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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Showalter, M. R. et al. New satellite of (134340) Pluto: S/2011 (134340). IAU Circ. 9221, (2011).
Weaver, H. et al. Discovery of two new satellites of Pluto. Nature 439, 943–945 (2006).
Showalter, M. R. et al. New satellite of (134340) Pluto: S/2012 (134340). IAU Circ. 9253, (2012).
Weaver, H. A. et al. New satellite of (134340) Pluto: S/2011 (134340). IAU Circ. 9221, (2011).
Buie, M. W., Grundy, W. M. & Tholen, D. J. Astrometry and orbits of Nix, Kerberos, and Hydra. Astron. J. 146, 152 (2013).
Brozović, M., Showalter, M. R., Jacobson, R. A. & Buie, M. W. The orbits and masses of satellites of Pluto. Icarus 246, 317–329 (2015).
Steffl, A. J. et al. New satellite of (134340) Pluto: S/2011 (134340). IAU Circ. 9221, (2011).
Lee, M. H. & Peale, S. J. On the orbits and masses of the satellites of the Pluto-Charon system. Icarus 184, 573–583 (2006).
Buie, M. W. et al. Orbits and photometry of Pluto’s satellites: Charon, S/2005 P1, and S/2005 P2. Astron. J. 132, 290–298 (2006).
Sinclair, A. T. The orbital resonance amongst the Galilean satellites of Jupiter. Mon. Not. R. Astron. Soc. 171, 59–72 (1975).
Rivera, E. J. et al. The Lick-Carnegie Exoplanet Survey: a Uranus-mass fourth planet for GJ 876 in an extrasolar Laplace configuration. Astrophys. J. 719, 890–899 (2010).
Youdin, A. N., Kratter, K. M. & Kenyon, S. J. Circumbinary chaos: using Pluto’s newest moon to constrain the masses of Nix and Hydra. Astrophys. J. 755, 17 (2012).
Quillen, A. C. & French, R. S. Resonant chains and three-body resonances in the closely-packed inner Uranian satellite system. Mon. Not. R. Astron. Soc. 445, 3959–3986 (2014).
French, R. G., Dawson, R. I. & Showalter, M. R. Resonances, chaos, and short-term interactions among the inner Uranian satellites. Astron. J. 149, 142–169 (2015).
Canup, R. M. A giant impact origin of Pluto-Charon. Science 307, 546–550 (2005).
Ward, W. R. & Canup, R. M. Forced resonant migration of Pluto’s outer satellites by Charon. Science 313, 1107–1109 (2006).
Kenyon, S. J. & Bromley, B. C. The formation of Pluto’s low-mass satellites. Astron. J. 147, 8–24 (2014).
Lithwick, Y. & Wu, Y. The effect of Charon’s tidal damping on the orbits of Pluto’s three moons. Preprint at http://arxiv.org/abs/0802.2939 (2008).
Lithwick, Y. & Wu, Y. On the origin of Pluto’s minor moons, Nix and Hydra. Preprint at http://arxiv.org/abs/0802.2951 (2008).
Walsh, K. & Levison, H. F. Formation and evolution of Pluto’s small satellites. Preprint at http://arxiv.org/abs/1505.01208 (2015).
Zhang, K. & Hamilton, D. P. Orbital resonances in the inner Neptunian system I. The 2:1 Proteus-Larissa mean-motion resonance. Icarus 188, 386–399 (2007).
Zhang, K. & Hamilton, D. P. Orbital resonances in the inner Neptunian system II. Resonant history of Proteus, Larissa, Galatea, and Despina. Icarus 193, 267–282 (2008).
Grundy, W. M., Noll, K. S. & Stephens, D. C. Diverse albedos of small trans-neptunian objects. Icarus 176, 184–191 (2005).
Lykawka, P. S. & Mukai, T. Higher albedos and size distribution of large transneptunian objects. Planet. Space Sci. 53, 1319–1330 (2005).
Stansberry, J. et al. in The Solar System beyond Neptune (eds Barucci, M. A. et al.) 161–179 (Univ. Arizona Press, 2007).
Lacerda, P. et al. The albedo–color diversity of transneptunian objects. Astrophys. J. 793, L2 (2014).
Stern, S. A. Ejecta exchange and satellite color evolution in the Pluto system, with implications for KBOs and asteroids with satellites. Icarus 199, 571–573 (2009).
Hedman, M. M., Burns, J. A., Thomas, P. C., Tiscareno, M. S. & Evans, M. W. Physical properties of the small moon Aegaeon (Saturn LIII). Eur. Planet. Space Congr. Abstr. 6, 531 (2011).
Wisdom, J., Peale, S. J. & Mignard, F. The chaotic rotation of Hyperion. Icarus 58, 137–152 (1984).
Klavetter, J. J. Rotation of Hyperion. I—Observations. Astron. J. 97, 570–579 (1989).
Dobrovolskis, A. R. Chaotic rotation of Nereid? Icarus 118, 181–198 (1995).
Buratti, B. J., Gougen, J. D. & Mosher, J. A. No large brightness variations on Nereid. Icarus 126, 225–228 (1997).
Grav, T., Holman, M. J. & Kavelaars, J. J. The short rotation period of Nereid. Astrophys. J. 591, L71 (2003).
Giuliatti Winter, S. M., Winter, O. C., Vieira Neto, E. & Sfair, R. Stable regions around Pluto. Mon. Not. R. Astron. Soc. 430, 1892–1900 (2013).
Krist, J. E., Hook, R. N. & Stoehr, F. 20 years of Hubble Space Telescope optical modeling using Tiny Tim. Proc. SPIE 8127, 1–16 (2011).
Space. Telescope Science Institute. Observatory Support: Tiny Tim HST PSF Modelinghttp://www.stsci.edu/hst/observatory/focus/TinyTim (2011).
Buie, M. W. et al. Pluto and Charon with the Hubble Space Telescope. II. Resolving changes on Pluto’s surface and a map for Charon. Astron. J. 139, 1128–1143 (2010).
Hamilton, D. P. A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances. Icarus 109, 221–240 (1994).
Levison, H. F. & Duncan, M. J. The long-term dynamical behavior of short-period comets. Icarus 108, 18–36 (1994).
Levison, H. F. SWIFT: A Solar System Integration Software Package http://www.boulder.swri.edu/∼hal/swift.html (2014).
French, R. S. & Showalter, M. R. Cupid is doomed: An analysis of the stability of the inner Uranian satellites. Icarus 220, 911–921 (2012).
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.
The authors declare no competing financial interests.
Extended data figures and tables
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.
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.
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.
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.
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.
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).
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)
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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