Comparison between the Shkuratov and Hapke Scattering Theories for Solid Planetary Surfaces: Application to the Surface Composition of Two Centaurs

This project examines the different approaches which deal with the theory of radiative transfer on atmosphereless bodies. We present the relative merits of two scattering theories based on the equivalent slab model: the extensively used Hapke theory (Hapke 1981, J. Geophys. Res.86, 3039-3054) and the Shkuratov theory (Shkuratov et al. 1999, Icarus141, 132-155). We found that their main difference is the role of the phase function of individual particles of regolith, which is predicted (and generally forward directed) in the case of the Shkuratov model instead of being a free parameter as formulated in the Hapke model. We also emphasize that different assumptions as to the manner in which different constituents are physically mixed in either model have a substantial effect on the synthetic spectra inferred. This leads to a significant extension of the validity of Hapke's or similar practical approaches to areas where these approaches are valid.We used two objects (the Centaurs 5145 Pholus and 8405 Asbolus) as examples. Previous modeling of the spectra of these two bodies with the Hapke approach gave suspect results in terms of the derived grain sizes, which were smaller than the wavelength, violating key assumptions of the model (Cruikshank et al. 1998, Icarus135, 389-407 for Pholus; Barucci et al. 2000, Astron. Astrophys.357, L53-56 for Asbolus). We considered several different types of powdered surfaces to interpret the surface composition of these two Centaurs. The effect of fine-scale contamination of water ice grains by small amounts of carbon and/or tholins is also explored. We can explain the strong red color and the rich near-infrared spectral signatures of Pholus using a five-component surface (contaminated water ice, amorphous carbon, Titan tholin, olivine, and methanol ice) where the grain sizes are consistent with the model assumptions. These components are similar to those inferred by Cruikshank et al. (1998), but we obtain very different grain sizes and relative abundances. For example, we obtain a relative abundance of water ice on the surface of Pholus of about 40% instead of 6% found with the Hapke model. Organic and carbonaceous components change by similar amounts. In the case of Asbolus, a tholin and amorphous carbon areal mixture can reproduce the spectrum, with water remaining at 9% or less. Using the albedo published by Fernandez et al. (2002, Astron. J.123, 1050-1055) which is higher than most workers assume for Centaurs and Kuiper belt objects, a surface composition similar to that of Pholus is found. It appears that model-based uncertainties in relative compositions must be regarded with more attention.     

Asteroid rotation rates

The dependence of rotational frequency on diameter, taxonomic type, and family membership is analyzed for 217 main-belt asteroids with statistically useful periods extracted from the file published by Harris and Young ((1983). Icarus54, 59–109). It is shown that for asteroids with diameters ? 120 km, mean rotational frequency increases with increasing diameter. This trend is equally present in all subsets of M-, S-, and C-type asteroids, for both family and nonfamily members alike, and cannot be accounted for by observational selection. For asteroids with diameters ? 120 km, mean rotational frequency increases with decreasing diameter; however, within this group there is a subset of asteroids with exceptionally long rotational periods. This marked change in the distribution at diameter ～ 120 km could separate primordial asteroids from their collision products. However, it is probable that the sample is biased in favor of small asteroids with short rotational periods and that the apparent increase of mean rotational frequency with decreasing diameter for small asteroids is at least partly the product of observational selection. An observational program that could test this hypothesis is described. If asteroids of any one diameter are considered, then, on average, M asteroids rotate faster than S asteroids which in turn rotate faster than C asteroids. This shows that asteroids which have been classified by their surface properties alone have different bulk properties. There is also some evidence that for all asteroidal types, of all diameters, family members rotate faster than nonfamily members.     

Analytical model of the long-period forced longitude librations of Mercury

The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/C_m. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/C_m. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.     

On Rotation of the Solar Corona

We have studied the rotation of the solar corona using the images taken at a 9.4?nm wavelength by the AIA 094 instrument on board the Solar Dynamics Observatory (SDO) satellite. Our analysis implies that the solar corona rotates differentially. It appears that ??, the angular rotation velocity of the solar corona, does not only depend on heliographic latitude but is also a function of time, while the nature of the latter dependence remains unclear. Besides measurement errors, deviations ???? from the mean rotational speed are also caused by proper motion of the observed point source (the tracer) with respect to its surroundings. The spread in ?? values at a particular heliographic latitude is a real effect, not caused by measurement errors. Most of the observations carry relative error less than 1?% in???.     

