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From 31 Earth-based and three Voyager 2 occultations spanning 1977--2006, we determine the orbital elements of the nine main Uranian rings with typical RMS residuals of 0.2 -- 0.4 km and 1-$\sigma$ errors in $a, ae,$ and $a\sin i$ of order 0.1 km, registered on an absolute radius scale accurate to 0.2 km at the 2-$\sigma$ level. The $\lambda$ ring shows more substantial scatter. In addition to the free modes $m=0$ in the $\gamma$ ring and $m=2$ in the $\delta$ ring, we find two additional outer Lindblad resonance (OLR) modes ($m=-1$ and $-2$) and a possible $m=3$ inner Lindblad resonance (ILR) mode in the $\gamma$ ring. No normal modes are detected for rings 6, 5, 4, $\alpha$, or $\beta$. Five normal modes are forced by small moonlets: the 3:2 inner ILR of Cressida with the $\eta$ ring, the 6:5 ILR of Ophelia with the $\gamma$ ring, the 23:22 ILR of Cordelia with the $\delta$ ring, the 14:13 ILR of Ophelia with the outer edge of the $\epsilon$ ring, and the counterpart 25:24 OLR of Cordelia with the ring's inner edge. We determine the width-radius relations for nearly all of the detected mode. We find no convincing evidence for librations of any of the rings. The Uranus pole direction at epoch TDB 1986 Jan 19 12:00 is $\alpha_P=77.311327\pm 0.000141^\circ$ and $\delta_P=15.172795\pm0.000618^\circ$. We determine the zonal gravitational coefficients $J_2=(3509.291\pm0.412)\times 10^{-6}, J_4=(-35.522\pm0.466)\times10^{-6}$, and $J_6$ fixed at $0.5\times 10^{-6}$, with a correlation coefficient $\rho(J_2,J_4)=0.9861$, for a reference radius $R=$25559 km. From the amplitudes and resonance radii of normal modes forced by moonlets, we determine the masses of Cressida, Cordelia, and Ophelia. Their estimated densities decrease systematically with increasing orbital radius and generally follow the radial trend of the Roche critical density for a shape parameter $\gamma=1.6$., Comment: 94 pages, 53 figures

Planet-planet scattering best explains the eccentricity distribution of extrasolar giant planets. Past literature showed that the orbits of planets evolve due to planet-planet scattering. This work studies the spin evolution of planets in planet-planet scattering in 2-planet systems. Spin can evolve dramatically due to spin-orbit coupling made possible by the evolving spin and orbital precession during the planet-planet scattering phase. The main source of torque to planet spin is the stellar torque, and the total planet-plane torque contribution is negligible. As a consequence of the evolution of the spin, planets can end up with significant obliquity (the angle between a planet's own orbit normal and spin axis) like planets in our Solar System., Comment: 7 pages, 9 figures

The innovative Saturn Ring Skimmer mission concept enables a wide range of investigations that address fundamental questions about Saturn and its rings, as well as giant planets and astrophysical disk systems in general. This mission would provide new insights into the dynamical processes that operate in astrophysical disk systems by observing individual particles in Saturn's rings for the first time. The Ring Skimmer would also constrain the origin, history, and fate of Saturn's rings by determining their compositional evolution and material transport rates. In addition, the Ring Skimmer would reveal how the rings, magnetosphere, and planet operate as an inter-connected system by making direct measurements of the ring's atmosphere, Saturn's inner magnetosphere and the material owing from the rings into the planet. At the same time, this mission would clarify the dynamical processes operating in the planet's visible atmosphere and deep interior by making extensive high-resolution observations of cloud features and repeated measurements of the planet's extremely dynamic gravitational field. Given the scientific potential of this basic mission concept, we advocate that it be studied in depth as a potential option for the New Frontiers program., Comment: White paper submitted to the Planetary Science and Astrobiology Decadal Survey (submission #420)

