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The Astronomical Journal, 132:614 - 619, 2006 August
# 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

A

NEW CONSTRAINTS ON ADDITIONAL SATELLITES OF THE PLUTO SYSTEM
A. J. Steff l,1 M. J. Mutchler,2 H. A. Weaver,3 S. A. Stern,4 D. D. Durda,1 D. Terrell,1 W. J. Merline, L. A. Young,1 E. F. Young,1 M. W. Buie,5 and J. R. Spencer1
Received 2005 November 30; accepted 2006 April 26
1

ABSTRACT Observations of Pluto and its solar-tidal stability zone were made using the Advanced Camera for Surveys (ACS) Wide Field Channel ( WFC ) on the Hubble Space Telescope on UT 2005 May 15 and May 18. Two small satellites of Pluto, provisionally designated S/2005 P1 and S/2005 P2, were discovered, as discussed by Weaver et al. and Stern et al. Confirming observations of the newly discovered moons were obtained using the ACS in the High Resolution Channel ( HRC ) mode on 2006 February 15 ( Mutchler et al.). Both sets of observations provide strong constraints on the existence of any additional satellites in the Pluto system. Based on the 2005 May observations using the ACS WFC, we place a 90% confidence lower limit of mV Ì 26:8 (mV Ì 27:4 for a 50% confidence lower limit) on the magnitude of undiscovered satellites greater than 500 (1:1 ; 105 km) from Pluto. Using the 2005 February 15 ACS HRC observations we place 90% confidence lower limits on the apparent magnitude of any additional satellites of mV Ì 26:4 between 300 and 500 (6:9 ; 104 1:1 ; 105 km) from Pluto, mV Ì 25:7 between 100 and 300 (2:3 ; 104 6:9 ; 104 km) from Pluto, and mV Ì 24 between 0B3 and 100 (6:9 ; 103 2:3 ; 104 km) from Pluto. The 90% confidence magnitude limits translate into upper limits on the diameters of undiscovered satellites of 29 km outside of 500 from Pluto, 36 km between 300 and 500 from Pluto, 49 km between 100 and 300 fromPluto,and 115kmbetween 0B3and 100 for a comet-like albedo of pV Ì 0:04. If potential satellites are assumedtohaveaCharon-likealbedoof pV Ì 0:38, the diameter limits are 9, 12, 16, and 37 km, respectively. Key words: Kuiper Belt -- planets and satellites: individual ( Pluto) Online material: color figure

1. INTRODUCTION Since its discovery in 1930 by Tombaugh (Slipher 1930), there have been surprisingly few published searches for satellites of Pluto. The first search was made at Lowell Observatory in 1930 February - March, immediately following Pluto's discovery ( Tombaugh 1960). It failed to discover Charon or any other satellite. Kuiper and Humason, working independently, conducted satellite searches in 1950 January ( Kuiper 1961). Using photographic plates from the two searches, Kuiper established magnitude limits of Plutonian satellites of mP Ì 19 between 0B3 and 200 from Pluto and mP Ì 22:4 for the region from 200 from Pluto to the edge of the stability zone. Curiously, despite the fact that the V magnitude of Charon in 1950 was about 17.5 (Stern et al. 1991) and that it was near its maximum northern elongation of 0B8from Pluto at the time of Kuiper 's observations ( Reaves 1997 ), no satellites were detected, although the presence of an unresolved Charon in Kuiper 's data may have resulted in his anomalously large measurement of Pluto's diameter ( Marcialis & Merline 1998). The first 50 years of Pluto-Charon observations are reviewed by Marcialis (1997). More recently, Stern et al. (1991) searched for satellites of Pluto out to the edge of Pluto's solar-tidal stability region using the MDM Observatory at Kitt Peak, Arizona, and the 2.1 m Struve telescope at McDonald Observatory in Texas. Using a nonDepartment of Space Studies, Southwest Research Institute, Boulder, CO 80302. 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 3 Applied Physics Laboratory, Space Department, The Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723-6099. 4 Space Science and Engineering Division, Southwest Research Institute, 1050 Walnut Street, Suite 400, Boulder, CO 80302. 5 Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, AZ 86001.
1

