Spin axis of (2953) Vysheslavia and its implications

Photometric observations made during the years 2000-2005 are used to determine the pole orientation of (2953) Vysheslavia, a ?15-km size member of the Koronis family. We find admissible solutions for ecliptic latitude and longitude of the rotation pole P₃: βp=−64°±10° and λp=11°±8° or P₄: βp=−68°±8° and λp=192°±8°. These imply obliquity values γ=154°±14° and γ=157°±11°, respectively. The sidereal rotation period is Psid=0.2622722±0.0000018 day. This result is interesting for two reasons: (i) the obliquity value between 90° and 180° is consistent with a prediction done by Vokrouhlický et al. [Vokrouhlický, D., Bro?, M., Farinella, P., Kne?evi?, Z., 2001. Icarus 150, 78-93] that Vysheslavia might have been transported to its unstable orbit by the Yarkovsky effect, and (ii) with the obliquity close to 180°, Vysheslavia seems to belong to one of the two distinct groups in the Koronis family found recently by Slivan [Slivan, S.M., 2002. Nature 419, 49-51], further supporting the case of dichotomy in the spin axis distribution in this family. We also argue against the possibility that Vysheslavia reached its current orbit by a recent collisional breakup.     

Spin vectors in the Koronis family: comprehensive results from two independent analyses of 213 rotation lightcurves

Observations of Koronis asteroid family members (158) Koronis, (277) Elvira, (311) Claudia, (321) Florentina, and (720) Bohlinia made during the period 1998-2001 yielded 61 new individual rotation lightcurves to augment previous surveys (R.P. Binzel, 1987, Icarus 72, 135-208; S.M. Slivan, R.P. Binzel, 1996, Icarus 124, 452-470) and allow determination of the senses of rotation and spin vector orientations for these objects. Spin vector reductions were performed on these five objects and also on family members (167) Urda, (208) Lacrimosa, (534) Nassovia, and (1223) Neckar using both a combination of amplitude-magnitude and epoch methods and a convex inversion method. A total of 213 individual lightcurves were analyzed to determine sidereal rotation periods, pole solutions and obliquities, associated photometric parameters, and model shapes for each object. We checked our methods and results using the (243) Ida Master Dataset of lightcurves (R. P. Binzel et al., 1993, Icarus 105, 310-325) and found that the true pole determined from the Galileo fly by of this irregularly shaped member of the Koronis family falls just at the edge of the estimated uncertainty of our own solution. Our findings for the spin vector distribution of 10 members within the Koronis family represent the first systematic study of spin states within a well-established Hirayama family, and provide observational constraints for models of the physics of family formation and spin vector evolution in the main belt.     

Evolution of the spin of Venus

Evolutionary sequences of the Venusian sidereal rotation period, and of its obliquity, under the action of solar gravitational torques on the body of the planet and on its atmosphere are here presented. They show that Venus initial configuration in the early history of the solar system may well have been of rotation period between 33 and 48 days with an angle of obliquity of about 170°.     

Possible dynamical evolution of the rotation of Venus since formation

The past evolution of the rotation of Venus has been studied by a numerical integration method using the hypothesis that only solar tidal torques and core-mantle coupling have been active since formation. It is found quite conceivable that Venus had originally a rotation similar to the other planets and has evolved in 4.5×10⁹ years from a rapid and direct rotation (12-hour spin period and nearly zero obliquity) to the present slow retrograde one.While the solid tidal torque may be quite efficient in despinning the planet, a thermally driven atmospheric tidal torque has the capability to drive the obliquity from 0° towards 180° and to stabilize the spin axis in the latter position. The effect of a liquid core is discussed and it is shown that core-mantle friction hastens the latter part of the evolution and makes even stronger the state of equilibrium at 180°. The model assumes a nearly stable balance between solid and atmospheric tides at the current rotation rate interpreting the present 243 day spin period as being very close to the limiting value.A large family of solutions allowing for the evolution, in a few billions years, of a rapid prograde rotation to the present state have been found. Noticeably different histories of evolution are observed when the initial conditions and the values of the physical parameters are slightly modified, but generally the principal trend is maintained.The proposed evolutionary explanation of the current rotation of Venus has led us to place constraints on the solid bodyQ and on the magnitude of the atmospheric tidal torque. While the constraints seem rather severe in the absence of core-mantle friction (aQ15 at the annual frequency is required, and a dominant diurnal thermal response in the atmosphere is needed), for a large range of values of the core's viscosity, the liquid core effect allows us to relax somewhat these constraints: a solid bodyQ of the order 40 can then be allowed. ThisQ value implies that a semi-diurnal ground pressure oscillation of 2 mb is needed in the atmosphere in order for a stable balance to occur between the solid and atmospheric tides at the current rotation rate. No model of atmospheric tides on Venus has been attempted in this study, however the value of 2 mb agrees well with that predicted by the model given in Dobrovolskis (1978).     