Photometric properties of outer planetary satellites

We present optical broadband photometry for the satellites J6, J7, J8, S7, S9, U3, U4, N1, and polarimetry for J6, obtained between 1970 and 1979. The outer Jovian satellites resemble C-type asteroids; J6 has a rotational lightcurve with period ～9.5 hr. The satellites beyond Jupiter also show C-like colors with the exception of S7 Hyperion. S9 Phoebe has a rotational lightcurve with period near either 11.25 or 21.1 hr. For U4 and N1 there is evidence for a lightcurve synchronous with the orbital revolution. The seven brighter Saturnian satellites show a regular relation between the ultraviolet dropoff and distance to the planet, probably related with differences in the rock component on their surfaces.     

Dynamic fission instability of dissipative protoplanets

All theories of fission require a catastrophic, dynamic phase in order to produce two separate bodies. We have used nonlinear numerical and linear analytical calculations to show that the dynamic fission instability probably does not occur in dissipative protoplanets. The numerical calculations were performed with a three-spatial-dimension hydrodynamical code, with the proto-planet represented by a fluid with a Murnaghan equation of state. The kinetic energy in the protoplanet (other than rigid body rotation) is dissipated throughout the evolution in order to simulate the effects of viscous dissipation. Protoplanets rotating above the limit for dynamic instability were given initial asymmetric density perturbations; in each case the asymmetry did not grow during a time on the order of the rotational period. This dynamical stability has been verified by including the dissipative terms in the tensor-virial equation analysis for the stability of a Maclaurin spheroid: the dynamic instability vanishes when the dissipative terms are included, while the secular instability (with a growth time much larger than the rotational period) remains. The result applies to bodies of radius R with a kinematic viscosity ν? 4 × 10¹³ (R/6400 km)²cm²sec^?1, and hence may be applicable to any terrestrial protoplanet which is not totally molten. Current thermal histories for the Earth predict a partially molten mantle with a viscosity greater than this critical value. Depending on the detailed rheology of the early Earth, our results appear to rule out the possibility of forming the Earth-Moon system through a dynamic fission instability.     

Distribution of spin axes and senses of rotation for 20 large asteroids

Pole determinations for 20 large asteroids are presented. This is the first determination of the sense of rotation for 11 of the objects, and a sense of rotation opposite to previous results is obtained for two of the remaining nine asteroids. The spin axes are fairly isotropically distributed, with a statistically uncertain preference for prograde rotation. The mean of the component of the spin angular velocity vectors toward the north ecliptic pole is 〈ω_z〉 = (0.8 ± 0.5) rev/day. This suggests that for large asteroids an original predominance of prograde rotators has not completely been randomized by collisions (the median diameter in the present sample is approximately 200 km). Two fundamentally different pole determination methods were combined in order to get as reliable results as possible. The first is an Amplitude-Magnitude method based on triaxial ellipsoidal models. The celestial sphere is scanned with trial poles and the one is chosen for which the best fit is obtained with semiempirical amplitude-aspect-phase and magnitude-aspect-phase relationships. Triaxial approximations to the true asteroidal shapes are also obtained with this method. The second method uses the variation of the observed synodic period of rotation to derive the axis and sense of rotation. A well-defined “standard feature” in the lightcurves is selected and is assumed to remain at a fixed rotational phase. An efficient algorithm for finding the correct number of rotational cycles between observations during different apparitions is used. This makes it possible to identify extrema observed during different apparitions with each other (it is not safe to assume that, e.g., the primary maximum at one opposition remains primary at other aspect angles). Discrimination between ambiguous rotation periods can also be made with this method. 4 Vesta is shown to have one maximum and one minimum per rotational cycle. The secular variations of the period of rotation for 7 Iris and 15 Eunomia are less than 3 × 10⁻⁴ and 2 × 10⁻⁴ sec/year, respectively.     