standard filter passband consisting of two separate transmission peaks at 5000 8 (FWHM Ì 350 8) and 6575 8 (FWHM Ì 225 8), they placed 90% confidence limits on satellites brighter than m Ì 20:6 Ö 0:5from 600 to 1000 from Pluto and m Ì 22:6 Ö 0:5for angular separations greater than 1000 from Pluto. These 90% confidence limiting magnitudes were improved by Stern et al. (1994) to mV Ì 21:7 between 100 and 200 from Pluto and mV Ì 21:9 between 200 and 1000 from Pluto through analysis of archival images from the Hubble Space Telescope ( HST ). No satellites (other than Charon) were detected in either of these searches. Nicholson & Gladman (2006) have also reported results from a Plutonian satellite search using the Hale 5 m telescope in June of 1999. They searched Pluto's entire Hill sphere and placed a 50% confidence detection limit of mR Ì 25:0 Ö 0:2 on additional satellites appearing more than $400 from Pluto, the point at which scattered light significantly degrades the sensitivity of their search. For potential undiscovered satellites with a solar V Ð R color, this limit translates into mV Ì 25:4 Ö 0:2. Previous satellite searches have used both the Hill radius, r H, and the stability radius, rS , to define the outer edge of the search region. Both of these radii derive from analytic solutions to the restricted three-body problem (i.e., a massless particle moving in the gravitational influence of the Sun with mass 1 M and a planet with mass Mp ). For a satellite to be gravitationally bound to a planet, it must have sufficiently low energy, so that its zero-velocity surface is closed. The largest , closed zero-velocity surface is the Hill sphere, whose radius is given by Ð Ñ r H Ì ap 1 Ð e p Mp 3 M
1=3

;

? 1î

where ap is the semimajor axis of the planet's orbit and ep is the planet's orbital eccentricity ( Hamilton & Burns 1992). Somewhat 614


CONSTRAINTS ON ADDITIONAL PLUTONIAN SATELLITES
TABLE 1 Observationa l Parameters r (AU ) 30.95 30.95 31.07 31.08 Ñ (AU ) 30.07 30.05 31.54 31.31 Phase Angle ( ) (deg) 0.96 0.88 1.59 1.77

615

Observation Date ( UT ) 2005 2005 2006 2006 May 15.045................... May 18.141................... Feb 15.659 .................... Mar 2.747 .....................

