Keck NIRC2 photometry of Uranus, uranian satellites, and Triton in August 2004

On August 11, 2004, we made adaptive optics observations of the Uranus and Neptune systems with the Keck II Near Infrared Camera. Uranus and Triton were observed in three broadband filters (J, H, and K-prime) and four narrowband filters [Hcont, FeII, He1_B, and H2(v=1-0)]. Miranda, Ariel, Umbriel, and Oberon were observed in the four narrowband filters only. To achieve the highest possible photometric accuracy, and thus the tightest possible constraints on atmospheric aerosol models and gas mixing ratios, we used aperture photometry that accounted for the dependence of point-spread functions and growth curves on the adaptive optics reference object, and accounted for recently determined phase curves of each object. The satellite albedos we determined were compared with published relative spectra to verify the relative consistency of our observations, which were subsequently used to convert published relative spectra to absolute spectra. We used these absolute spectra and synthetic photometry methods to compare published values in dissimilar photometric systems to each other and to our observations. We find our satellite albedos in best agreement with photometry from Karkoschka [Karkoschka, E., 2001. Icarus 151, 51-68], which is the best characterized and most contemporaneous data set. Our estimated absolute accuracy of 5% to 8% is consistent with these intercomparisons. We obtained the following ring-subtracted and discrete feature-free albedos of Uranus: J: (1.66±0.07)×¹⁰⁻², H: (1.09±0.05)×¹⁰⁻², K^′: (2.08±0.15)×¹⁰⁻⁴, Hcont: (3.71±0.23)×¹⁰⁻², FeII: (1.14±0.07)×¹⁰⁻³, He1_B: (2.06±0.16)×¹⁰⁻⁴, and H2: (1.27±0.10)×¹⁰⁻⁴.     

Photometric variability of Uranus and Neptune, 1950-2004

Photoelectric intermediate-band b and y photometry of Uranus and Neptune obtained at each apparition since 1972, combined with broadband B and V photometry from 1950 to 1966, provide a record of planetary variability covering 2/3 of Uranus' 84-year orbital period and 1/3 of Neptune's 165-year orbital period. Almost all of the data were obtained with a dedicated 21-inch photometric telescope at Lowell Observatory. The data are quite homogeneous, with yearly uncertainties typically smaller than 0.01 mag (1%). The lightcurve of Uranus is sinusoidal with peaks at the solstices. The b amplitude slightly exceeds the expected 0.025 mag purely geometrical variation caused by oblateness as the planetary aspect changes, seen from Earth. The y amplitude is several times larger, indicating a strong equator-to-pole albedo gradient. The lightcurve is asymmetrical with respect to southern solstice, evidence of a temporal albedo variation. Neptune's post-1972 lightcurve exhibits a generally rising trend since 1972 interpreted by Sromovsky et al. [Sromovsky, L.A., Fry, P.M., Limaye, S.S., Baines, K.H., 2003. Icarus 163, 256-261] as a lagged sinusoidal seasonal variation. However, the 1950-1966 lightcurve segments are much fainter than expected, missing the proposed seasonal sinusoid by 0.1-0.2 mag. A major unknown component is therefore needed to explain Neptune's long-term variation. The apparent relationship between Neptune's brightness variation and the 11-year solar cycle seen in cycles 21-22 (1972-1996) has apparently now faded away. Further interpretation of the data in this paper will be found in a companion paper by Hammel and Lockwood [Hammel, H.B., Lockwood, G.W., 2005. Icarus. Submitted for publication].     

Dynamical objectives of observation of mutual events

Recently the motion of the main satellites of Jupiter, Saturn and Uranus have been modelled in order to get accurate ephemerides. These models have been fitted over a large amount of observations. Among these ones, the positions issued from the observations of mutual events are the most accurate. We can then expect to obtain a new kind of dynamical informations directly linked to planetological questions. We have to determine what information is used in these observations to get the still unknown dynamical parameters. We look after these questions especially in the Jovian and Saturnian systems.     