Testing quantised inertia on galactic scales

Galaxies and galaxy clusters have rotational velocities (v) apparently too fast to allow them to be gravitationally bound by their visible matter (M). This has been attributed to the presence of invisible (dark) matter, but so far this has not been directly detected. Here, it is shown that a new model that modifies inertial mass by assuming it is caused by Unruh radiation, which is subject to a Hubble-scale (Θ) Casimir effect predicts the rotational velocity to be: v ⁴=2GMc ²/Θ (the Tully-Fisher relation) where G is the gravitational constant, M is the baryonic mass and c is the speed of light. The model predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy clusters, within error bars, without dark matter or adjustable parameters, and makes a prediction that local accelerations should remain above 2c ²/Θ at a galaxy’s edge.     

The rotation,color, phase coefficient,and diameter of 1915 quetzalcoatl

Photoelectric observations of 1915 Quetzalcoatl on March 2, 1981 show that this asteroid has a rotational period of 4.9 ± 0.3 hr and a lightcurve amplitude of 0.26 magnitudes. B-V and U-B colors are found to be 0.83 ± 0.04 and 0.43 ± 0.03, respectively, consistent with Quetzalcoatl being an S-type asteroid. Additional observations from March 31, 1981 give a linear phase coefficient of 0.033 mag deg^?1 and a mean B(1,0) magnitude of 20.10. The resulting estimated mean diameter for Quetzalcoatl is only 0.37 km, making it one of the smallest asteroids for which physical observations have yet been made.     

Rotational properties of asteroids: Correlations and selection effects

Rotational data on 321 asteroids observed as of late 1978 are analyzed. Selection effects within the sample are discussed and used to define a data set consisting of 134 main-belt, nonfamily asteroids having reliably determined periods and amplitudes based on photoelectric observations. In contrast to A. W. Harris and J. A. Burns (1979, Icarus40, 115–144) we found no significant correlation between rotational properties and compositional type. Smaller asteroids have a greater range of rotational amplitudes than the largest asteroids but are not, on the average, appreciably more elongated. While no definite relationship between asteroid size and rotation rate was found the distribution is not random. The largest asteroids have rotation periods near 7 hr compared with 10 hr for the smaller. A group of large, rapidly rotating, high-amplitude asteroids is recognized. A pronounced change in rotational properties occurs near this size range (diam = 200 ± 50 km) which also corresponds to the size at which a change of slope occurs in the size frequency distribution. We believe this size range represents a transition region between very large, rapidly rotating, low-amplitude (primordial?) objects and smaller ones having a considerably greater range of periods and amplitudes. Asteroids in this transition size range display an increase in rotational amplitude with increasing spin rate; other than this, however, there is no correlation between period and amplitude. The region of low spatial density in the asteroid belt centered near 2.9 AU and isolated from the inner and outer belt by the 2:5 and 3:7 commensurabilities is shown to be a region in which non-C or -S asteroids are overrepresented and which have marginally higher rotational amplitudes than those located in more dense regions. We attribute disagreements between our results and other studies of this type to the inclusion of non-main-belt asteroids and photographic data in the earlier analyses.     

On the detection of newly created CN radicals in comets

Laboratory investigations of CN radical formation by photodissociation of parent molecules have suggested the possibility of observing emission lines in cometary spectra from newly formed CN radicals. These laboratory studies have shown that high initial internal excitation of CN is the rule with excitation of rotational levels N up to 70. In the collisionless environment of the cometary atmosphere this initial excitation would yield a corresponding distribution for the lowest vibrational level of the ground X²Σ⁺ state. Our calculations show that it is feasible with present observational techniques to detect photochemically excited lines with N ～ 30 in the 0-0 band of the violet system.     

Clues to Substellar Formation: Rotation and the Low-Mass End of the Initial Mass Function

We have monitored S Ori 45, a young, low-mass (20 M _j up) brown dwarf of the σ Orionis cluster (～3 Myr, 352 pc), using optical and near-infrared filters. S Ori 45 (spectral type M8.5) is found to be multi-periodic with a dominant modulation at 2.5–3.5 h, and a short modulation at about 46 min. We ascribe the longer of these modulations to a rotation period. After comparing these results with observations of more massive cluster brown dwarfs and field brown dwarfs, we conclude that substellar objects present rotational and angular momentum evolution. We have also obtained intermediate-resolution near-infrared spectroscopy of S Ori 70, which is a T-class, free-floating planetary candidate member in the σ Orionis cluster. Its observed spectrum has been compared to data of field brown dwarfs of similar types and to theoretical spectra computed for different surface temperatures and gravities. We conclude that S Ori 70 has a significantly cool, low-gravity atmosphere. This supports the young age of this object and its membership in the cluster. From state-of-the-art evolutionary models, the mass of S Ori 70 is estimated at 3 times the Jovian mass (⁺⁵ _?2 M _j up), challenging current stellar/substellar formation models. S Ori 70 remains the lowest mass object so far identified in any open cluster.     