We have analyzed the complete Visual and Infrared Mapping Spectrometer (VIMS) data archive of Titan. Our objective is to build global surface cartographic products, by combining all the data gathered during the 127 targeted flybys of Titan into synthetic global maps interpolated on a grid at 32 pixels per degree (~1.4 km/pixel at the equator), in seven infrared spectral atmospheric windows. Multispectral summary images have been computed for each single VIMS cube in order to rapidly identify their scientific content and assess their quality. These summary images are made available to the community on a public website (vims.univ-nantes.fr). The global mapping work faced several challenges due to the strong absorbing and scattering effects of the atmosphere coupled to the changing observing conditions linked to the orbital tour of the Cassini mission. We determined a surface photometric function which accounts for variations in incidence, emergence and phase angles, and which is able to mitigate brightness variations linked to the viewing geometry of the flybys. The atmospheric contribution has been reduced using the subtraction of the methane absorption band wings, considered as proxies for atmospheric haze scattering. We present a new global three color composite map of band ratios (red: 1.59/1.27 {\mu}m; green: 2.03/1.27 {\mu}m; blue: 1.27/1.08 {\mu}m), which has also been empirically corrected from an airmass (the solar photon path length through the atmosphere) dependence. This map provides a detailed global color view of Titan's surface partially corrected from the atmosphere and gives a global insight of the spectral variability, with the equatorial dunes fields appearing in brownish tones, and several occurrences of bluish tones localized in areas such as Sinlap, Menvra and Selk craters. (...)

We have analyzed the complete archive of the Visual and Infrared Mapping Spectrometer (VIMS) data in order to monitor and analyze the evolution of the clouds and haze coverage at both poles of Titan during the entire Cassini mission. Our objective is to give a cartographic synopsis from a VIMS perspective, to provide a global view of the seasonal evolution of Titan's atmosphere over the poles. We leave the detailed comparison with the Imaging Science Subsystem (ISS) and the Composite Infrared Spectrometer (CIRS) data sets to further studies. We have computed global hyperspectral mosaics for each of the 127 targeted flybys of Titan to produce synthetic color maps emphasizing the main atmospheric features. The north pole appears fully covered by a huge cloud as soon as the first observations in 2004 and up to the equinox in 2009 (Le Mou\'elic et al. 2012). The northern skies then became progressively clearer, after the circulation turnover in 2009, revealing the underlying lakes and seas to the optical instruments up to 2017. The reverse situation is observed over the south pole, which was mostly clear of such a high obscuring cloud during the first years of the mission, but started to develop a polar cloud in 2012. This feature grew up month after month until the end of the mission in 2017, with a poleward latitudinal extent of 75$^\circ$S in 2013 up to 58$^\circ$S in April 2017. Thanks to the spectral capabilities of VIMS, we have detected HCN spectral signatures over the north pole in almost all flybys between 2004 and 2008. These HCN signatures started then to show up over the south pole in almost all flybys between 2012 and 2017, so perfectly matching the timing and spatial extent of the northern and southern polar atmospheric features.

Planet-planet scattering is the leading mechanism to explain the broad eccentricity distribution of observed giant exoplanets. Here we study the orbital stability of primordial giant planet moons in this scenario. We use N-body simulations including realistic oblateness and evolving spin evolution for the giant planets. We find that the vast majority (80-90% across all our simulations) of orbital parameter space for moons is destabilized. There is a strong radial dependence, as moons past 0.1 Hill radii are systematically removed. Closer-in moons on Galilean-moon-like orbits (< 0.04 Hill radii) have a good ( 20-40%) chance of survival. Destabilized moons may undergo a collision with the star or a planet, be ejected from the system, be captured by another planet, be ejected but still orbiting its free-floating host planet, or survive on heliocentric orbits as "planets." The survival rate of moons increases with the host planet mass but is independent of the planet's final (post-scattering) orbits. Based on our simulations we predict the existence of an abundant galactic population of free- floating (former) moons., Comment: 15 pages, 9 figures, 1 table, accepted for publication in ApJ

