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 UT 2005 May 18. Two small satellites of Pluto, provisionally designated S/2005 P 1 and S/2005 P 2, were discovered, as discussed by Weaver et al. (2006) and Stern et al. (2006a). Confirming observations of the newly discovered moons were obtained using the ACS in the High Resolution Channel (HRC) mode on 2006 Feb 15 (Mutchler et al. 2006). Both sets of observations provide strong constraints on the existence of any additional satellites in the Pluto system. Based on the May 2005 observations using the ACS/WFC, we place a 90%-confidence lower limit of m_V = 26.8 (m_V = 27.4 for a 50%-confidence lower limit) on the magnitude of undiscovered satellites greater than 5 (1.1x10^5 km) from Pluto. Using the 2005 Feb 15 ACS/HRC observations we place 90%-confidence lower limits on the apparent magnitude of any additional satellites of m_V = 26.4 between 3-5 (6.9x10^4-1.1x10^5 km) from Pluto, m_V = 25.7 between 1-3 (2.3x10^4-6.9x10^4 km) from Pluto, and m_V = 24. between 0.3-1 (6.9x10^3-2.3x10^4 km) from Pluto. The 90%-confidence magnitude limits translate into upper limits on the diameters of undiscovered satellites of 29 km outside of 5 from Pluto, 36 km between 3-5 from Pluto, 49 km between 1-3 from Pluto, and 115 km between 0.3-1 for a comet-like albedo of p_V = 0.04. If potential satellites are assumed to have a Charon-like albedo of p_V = 0.38, the diameter limits are 9 km, 12 km, 16 km, and 37 km, respectively.
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