Neptune's rotation period: A correction and a speculation on the difference between photometric and spectroscopic results

An error in the Hayes and Belton (1977), Icarus32, 383–401) estimate of the rotation period of Neptune is corrected. If Neptune exhibits the same degree of limb darkening as Uranus near 4900 Å, the rotation period is 15.4 ± 3 hr. This value is compatible with a recent spectroscopic determination of Munch and Hippelein (1979) who find a period of 11.2_?1.2^+1.8 hr. However, if, as indirect evidence suggests, the law of darkening on Neptune at these wavelengths is less pronounced than on Uranus, then the above estimates may need to be lengthened by several hours. Recent photometric data are independently analyzed and are found to admit several possible periods, none of which can be confidently assumed to be correct. The period of Neptune most probably falls somewhere in the range 15–20 hr. The Hayes-Belton estimate of the period of Uranus is essentially unaffected by the above-mentioned error and remains at 24 ± 4 hr. All observers agree that the rotation period of Uranus is longer than that of Neptune.     

The internal structures and the relative rotation rates of Uranus and Neptune

The difference between the interior structures of Uranus and Neptune is presented, based on models which fit the observed mass, radius, and gravitational moments for the assumed rotation periods of these planets. If Uranus and Neptune are assumed to be as similar in internal structure as they are in mass and radius, the rotation period for Neptune must be shorter than that for Uranus. It is suggested that the true rotation period is given by Neptune's oblateness, while the photometric period corresponds to the motion of Rossby waves in the upper atmosphere.     

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.     

Mars data analysis program special issue no. 2

An extended photometric time series in the J and K bands of Neptune has a complex appearance which appears to require the simultaneous presence of three periodicities plus related harmonics in the (J-K) color. The most apparent of the fundamental periods is N1 = 17.73 hr. The two others are at N2 = 18.56 and N3 = 18.29 hr and may be the result of amplitude modulation of a previously reported period of 18.42 hr. We interpret the presence of multiple periodicity as indicating that distinct systems of zonal winds exist on the planet. We argue that these wind systems are probably confined to moderate or high latitudes on the basis of recent omages of the planet taken in a spectral region of strong CH₄ absorption, and, by analogy to the zonal wind systems that exist in Jupiter's atmosphere, deduce a period of rotation for the body of the planet of 18.2 ± 0.4 hr. Zonal wind contrasts of up to 109 m sec^?1 are implied in the atmosphere of Neptune by these observations.     

The rotation period of Neptune's upper atmosphere

Significant variations in the near-infrared brightness of Neptune during July and August 1980 were observed. These observations show a well-defined, large-amplitude variation in Neptune's J-K color, with a period of 17.73 ± 0.1 hr and are interpreted as diurnal variations resulting from the 17.73-hr rotation period of the upper atmosphere of Neptune in the presence of inhomogeneous weather. These results qualitatively corroborate those of D. P. Cruikshank (1978, Astrophys. J.220, L57-L59) in an earlier study using similar techniques. In addition, variations were observed in the 5-μm spectral region which are in phase with the variations seen at shorter wavelengths. A new 5-μm measurement of Uranus is also reported.     

The rotation period and pole orientation of asteroid 4 Vesta

In 1971 asteroid Vesta was observed in a region of the sky in which it had never been observed before. Its photometric lightcurve had two distinct maxima. Those observations have been the only strong evidence to support a rotation period of about 10 hr 41 min. Lightcurves made in 1982, when Vesta was at the same aspect as 1971, do not show two different maxima. It is concluded that there was a systematic error in the 1971 observations. At this time a definitive statement cannot be made about the true period of Vesta, although the 5 hr 20 min period does appear more plausible. Radar echoes in 1988 and 1992 should resolve the problem. The shorter rotation period was assumed and the photometric astrometry method applied. The sidereal period is 5 hr 20 min 31.68 sec 0.2225889 ± 0.0000002 days, the rotation is prograde, and the coordinates of the north pole are 103° longitude and +43° latitude with an uncertainty of abour 6°.     

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.     

Submillimeter and millimeter observations of Uranus and Neptune

We have made narrowband photometric measurements of Uranus and Neptune covering the wavelength range from 0.35 to 3.3 mm. The observations provide accurate comparative radiometry of these planets. Absolute calibration was referenced to Mars, and to Jupiter as a secondary standard. The results establish Uranus and Neptune as reliable secondary calibrators in their own right. We have combined our observations with other measurements made in the period 1978 through 1984 in the spectral range of 17 μm through 3 mm to form models for atmospheric temperature structure in the vertical range from 100 mbar to 8 bar. The simplest models imply that the tropospheres of both planets are consistent with “frozen” equilibrium H₂ and a mixing ratio of CH₄ of about 2% by volume in the deep atmosphere. There is some evidence in the Uranus data which implies the presence of discrete spectral lines. These could be due to CH₄ pure rotational or dimer transitions or to minor constituents such as CO, which remain uncondensed even at the cold temperatures in the atmosphere of Uranus.     