The viscous spreading of planetary rings is believed to be counteracted by satellite torques, either through an individual resonance or through overlapping resonances. For the A ring of Saturn, it has been commonly believed that the satellite Janus alone can prevent the ring from spreading via its 7:6 Lindblad resonance. We discuss this common misconception and show that, in reality, the A ring is confined by the contributions from the group of satellites Pan, Atlas, Prometheus, Pandora, Janus, Epimetheus, and Mimas, whose cumulative torques from various resonances gradually decrease the angular momentum flux transported outward through the ring via density and bending waves. We further argue that this decrease in angular momentum flux occurs through 'flux reversal'. Furthermore, we use the magnitude of the satellites' resonance torques to estimate the effective viscosity profile across the A ring, showing that it decreases with radius from ~50 cm2 s-1 to less than ~10 cm2 s-1. The gradual estimated decrease of the angular momentum flux and effective viscosity are roughly consistent with results obtained by balancing the shepherding torques from Pan and Daphnis with the viscous torque at the edges of the Encke and Keeler gaps, as well as the edge of the A ring. On the other hand, the Mimas 2:1 Lindblad resonance alone seems to be capable of confining the edge of the B ring, and contrary to the situation in the A ring, we show that the effective viscosity across the B ring is relatively constant at ~24-30 cm2 s-1., Comment: 38 pages, 3 figures

We analyze several thousand Cassini ISS images in order to study the inner edge of the Keeler gap in Saturn's outer A ring. We find strong evidence for an m=32 perturbation with a mean amplitude of radial variation of 4.5 km. Phase analysis yields a pattern speed consistent with the mean motion of Prometheus, indicating that this pattern is generated by the 32:31 Inner Lindblad resonance with Prometheus. In addition, we find evidence of 18-lobed and 20-lobed patterns with amplitudes of ~1.5 km. These patterns, whose rotation rates correspond to resonance locations ~4 km interior to the gap edge, are believed to be normal modes. The former is probably related to the nearby 18:17 (m=18) resonance with Pandora. In addition to these resonant and normal mode patterns, we also observe multiple localized features that appear to move at the local keplerian rate and that persist for only a few months. One hypothesis is that different groups of ring particles at the inner edge of the gap may be reacting differently to the resonance with Prometheus, with local variations in the forced eccentricity and/or pericenter; an alternative hypothesis is the existence of several unseen objects embedded at or near the inner edge of the Keeler gap, similar to those suspected to exist at the outer edges of the A and B rings (Spitale and Porco 2009, 2010). In either case, observations of the ring edge at opposite ansae demonstrate that the localized features must be on eccentric orbits.

We present the Cassini Atlas Of Stellar Spectra (CAOSS), comprised of near-infrared low-resolution spectra of bright stars recovered from space-based observations by the Cassini spacecraft. The 65 stellar targets in the atlas are predominately M, K and S giants. However it also contains spectra of other bright nearby stars including carbon stars and main sequence stars from A to F. The spectra presented are free of all spectral contamination caused by the Earth's atmosphere, including the detrimental telluric molecular bands which put parts of the near-infrared spectrum out of reach of terrestrial observations. With a single instrument, a spectro-photometric dataset is recovered that spans the near-infrared from 0.8 to 5.1 microns with spectral resolution ranging from R=53.5 to R=325. Spectra have been calibrated into absolute flux units after careful characterisation of the instrumental spectral efficiency. Spectral energy distributions for most stars match closely with literature values. All final data products have been made available online., Comment: 10 emulateapj pages, 4 figures, 4 tables. Accepted by ApJS. Full atlas available at http://www.physics.usyd.edu.au/sifa/caoss/

