The Pluto System

Rotational Variability of Nix and Hydra

Generals Paper I

Alessondra Springmann

July 1, 2008

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1 Introduction

Once thought to be a remote oddball of our outer Solar System, Pluto is now known

to be one of many objects in the Kuiper Belt. [Its three moons—previously thought to be

unique for such a small, remote body—make Pluto one of the numerous binary or multiple-

body Kuiper Belt objects (KBOs) that have been discovered in the last 16 years.] [clarify...

awkward phrasing] Up to 20% of KBOs in various dynamical classes are multiple systems

(Noll et al., 2008), implying that it is not uncommon for a body residing in this region of

the Solar System to have multiple moons or be a binary object.

Pluto’s largest moon Charon was discovered in 1978 (Christy & Harrington, 1978), mak-

ing Pluto a double planet until the 2005 discovery of Pluto’s smallest moons, Nix and Hydra

(Weaver et al., 2005). Nix and Hydra not only make Pluto part of a quadruple system, but

also present new constraints on the formation of the Pluto system from dynamical simula-

tions. The satellites’ circular orbits, coplanar with the orbit of Charon, suggest that these

moons all formed from material ejected into orbit around Pluto by a giant impact event.

1.1 Motivation

Nix and Hydra’s recent discovery and their importance in our understanding the Pluto

system make them an important and timely mission goal for New Horizons, set for a 2015

encounter with Pluto. In this paper, we discuss a method for constraining the rotation

periods of Nix and Hydra from data obtained with the 6.5-meter Baade telescope at Las

Campanas Observatory in July 2007. Providing limits on the rotation periods of these

moons allows for more efficient imaging of their surfaces by the New Horizons cameras, in

addition to confirming the period constraints determined by Buie et al. (2007) and allowing

for more precise simulations to be carried out of the Pluto system’s formation and evolution.

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2 Pluto System Origin and Evolution

2.1 Formation

It is widely accepted that the Pluto system was formed in a giant impact collision (Canup,

2005; Stern et al., 2006) with little or no exchange of heat or heating of the bodies’ materials

occuring, resulting in the formation of not only Pluto and Charon, but also Hydra and Nix.

This assumption is valid because the angular momentum of the Pluto system is quite high

(see references 9-12 in Stern et al., 2006), thus Charon must have formed from a collision

with Pluto and was therefore likely not captured into orbit. The largest body in the 3:2

mean-motion resonance with Neptune (Brown, 2008), Pluto is part of the only quadruple

system known to date in the Kuiper Belt (2003 EL61, the only known triple system, has two

small companions, and also has a collisional family).

2.2 Charon

Charon formed from mantle material leftover from the collision that formed the entire

Pluto system. As this collision resulted in little or no melting of the impactors’ material,

there was little heat exchange, and thus a good deal of the impactors’ icy mantles remained

water ice and became the major constituents of Charon (Stern et al., 2006).

Charon’s surface is dominated by water ice, in addition to a bit of ammonia (see

McKinnon et al., 2008, and references therein); quite a different surface from Pluto. Both

Pluto and Charon are tidally locked, the same faces of these two bodies always facing the

companion, making these two objects part of what is occasionally called a “double planet”.

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2.3 Nix & Hydra

Nix and Hydra likely formed in the same collision that produced Charon, probably origi-

nating as debris from this giant impact between two large, differentiated bodies (Stern et al.,

2006). Their coplanar orbits with Charon also suggest that they formed in the same impact

from which formed Charon. Combining their coplanar orbits with their neutral colors, it

can be assumed that Nix and Hydra are similar in composition to Charon, i.e. that their

constituents are mostly water ice.

Another argument for Nix and Hydra forming at the same time as Charon is that they

are larger than the critical size boundary for catastrophic breakup over the age of the solar

system (Durda & Stern, 2000; Stern et al., 2006). Forming along with Pluto and Charon, Nix

and Hydra are likely the same age as the former two bodies and have withstood disruption

forces that would have torn apart smaller bodies.

Even if Nix and Hydra have resisted disruption by impacts or tidal forces, they may have

lost up to 10% of their masses due to impact erosion (Stern, 2008a,b). Material ejected

from their surfaces by collisions with other KBO fragments could help feed the hypothetical,

tenuous rings or ring arcs in the Pluto system1.

