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].     

High-Resolution Infrared Imaging of Neptune from the Keck Telescope

We present results of infrared observations of Neptune from the 10-m W. M. Keck I Telescope, using both high-resolution (0.04 arcsecond) broadband speckle imaging and conventional imaging with narrowband filters (0.6 arcsec resolution). The speckle data enable us to track the size and shape of infrared-bright features (“storms”) as they move across the disk and to determine rotation periods for latitudes −30 and −45°. The narrowband data are input to a model that allows us to make estimates of Neptune's stratospheric haze abundance and the size of storm features. We find a haze column density of ∼10⁶ cm⁻² for a haze layer located in the stratosphere, and a lower limit of 10⁷ cm⁻² and an upper limit of 10⁹ cm⁻² for a layer of 0.2 μm particles in the troposphere. We also calculate a lower limit of 7×10⁶ km² for the size of a “storm” feature observed on 13 October 1997.     

The Unusual Dynamics of Northern Dark Spots on Neptune

Hubble Space Telescope (HST) and ground-based observations of Neptune from 1991 to 2000 show that Neptune's northern Great Dark Spots (NGDS) remained remarkably stable in latitude and longitudinal drift rate, in marked contrast to the 1989 southern Great Dark Spot (GDS), which moved continuously equatorward during 1989 and dissipated unseen during 1990. NGDS-32, discovered in October 1994 HST images, (H. B. Hammel et al., 1995, Science268, 1740-1742), stayed at ∼32°N from 1994 through at least 1996, and possibly through 2000. The second northern GDS (NGDS-15), discovered in August 1996 HST images, (L. A. Sromovsky et al. 2001, Icarus146, 459-488), appears to have existed as early as 8 March 1996 and remained near 15°N for the 16 months over which it was observed. NGDS-32 had a very uniform longitudinal drift rate averaging −36.28±0.04°/day from 10 October 1994 to 2 November 1995, and −35.84±0.02°/day from 1 September 1995 through 24 November 1995. A single circulation feature certainly exists during each of the first two periods, though it is not certain that it is the same feature. It is probable, but less certain, that only a single circulation feature was tracked during the 1996-1998 period, during which positions are consistent with a modulated drift rate averaging −35.401±0.001°/day, but with a peak-to-peak modulation of 1.5°/day with an ∼760-day period. If NDS-32 varied its drift rate in accord with the local latitudinal shear in the zonal wind, then all its drift-rate changes might be due to only ∼0.4° of latitudinal motion. The movement of NGDS-15 is also not consistent with a uniform longitudinal drift rate, but the nature of its variation cannot be estimated from the limited set of observations. The relatively stable latitudinal positions of both northern dark spots are not consistent with current numerical model calculations treating them as anticyclonic vortices in a region of uniform potential vorticity gradient (R. P. Lebeau and T. E. Dowling 1998, Icarus132, 239-265). Possible explanations include unresolved latitudinal structure in the zonal wind background or unaccounted-for variations in vertical stability structure.     

Sizes, shapes, and albedos of the inner satellites of Neptune

Based on 87 resolved Voyager images of the five innermost satellites of Neptune, their shapes were measured and fit by tri-axial ellipsoids with the semi-axes of 48 × 30 × 26 km for Naiad, 54 × 50 × 26 km for Thalassa, 90 × 74 × 64 km for Despina, 102 × 92 × 72 km for Galatea, and 108 × 102 × 84 km for Larissa. Thomas and Veverka published a similar shape for Larissa (104 × 89 km, J. Geophys. Res. 96, 19261-19268, 1991). The other satellites had no published shapes. Using Voyager photometry of the six inner satellites by the same authors and the revised sizes, including the published size of Proteus, the reflectivity within this inner system was found to vary by about 30%. Geometric albedos in the visible are estimated between 0.07 for Naiad and 0.10 for Proteus. The rotational lightcurves of these satellites seem to be due to satellite shapes.     

Predictions for eclipses of Nereid by Neptune

Neptune will eclipse its satellite Nereid (Neptune II) on 2007 April 27 from 00 to 06 h UT and on 2008 April 21 from 12 to 17 h UT, with uncertainties of about 3 h; and a third eclipse may occur on 2009 April 17. These events offer unique opportunities for astrometric and geophysical measurement.     