Asteroid age distributions determined by space weathering and collisional evolution models

We provide evidence of consistency between the dynamical evolution of main belt asteroids and their color evolution due to space weathering. The dynamical age of an asteroid’s surface (Bottke, W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H. [2005]. Icarus 175 (1), 111-140; Nesvorný, D., Jedicke, R., Whiteley, R.J., Ivezi?, ?. [2005]. Icarus 173, 132-152) is the time since its last catastrophic disruption event which is a function of the object’s diameter. The age of an S-complex asteroid’s surface may also be determined from its color using a space weathering model (e.g. Willman, M., Jedicke, R., Moskovitz, N., Nesvorný, D., Vokrouhlický, D., Mothé-Diniz, T. [2010]. Icarus 208, 758-772; Jedicke, R., Nesvorný, D., Whiteley, R.J., Ivezi?, ?., Juri?, M. [2004]. Nature 429, 275-277; Willman, M., Jedicke, R., Nesvorny, D., Moskovitz, N., Ivezi?, ?., Fevig, R. [2008]. Icarus 195, 663-673. We used a sample of 95 S-complex asteroids from SMASS and obtained their absolute magnitudes and u, g, r, i, z filter magnitudes from SDSS. The absolute magnitudes yield a size-derived age distribution. The u, g, r, i, z filter magnitudes lead to the principal component color which yields a color-derived age distribution by inverting our color-age relationship, an enhanced version of the ‘dual τ’ space weathering model of Willman et al. (2010).We fit the size-age distribution to the enhanced dual τ model and found characteristic weathering and gardening times of τ_w = 2050 ± 80 Myr and respectively. The fit also suggests an initial principal component color of −0.05 ± 0.01 for fresh asteroid surface with a maximum possible change of the probable color due to weathering of ΔPC = 1.34 ± 0.04. Our predicted color of fresh asteroid surface matches the color of fresh ordinary chondritic surface of PC₁ = 0.17 ± 0.39.     

High-Latitude Solar Rotation Traced by Magnetic Elements

Sequential observations at Huairou Solar Observation Station, China, and Kitt Peak, U.S.A., show that polar magnetic elements can live from several to more than 58 hours. This enables measurement of the solar rotation rate near the polar region by tracing magnetic element motions. With observations carried out on 8–15 July 1997, we identify and trace more than 1300 elements at north heliographic latitudes between 55°–85° using two methods, and fit the mean sidereal rotation rate as =14.0±0.54–(2.24±1.22)sin²–(1.78±0.79)sin⁴ deg per day.     

Additional measurements of the high-latitude sunspot rotation rate

We report measurements of the sunspot rotation rate at high sunspot latitutdes for the years 1966–1968. Ten spots at ¦latitude¦ 28 deg were found in our Mees Solar Observatory H patrol records for this period that are suitable for such a study. On the average we find a sidereal rotation rate of 13.70 ± 0.07 deg day^-1 at 31.05 ± 0.01 deg. This result is essentially the same as that obtained by Tang (1980) for the succeeding solar cycle, and significantly larger than Newton and Nunn's (1951) results for the 1934–1944 cycle. Taken together, the full set of measurements in this latitude regime yield a rotation rate in excellent agreement with the result =14^°.37₇–2^°.77 sin², derived by Newton and Nunn from recurrent spots predominatly at lower latitudes throughout the six cycles from 1878–1944.Summer Research Assistant.     

Radar observations and a physical model of Asteroid 1580 Betulia

We report Arecibo (2380-MHz, 13-cm) observations of Asteroid 1580 Betulia in May-June 2002. We combine these continuous-wave Doppler spectra and delay-Doppler images with optical lightcurves from the 1976 and 1989 apparitions in order to estimate Betulia's shape and spin vector. We confirm the spin vector solution of Kaasalainen et al. [Kaasalainen, M., and 21 colleagues, 2004. Icarus 167, 178-196], with sidereal period P=6.13836 h and ecliptic pole direction (λ,β)=(136°,+22°), and obtain a model that resembles the Kaasalainen et al. convex-definite shape reconstruction but is dominated by a prominent concavity in the southern hemisphere. We find that Betulia has a maximum breadth of 6.59±0.66 km and an effective diameter of 5.39±0.54 km. These dimensions are in accord with reanalyzed polarimetric and radar data from the 1970s. Our effective diameter is 15% larger than the best radiometric estimate of Harris et al. [Harris, A.W., Mueller, M., Delbó, M., Bus, S.J., 2005. Icarus 179, 95-108], but this difference is much smaller than the size differences between past models. Considering orbits of test particles around Betulia, we find that this asteroid's unusual shape results in six equilibrium points close to its equatorial plane rather than the usual four points; two of these six points represent stable synchronous orbits while four are unstable. Betulia's close planetary encounters can be predicted for over four thousand years into the future.     