Detecting the signatures of Uranus and Neptune

With more than 15 years since the first radial velocity discovery of a planet orbiting a Sun-like star, the time baseline for radial velocity surveys is now extending out beyond the orbit of Jupiter analogs. The sensitivity to exoplanet orbital periods beyond that of Saturn orbital radii however is still beyond our reach such that very few clues regarding the prevalence of ice giants orbiting solar analogs are available to us. Here we simulate the radial velocity, transit, and photometric phase amplitude signatures of the Solar System giant planets, in particular Uranus and Neptune, and assess their detectability. We scale these results for application to monitoring low-mass stars and compare the relative detection prospects with other potential methods, such as astrometry and imaging. These results quantitatively show how many of the existing techniques are suitable for the detection of ice giants beyond the snow line for late-type stars and the challenges that lie ahead for the detection true Uranus/Neptune analogs around solar-type stars.     

Near-infrared adaptive optics imaging of the satellites and individual rings of Uranus

We present the first Earth-based images of several of the individual faint rings of Uranus, as observed with the adaptive optics system on the W.M. Keck II telescope on four consecutive days in October 2003. We derive reflectivities based on multiple measurements of 8 minor moons of Uranus as well as Ariel and Miranda in filters centered at wavelengths of 1.25(J), 1.63(H), and 2.1(Kp) μm. These observations have a phase angle of 1.84°-1.96°. We find that the small satellites are somewhat less bright than in observations made by the HST at smaller phase angles, confirming an opposition surge effect. We calculate albedoes for the ring groups and for each ring separately. We find that the ε ring particles, as well as the particles in the three other ring groups, have albedoes near 0.043 at these phase angles. The equivalent depths of some of the individual rings are different than predicted based upon ring widths from occultation measurements (assuming a constant particle ring brightness); in particular the γ ring is fainter and the η ring brighter than expected. Our results indicate that q, the ratio of ε ring intensity at apoapse vs. periapse, is close to 3.2±0.16. This agrees well with a model that has a filling factor for the ε ring of 0.06 (Karkoschka, 2001, Icarus 151, 78-83). We also determine values of the north to south brightness ratio for the individual rings and find that in most cases they are close to unity.     

Models for planetary eclipses of the uranian satellites

A model for computing the brightness of a satellite in the shadow of a planet is described, which takes into account the Sun–planet–satellite–sensor geometry, the satellite bi-directional reflectance function, and the refraction of sunlight in the planetary atmosphere. Synthetic light curves for eclipse ingress or egress of the five large satellites of Uranus are generated. The model luminosities can be fitted to photometric observations in order to calculate a precise distance between the centers of the satellite and the planet. Alternately, when the satellite ephemeris is accurately known the atmospheric state of the planet can be studied.     

Near-IR methane absorption in outer planet atmospheres: Improved models of temperature dependence and implications for Uranus cloud structure

Near-IR absorption of methane in the 2000-9500 cm⁻¹ spectral region plays a major role in outer planet atmospheres. However, the theoretical basis for modeling the observations of reflectivity and emission in these regions has had serious uncertainties at temperatures needed for interpreting observations of the colder outer planets. A lack of line parameter information, including ground-state energies and the absence of weak lines, limit the applicability of line-by-line calculations at low temperatures and for long path lengths, requiring the use of band models. However, prior band models have parameterized the temperature dependence in a way that cannot be accurately extrapolated to low temperatures. Here we use simulations to show how a new parameterization of temperature dependence can greatly improve band model accuracy and allow extension of band models to the much lower temperatures that are needed to interpret observations of Uranus, Neptune, Titan, and Saturn. Use of this new parameterization by Irwin et al. [Irwin, P.G.J., Sromovsky, L.A., Strong, E.K., Sihra, K., Bowles, N., Calcutt, S.B., 2005b. Icarus. In press] has verified improved fits to laboratory observations of Strong et al. [Strong, K., Taylor, F.W., Calcutt, S.B., Remedios, J.J., Ballard, J., 1993. J. Quant. Spectrosc. Radiat. Trans. 50, 363-429] and Sihra [1998. Ph.D. Thesis, Univ. of Oxford], which cover the temperature range from 100 to 340 K. Here we compare model predictions to 77 K laboratory observations and to Uranus spectra, which show much improved agreement between observed and modeled spectral features, allowing tighter constraints on pressure levels of Uranus cloud particles, implying that most scattering contributions arise from pressures near 2 bars and 6 bars rather than expected pressures near 1.25 and 3.1 bars. Between visible and near-IR wavelengths, both cloud layers exhibit strong decreases in reflectivity that are indicative of low opacity and submicron particle sizes.     