Channel ACS ACS ACS ACS WFC WFC HRC HRC

Filter F606W F606W F606W F475W, F606W

less well known is the solar-tidal stability radius given by Szebehely's stability criterion: rS Ì 1 r H (Szebehely 1967, 1978). 3 Satellite orbits with semimajor axis as less than rS will be stable over long time spans, whereas for orbits with rS < as < r H , instability can develop. (At distances greater than r H, the satellite is no longer bound gravitationally to the planet.) Analytical arguments by Hamilton & Krivov (1997) showed that satellites on initially circular orbits will become unstable if as k 0:53r H for prograde orbits or as k 0:69r H for retrograde orbits. Numerical simulations also show that the orbits of satellites with as k 0:4r H for prograde orbits or as k 0:7r H for retrograde orbits become Ä unstable on timescales of $106 yr (Carruba et al. 2002; Nesvorny et al. 2003). Thus, the stability radius, rS , provides a better approximation to the size of the satellite orbital stability zone than the Hill radius, r H, and following Stern et al. (1991) we adopt rS when referring to the region of stable orbits in the discussion below. For Pluto, ap Ì 39:5 AU, ep Ì 0:248, and the combined mass of the Pluto-Charon system, Mp , is ?1:4570 Ö 0:0009î ; 1022 kg ( Buie et al. 2006), yielding a stability radius of rS Ì 2:0 ; 106 km. Pluto's first discovered moon, Charon (Christy & Harrington 1978), orbits with a semimajor axis a0 of 19; 571 Ö 4 km ( Buie et al. 2006), within the inner 1% of Pluto's orbital stability region (Stern et al. 1991). Dynamical interactions with Charon cause satellite orbits between 0.47a0 and $2.0a0 to become unstable (Stern et al. 1994). Thus, satellites may be found orbiting Pluto out to a distance of 0.47a0 and orbiting the Pluto-Charon barycenter between $2.0a0 and the stability radius, rS, although satellites on orbits closer to Pluto than Charon would be difficult to explain unless they postdate Charon's outward orbital migration. The relatively large size of this region, the relatively bright limits reached by previous searches (except for Nicholson & Gladman [2006], which was not published when we submitted our proposal), and the launch of the New Horizons Pluto mission in 2006 January motivated our search for additional satellites of Pluto. 2. OBSERVATIONS We conducted a search for additional satellites of Pluto using the F606W filter ( broad V ) in the Wide Field Channel ( WFC ) of the Advanced Camera for Surveys (ACS) on the HST during two separate visits on UT 2005 May 15 and May 18 (guest observer program 10427). Observational details can be found in Table 1. The ACS WFC has a field of view of 202 00 ; 202 00 and a plate scale of 0B049 pixelÐ1. This is well matched to the angular size of Pluto's stability region (18500 in angular diameter, as seen from Earth in 2005 May), allowing the entire stability region to be imaged in a single HST pointing. A total of five images were obtained per HST visit: one short (0.5 s) exposure with Pluto and Charon unsaturated and four long (475 s) exposures. Pluto's apparent motion, seen from HST and averaged over the visibility period, is 4B2hrÐ1. This caused stars to appear as streaks $11 pixels long, while unresolved objects moving with Pluto appeared as point sources in all four long images. A sample long exposure from this data set can be seen in Figure 1.

With the detection of two additional satellites of Pluto in the ACS WFC observations ( Weaver et al. 2006), we obtained two additional HST visits to the Pluto system on 2006 February 15 and March 2 from the Director's Discretionary Time (GO/ DD program 10774). These observations were designed to confirm the existence of the two satellites ( Mutchler et al. 2006) and were obtained using the ACS High Resolution Channel ( HRC ). The observations in 2006 February consisted of four 475 s integrations taken with the F606W filter with additional 1 s integrations (to allow for accurate image registration with Pluto and Charon unsaturated ) at each position in a four-point dither pattern. The final drizzlecombined image from the 2006 February 15 observations, with labels indicating the positions of S/2005 P1 and S/2005 P2, is shown in Figure 2. The observations in 2006 March were also designed to measure the B Ð V colors of the satellites, and therefore alternated between 145 s integrations using the F606W filter and 475 s integrations using the F435W (Johnson B) filter. As such, the March 2 observations are less sensitive to faint satellites and were

Fig. 1.-- ACS WFC image of Pluto and its stability region on UT 2005 May 15. The image has been corrected for the geometric distortion of the ACS and rotated so that north is up and east to the left. The ACS WFC consists of two independent 4096 ; 2048 pixel CCDs butted together to form an effective 4096 ; 4096 pixel CCD with an approximately 50 pixel gap separating the two chips. The large field of view of the ACS WFC (202 00 ; 202 00 ) allowed Pluto's entire stability zone, delineated by the large circle, to be imaged in a single exposure. The square at the center of the image represents the approximate size and location of the image in Fig. 2. [See the electronic edition of the Journal for a color version of this figure.]


