1 New Ephemerides of Nix and Hydra During the 1985 to 1990 Mutual

New Ephemerides of Nix and Hydra During the 1985 to 1990 Mutual Events Between Pluto and Charon

Garrett T. Elliott1 and David J. Tholen2 1The Ohio State University, 2Univ. of Hawaii.

ABSTRACT

Acknowledging the non-Keplerian orbits for the Plutonian moons Nix and Hydra due to significant perturbations by Charon, new ephemeris positions were calculated to assist with their detection in previous observations of the Pluto system. To compensate for unknown albedo and density, we varied their masses from 1.0x1016 kg to 2.5x1018 kg to allow for extremes of Pluto-like albedo and a water- ice density to comet-like albedo and Pluto-like density, respectively. New ephemeris positions of Nix and Hydra should allow us to identify them in stacked images from archival Hubble Space Telescope data. Also, the coplanar orbits of Nix, Hydra, and Charon result in a shared season of mutual events. In Pluto and Charon mutual event observations made between 1985 and 1990, Nix or Hydra mutual events with Pluto may have been unknowingly observed, however these events would be shallow if detectable at all. Even though mutual events between Nix or Hydra and Charon did occur, the focus of the observations during this time was on the events between Charon and Pluto. This situation makes for the possibility that there were observations of one of these Nix or Hydra and Charon events very remote.

INTRODUCTION

Nix and Hydra were discovered in close orbit around the Pluto and Charon system in June of 2005 after analyzing images taken in May of 2005 by the HST Pluto Companion Search Team. Orbits fit to these discovery observations provided a starting point to stack archived images of the system from 2002 and 2003 data. The new positional data were fit to Keplerian orbit solutions, which yielded three non-overlapping mass estimates for the system. Further investigation by Man Hoi Lee and S. J. Peale shows that, even if Nix and Hydra have negligible mass, perturbations from Charon would occur, resulting in non-Keplerian orbits. A serendipitous Nix or Hydra detection during Pluto and Charon’s 1985-1990 mutual event season could improve the orbital fits by having a larger arc of observations. Acknowledging the persistent perturbations, N- body calculations would have to be made for any orbital data calculations.

BACKGROUND

In studying the four-body system of Pluto, we are aided by the fact that at least two of the bodies have been successfully observed to provide quality orbital data since 2

1984. The majority of this data was taken due to the orbital plane of Charon passing through the orbit of the Earth. This allowed for many partial eclipses to be observed, and a few edge-on events occurred in 1987 and 1988. This wealth of data significantly aided in determining the radius of Pluto and Charon. The archived data of these mutual events were supplied by Dr. David Tholen and are accessible on the Planetary Data System (PDS).

Charon Nix Hydra Apparent Magnitude 16.2 23.4 23.3 Semi major Axis (km)1 19,570 48,700 64,800 Period (day) 6.387 24.86 38.21 Eccentricity2 .003 .002 .005 Inclination (deg)3 96.1 96.2 96.4

Table 1: The orbital data provided in this table was produced fitting the positional data of Nix and Hydra to Keplerian orbits. These values only provide a scale of reference into the Pluto system.

1Measured from Pluto, for Charon, and the Pluto-Charon barycenter, for Nix and Hydra 2 Charon eccentricity reported in Buie et al. 2006 was later corrected from .000 to .003 3As measured relative to the Earth’s equator

ANALYSIS

Our derived starting position and velocity vectors for the three satellites are from the orbits computed by Buie et al. Those orbits are barycentric, which minimizes the indirect perturbation on Pluto by Charon, but are two-body, which ignores direct perturbations. After converting these vectors from the barycentric frame to the Plutocentric frame, using Buie et al.'s mass ratio of 0.1165, they were compatible with Everhart's 15th-order Gauss-Radau integrator. We numerically integrated the motions of the satellites back to the epoch of the mutual events starting with the starting epoch of 2452600.5 JD, November 22, 2002. The masses of Pluto and Charon were taken from the work of Buie et al. Estimates for the mass of Nix and Hydra are limited by setting up a range with reasonable physical properties of a Kuiper Belt object. The range of albedo was matched to the lowest possible being that of a comet and highest possible being that of Pluto. This puts an average in the vicinity of Charon’s albedo. Now accompanied with the observed magnitudes, we calculate the possible radii being between thirteen to sixty-five kilometers. The bounds used for density are derived from the highest possible being that of Pluto’s and the lowest possible being near the density of water-ice. The final culmination of these estimates results in the mass range of 1.0 x 1016 to 2.5 x 1018 kilograms. 3

Comet-like Albedo Pluto-like Albedo

.04 .35 .65

Radius Range

65km  22km  13km

Pluto Density Water-Ice Density

3 3 2.03 g/cm 1.0 g/cm

Mass Range

2.5 x 1018 kg  1.0 x 1016 kg

Table 2: This table illustrates the method to derive the mass estimates for Nix and Hydra. These left hand values provide the upper mass boundaries and right hand values provide low mass boundaries.