Post-equinox observations of Uranus: Berg’s evolution, vertical structure, and track towards the equator

We present observations of Uranus taken with the near-infrared camera NIRC2 on the 10-m W.M. Keck II telescope, the Wide Field Planetary Camera 2 (WFPC2) and the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) from July 2007 through November 2009. In this paper we focus on a bright southern feature, referred to as the “Berg.” In Sromovsky et al. (Sromovsky, L.A., Fry, P.M., Hammel, H.B., Ahue, A.W., de Pater, I., Rages, K.A., Showalter, M.R., van Dam, M. [2009]. Icarus 203, 265-286), we reported that this feature, which oscillated between latitudes of −32° and −36° for several decades, suddenly started on a northward track in 2005. In this paper we show the complete record of observations of this feature’s track towards the equator, including its demise. After an initially slow linear drift, the feature’s drift rate accelerated at latitudes ∣θ∣ < 25°. By late 2009 the feature, very faint by then, was spotted at a latitude of −5° before disappearing from view. During its northward track, the feature’s morphology changed dramatically, and several small bright unresolved features were occasionally visible poleward of the main “streak.” These small features were sometimes visible at a wavelength of 2.2 μm, indicative that the clouds reached altitudes of ∼0.6 bar. The main part of the Berg, which is generally a long sometimes multipart streak, is estimated to be much deeper in the atmosphere, near 3.5 bars in 2004, but rising to 1.8-2.5 bars in 2007 after it began its northward drift. Through comparisons with Neptune’s Great Dark Spot and simulations of the latter, we discuss why the Berg may be tied to a vortex, an anticyclone deeper in the atmosphere that is visible only through orographic companion clouds.     

The Dark Spot in the atmosphere of Uranus in 2006: Discovery, description, and dynamical simulations

We report the first definitive detection of a discrete dark atmospheric feature on Uranus in 2006 using visible and near-infrared images from the Hubble Space Telescope and the Keck II 10-m telescope. Like Neptune's Great Dark Spots, this Uranus Dark Spot had bright companion features that exhibited considerable variability in brightness and location relative to the Dark Spot. We detected the feature or its bright companions on 16 June (Hubble), 30 July and 1 August (Keck), 23-24 August (Hubble), and 15 October (Keck). The dark feature—detected at latitude ∼28±1° N with an average physical extent of roughly 2° (1300 km) in latitude and 5° (2700 km) in longitude—moved with a nearly constant zonal velocity of , which is roughly 20 m s⁻¹ greater than the average observed speed of bright features at this latitude. The dark feature's contrast and extent varied as a function of wavelength, with largest negative contrast occurring at a surprisingly long wavelength when compared with Neptune's dark features: the Uranus feature was detected out to 1.6 μm with a contrast of −0.07, but it was undetectable at 0.467 μm; the Neptune GDS seen by Voyager exhibited its most prominent contrast of −0.12 at 0.48 μm, and was undetectable longward of 0.7 μm. Computational fluid dynamic simulations of the dark feature on Uranus suggest that structure in the zonal wind profile may be a critical factor in the emergence of large sustained vortices.     

Photometric and astrometric analysis of a mutual event between the Uranian satellites Miranda and Oberon

Observations of the predicted occultation between the satellites Miranda and Oberon were performed on 2007 July 30. Data analysis reveals that the predicted magnitude drop for this phenomenon was overestimated and we establish an upper limit of 0^m. 05 for the phenomenon, perhaps due to a non‐lambertian limb scattering. The new astrometry obtained from this run is in good agreement with the LA06 numerical model and these new data will improve the dynamical models of the Uranus system. The paper concludes with an uncertainty analysis on the parameters for the event, determined by the uncertainty of the magnitude drop of about 0.04 mag, and the difficulty to observe mutual phenomena between satellites in the Uranian system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The phase diagram of water and the magnetic fields of Uranus and Neptune