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Fig. 2.-- Drizzle-combined ACS HRC image of the Pluto system on 2006 February 15. This image shows a 512 ; 512 pixel region near the center of the ACS HRC detector. Pluto is centered on the image, while Charon is located 0B77 from Pluto at a position angle of 313 .P1 (2B86 from Pluto at a position angle of 343 ) and P2 (2B03 from Pluto at a position angle of 356 ) can be clearly seen. No other satellites are detected.

not used in the subsequent analysis. Some observational details about the ACS HRC observations are also presented in Table 1. 3. DATA ANALYSIS To estimate the sensitivity of our satellite search using the 2005 May ACS WFC data, we generated synthetic point-spread functions ( PSFs) at 400 locations in the plane of the sky using the Tiny Tim, version 6.3, software package ( Krist & Hook 2004), with the assumption that the sources have the same spectral distribution as the Sun. These PSFs were randomly spaced in separation and position angle from Pluto and were scaled to uniformly span the range in WFC STMAG magnitudes of 25.5- 29.5. To ensure proper subpixel alignment of the synthetic PSFs in the geometrically distorted ACS images (i.e., FLT images) the PSFs were subsampled by a factor of 5, resampled at the proper pixel locations, rebinned to normal size, and then convolved with the CCD charge diffusion kernel generated by the Tiny Tim program. Independent Poisson noise was applied to the synthetic PSFs before they were added, at the appropriate locations, to each of the four deep (475 s) exposures in the two ACS WFC visits. The four images were then ``drizzled'' together using the multidrizzle procedure supplied with the PyRAF software package ( Koekemoer et al. 2002). In the multidrizzle procedure the individual images are corrected for the geometric distortion of the ACS instrument, rotated so that north is up and east to the left, sky-background-subtracted, coregistered relative to Pluto, and combined using a median filter. In addition, pixels that have anomalously low sensitivity, have high dark counts, or are saturated are excluded. The median combination removes artifacts, such as cosmic-ray events or star trails, that do not appear in same position on the plane of the sky in at least two of the images. We then visually searched the final drizzle-combined image for objects (real or synthetic) with a PSF-like appearance. Adding synthetic PSFs to the data before conducting the actual satellite search results in a more accurate estimate of the lim-

iting magnitude of the search (since the conditions during the satellite search and the limiting magnitude estimation are identical). However, there is a small chance that one of the synthetic PSFs will be coincident with a real source, thus preventing the detection of the real source. Given the size of the ACS WFC images and the relatively compact nature of the ACS WFC PSF (0:796 Ö 0:003 of the total flux from a point source is contained within a circle of radius 3 pixels for the ACS WFC using the F606W filter [Sirianni et al. 2005]), only 0.06% of the pixels in the ACS WFC images change by more than 0.1 times the standard deviation in the sky background when the synthetic PSFs are added. Thus, we feel the benefit of obtaining a more accurate estimate of the limiting magnitude vastly outweighs the small risk of masking a real object with a synthetic PSF. Visual identification of point sources is generally more reliable than identification by automated detection algorithms. However, it can also be more subjective and prone to operator error/fatigue. To minimize the possibility that a bona fide satellite of Pluto would be missed on account of operator error or some systematic error introduced via the multidrizzle analysis procedure, the data were searched a second time using an independent technique: the four deep exposures were manually coregistered, displayed to the screen, and then cycled rapidly between images at roughly 15 frames sÐ1. As a result, stars would appear as trails moving through the displayed region, and cosmic-ray events and bad pixels would appear and disappear. Objects comoving with Pluto (whether real satellites or synthetic PSFs) would appear in the same location in each of the four frames. Although this technique proved to be somewhat less sensitive than the drizzle combination technique, it yielded consistent results. The field of view of the ACS HRC is 29 00 ; 26 00 , compared to 202 00 ; 202 00 with the ACS WFC. With the smaller field of view, there is an increased risk that a synthetic PSF added to the data will be coincident with a real source in the data, thus preventing the detection of the real source. To avoid this possibility, data from the 2006 February ACS HRC observations were first searched for satellites using the drizzle technique without the addition of synthetic PSFs. The data were then analyzed a second time, this time with synthetic PSFs added to provide an estimate of the sensitivity. A total of 200 PSFs, uniformly spaced between magnitudes 24.5 and 28.5, were added at random locations in each of two annuli centered on Pluto: one extending from 100 to 300 and the other from 300 to 500 . Since placing so many synthetic PSFs in such a small area would result in a high probability of overlapping PSFs, the ACS HRC data were analyzed 10 separate times, with only 20 randomly selected PSFs in each annulus for each analysis run. After the synthetic PSFs were added, the ACS HRC images were drizzlecombined, and the resulting image was visually inspected for point sources in a manner similar to that for the ACS WFC images. Finally, to estimate the limiting magnitude within 100 of Pluto, we placed 12 synthetic PSFs in a ring at an angular distance of 0B5 from Pluto, using the techniques described above. The magnitude of the individual PSFs in the ring pattern was then varied until at least one of the PSFs could no longer be easily identified. Although this technique is not as statistically rigorous, it provides a reasonable estimate of the limiting magnitude in this region. Scattered light from Pluto prevents us from assigning meaningful upper limits within $0B3 of Pluto. 4. RESULTS AND DISCUSSION As mentioned above, two satellites of Pluto, provisionally designated S/2005 P1 and S/2005 P2 ( hereafter P1 and P2), were discovered during the analysis of the 2005 May ACS WFC images ( Weaver et al. 2006). During the discovery epoch, P1 had