Differential rotation of the solar atmosphere as determined from millimeter data

Radiospectroheliograms obtained at millimeter wavelengths were used to determine the rotation of the solar atmosphere. Regions observed in both emission as well as absorption (associated with H dark filaments) were followed across the disk. The average sidereal rotation rate deduced from emissive regions is given by (deg day^-1)=14.152(±0.270)-4.194(±3.017)sin² B, where B is the heliographic latitude and the quoted errors are the standard deviations of a least squares fit to the data. The rate deduced from absorption regions is given by =14.729(±0.286)-1.050(±1.611)sin² B. This rate is larger than that of emissive regions at all latitudes and shows smaller differential rotation. This apparent difference in the rotation rates is probably due to the difference in the height of formation of the emissive and absorption regions. This difference could be used to estimate the difference in height between an emissive region and an absorption feature in millimeter radiation.     

Long-term evolution of the spin of Venus: II. numerical simulations

We present here the numerical application of the theoretical results derived in Correia et al. (2003, Icarus 163, 1-23) for the spin evolution of Venus since its formation. We explore a large variety of initial conditions to cover the possible formation and evolutionary scenarios. In particular, we pay special attention to the evolutions which cross the chaotic zone resulting from secular planetary perturbations (Laskar and Robutel, 1993, Nature 361, 608-612). We demonstrate that Venus’ axis can be temporarily trapped in a secular resonance with the node of Neptune’s orbit, which can prevent it from being tilted to 180° and will drive it toward 0°. We test several dissipation models and parameters to evaluate their contribution to the planet’s spin history. We confirm that despite the variations in the models, only three of the four final spin states of Venus are possible (Correia and Laskar, 2001, Nature 411, 767-770) and that the present observed retrograde spin state of Venus can be attained by two different processes. In the first scenario (π−), the axis is tilted toward 180° while its rotation rate slows down, while in the second one, the axis is driven toward 0° obliquity and the rotation rate decreases, stops, and increases again in the reverse direction to a final equilibrium value (0−).     

Size-frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families

We investigate the morphology of size-frequency distributions (SFDs) resulting from impacts into 100-km-diameter parent asteroids, represented by a suite of 161 SPH/N-body simulations conducted to study asteroid satellite formation [Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M., 2004. Icarus 170, 243-257]. The spherical basalt projectiles range in diameter from 10 to 46 km (in equally spaced mass increments in logarithmic space, covering six discrete sizes), impact speeds range from 2.5 to 7 km/s (generally in 1 km/s increments), and impact angles range from 15° to 75° (nearly head-on to very oblique) in 15° increments. These modeled SFD morphologies match very well the observed SFDs of many known asteroid families. We use these modeled SFDs to scale to targets both larger and smaller than 100 km in order to gain insights into the circumstances of the impacts that formed these families. Some discrepancies occur for families with parent bodies smaller than a few tens of kilometers in diameter (e.g., 832 Karin), however, so due caution should be used in applying our results to such small families. We find that ∼20 observed main-belt asteroid families are produced by the catastrophic disruption of D>100 km parent bodies. Using these data as constraints, collisional modeling work [Bottke Jr., W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H.F., 2005b. Icarus 179, 63-94] suggests that the threshold specific energy, , needed to eject 50% of the target body's mass is very close to that predicted by Benz and Asphaug [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20].     

Radar observations and a physical model of contact binary Asteroid 4486 Mithra

Arecibo (2380 MHz, 12.6 cm) and Goldstone (8560 MHz, 3.5 cm) delay-Doppler radar images obtained in July and August of 2000 reveal that 4486 Mithra is an irregular, significantly bifurcated object, with a central valley ∼380 m deep and a long axis potentially exceeding 2 km. With its bimodal appearance, Mithra is a strong candidate for a contact binary asteroid. Sequences of Goldstone images spanning up to 3 h per day show very little rotation and establish that Mithra is an unusually slow rotator. We used Goldstone and Arecibo data to estimate Mithra’s 3D shape and spin state. We obtain prograde (λ = 337°, β = 19°) and retrograde (λ = 154°, β = −19°) models that give comparable fits, have very similar shapes roughly resembling an hourglass, and have a rotation period of 67.5 ± 6.0 h. The dimensions of these two models are very similar; for the prograde solution the maximum dimensions are X = 2.35 ± 0.15 km, Y = 1.65 ± 0.10 km, Z = 1.44 ± 0.10 km. Dynamical analysis of our models suggests that in the past, Mithra most likely went through a period of even slower rotation with its obliquity close to 90°. The spin rate is predicted to be increasing due to thermal torque (YORP), while the obliquity, which is currently +68° and +106° for the prograde and retrograde models, respectively, is predicted to move away from 90°.     