The method for detection was to rotate the position vectors to be viewed as they would be on the plane of the sky. An event between Nix and Hydra would be documented if their positions came within a radius of 1215 km to the center of Pluto’s mass. The mass and size of Nix and Hydra were always held equal in all calculations. Honing in on more accurate and differentiated values of Nix and Hydra would be left for later fine tuning of the orbits. Matching the expected times of a mutual event for Nix or Hydra with those observed for Charon, we have candidates for determining whether or not the light curve dipped further than predicted. The most relative question to ask when investigating a possible observed mutual event of Nix and Hydra is whether or not they were capable of being detected from the Pluto and Charon observations retrieved off PDS. For a suitable detection above the noise, there would have to be a discrepancy between the observed and theorized magnitudes of at least .002 magnitudes. If the best case scenario is achieved and Nix and Hydra cross over Pluto with a full shadow, then the surface area reduction for Pluto would be doubled and the odds of possible detection would increase. This being the case, the minimum radius that these satellites could be and still be detectable is roughly forty kilometers. Anything below will most likely be indistinguishable. The benefit of such as boundary is that it lies within our estimates for the radius and provides an opportunity to narrow down the mass range even further. If there is an observed event for Nix and Hydra and no difference in magnitude is recorded, from what is theorized, this would indicate a radius near the lower estimates.

RESULTS

When checking the validity of our output, it became apparent that integrating using high mass values for Nix and Hydra caused a severe offset for the prediction of 4 when Charon’s mutual events with Pluto were to occur. Compared to observed data from a February 20th observation in 1985, the high mass data set predicts a mutual event over 4hrs prior to when it was recorded. Integrating with a low mass value brings this offset down to nearly fifteen minutes. Comparing the high mass predictions versus the low mass predictions for all mutual events from 1985 to 1990 shows a diminishing difference between the two times. A four hour difference in 1985 shrinks to less than three hours by 1990.

CONCLUSIONS

The perturbations of Nix and Hydra are expected, even at negligible mass, but what was not anticipated is how strongly the high mass values can perturb the orbit of Charon. This now provides an opportunity to narrow the mass range even further since the orbit of Charon is known to a high degree. An unknown mass may not be the only culprit for the time inconsistencies; even the low mass calculations still contain an offset. Proposals to fix the prediction values are to start with an N-body solution to determine the initial vectors and include more data for Nix and Hydra’s positions to gain a greater arc of time in their observation. One must recognize the possibility that if Kepler’s equations are incorporated to solve the orbit of Charon with 1992-93 and 2002-3 data and Nix and Hydra with just 2002-2003 data, perhaps the reason they work best with low mass is that Kepler’s equations are the same as an N-body solution if Nix and Hydra had negligible mass. It is important to note that the original intent of this research has been put on hold. High mass and low mass variations for Nix and Hydra can shift the predictions for their mutual events with Pluto by as much as 3 days. The range needs to be narrowed even further by investigation into the dynamics of the Pluto system. Future work will be to improve the initial position values by incorporating a longer arc of time between observations of Nix and Hydra. New observations with Hubble Space Telescope are set for earlier 2007 and will provide an arc of over four years from the 2002- 2003 data. 5

APPENDIX 1

Figure 1: A plot showing the orbital paths of Charon, Nix, and Hydra in a Plutocentric reference frame. The time step for each point is one hundredth of a day. This plot’s orientation is in the plane of Charon’s orbit. 6

APPENDIX 2

Figure 2: A plot showing the orbital paths of Charon, Nix, and Hydra with the orientation of the Pluto system as seen from the Earth. Each point goes by a time step of one hundredth of a day over the course of 1987. The paths show how the orbital planes begin to pass through the orbit of the Earth. This point of view resulted in the observed mutual events. 7

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