We use solar occultations observed by the Visual and Infrared Mapping Spectrometer aboard the Cassini Spacecraft to extract the 1 to 5 micron transmission spectrum of Saturn, as if it were a transiting exoplanet. We detect absorption from methane, ethane, acetylene, aliphatic hydrocarbons, and possibly carbon monoxide with peak-to-peak features of up to 90 parts-per-million despite the presence of ammonia clouds. We also find that atmospheric refraction, as opposed to clouds or haze, determines the minimum altitude that could be probed during mid-transit. Self-consistent exoplanet atmosphere models show good agreement with Saturn's transmission spectrum but fail to reproduce a large absorption feature near 3.4 microns likely caused by gaseous ethane and a C-H stretching mode of an unknown aliphatic hydrocarbon. This large feature is located in one of the Spitzer Space Telescope bandpasses and could alter interpretations of transmission spectra if not properly modeled. The large signal in Saturn's transmission spectrum suggests that transmission spectroscopy of cold, long-period gaseous exoplanets should be possible with current and future observatories. Motivated by these results, we briefly consider the feasibility of a survey to search for and characterize cold exoplanets analogous to Jupiter and Saturn using a target-of-opportunity approach., Comment: 15 pages, 9 figures. Accepted to ApJ. Data available in the source files

We present a study of the behavior of Saturn's A ring outer edge, using images and occultation data obtained by the Cassini spacecraft over a period of 8 years from 2006 to 2014. More than 5000 images and 170 occultations of the A ring outer edge are analyzed. Our fits confirm the expected response to the Janus 7:6 Inner Lindblad resonance (ILR) between 2006 and 2010, when Janus was on the inner leg of its regular orbit swap with Epimetheus. During this period, the edge exhibits a regular 7-lobed pattern with an amplitude of 12.8 km and one minimum aligned with the orbital longitude of Janus, as has been found by previous investigators. However, between 2010 and 2014, the Janus/Epimetheus orbit swap moves the Janus 7:6 LR away from the A ring outer edge, and the 7-lobed pattern disappears. In addition to several smaller-amplitudes modes, indeed, we found a variety of pattern speeds with different azimuthal wave numbers, and many of them may arise from resonant cavities between the ILR and the ring edge; also we found some other signatures consistent with tesseral resonances that could be associated with inhomogeneities in Saturn's gravity field. Moreover, these signatures do not have a fixed pattern speed. We present an analysis of these data and suggest a possible dynamical model for the behavior of the A ring's outer edge after 2010.

The spatial distribution of the tropospheric methane on Titan was measured using near-infrared spectroscopy. Ground-based observations at 1.5$\mu{\rm m}$ (H-band) were performed during the same night using instruments with adaptive optics at both the W. M. Keck Observatory and at the Paranal Observatory on 17 July 2014 UT. The integral field observations with SINFONI on the VLT covered the entire H-band at moderate resolving power, $R=\lambda/\Delta\lambda\approx1,500$, while the Keck observations were performed with NIRSPAO near 1.55254$\mu{\rm m}$ at higher resolution, $R\approx25,000$. The moderate resolution observations are used for flux calibration and for the determination of model parameters that can be degenerate in the interpretation of high resolution spectra. Line-by-line calculations of CH$_4$ and CH$_3$D correlated $k$ distributions from the HITRAN 2012 database were used, which incorporate revised line assignments near 1.5$\mu{\rm m}$. We fit the surface albedo and aerosol distributions in the VLT SINFONI observations that cover the entire H-band window and used these quantities to constrain the models of the high-resolution Keck NIRSPAO spectra when retrieving the methane abundances. Cassini VIMS images of the polar regions, acquired on 20 July 2014 UT, are used to validate the assumption that the opacity of tropospheric aerosol is relatively uniform below 10 km. We retrieved methane abundances at latitudes between 42$^{\circ}$ S and 80$^{\circ}$ N. The tropospheric methane in the Southern mid-latitudes was enhanced by a factor of $\sim$10--40% over the nominal profile that was measured using the GCMS on Huygens. The Northern hemisphere had $\sim$90% of the nominal methane abundance up to polar latitudes (80$^{\circ}$N). These measurements suggest that a source of saturated polar air is equilibrating with dryer conditions at lower latitudes., Comment: Accepted for publication in Icarus on May 22, 2015