Restored methane band images of Uranus and Neptune

Charge-coupled device images of Uranus and Neptune taken in the 8900-Å absorption band of methane are presented. The images have been digitally processed by means of nonlinear deconvolution techniques to partially remove the effects of atmospheric seeing. The restored Uranus images show strong limb brightening consistent with previous observations and theoretical models of the planet's atmosphere. The computer-processed images of Neptune show discreted cloud features similar to those reported previously by B. A. Smith, H. J. Reitsema and S. M. Larson (1979 Bull. Amer. Astron. Soc.11, 570). A time series of the restored Neptune images shows a continuous variation which may be due to the planet's rotation.     

Observations of Ganymede,Callisto, Ceres,Uranus, and Neptune at 3.33 mm wavelength

We have measured the 3.33 mm wavelength disk brightness temperatures of Ganymede (136 ± 21°K), Callisto (95 ± 17°K), Ceres (137 ± 25°K), Uranus (125 ± 9°K), and Neptune (126 ± 9°K). Our observations of Ganymede are consistent with the radiation from a blackbody in solar equilibrium, whereas Callisto's microwave spectrum indicates a surface similar to that of the Moon. The disk temperature for Ceres agrees with that expected from a rapidly rotating blackbody. The millimeter temperatures of Uranus and Neptune greatly exceed solar equilibrium values, implying atmospheres with large temperature gradients.     

The Near-Earth Objects Follow-Up Program

We present the results of photometric observations of the near-Earth asteroids (1943) Anteros, (2102) Tantalus, (2212) Hephaistos, (3199) Nefertiti, (5751) Zao = 1992 AC, (6322) 1991 CQ, (7474) 1992 TC, and 1989 VA made between 1982 and 1995. Synodic rotation periods in the range from 2.39 to 5.54 hr were derived for five of them, and we were able to place lower limits on periods of (2212) and (5751)—both > 20 hr. Only the period of the low amplitude case of (1943) was not constrained. The most interesting results were obtained for the following objects: (2102), a fast rotator (period 2.39 hr) in an extremely inclined orbit (i≈ 64°); (2212), a low amplitude slow rotator considered as an inactive cometary nucleus candidate; (3199), which showed similar lightcurves at quite different positions of the phase angle bisector, constraining its rotational pole; and 1989 VA, an unusual Aten asteroid with a rotation period of 2.51 hr and a relatively large amplitude. Overall, these results continue the pattern that NEO spins exhibit a bimodal distribution of spin rates.     

Infrared radiometry of Uranus and Neptune at 21 and 32 μm

Radiometric measurement of Uranus and Neptune near 21 and 32 μm have been made with filters with widths of 8 and 5 μm, respectively. The observations at 21 μm, made on 1985 June 19 at the NASA Infrared telescope facility at Mauna Kea, Hawaii, were calibrated against α Boo and corresponded to brightness temperatures of 54.1 ± 0.3 K for Uranus and 58.1 ± 0.3 K for Neptune. The observations at 32 μm were made on three nights: 1983 May 1 and 1984 May 30 and 31, also at the NASA IRTF. Calibrated against the Jovian satellites Callisto (J4) and Ganymede (J3), these measurements corresponded to brightness temperatures of 51.8 ± 1.5 K for Uranus and 55.6 ± 1.2 K for Neptune. The observations are consistent with higher-resolution studies and confirm the general decrease of brightness temperatures going from about 20 to 30 μm.     

Asteroid 532 Herculina: Lightcurves,pole orientation and a model

Photoelectric lightcurves of 532 Herculina in 1984 show two maxima and two minima with a synodic rotation period of 0.39185 ± 0.00002 day (1σ). During some other oppositions the Herculina lightcurve has only one maximum and one minimum over that same rotation period. The absolute magnitude in V is 6.13 ± 0.02 mag, the phase coefficient in V is 0.037 ± 0.002, and the mean colors are B−V = +0.86 ± 0.04 and U−B = +0.43 ± 0.02. We applied photometric astrometry and the results indicate a sideral period of 0.3918711 ± 0.0000001 day with retrograde rotation for a north pole at 276° long and +1° lat. The uncertainty of the pole is ±1°. A model of Herculina is presented that generates lightcurves consistent with both the observed amplitudes and the timings of extrema over precisely 28,630 sideral rotations during 30 years. The model is a sphere with two dark regions that are each about 0.13 times the brightness of the surrounding surface. The regions are at 0° asterocentric longitude, +15° lat, with a radius of 30°, and 170° long, −38° lat, with a radius of 26°. With the photometric astrometry pole and the model with two dark regions, predicted lightcurves are shown for the next four oppositions.     