Measurement of weak airglow emissions with a programmable scanning spectrometer

We demonstrate how the radiance response of a wavelength scanning instrument may be improved with a programmable scanning system. A minicomputer with a high level language offers a versatile software package that can be readily modified for any specific problem. We illustrate the technique with the application of the one meter Ebert Fastie spectrophotometer at the Arecibo Observatory's airglow facility to the measurements of the peak spectral emissions of the 5200 Å doublet of N(²D) in the nightglow and the 7320 Å doublet of O⁺(²P) in twilight. Typical measurement errors were ±0.2 R and ±0.5 R, respectively. We have also applied this method to measurements of the OH rotational temperature from the ratio of the P₁(2) and the P₁(5) rotational lines in the Meinel 8-3 band and obtained a precision of ±3 K within a time period of 6 min. The required modifications to the wavelength drive were not extensive, the costs were not high, and the technique may be applied to any wavelength scanning instrument in operation today.     

Stars with discrepant v sin i as derived from the Ca II λ3933 Å and Mg II λ4481 Å lines. IV. HD8837—a shell star, HD47964 and HD183986—new binaries

Axial rotation of a star plays an important role in its evolution, physical conditions in its atmosphere, and appearance of its spectrum. We have analyzed CCD spectra of three stars for which their projected rotational velocity remarkably differs when derived from the Ca II λ 3933 Å and MgII λ 4481 Å lines. We derived effective temperatures and surface gravities using published uvbyβ photometries and computed synthetic spectra. Comparing observed line profiles of the two lines with the computed ones, we estimated values of v sin i. We also derived radial velocities by means of the cross-correlation function. HD8837 is known to be a shell star with pronounced narrow absorption cores in the Balmer lines as well as in the strong metal lines; however, we do not confirm the emission component in the core of Hβ. HD47964 has been discovered by Hipparcos to be a double. However, in our spectra we do not find traces of the other star. Based on the Hipparcos data, we estimated that the other star would be a main sequence A4 star with an extremely high rotational velocity resulting in wiping out any traces of spectral lines of the companion. HD183986 is known to be a triple star. However, we have found a manifestation of a so far not discovered companion of the component HD183986A and estimated it as a main sequence A5 star having v sin i of about 150 km/s.     

Nature of the small main belt Asteroid 3169 Ostro

We present a set of rotational lightcurve measurements of the small main belt Asteroid 3169 Ostro. Our observations reveal an unambiguous, double-peaked rotational lightcurve with a peak-to-peak variation up to 1.2±0.05 mag and a synodic period of 6.509±0.001 h. From the large flux variation and the overall shape of the lightcurves, we suggest that 3169 Ostro could be a tightly bound binary or a contact binary, similar to the Trojan Asteroid 624 Hektor. A shape model of this system is proposed on the assumption that 3169 Ostro is a Roche binary described by a pair of homogeneous elongated bodies, with a size ratio of 0.87, in hydrostatic equilibrium and in circular synchronous motion around each other. The direction of the spin axis is determined modulo 180° by its J2000 ecliptic coordinates λ₀=50±10°, β₀=±54±5°. The binary interpretation and the pole solution adequately fit the earlier photometric observations made in 1986 and 1988. However, additional supporting lightcurves are highly desirable especially in the next mutual events occurrence of 2008 and 2009 in order to remove the pole ambiguity and to confirm unambiguously the binary nature of 3169 Ostro.     