The proximity of Nix and Hydra to the corotation (more literally, co-orbital) resonances

also implies a common impact origin for these smaller moons, meaning that Nix and Hydra

were driven outward by Charon’s migration (Ward & Canup, 2006). At some point, the

outward migration of Nix and Hydra ceased, most likely due to the end of Charon’s outward

migration. Nix likely escaped from its corotation resonance with Charon first, before the

end of Charon’s outward semi-major axis migration due to tidal expansion. [EXPAND ME]

1Binzel (2006) and Stern et al. (2006) propose the possibility of rings (or ring arcs) in the Pluto system,of time-varying optical depth of approximately τ = 5× 10−6, of the same order of magnitude as the opticaldepth of the tenuous rings around Jupiter (Showalter et al., 1987; Throop et al., 2004). As Pluto is far awayfrom the perturbing forces of the Sun, the possibility of there existing rings of collisional ejecta from Nix andHydra in the Pluto system is high, though the arrival of New Horizons will ultimately confirm or deny theprescence of rings. Stern (2008a) also suggests the potential resurfacing of Nix and Hydra by impact ejecta[EXPAND ME].

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Ward & Canup (2006) also show that these particular corotation resonances (4:1 and 6:1)

are the most conducive to moon formation around Pluto, as other corotation resonances are

close to the Hill sphere and other dynamically unstable regions. Nix and Hydra’s probable

initial locations in the 4:1 and 6:1 corotation resonances could have lead to the aggregation

of material at these points and thus helped contribute to the long-term survival of these

moons over the age of the Solar System.

Formation of these moons alongside Pluto and Charon was likely, as they are presently

in highly circular orbits—e = 0.01504 for Nix and e = 0.00870 for Hydra (Tholen et al.,

2008)—implying that they were not dynamically captured, as the circularization timescales

are greater than the age of the Solar System (Stern et al., 2006).

Though the orbits of these two small moons are relatively well known (Tholen et al.,

2008), not much is known about either the exact dimensions of Nix and Hydra or their

rotation rates. Stern et al. (2006) assume minimal masses for Nix and Hydra and calculate

that these moons are likely not in synchronous rotation with Pluto, unless they formed

much closer to Pluto and migrated outward (Ward & Canup, 2006). Thus, understanding

the rotation rates of Nix and Hydra helps [EXPAND ME] ...

2.4 Other Kuiper Belt Binaries

Because up to a fifth of Kuiper Belt objects are binary or have multiple satellites

(Stephens & Noll, 2006), studying the multiple system of Pluto allows us to better under-

stand the evolution and current states of not only the Pluto system but also other multiple

Kuiper Belt objects. Although there are plenty of binary KBOs, it is significantly harder to

observe smaller satellites of 100-km class TNOs (Noll et al., 2008), especially for narrowly-

separated objects. Comparing the frequencies of nearly equal-sized binaries with objects

with smaller companions is difficult, due to observational limits from seeing, telescope size,

differences in detectors, etc. Pluto, being one of the brightest KBOs, allows us to most

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readily study its multiple satellites, making it an ideal target for New Horizons (Section 3).

3 New Horizons

A collaboration between the John Hopkins Applied Physics Laboratory and the South-

west Research Institute, New Horizons was launched in January 2006 and is expected to fly

by Pluto on Bastille Day in 2015. New Horizons’ science goals include imaging the surfaces

and thus mapping the compositions of the four main bodies in the Pluto system, studying

Pluto’s atmosphere, searching for an atmosphere around Charon, along with imaging the en-

tire Pluto Hill sphere, searching for presently undiscovered moons and probable rings (Stern

et al., 2006; Young et al., 2007; Stern, 2008a).

The recent discovery of Nix and Hydra is very timely in allowing target planning and

new science goals for the New Horizons mission. Once the rotation rates of these moons are

verified, New Horizons will be able to optimally image their surfaces. Knowing the rotation

rates of these moons will help verify whether they are in any sort of spin-orbit resonances

with Pluto, and place important constraints on the rotation rates of moons of other KBOs.