Pole orientation of asteroid 44 Nysa via photometric astrometry,including a discussion of the method's application and its limitations

The results of photometric astrometry, a method of determining the orientation of a rotation axis, as applied to asteroid 44 Nysa are presented. The pole orientation of Nysa was found to be λ₀ = 100°, β₀ = +60° with an uncertainty of 10°. The sidereal period is 0^d.26755902 ± 0.00000006, and the rotation prograde. Refinements to, and limitations of, the application of the method of photometric astrometry are discussed. In light of the results presented herein, we believe that all photometric astrometry pole determinations of the past should be redone.     

Measurements of the H2 4-0 quadrupole bands of Uranus and Neptune

We find that the equivalent widths of the lines of the 4-0 H₂ quadrupole band on Uranus and Neptune are substantially smaller than the values found by some previous observers. An analysis of our results based on a range of atmospheric models yields H₂ abundances of 240 ± 60 km-amagats for Uranus and ?200 km amagats for Neptune.     

Rotation of the nucleus of comet p/Arend-Rigaux

Time-resolved charge-coupled device photometry of Comet p/Arend-Rigaux shows a cyclic variation in cometary brightness consistent with the periods T₁ = 574 ± 5 min (9.58 ± 0.08 hr) and T₂ = 407 ± 5 min (6.78 ± 0.08 hr). The variation has a 30% range and is confined to the inner coma. The relative photometric stability of the outer coma indicates that the variations in the inner coma are associated with the nucleus and probably result from its rotation at, or at a multiple of, one of the above periods.     

New observational constraints on the temperature inversions of Uranus and Neptune

We present 20-μm photometry of Uranus and Neptune which confirms the presence of a temperature inversion in the lower stratospheres in both planets. We find the brightness temperature difference between 17.8 and 19.6 μm to be 0.8 ± 0.5°K for Uranus and 1.8 ± 0.6°K for Neptune. These results indicate that the temperature inversions on both planets are weaker than previously thought. Comparison to model atmospheres by J. Appleby [Ph.D. thesis, SUNY at Stony Brook 1980] indicates that the temperature inversions can be understood as arising from heating by the absorption of sunlight by CH₄ and aerosols. However, the stratospheric CH₄ mixing ratio on Neptune must be higher than that at the temperature minimum.     

An atmospheric rotation period of Neptune determined from methane-band imaging

Direct imaging of Neptune through an 8900-Å methane-band filter with the University of Hawaii 2.24-m telescope at Mauna Kea Observatory shows discrete atmospheric cloud features. A rotation period of 17.86 ± 0.02 hr is derived from the observations of two transits of a bright feature in the southern hemisphere during May and June 1986. This period is consistent with earlier observations of cloud motion on Neptune. The imaging also shows that bright features in Neptune's northern hemisphere seen as recently as in 1983 by earlier investigations have disappeared, markedly changing the overall distribution of reflected light from the planetary disk.     

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.     

Long‐term photometry of three active red giants in close binary systems: V2253 Oph,IT Com and IS Vir

We present and analyze long‐term optical photometric measurements of the three active stars V2253 Oph, IT Com and IS Vir. All three systems are single‐lined spectroscopic binaries with an early K giant as primary component but in different stages of orbital‐rotational synchronization. Our photometry is supplemented by 2MASS and WISE near‐IR and mid‐IR magnitudes and then used to obtain more accurate effective temperatures and extinctions. For V2253 Oph and IT Com, we found their spectral energy distributions consistent with pure photospheric emission. For IS Vir, we detect a marginal mid‐IR excess which hints towards a dust disk. The orbital and rotational planes of IT Com appear tobe coplanar, contrary to previous findings in the literature. We apply a multiple frequency analysis technique to determine photometric periods, and possibly changes of periods, ranging from days to decades. New rotational periods of 21.55±0.03 d, 65.1±0.3 d, and 23.50±0.04 d were determined for V2253 Oph, IT Com, and IS Vir, respectively. Splitting of these periods led to tentative detections of differential surface rotations of δP/P ≈ 0.02 for V2253 Oph and 0.07 for IT Com. Using a time‐frequency technique based on short‐term Fourier transforms we present evidence of cyclic light variations of length ≈ 10 yr for V2253 Oph and 5–6 yr for IS Vir. A single flip‐flop event has been observed for IT Com of duration 2–3 yr. Its exchange of the dominant active longitude had happened close to a time of periastron passage, suggesting some response of the magnetic activity from the orbital dynamics. The 21.55‐d rotational modulation of V2253 Oph showed phase coherence also with the orbital period, which is 15 times longer than the rotational period, thus also indicating a tidal feedback with the stellar magnetic activity. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)