Long-term atmospheric variability on Uranus and Neptune

Long-term photometric measurements of Uranus and Neptune through 2005 show variations in brightness. For Uranus, much of the variation can be interpreted as seasonal, i.e., caused by viewing angle changes of an oblate planet. The photometry suggests that if seasonal variations on Uranus are north-south symmetric, then the northern pole should begin to brighten in 2006. However, seasonal “aspect” changes cannot explain all the variation; the Uranus observations require intrinsic atmospheric change. Furthermore, Uranus observations spanning many scale heights in the atmosphere may show similar change. For Neptune, variations in sub-solar latitude may explain the general shape of the long-term light curve, but significant deviations occur that have no explanation at present. Observations are needed over a longer temporal baseline than currently exists to fully characterize both atmospheres.     

Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune

Raman scattering by H₂ in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ∼20% in a clear atmosphere and ∼10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH₄ bands is mainly Raman scattered is not valid for current estimates of the CH₄ vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ∼6% in the 0.22-0.26 μm range and by ∼13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH₄ absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ∼5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new approximation based on spectral tuning of the effective molecular single scattering albedo provides low errors for zenith angles below 70° in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

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.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

Variability of Neptune

Earth-based observers of Neptune have found that the planet varies in brightness at various wavelengths in ways that suggest that changes occur in the planet's atmosphere on several different time scales. Global inhomogeneities in high-altitude haze distribution that are stable for several days permit measurements of the planet's rotation period (about 18 hr), but this stability sometimes breaks down, obscuring the diurnal lightcurve. In addition, there is an apparent long-term variability of the brightness of Neptune in anticorrelation with the cycle of solar activity. This slow variability of low amplitude may be punctuated by outburst of high-altitude condensation of particles in the atmosphere whose decay time is several months.     

The haze and methane distributions on Neptune from HST-STIS spectroscopy

We analyzed a data cube of Neptune acquired with the Hubble STIS spectrograph on August 3, 2003. The data covered the full afternoon hemisphere at 0.1 arcsec spatial resolution between 300 and 1000 nm wavelength at 1 nm resolution. Navigation was accurate to 0.004 arcsec and 0.05 nm. We constrained the vertical aerosol structure with radiative transfer calculations. Ultraviolet data confirmed the presence of a stratospheric haze of optical depth 0.04 at 370 nm wavelength. Bright, discrete clouds, most abundant near latitudes −40° and 30°, had their top near the tropopause. They covered 1.7% of the observed disk if they were optically thick. The methane abundance above the cloud tops was 0.0026 and 0.0017 km-am for southern and northern clouds, respectively, identical to earlier observations by Sromovsky et al. (Sromovsky, L.A., Fry, P.M., Dowling, T.E., Baines, K.H., Limaye, S.S., [2001b]. Icarus 149, 459-488). Aside from these clouds, the upper troposphere was essentially clear. Below the 1.4-bar layer, a vertically uniform haze extended at least down to 10 bars with optical depth of 0.10-0.16/bar, depending on the latitude. Haze particles were bright at wavelengths above 600 nm, but darkened toward the ultraviolet, at the equator more so than at mid and high latitudes. A dark band near −60° latitude was caused by a 0.01 decrease of the single scattering albedo in the visible, which was close to unity. A comparison of methane and hydrogen absorptions contradicted the current view that methane is uniformly mixed in latitude and altitude below the ∼1.5-bar layer. The 0.04 ± 0.01 methane mixing ratio is only uniform at low latitudes. At high southern latitudes, it is depressed roughly between the 1.2 and 3.3-bar layers compared to low-latitude values. The maximum depression factor is ∼2.7 at 1.8 bars. We present models with 2° latitude sampling across the full sunlit globe that fit the observed reflectivities to 2.8% rms.     