The interior of giant planets can give valuable information on formation and evolution processes of planetary systems. However, the interior and evolution of Uranus and Neptune is still largely unknown. In this paper, we compare water-rich three-layer structure models of these planets with predictions of shell structures derived from magnetic field models. Uranus and Neptune have unusual non-dipolar magnetic fields contrary to that of the Earth. Extensive three-dimensional simulations of Stanley and Bloxham (Stanley, S., Bloxham, J. [2004]. Nature 428, 151-153) have indicated that such a magnetic field is generated in a rather thin shell of at most 0.3 planetary radii located below the H/He rich outer envelope and a conducting core that is fluid but stably stratified. Interior models rely on equation of state data for the planetary materials which have usually considerable uncertainties in the high-pressure domain. We present interior models for Uranus and Neptune that are based on ab initio equation of state data for hydrogen, helium, and water as the representative of all heavier elements or ices. Based on a detailed high-pressure phase diagram of water we can specify the region where superionic water should occur in the inner envelope. This superionic region correlates well with the location of the stably-stratified region as found in the dynamo models. Hence we suggest a significant impact of the phase diagram of water on the generation of the magnetic fields in Uranus and Neptune.     

Vertical cloud structure of Uranus from UKIRT/UIST observations and changes seen during Uranus’ northern spring equinox from 2006 to 2008

Long-slit spectroscopy observations of Uranus by the United Kingdom Infrared Telescope UIST instrument in 2006, 2007 and 2008 have been used to monitor the change in Uranus’ vertical and latitudinal cloud structure through the planet’s northern spring equinox in December 2007.The observed reflectance spectra in the Long J (1.17-1.31 μm) and H (1.45-1.65 μm) bands, obtained with the slit aligned along Uranus’ central meridian, have been fitted with an optimal estimation retrieval model to determine the vertical cloud profile from 0.1 to 6-8 bar over a wide range of latitudes. Context images in a number of spectral bands were used to discriminate general zonal cloud structural changes from passing discrete clouds. From 2006 to 2007 reflection from deep clouds at pressures between 2 and 6-8 bar increased at all latitudes, although there is some systematic uncertainty in the absolute pressure levels resulting from extrapolating the methane coefficients of Irwin et al. (Irwin, P.G.J., Sromovsky, L.A., Strong, E.K., Sihra, K., Teanby, N.A., Bowles, N., Calcutt, S.B., Remedios, J.J. [2006] Icarus, 181, 309-319) at pressures greater than 1 bar, as noted by Tomasko et al. and Karkoschka and Tomasko (Tomasko, M.G., Bezard, B., Doose, L., Engel, S., Karkoschka, E. [2008] Planet. Space Sci., 56, 624-647; Karkoschka, E., Tomasko, M. [2009] Icarus). However, from 2007 to 2008 reflection from these clouds throughout the southern hemisphere and from both northern and southern mid-latitudes (30° N,S) diminished. As a result, the southern polar collar at 45°S has diminished in brightness relative to mid-latitudes, a similar collar at 45°N has become more prominent (e.g. Rages, K.A., Hammel, H.B., Sromovsky, L. [2007] Bull. Am. Astron. Soc., 39, 425; Sromovsky, L.A., Fry, P.M., Ahue, W.M., Hammel, H.B., de Pater, I., Rages, K.A., Showalter, M.R., van Dam, M.A. [2008] vol. 40 of AAS/Division for Planetary Sciences Meeting Abstracts, pp. 488-489; Sromovsky, L.A., Ahue, W.K.M., Fry, P.M., Hammel, H.B., de Pater, I., Rages, K.A., Showalter, M.R. [2009] Icarus), and the lowering reflectivity from mid-latitudes has left a noticeable brighter cloud zone at the equator (e.g. Sromovsky, L.A., Fry, P.M. [2007] Icarus, 192, 527-557;Karkoschka, E., Tomasko, M. [2009] Icarus). For such substantial cloud changes to have occurred in just two years suggests that the circulation of Uranus’ atmosphere is much more vigorous and/or efficient than is commonly thought. The composition of the main observed cloud decks between 2 and 6-8 bar is unclear, but the absence of the expected methane cloud at 1.2-1.3 bar (Lindal, G.F., Lyons, J.R., Sweetnam, D.N., Eshleman, V.R., Hinson, D.P. [1987] J. Geophys. Res., 92, 14987-15001) is striking (as previously noted by, among others, Sromovsky, L.A., Irwin, P.G.J., Fry, P.M. [2006] Icarus, 182, 577-593; Sromovsky, L.A., Fry, P.M. [2007] Icarus, 192, 527-557; Sromovsky, L.A., Fry, P.M. [2008] Icarus, 193, 252-266; Karkoschka, E., Tomasko, M. [2009] Icarus) and suggests that cloud particles may be considerably different from pure condensates and may be linked with stratospheric haze particles drizzling down from above, or that tropospheric hazes are generated near the methane condensation level and then drizzle down to deep pressures as suggested by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2009] Icarus).The retrieved cloud structures were also tested for different assumptions of the deep methane mole fraction, which Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2009] Icarus) find may vary from ∼1-2% in polar regions to perhaps as much as 4% equatorwards of 45°N,S. We found that such variations did not significantly affect our conclusions.     