We present an advance in the use of Cassini observations of stellar occultations by the rings of Saturn for stellar studies. Stewart et al. (2013) demonstrated the potential use of such observations for measuring stellar angular diameters. Here, we use these same observations, and tomographic imaging reconstruction techniques, to produce two dimensional images of complex stellar systems. We detail the determination of the basic observational reference frame. A technique for recovering model-independent brightness profiles for data from each occulting edge is discussed, along with the tomographic combination of these profiles to build an image of the source star. Finally we demonstrate the technique with recovered images of the {\alpha} Centauri binary system and the circumstellar environment of the evolved late-type giant star, Mira., Comment: 8 pages, 8 figures, Accepted by MNRAS

This work shows the dynamical instability that can happen to close-in satellites when planet oblateness is not accounted for in non-coplanar multiplanet systems. Simulations include two secularly interacting Jupiter-mass planets mutually inclined by 10 degrees, with the host planet either oblate or spherical. With a spherical host planet, moons within a critical planetocentric distance experience high inclinations and in some cases high eccentricities, while more distant moons orbit stably with low inclinations and eccentricities, as expected. These counter-intuitive dynamical phenomena disappear with an oblate host planet, in which case the moons' Laplace plane transitions from the host planet's equatorial plane to the host planet's precessing orbital plane as their semi-major axes increase, and all moons are dynamically stable with very mild changes in orbits. Direct perturbation from the perturbing planet has been investigated and ruled out as an explanation for the behavior of the innermost satellites, therefore leaving the central star's perturbation as the cause. Instability occurs while the nodal precession of the satellite and the central star (as seen from the host planet's frame) approaches the 1:1 secular resonance. In non-coplanar systems, around a non-oblate planet, the nodal precession of the moon becomes slow and comparable to that of the planet, giving rise to resonant configurations. The above effect needs to be taken into account in setting up numerical simulations., Comment: 7 pages, 6 figures. Accepted for publication in MNRAS

Image photometry reveals that the F ring is approximately twice as bright during the Cassini tour as it was during the Voyager flybys of 1980 and 1981. It is also three times as wide and has a higher integrated optical depth. We have performed photometric measurements of more than 4,800 images of Saturn's F ring taken over a five-year period with Cassini's Narrow Angle Camera. We show that the ring is not optically thin in many observing geometries and apply a photometric model based on single-scattering in the presence of shadowing and obscuration, deriving a mean effective optical depth tau = 0.033. Stellar occultation data from Voyager PPS and Cassini VIMS validate both the optical depth and the width measurements. In contrast to this decades-scale change, the baseline properties of the F ring have not changed significantly from 2004 to 2009. However, we have investigated one major, bright feature that appeared in the ring in late 2006. This transient feature increased the ring's overall mean brightness by 84% and decayed with a half-life of 91 days., Comment: 27 pages, 12 figures, 2 tables

The James Webb Space Telescope (JWST) will provide unprecedented opportunities to observe the rings and small satellites in our solar system, accomplishing three primary objectives: 1) discovering new rings and moons, 2) unprecedented spectroscopy, and 3) time-domain observations. We give details on these science objectives and describe requirements that JWST must fulfill in order to accomplish the science objectives, Comment: 14 pages, 5 figures; Accepted by Publications of the Astronomical Society of the Pacific. arXiv admin note: text overlap with arXiv:1403.6845