The altitude of Neptune cloud features from high-spatial-resolution near-infrared spectra

We report on observations of Neptune from the 10-meter W.M. Keck II Telescope on June 17-18 (UT) 2000 and August 2-3 (UT) 2002 using the adaptive optics (AO) system to obtain a spatial resolution of 0.06 arcseconds. With this spatial resolution we can obtain spectra of individual bright features on the disk of Neptune in a filter centered near 2 microns. The use of a gas-only, simple reflecting layer radiative transfer model allows us to estimate the best fit altitudes of 18 bright features seen on these 4 nights and to set a constraint on the fraction of hydrogen in ortho/para equilibrium. On these nights there were three main types of features observed: northern hemisphere features in the range from +30 to −45 degrees; southern hemisphere features in the range from −30 to −50 degrees; and small southern features at −70 degrees. We find that the altitudes of the northern features are in the range from 0.023-0.064 bar, which places them in Neptune's stratosphere. Southern features at −30 to −50 degrees are mainly at altitudes from 0.10 to 0.14 bars. The small features at −70 degrees are somewhat deeper in the upper troposphere, at 0.17 and 0.27 bars. This pattern of features located at higher altitudes in the northern hemisphere and lower altitudes in the south has also been noted by previous observers. The best fits for all the observed spectra give a value of 1.0 for the fraction of hydrogen in ortho/para equilibrium; the value of the helium fraction is less well constrained by the data at 0.24. We suggest that the southern mid-latitude features are methane haze circulated up from below, while the −70° features may be isolated areas of upwelling in a general area of subsidence. Northern bright features may be due to subsidence of stratospheric haze material rather than upwelling and condensation of methane gas. We suggest that convection efficiently transports methane ice clouds to the tropopause in the Southern mid latitudes and thus plays a key role in the stratospheric haze production cycle.     

冥族小天体与海王星特洛伊的近密交会

海王星外天体中的冥族小天体与海王星成2:3的平运动轨道共振,且具有较大的轨道偏心率,因此它们能与海王星特洛伊的轨道发生重叠,导致近密交会和碰撞,从而深刻地影响两者的动力学演化。利用数值模拟的方法,有效地获得了这两群小天体间近密交会的信息,讨论了可能影响两者近密交会频率的因素,包括小天体质量、轨道倾角和轨道偏心率等。在合理近似条件下,建立了估算两群小天体近密交会和碰撞次数的理论公式。结合已有的数值模拟结果,以及对冥族小天体观测数据的分析,对实际情况下冥族小天体群与典型特洛伊小天体之间的近密交会和碰撞次数进行了估算,证明近密交会较为频繁地发生,而碰撞则极其罕见,并且各尺寸范围的小天体对近密交会和碰撞次数的贡献各有不同。这一套分析和估算的方法可以直接应用在其他类似小天体间交会过程的估算上。     

Neptune migration model with one extra planet

We explore conventional Neptune migration model with one additional planet of mass at 0.1-2.0M_⊕. This planet inhabited in the 3:2 mean motion resonance with Neptune during planet migration epoch, and then escaped from the Kuiper belt when jovian planets parked near the present orbits. Adding this extra planet and assuming the primordial disk truncated at about 45 AU in the conventional Neptune migration model, it is able to explain the complex structure of the observed Kuiper belt better than the usual Neptune migration model did in several respects, which are the following. (1) High-inclination Plutinos with i?15-35° are produced. (2) Generating the excitation of the classical Kuiper belt objects, which have moderate eccentricities and inclinations. (3) Producing the larger ratio of Neptune’s 3:2 to 2:1 resonant particles, and the lower ratio of particles in the 3:2 resonance to those in the classical belt, which may be more consistent with observations. (4) Finally, several Neptune’s 5:2 resonant particles are obtained. However, numerical experiments imply that this model is a low-probability event. In addition to the low probability, two features produced by this model may be inconsistent with the observations. They are small number of low-inclination particles in the classical belt, and the production of a remnant population with near-circular and low-inclination orbit within . According to our present study, including one extra planet in the conventional Neptune migration model as the scenario we explored here may be unsuitable because of the low probability, and the two drawbacks mentioned above, although this model can explain better several features which is hard to produce by the conventional Neptune migration model. The issues of low-probability event and the lack of low-inclination KBOs in the classical belt are interesting and may be studied further under a more realistic consideration.     