Methane on Uranus: The case for a compact CH4 cloud layer at low latitudes and a severe CH4 depletion at high-latitudes based on re-analysis of Voyager occultation measurements and STIS spectroscopy

Lindal et al. (Lindal, G.F., Lyons, J.R., Sweetnam, D.N., Eshleman, V.R., Hinson, D.P. [1987]. J. Geophys. Res. 92 (11), 14987-15001) presented a range of temperature and methane profiles for Uranus that were consistent with 1986 Voyager radio occultation measurements of refractivity versus altitude. A localized refractivity slope variation near 1.2 bars was interpreted to be the result of a condensed methane cloud layer. However, models fit to near-IR spectra found particle concentrations much deeper in the atmosphere, in the 1.5-3 bar range (Sromovsky, L.A., Irwin, P.G.J., Fry, P.M. [2006]. Icarus 182, 577-593; Sromovsky, L.A., Fry, P.M. [2010]. Icarus 210, 211-229; Irwin, P.G.J., Teanby, N.A., Davis, G.R. [2010]. Icarus 208, 913-926), and a recent analysis of STIS spectra argued for a model in which aerosol particles formed diffusely distributed hazes, with no compact condensation layer (Karkoschka, E., Tomasko, M. [2009]. Icarus 202, 287-309). To try to reconcile these results, we reanalyzed the occultation observations with the He volume mixing ratio reduced from 0.15 to 0.116, which is near the edge of the 0.033 uncertainty range given by Conrath et al. (Conrath, B., Hanel, R., Gautier, D., Marten, A., Lindal, G. [1987]. J. Geophys. Res. 92 (11), 15003-15010). This allowed us to obtain saturated mixing ratios within the putative cloud layer and to reach above-cloud and deep methane mixing ratios compatible with STIS spectral constraints. Using a 5-layer vertical aerosol model with two compact cloud layers in the 1-3 bar region, we find that the best fit pressure for the upper compact layer is virtually identical to the pressure range inferred from the occultation analysis for a methane mixing ratio near 4% at 5°S. This strongly argues that Uranus does indeed have a compact methane cloud layer. In addition, our cloud model can fit the latitudinal variations in spectra between 30°S and 20°N, using the same profiles of temperature and methane mixing ratio. But closer to the pole, the model fails to provide accurate fits without introducing an increasingly strong upper tropospheric depletion of methane at increased latitudes, in rough agreement with the trend identified by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2009]. Icarus 202, 287-309).     

The web of three-planet resonances in the outer Solar System: II. A source of orbital instability for Uranus and Neptune

The motion of the giant planets from Jupiter to Neptune is chaotic with Lyapunov time of approximately 10 Myr. A recent theory explains the presence of this chaos with three-planet mean-motion resonances, i.e. resonances among the orbital periods of at least three planets. We find that the distribution of these resonances with respect to the semi-major axes of all the planets is compatible with orbital instability. In particular, they overlap in a region of 10⁻³ AU with respect to the variation of the semi-major axes of Uranus and Neptune. Fictitious planetary systems with initial conditions in this region can undergo systematic variations of semi-major axes. The true Solar System is marginally in this region, and Uranus and Neptune undergo very slow systematic variations of semi-major axes with speed of order 10⁻⁴ AU/Gyr.     