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CONSTRAINTS ON ADDITIONAL PLUTONIAN SATELLITES

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Fig. 3.-- Detection efficiency as a function of STMAG magnitude for PSFs more than 500 from Pluto. Points on the graph represent the running average of the detection efficiency, in bins 0.5 mag in width centered on points spaced every 0.01 mag. A total of 400 synthetic PSFs, distributed randomly in the plane of the sky and uniformly in flux between magnitudes 25.5 and 29.5, were added to each of the four ACS WFC images per HST visit. Data from each visit were analyzed twice. The 90% and 50% levels of detection efficiency are marked by horizontal dotted lines. The 90% confidence magnitude limit is m lim;90% Ì 26:9, while the 50% confidence magnitude limit, i.e., the limiting magnitude as defined by Harris (1990), is m lim; 50% Ì 27:5. These magnitude limits use the STMAG magnitude system with the F606W passband. Magnitude limits transformed into the Johnson V passband are presented in Table 2.

nitude at which the detection efficiency drops below 50% ( Harris 1990), then the limiting magnitude of our search is mF606W Ì 26:9. Both Pluto and Charon are severely overexposed in the 475 s integrations. Scattered light from these objects significantly degrades the sensitivity of the ACS WFC satellite search within 500 (1:1 ; 105 km) of Pluto. Since the plate scale of the ACS HRC is roughly twice that of the ACS WFC (the ACS HRC plate scale is $0B025 pixelÐ1 vs. $0B049 pixelÐ1 for the ACS WFC), it is less severely affected by scattered light from Pluto and Charon, and so the 2006 February ACS HRC observations were used to search for potential satellites within 500 of Pluto. Between 100 and 300 (a projected distance of 2:3 ; 104 6:9 ; 104 km) the 90% confidence limiting magnitude is mF606W Ì 25:8 (mF606W Ì 27:0 for 50% confidence), while between 300 and 500 (6:9 ; 104 1:1 ; 105 km) from Pluto the 90% confidence limiting magnitude is mF606W Ì 26:5 (mF606W Ì 27:3 for 50% confidence). Between 0B3 and 100 (6:9 ; 103 2:3 ; 104 km) from Pluto the 90% confidence limiting magnitude is mF606W Ì 24. 4.1. Conversion of STMAG to V Magnitudes The above magnitude limits use the STMAG magnitude system with the ACS WFC and HRC F606W filters ( Koornneef et al. 1986). These can be converted into standard Johnson V magnitudes via the equation mV Ì mF606W ? c0 ? c1 (B Ð V ) ? c2 (B Ð V )2 Ð ZST ; ? 2î