Nix and Hydra’s recent discovery and their importance in understanding of the Pluto

system make them an important and timely mission goal for New Horizons. Until New Hori-

zons arrives at Pluto, a good deal will remain uncertain about the Pluto system, including

the absolute radius of Pluto, the nature of its atmosphere, the rotation rates of Nix and

Hydra, and the masses and composition of these moons.

After visiting Pluto New Horizons will swing by at least one yet-to-be-determined KBO

to further study the other icy bodies of the outer Solar System, linking them with other

dynamical populations such as Centaurs and comets. Hopefully in the process, New Horizons

will begin to answer our questions about the origins and compositions of the cold leftovers

of our Solar System’s formation and evolution.

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4 Observations

To determine or constrain potential short period rotation of Nix and Hydra, images of

the Pluto system were obtained with the 6.5-meter Walter Baade Magellan telescope at the

Las Campanas Observatory, Chile. Repeated imaging sequences covering a total of 10 hours

on UT 2007 July 11 and 12 were executed using the Inamori Magellan Areal Camera and

Spectrograph (IMACS) in the Baade f/4 direct imaging mode. A total of 815 images with

integration times of 6 seconds (cadence of 30 seconds) in a Sloan i′ filter were collected under

0.4-0.7 arcsecond seeing. Only Chip 2 out of the eight chips that compose IMACS was used

and was further subrastered to reduce image readout time. A sample image sequence is

[shown] in Fig. 1, moving 0.44 arcseconds per hour.

Figure 1: Six-second integrations of the Pluto system taken 6 minutes apart on UT 2007July 11. The Pluto-Charon system is the bright object near the center of the frames thatchanges position between exposures. The IMACS plate scale is 0.11 arcseconds per pixel.[FIX FINAL FIGURE - I know it’s wrong!]

[Observation circumstances table goes here.]

[Complements HST program 10786 - Buie team and cadence thereof]

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5 Data Analysis

5.1 Reduction

The data were calibrated using bias and flat frame images. [EXPAND?] Routines from

the IRAF/DAOPHOT package were used to perform stellar photometry on the Pluto fields.

First, the daofind task creates an initial star list by locating all the star-like sources in

an image within a certain width and range of counts, then tvmark marks the stars from the

star list on the displayed FITS file. Using both phot and daofind, the background values

and initial magnitudes for the stars in the star list are calculated.

To generate a PSF from the stars in the image, between seven and nine stars brighter

than Pluto are manually selected with pstselect and an initial PSF is created with the psf

routine, where the type of PSF (Lorentz, Gauss, or Moffat) can be specified.

The nstar task then takes the PSF generated in the previous step and fits it to the rest

of the stars in the field. The PSFs of the fitted PSF stars and their neighbors are then

subtracted from the image using substar. This process is then repeated on the subtracted

images until a clean PSF is obtained, usually after three or four iterations.

After the stars have been modeled and subtracted in each frame, approximately 12 min-

utes (integration time, not clock time) of images are coadded together to obtain sufficient

signal to noise with respect to Nix and Hydra. [Expand]

Several different point spread function (PSF) types were used to accurately model the

light from Pluto and Charon and thus subtract these two bodies’ PSFs. As Pluto appears

as a disk, rather than a point source, a simple Gaussian model does not suffice to model the

“disk spread function” of Pluto. [Expand]

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5.2 Point Spread Function Models

Three different models have been tried to approximate the point spread functions of the

data. Davis (1994) describe Gaussian, Moffat, and Lorentz models for IRAF/DAOPHOT

PSF modeling as discussed below. A is a normalization constant for each model and pn are

parameters fit during the PSF modeling process.

[Should this go in an appendix?]

[Soon to appear here: plots comparing the three models!]

5.2.1 Moffat

A typical Moffat function, as described by Trujillo et al. (2001), is

PSF(r) =β − 1

πα2

[1 +

(r

α

)2]−β

, (1)

with the full width at half maximum, FWHM=2α√

21/β − 1, where PSF(FWHM/2) =

(1/2)PSF(0) and the total flux is normalized to 1. IRAF uses a simplified version of this

function,

[Math goes here]

for its Moffat25 model.