Magnetic fields and rotation of the white dwarfs 40 Eri B and WD 0009+501

We describe the results of our magnetometric monitoring of two white dwarfs: 40 Eri B and WD 0009+501. We found periodic variations in the longitudinal magnetic field of 40 Eri B. The field variability with an amplitude of ～4 kG and a zero mean is discussed in terms of an oblique rotator model. The rotation period is ～5 h 17 min, but there is another period of 2 h 25 min that may be related to nondipolar field components. The published projected rotational velocities of 40 Eri B measured from a narrow non-LTE Hα peak V sin i?8 km s^?1 are in good agreement with our measurements of the magnetic field and the rotation period. The combined effect of magnetic and rotational broadening of the central Hα component constrains the rotation period, P? 5.2 h. We discovered the rotation period (1.83 h) of the magnetic white dwarf WD 0009+501. The period was found from the periodically varying magnetic field of the star with a mean 〈B_e〉 = ?42.3±5.4 kG and a half-amplitude of 32.0±6.8 kG.     

Photoelectric photometry of asteroids 9 Metis, 18 Melpomene, 60 Echo, 116 Sirona, 230 Athamantis, 694 Ekard,and 1984 KD

Photoelectric observations of seven asteroids were made from Gila Observatory between October 14, 1983, and June 21, 1984. The following synodic rotational periods and amplitudes are reported: 9 Metis, P = 5.04 hr, ΔM = 0.05; 18 Melpomene, P = 11.570 hr, ΔM = 0.22; 60 Echo, P = 25.208 hr, ΔM = 0.22; 116 Sirona, P = 12.028 hr, ΔM = 0.42; 230 Athamantis, P = 23.99 hr, ΔM > 0.20; 694 Ekard, P = 5.925 hr, ΔM = 0.50; 1984 KD, P = 1.97 hr, ΔM = 0.26. The rotational periods reported for asteroid 60 Echo, 116 Sirona, 694 Ekard, and 1984 KD represent completely new results. The synodic rotational period reported for asteroid 1984 KD is tentative and is based largely upon the observations of a single night. The reported synodic periods of the remaining six asteroids are based upon a minimum of 3 nights of photometric observations.     

Theoretical brightness temperature profiles of atmospheric pure H2 rotational quadrupole lines: Jupiter and Uranus

With the advent of high-resolution instruments and their use high above most of the telluric water vapor, we can expect to observe the hydrogen pure rotational quadrupole lines at 28, 17, and 12 μm from the atmospheres of the outer planets. We have calculated the best values for the line strengths, pressure-broadening coefficients, diffusion constants, and pressure shifts for these rotational transitions. We have used the collisionally narrowed Galatry profile to calculate brightness temperature line profiles for these H₂ transitions for the outer planets Jupiter and Uranus. We have also included the effect of the H₂ rotational-translational continuum and the NH₃ν₂ band.     

Rotation effects in classical T Tauri stars

Surface temperature inhomogeneities in classical T Tauri stars (CTTS) induced by magnetic activity andmass accretion lead to rotationalmodulation of both photometric and spectroscopic parameters of these stars. Using the extended photometric catalogue byGrankin et al., we have derived the periods and amplitudes of the rotational modulation of brightness and color for 31 CTTS; for six of them, the periods have been revealed for the first time. The inclinations of the rotation axis and equatorial rotational velocities of CTTS have been determined. We show that the known periods of brightness variations for some of the CTTS are not the axial rotation periods but are the Keplerian periods near the inner boundary of the dusty disk. We have found that the angular velocity of CTTS with a mass of 0.3?3M _?? in the Taurus-Auriga complex remains constant in the age range 1?C10 Myr. CTTS on radiative evolutionary tracks rotate faster than completely convective CTTS. The specific angular momentum of CTTS depends on the absolute luminosity in the H?? line.     

A semi-analytic approach to angular momentum transport in stellar radiative interiors

A novel semi-analytic spectral method, based on eigenfunction expansions, is applied to model the angular momentum transport in stellar radiative interiors. The advantages of our approach are shown by applying it to a spin-down model for a 1M _⊙ main-sequence star. The evolution of the coupling between core and envelope is investigated for different values of the viscosity and different geometries and intensities of the poloidal field. We suggest that a quadrupolar poloidal field may explain the short coupling timescale (τ _c～10 Myr) needed to reproduce the observed rotational evolution of fast rotators on the zero age main sequence, while a dipolar geometry is indicated in the case of slow rotators (τ _c～100 Myr). Our method provides a rigorous analytic treatment of a classic MHD problem and allows us to explore the influence of various parameters on the rotational history of radiative interiors.