an apparent magnitude of mV Ì 22:93 Ö 0:12 and P2 had an apparent magnitude of mV Ì 23:38 Ö 0:17 ( Weaver et al. 2006). Analysis of the discovery observations and archival HST observations yielded provisional orbits with semimajor axes of 64; 780Ö 88 km for P1 and 48; 675 Ö 121 km for P2 (Buie et al. 2006). The orbits of P1 and P2 are circular (or nearly so) and coplanar with Pluto's other large moon, Charon, implying that these moons share a giant impact origin (Stern et al. 2006b). This hypothesis is supported by the observation that P1 and P2 are essentially neutral in color with B Ð V values of 0:653 Ö 0:026 for P1 and 0:654 Ö 0:065 for P2 (Stern et al. 2006a). No other satellites were detected, out to the edge of Pluto's stability region. The efficiency of detecting the synthetic point sources planted in the ACS images is used to estimate the sensitivity of our search. The detection efficiency, as a function of PSF magnitude (in the F606W passband), is shown in Figure 3. Defining the limiting magnitude to be the level at which the detection efficiency drops to 90%, we find that the limiting magnitude, in the ACS WFC F606W passband and using the STMAG magnitude system ( Koornneef et al. 1986), of our search is mF606W Ì 27:5. If we adopt a less stringent definition of limiting magnitude as the mag-

where mF606W is the magnitude in the F606W passband using the STMAG system and B Ð V is the object's color in the Johnson system. The coefficients c0 , c1 , and c2 , as well as the magnitude system zero point ZST, are given by Sirianni et al. (2005). Objects in the outer solar system exhibit a wide range of B Ð V colors, e.g., B Ð V Ì 0:65 for P1 and P2 (Stern et al. 2006a), and B Ð V Ì 1:23 for 5145 Pholus ( Barucci et al. 2005). Since all three of Pluto's known satellites exhibit roughly neutral colors (Charon has a B Ð V of 0.71 [ Buie et al. 1997] compared with the solar B Ð V color of 0.67 [ Hardorp 1980]) it is reasonable to assume that any as yet undetected satellites of Pluto would have B Ð V % 0:7. Substituting the appropriate values into equation (2), we find mV Ð mF606W Ì Ð0:096 for the ACS WFC and mV Ð mF606W ÌÐ0:092 for the ACS HRC. If instead the undetected satellites have extremely red B Ð V colors (i.e., similar to 5145 Pholus), then mV would be %0.2 mag fainter. The limiting magnitudes of the satellite search, converted into Johnson V magnitudes, are given in Table 2. 4.2. Limiting Satellite Diameter Once a limiting magnitude has been determined, the diameter in kilometers of a spherical satellite, in the absence of significant

TABLE 2 Limits on Additional Sate ll ites Angular Separation from Pluto Quantity Projected distance ( km) ................................................... 50% confidence limit V mag. .......................................... 90% confidence limit V mag. .......................................... Max. diameter ( km)a ( V Ì 0:38) .................................. Max. diameter ( km)a ( V Ì 0:04) ..................................
a

0B3-100 6.9 ; 103 -2.3 ; 104 24 37 115

100 -300 2.3 ; 104 -6.9 ; 104 26.9 25.7 16.0 49.4

300 -500 6.9 ; 104 -1.1 ; 105 27.2 26.4 11.7 36.1

>500 >1.1 ; 105 27.4 26.8 9.3 28.6

Maximum satellite diameters calculated using eq. (3) and 90% confidence limiting magnitudes, assuming spherical satellites and no limb darkening.