5.2.2 Gaussian

The Gaussian model for a PSF is a limiting case of the Moffat PSF (when β →∞) (Trujillo

et al., 2001):

PSF(r) = 4(21/β − 1

) β − 1

πF 2

[1 + 4(21/β − 1)

(r

F

)2]−β

, (2)

which becomes:

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limβ→∞

PSF(r) =1

2πσ2e−

12( rσ )

2

. (3)

5.2.3 Lorentz

[Math goes here.]

5.3 Limiting Magnitude Calculation

In order to determine if Nix and Hydra are detectable in our science images, we calculated

how many images would need to be coadded to obtain sufficient signal-to-noise on these

moons to bring them to the same brightness as the dimmest stars in our exposures.

Using IDL astron routines from Marc Buie, we matched the locations of the stars in our

frames to US Naval Observatory stellar locations. Initally, the predicted catalog positions

do not match the positions of the stars on the chip very well (Figure N).

The positions of the stars on the chip are manually aligned with the predicted catalog

positions. (Figure N+1). astron then calculates the vectors between the catalog and chip

locations of the stars and also plots the correlations between the instrumental magnitude

and how red the stars are in the USNO catalog (Figure N+2).

(Figure N+3: Stars used for solving for the positions of the stars are in yellow, rejected

in red.)

[I’m in the process of cleaning up this calculation. Shall be improved Monday.]

One of the dimmest, isolated stars in a frame had an instrumental magnitude of 11.8

which corresponds to a visual magnitude of 15.3 and a signal of S0 = 75, 000 counts for an

integration time of 10 seconds. The magnitude of Hydra is 24, so this means that ∆m =

-8.7.

m = m0 − 2.5 logS0

10

15.3 = 24.0− 2.5 logS0

1015.3−24.0−2.5 = S0

[... I’ll flush this out soon, I promise.]

[Figures will go here soon.]

6 Results

[None, yet.(. ._

). Stay tuned for more...]

7 Discussion/Conclusions

Our observations yield continuous coverage with integration times of six seconds over a

span of seven hours on the first night of observing. The high sampling frequency should

allow or constrain rotation periods of Nix and Hydra under 24 hours.

This high cadence of observations complements the observing sequence of the Hubble

telescope by Buie et al. (2007), which should constrain the moons’ rotation rates on the

order of days or longer. Between our measurements and those of the Buie team, the rotation

rates of these moons should be discerned in the near future and made available to the New

Horizons team in order to maximize the imaging capabilities of this spacecraft during its

flyby of these moons.

[Something about how the Buie team can measure rotation rates over 24 hours and we

can constrain rotation rates under that amount of time, should we find these moons.]

The arrival of New Horizons at Pluto will begin the in situ exploration of the Kuiper

Belt and the icy regions beyond Neptune, helping us understand better the nature of not

only Plutos moons but also their dwarf planet companion and other Kuiper Belt objects.

By imaging the surfaces of these moons and other objects beyond Pluto, we will be able to

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determine the compositions of these moons and also their orbital characteristics, giving us

further clues as to their dynamical evolutions as well as those of other Kuiper Belt objects.

Almost 30 years after the realization that Pluto was a double planet, the discovery of

1998 WW31 demonstrated that Pluto was no longer unique in its binary status (Veillet et al.,

2001). According to the frequency predictions of Noll et al. (2008), there could be up to tens

of thousands of Kuiper Belt objects with satellites or that are binaries (Stephens & Noll,

2006). Though we know of only three moons in orbit around Pluto, there could have been

more moons that were disrupted or destabilized throughout the dynamical history of the

Pluto system. In addition to moons that once were, more satellites could be lurking below

the detection thresholds of current telescopes, along with rings or ring arcs, not just around

the tightly-bound Pluto system but around other KBOs. Maybe there exist KBO systems

less tightly-bound than Pluto, such as ones with captured satellites in highly eccentric orbits.

The arrival of New Horizons in the Kuiper Belt will answer numerous questions about

the history of this region, but will likely also raise new ones as the spacecraft’s science

instruments begin to probe the chilly remnants of planet formation.

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