature at the synodic period and its overtones: SSK = 53.98 days (green); SNK = 109.24 days (red); SKH = 203.92 days (blue). b, Harmonics of the second resonance, with period 42SNK ≈ 43SSN ≈ 4,590 days, are also visible. The 3/2 harmonic is unexplained.

Extended Data Figure 4 Satellite phase curves.

Raw disk-integrated photometry has been plotted versus phase angle α for Nix (a) and Hydra (b). Vertical bars are ±1σ. An opposition surge is apparent. A simple parametric model for the phase curve is shown: c(1 + d/α), where d is fixed but c is scaled to fit each moon during each year. Measurements and curves are colour-coded by year: red for 2010, green for 2011, and blue for 2012. Source data

Extended Data Figure 5 Distribution of photometric measurements by year.

The black curves show the theoretical probability density function (PDF) of A by year for Nix (a, 2010; b, 2011; c, 2012) and Hydra (d, 2010; e, 2011; f, 2012), after convolution with the measurement uncertainties. The histogram of measurements from each year is shown in red. In spite of small number statistics, the measurements appear to be well described by the models, which have been derived via Bayesian analysis. Source data

Extended Data Figure 6 Searches for rotation periods in the light curves.

We fitted a simple model involving a frequency and its first harmonic to the photometry (see equation (6)) of Nix (a) and Hydra (b). Curves are plotted for data from 2010 (red), 2012 (blue) and for three years 2010–2012 (black). Local minima with RMS residuals 1 indicate a plausible fit. The orbital periods and half-periods are identified; if either moon were in synchronous rotation, we would expect to see minima near either P (for albedo variations) or P/2 (for irregular shapes).

Extended Data Table 1 Orbital elements based on coupling various orbital elements and based on subsets of the data.

Supplementary information

Supplementary Table 1

This table contains data concerning the Hubble images used in the study. The file name is as defined by Space Telescope Science Institute (STScI) in their Mikulski Archive for Space Telescopes (MAST). However, coadded images contain a "_coadd" suffix; in these cases, the Exposure Time column identifies the number of images obtained nearby in time that have been combined. Program ID is defined by STScI. Visit IDs are as designated by the Principal Investigator; most visits consist of a single orbit of Hubble, but two or more consecutive orbits sometimes fall within the same visit. Orbit Number identifies these sequences of consecutive orbits. The last four columns indicate which of the four small moons were measured in the image: S = Styx, N = Nix, K = Kerberos, H = Hydra. (XLSX 534 kb)

Simulated rotation of Nix

This video shows the orientation of Nix as viewed from the system barycenter. Nix has an assumed axial ratio of 5 × 6 × 10 and starts at rest in the rotating frame, but with the long axis pointed away from the barycenter. The video plays at 12.5 days (~ half an orbital period) per second. (MOV 3642 kb)

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Showalter, M., Hamilton, D. Resonant interactions and chaotic rotation of Pluto’s small moons. Nature 522, 45–49 (2015). https://doi.org/10.1038/nature14469

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