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limb darkening, can be derived via the following equation ( Russell 1916 ): d Ì 2:99 ; 108 rÑp
Ð1=2 V

10(

m ÐmV ? )=5

;

? 3î

where r and Ñ are the distances from Pluto to the Sun and Pluto to the Earth, respectively, in units of AU, pV is the geometric visual albedo, m Ì Ð26:75 is the V magnitude of the Sun at a distance of 1 AU (Colina et al. 1996),  is the phase law (in mag degÐ1), and is the phase angle of the object (i.e., the Sun-objectobserver angle). We assume the phase law for potential satellites to be identical to that for Charon, i.e.,  Ì 0:0866 Ö 0:0078 mag degÐ1 ( Buie et al. 1997). Thus, assuming a very dark albedo of pV Ì 0:04, comparable to cometary nuclei (Lamy et al. 2004), we can rule out, at the 90% level of confidence, the existence of additional satellites in the Pluto system larger than 49.4 km in diameter over the span of separations from Pluto of 100 -300 , 36.1 km over the span of 300 -500 , and 28.6 km in diameter at separations of more than 500 from Pluto. If instead we assume that potential satellites are as reflective as Charon, i.e., having pV Ì 0:38 ( Buie et al. 1997 ), then we can rule out satellites in these three regions larger than 16.0, 11.7, and 9.3 km in diameter, respectively. Within 100 of Pluto, the limiting diameters are 115 km for an albedo of pV Ì 0:04 and 37 km for an albedo of pV Ì 0:38. Our limiting diameters in this region are comparable to the limits obtained by Stern et al. (1994) using dynamical arguments and an assumed orbital eccentricity of Charon of 10Ð4, which is reasonable given the uncertainty of 7 ; 10Ð5 in the recently published finding of zero eccentricity in the orbit of Charon ( Buie et al. 2006 ). These results are summarized in Table 2, and the limiting diameter for Plutonian satellites for the four regions, as a function of satellite albedo, is shown in Figure 4. The above discussion has assumed a zero-amplitude light curve for potential satellites. While Charon exhibits a relatively small light-curve amplitude (defined as the difference between maximum and minimum magnitude and not the absolute deviation from the mean) of only 0.08 mag in V ( Buie et al. 1997 ), other Kuiper Belt objects (KBOs) exhibit much larger lightcurve effects (Trilling & Bernstein 2006). An extreme example is the KBO 2001 QG298, which exhibits a light curve with an amplitude of 1.14 mag in R (Sheppard & Jewitt 2004). If an object with a similarly extreme light curve exists within the Pluto system and was at the minimum of its light curve during the ACS WFC (if the object is located more than 500 from Pluto) or ACS HRC visits (if the object is within 500 of Pluto), it could have escaped detection, although its peak brightness would be nearly 3 times greater than the upper limits quoted above. In this pathological case, the length of the satellite in two dimensions

Fig. 4.-- Maximum diameter of undiscovered satellites of Pluto as a function of geometric albedo, assuming a light-curve amplitude of zero and a limiting magnitude defined by the 90% detection efficiency criterion. Circles mark the locations of pV Ì 0:04 (comet-like albedo) and pV Ì 0:38 (Charon-like albedo).

could be as large as the limiting diameters quoted above, while the length in the third dimension could be up to a factor of 3 greater. The effective diameter of such a cigar-shaped satellite would be approximately 44% greater than the above size limits. The 90% confidence limit of mV Ì 25:7 at separations greater than 100 from Pluto places an upper limit of roughly 49 km on the diameter of undetected satellites in this region. Assuming bulk properties (albedo, light curve, phase effect, density, etc.) similar to Pluto's smallest known moon, P2, potential undetected satellites in this region must be less than 40% the size of P2 with a mass 2.5% that of P2. Such a small satellite would be unable to strongly perturb the orbits of either P1 or P2, and therefore the proposed circular, or near-circular, orbits of P1 and P2 ( Weaver et al. 2006; Buie et al. 2006) do not necessarily preclude the existence of other very small satellites in the Pluto system. Finally, we note that both P1 and P2 appear to be in, or near, meanmotion resonance with Charon, and therefore, we suggest that satellites below the detection limit of our search may occupy the other mean-motion resonances. We suggest further observations with greater sensitivity to investigate this possibility.

Financial support for this work was provided by the New Horizons Pluto - Kuiper Belt mission. Additional support was provided by NASA through grants GO-10427 and GO-10774 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.

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