Radio occultations of Saturn's main rings by spacecraft suggest a power law particle size-distribution down to sizes of the order of 1 cm (Marouf et al., 1983), (Zebker et al., 1985). The lack of optical depth variations between ultraviolet and near-IR wavelengths indicate a lack of micron-sized particles. Between these two regimes, the particle-size distribution is largely unknown. A cutoff where the particle-size distribution turns over must exist, but the position and shape of it is not clear from existing studies. Using a series of solar occultations performed by the VIMS instrument on-board Cassini in the near-infrared, we are able to measure light forward scattered by particles in the A and C rings. With a model of diffraction by ring particles, and the previous radio work as a constraint on the slope of the particle size distribution, we estimate the minimum particle size using a truncated power-law size distribution. The C Ring shows a minimum particle size of $4.1^{+3.8}_{-1.3}$ mm, with an assumed power law index of q=3.1 and a maximum particle size of 10 m. The A Ring signal shows a similar level of scattered flux, but modeling is complicated by the presence of self-gravity wakes and higher optical depths. If q<3, our A Ring model requires a minimum particle size below one millimeter (< 0.34 mm for an assumed q=2.75, or $0.56^{+0.35}_{-0.16}$ mm for a steeper q=2.9) to be consistent with VIMS observations. These results might seem to contradict previous optical(Dones et al., 1993) and infrared (French and Nicholson, 2000) work, which implied that there were few particles in the A Ring smaller than 1 cm. But, because of the shallow power law, relatively little optical depth (between 0.03 and 0.16 in extinction, or 0.015 - 0.08 in absorption) is provided by these particles., Comment: 47 pages, 16 figures, 3 Tables

We present a photometric model of the rings of Saturn which includes the main rings and an F ring, inclined to the main rings, with a Gaussian vertical profile of optical depth. This model reproduces the asymmetry in brightness between the east and west ansae of the rings of Saturn that was observed by the Hubble Space Telescope (HST) within a few hours after the Earth ring-plane crossing (RPX) of 10 August 1995. The model shows that during this observation the inclined F ring unevenly blocked the east and west ansae of the main rings. The brightness asymmetry produced by the model is highly sensitive to the vertical thickness and radial optical depth of the F ring. The F ring model that best matches the observations has a vertical full width at half maximum of 13 +/- 7 km and an equivalent depth of 10 +/- 4 km. The model also reproduces the shape of the HST profiles of ring brightness vs. distance from Saturn, both before and after the time of ring-plane crossing. Smaller asymmetries observed before the RPX, when the Earth was on the dark side of the rings, cannot be explained by blocking of the main rings by the F ring or vice versa and are probably instead due to the intrinsic longitudinal variation exhibited by the F ring., Comment: 36 pages, 13 figures

We present novel observations utilising the Cassini spacecraft to conduct an observing campaign for stellar astronomy from a vantage point in the outer solar system. By exploiting occultation events in which Mira passed behind the Saturnian ring plane as viewed by Cassini, parametric imaging data were recovered spanning the near-infrared. From this, spatial information at extremely high angular resolution was recovered enabling a study of the stellar atmospheric extension across a spectral bandpass spanning the 1 - 5 {\mu}m spectral region in the near-infrared. The resulting measurements of the angular diameter of Mira were found to be consistent with existing observations of its variation in size with wavelength. The present study illustrates the validity of the technique; more detailed exploration of the stellar physics obtained by this novel experiment will be the subject of forthcoming papers., Comment: 9 pages, 6 figures

High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations---large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 degrees, orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68.875 degrees. Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. We find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this is occurs because radiation pressure modifies the equilibrium Laplace plane., Comment: 39 pages, 9 figures. Accepted for publication in AJ

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r~118,800 km, 4.5 m at r~120,700 km) and the inner A Ring (10 to 15 m for r<127,000 km)., Comment: 43 pages, 21 figures; To appear in Icarus

We describe a model that accounts for the complex morphology of spiral density waves raised in Saturn's rings by the co-orbital satellites, Janus and Epimetheus. Our model may be corroborated by future Cassini observations of these time-variable wave patterns., Comment: 9 pages, 5 figures; In press at Astrophysical Journal Letters

We have conducted pencil-beam searches for outer solar system objects to a limiting magnitude of R ~ 26. Five new trans-neptunian objects were detected in these searches. Our combined data set provides an estimate of ~90 trans-neptunian objects per square degree brighter than ~ 25.9. This estimate is a factor of 3 above the expected number of objects based on an extrapolation of previous surveys with brighter limits, and appears consistent with the hypothesis of a single power-law luminosity function for the entire trans-neptunian region. Maximum likelihood fits to all self-consistent published surveys with published efficiency functions predicts a cumulative sky density Sigma(