Astrometric results of observations of mutual occultations and eclipses of the Galilean satellites of Jupiter in 2002-2003

We suggest a new approach and develop an original method for deriving astrometric data from the photometry of mutual occultations and eclipses of planetary satellites. We decide to model not the relative apparent motion of one satellite with respect to another satellite but the deflection of the observed relative motion with respect to the theoretical motion implied by appropriate ephemerides.We have attempted to reduce the results of photometric observations of the Gallilean satellites during their mutual occultations and eclipses in 2002-2003. The data of observation for 319 light curves of 106 mutual events were received from the observers. The reliable 245 light curves were processed with our method. Eighty six apparent relative positions have been obtained.Systematic errors arise inevitably while deriving astrometric data. Most of them are due to factors that are unrelated to the methods for deriving astrometric data. The systematic errors are more likely due to incorrect excluding the effect of background on photometric counts. In the case of mutual occultations, the flux drop is determined to a considerable degree by the ratio of the mean albedos of the two satellites. Some mutual event observations revealed wrong adopted values of the mean albedos.     

Resolving dynamic parameters of the August 2007 Titania and Ariel occultations by Umbriel

We observed the 15 August 2007 occultation of the uranian satellite Titania and the 19 August 2007 occultation of Ariel by Umbriel using the Agile high-speed photometer on the APO 3.5 m telescope. We find that the Titania event midpoint occurred at 09:16:39.20 UT and the Ariel event midpoint at 07:59:49.4 UT, which was 26.2 s and 37.4 s later than predicted, respectively. Our best fit impact parameter was 71.0 km for the Titania occultation and 476.9 km for the Ariel event, both of which were less than predicted.     

Revised vertical cloud structure of Uranus from UKIRT/UIST observations and changes seen during Uranus’ Northern Spring Equinox from 2006 to 2008: Application of new methane absorption data and comparison with Neptune

Long-slit spectroscopy observations of Uranus by the United Kingdom InfraRed Telescope UIST instrument in 2006, 2007 and 2008 have been used to monitor the change in Uranus’ vertical and latitudinal cloud structure through the planet’s Northern Spring Equinox in December 2007.These spectra were analysed and presented by Irwin et al. (Irwin, P.G.J., Teanby, N.A., Davis, G.R. [2009]. Icarus 203, 287-302), but since publication, a new set of methane absorption data has become available (Karkoschka, E., Tomasko, M. [2010]. Methane absorption coefficients for the jovian planets from laboratory, Huygens, and HST data. Icarus 205, 674-694.), which appears to be more reliable at the cold temperatures and high pressures of Uranus’ deep atmosphere. We have fitted k-coefficients to these new methane absorption data and we find that although the latitudinal variation and inter-annual changes reported by Irwin et al. (2009) stand, the new k-data place the main cloud deck at lower pressures (2-3 bars) than derived previously in the H-band of ∼3-4 bars and ∼3 bars compared with ∼6 bars in the J-band. Indeed, we find that using the new k-data it is possible to reproduce satisfactorily the entire observed centre-of-disc Uranus spectrum from 1 to 1.75 μm with a single cloud at 2-3 bars provided that we make the particles more back-scattering at wavelengths less than 1.2 μm by, for example, increasing the assumed single-scattering albedo from 0.75 (assumed in the J and H-bands) to near 1.0. In addition, we find that using a deep methane mole fraction of 4% in combination with the associated warm ‘F’ temperature profile of Lindal et al. (Lindal, G.F., Lyons, J.R., Sweetnam, D.N., Eshleman, V.R., Hinson, D.P. [1987]. J. Geophys. Res. 92, 14987-15001), the retrieved cloud deck using the new (Karkoschka and Tomasko, 2010) methane absorption data moves to between 1 and 2 bars.The same methane absorption data and retrieval algorithm were applied to observations of Neptune made during the same programme and we find that we can again fit the entire 1-1.75 μm centre-of-disc spectrum with a single cloud model, providing that we make the stratospheric haze particles (of much greater opacity than for Uranus) conservatively scattering (i.e. ω = 1) and we also make the deeper cloud particles, again at around the 2 bar level more reflective for wavelengths less than 1.2 μm. Hence, apart from the increased opacity of stratospheric hazes in Neptune’s atmosphere, the deeper cloud structure and cloud composition of Uranus and Neptune would appear to be very similar.     