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.     

Significant science at Titan and Neptune from aerocaptured missions

In 2001, NASA began assembling the Aerocapture Systems Analysis Team, a team of scientists and engineers from multiple NASA centers. Their charter is to perform high-fidelity analyses of delivering scientifically compelling orbital missions that use aerocapture for orbit insertion at their destinations. After establishing scientific credibility, studies focus on aerocapture systems design and performance, including approach navigation, flight mechanics, aerothermodynamics, and thermal protection. The team's October 2001-September 2002 study examined a mission to explore the organic environment of Titan and its chemical, geological, and dynamical context. Its architecture includes a Titan polar orbiter that would complete and extend Cassini's soon-to-begin global mapping, aiding global extrapolation of findings from a mobile in situ element (rover, blimp, etc.). The in situ element would perform remote sensing and in situ investigations, for analysis and characterization of Titan's surface, shallow subsurface, atmosphere, processes occurring there, and energy sources driving it all. The study concentrated on the orbiter and orbit insertion, largely treating the in situ element as a black box with data relay requirements. October 2002-September 2003 the team studied a mission to perform Cassini/Huygens-level exploration of the Neptune system. Before aerocapture this mission would deploy and support multiple Neptune atmospheric entry probes. After aerocapture the orbiter uses Triton as a “tour engine”, in much the same manner as Cassini uses Titan, to provide many Triton flybys and orbit evolution for detailed investigation of Neptune's interior, atmosphere, magnetosphere, rings, and satellites.This presentation summarizes the missions’ science objectives, instrumentation, and data requirements that served as the foundations for the studies, and describes mission design requirements and constraints that affect the science investigations.     

Survival of Trojan-type companions of Neptune during primordial planet migration

We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus ∼1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune's Trojans as a function of migration rate. We find that orbital migration with the characteristic time scale τ=10⁶ years allows about 35% of preexisting Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with τ=10⁷ years yields only a ∼5% probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we find that the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. These secondary resonances arise when the circulation frequencies, f, of critical arguments for Uranus-Neptune mean-motion near-resonances (e.g., f^UN_1:2, f^UN_4:7) are commensurate with harmonics of the libration frequency of the critical argument for the Neptune-Trojan 1:1 mean-motion resonance (f^NT_1:1). Trojans trapped in the secondary resonances typically have their libration amplitudes amplified until they escape the 1:1 resonance with Neptune. Trojans with large libration amplitudes are susceptible to loss during sweeping by numerous high-order secondary resonances (e.g., f^UN_1:2≈11f^NT_1:1). However, for the slower migration, with τ=10⁷ years, even tightly bound Neptune Trojans with libration amplitudes below 10° can be lost when they become trapped in 1:3 or 1:2 secondary resonances between f^UN_1:2 and f^NT_1:1. With τ=10⁷ years the 1:2 secondary resonance was responsible for the single greatest episode of loss, ejecting nearly 75% of existing Neptune Trojans. This episode occurred during the late stages of planetary migration when the remnant planetesimal disk would have been largely dissipated. We speculate that if the number of bodies liberated during this event was sufficiently high they could have caused a spike in the impact rate throughout the Solar System.     

The spectral variability of Triton from 1997-2000

We present the results of a three-year observational program of long-slit spectroscopy and UBVRI photometry of Triton. We find evidence for short-lived albedo variations at wavelengths less than 0.5 μm with the most notable reddening event measured in October 1997 and “normal” colors returning by May 1998. We report a possible variation in the relative 0.73/0.89 μm methane absorption band strengths, suggesting that the transport or denudation of this species may play a major role in the reddening events.     

First Spitzer observations of Neptune: Detection of new hydrocarbons

We present the first spectra of Neptune taken with the Spitzer Space Telescope, highlighting the high-sensitivity, moderate-resolution 10-20 μm (500-1000 cm⁻¹) spectra. We report the discovery of methylacetylene (CH₃C₂H) and diacetylene (C₄H₂) with derived 0.1-mbar volume mixing ratios of (1.2±0.1)×¹⁰⁻¹⁰ and (3±1)×¹⁰⁻¹² respectively.