Nonhydrostatic effects and the determination of icy satellites’ moment of inertia

We compare the moment of inertia (MOI) of a simple hydrostatic, two layer body as determined by the Radau–Darwin Approximation (RDA) to its exact hydrostatic MOI calculated to first order in the parameter q = Ω²R³/GM, where Ω, R, and M are the spin angular velocity, radius, and mass of the body, and G is the gravitational constant. We show that the RDA is in error by less than 1% for many configurations of core sizes and layer densities congruent with those of solid bodies in the Solar System. We then determine the error in the MOI of icy satellites calculated with the RDA due to nonhydrostatic effects by using a simple model in which the core and outer shell have slight degree 2 distortions away from their expected hydrostatic shapes. Since the hydrostatic shape has an associated stress of order ρΩ²R² (where ρ is density) it follows that the importance of nonhydrostatic effects scales with the dimensionless number σ/ρΩ²R², where σ is the nonhydrostatic stress. This highlights the likely importance of this error for slowly rotating bodies (e.g., Titan and Callisto) and small bodies (e.g., Saturn moons other than Titan). We apply this model to Titan, Callisto, and Enceladus and find that the RDA-derived MOI can be 10% greater than the actual MOI for nonhydrostatic stresses as small as ∼0.1 bars at the surface or ∼1 bar at the core–mantle boundary, but the actual nonhydrostatic stresses for a given shape change depends on the specifics of the interior model. When we apply this model to Ganymede we find that the stresses necessary to produce the same MOI errors as on Titan, Callisto, and Enceladus are an order of magnitude greater due to its faster rotation, so Ganymede may be the only instance where RDA is reliable. We argue that if satellites can reorient to the lowest energy state then RDA will always give an overestimate of the true MOI. Observations have shown that small nonhydrostatic gravity anomalies exist on Ganymede and Titan, at least at degree 3 and presumably higher. If these anomalies are indicative of the nonhydrostatic anomalies at degree 2 then these imply only a small correction to the MOI, even for Titan, but it is possible that the physical origin of nonhydrostatic degree 2 effects is different from the higher order terms. We conclude that nonhydrostatic effects could be present to an extent that allows Callisto and Titan to be fully differentiated.     

New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses

In 2007, the M-type binary Asteroid 22 Kalliope reached one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, was aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. A dedicated international campaign of photometric observations, based on amateur-professional collaboration, was organized and coordinated by the IMCCE in order to catch several of these events. The set of the compiled observations is released in this work. We developed a relevant model of these events, including a topographic shape model of Kalliope refined in the present work, the orbit solution of Linus as well as the photometric effect of the shadow of one component falling on the other. By fitting this model to the only two full recorded events, we derived a new estimation of the equivalent diameter of Kalliope of 166.2±2.8 km, 8% smaller than its IRAS diameter. As to the diameter of Linus, considered as purely spherical, it is estimated to 28±2 km. This substantial “shortening” of Kalliope, gives a bulk density of 3.35±0.33 g/cm³, significantly higher than past determinations but more consistent with its taxonomic type. Some constraints can be inferred on the composition.     

Predictions and observations of events and configurations occurring during the Uranian equinox

The occurrence of the Earth and Sun transits through the equatorial plane of Uranus will bring us the opportunity for observations only possible at that time: mutual events of the satellites, search for new faint satellites and measurement of the thickness of the rings.The predictions of the mutual events need a theoretical model of the motion of the satellites. The calculated occurrences of the occultations and eclipses highly depend on the model since these predictions are very sensitive to the relative positions of the satellites. A difference of 0.05 arcsec in latitude may make an event inexistent and the accuracy of the theoretical models is around 0.1 arcsec.In order to be sure of the occurrence of each event, we made the predictions using three theoretical models: the first one is GUST86 made by Laskar and Jacobson in 1986, the second is GUST06 based on the former model fitted by Emelianov on new observations and the third one is LA06 based on a brand new theory with an accuracy 10 times better than GUST and fitted on recent observations made since 1950.This comparison shows that some events predicted with one model are not predicted using another one. We try to select the events which will occur surely in order to help the observers to catch the best phenomena.The search for new satellites and the measurement of the thickness of the rings are planned by means of observations at the time of the transit of the Earth in the ring plane.