Measurement of the solar rotation, 1978, from recurrent and non-recurrent sunspots

Results are presented for the solar rotation, 1978, as derived from sunspots by two different methods. Using recurrent spots only, the latitude dependence of the sidereal rotation rate was calculated to be =(14.41±0.05)–(3.13±0.26) sin² . Using recognizable spots, both recurrent and non-recurrent, average rotation rates were obtained for 5-degree intervals of latitude. The results from these two approaches were found to be in agreement with observations made between 1878 and 1951, suggesting that the solar rotation has not changed in the past 100 years.Currently at Northwestern University, Evanston, Ill., U.S.A.     

Dynamical evolution of the rotation of Venus

By considering the torque of the bodily tides, the effect of the core-mantle viscous coupling and the torque of the atmospheric tides have been obtained by numerical calculation: the evolution of the spin angular velocity and the obliquity of the Venus are calculated numerically with the step-variable Runge-Kutta method of 7th order; and 7 sets of the probable Cytherean spin evolution have been obtained. It is indicated that the present spin state of Venus is the result of long-term evolution within the reasonable ranges of some disposable parameters. The early spin period is between 7 h to 2 d and the corresponding obliquity is about 90 ° ~ 100 °. The effects of the torques of body and atmospheric tides and the core-mantle viscous coupling of Venus on its spin angular velocity could nearly cancel out each other about a billion years ago. Therefore, Venus could have been captured in a spin-orbit resonant state by the gravitational torque of the Earth on the permanent deformation part of Venus; and this resonant state has lasted up to the present time.     

On the relation between the synodic and sidereal rotation period of the Sun

It is pointed out that by taking Kepler's second law into account, the sidereal correction, i.e., the correction to be added to the observed synodic rotation rate of the Sun in order to get the sidereal rate, can be calculated more directly than described in a recent paper by Roa et al. (1995).     

Spectroscopic determinations of solar rotation

Spectral line shift data obtained from full-disk magnetograms recorded at Mt. Wilson are analyzed for differential rotation. The method of analysis is discussed and the results from the data for 1966 through 1968 are presented. The average equatorial velocity over this period is found to be 1.93 km/sec or 13.76 deg/day (sidereal). This corresponds to a sidereal period of 26.16 days. The average results are = 2.78 × 10^-6 - 3.51 × 10^-7 sin² B - 4.43 × 10^-7 sin⁴ B rad/sec, whereB is the solar latitude. This indicates a smaller decrease of angular velocity with latitude than found by earlier investigators. Variations from day to day are caused by large-scale short-lived velocity fields on the solar surface. There also appear to be secular variations.Currently at the Kitt Peak National Observatory, Tucson, Arizona.     

The peculiarities of rotation of the solar polar regions

The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s^–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s^–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s^–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator.     

Thermal inertia of main belt asteroids smaller than 100 km from IRAS data

Recent works have shown that the thermal inertia of km-sized near-Earth asteroids (NEAs) is more than 2 orders of magnitude higher than that of main belt asteroids (MBAs) with sizes (diameters) between 200 and 1000 km. This confirms the idea that large MBAs, over hundreds millions of years, have developed a fine and thick thermally insulating regolith layer, responsible for the low values of their thermal inertia, whereas km-sized asteroids, having collisional lifetimes of only some millions years, have less regolith, and consequently a larger surface thermal inertia.Because it is believed that regolith on asteroids forms as a result of impact processes, a better knowledge of asteroid thermal inertia and its correlation with size, taxonomic type, and density can be used as an important constraint for modeling of impact processes on asteroids. However, our knowledge of asteroids’ thermal inertia values is still based on few data points with NEAs covering the size range 0.1-20 km and MBAs that .Here, we use IRAS infrared measurements to estimate the thermal inertia values of MBAs with diameters and known shapes and spin vector, filling an important size gap between the largest MBAs and the km-sized NEAs. An update to the inverse correlation between thermal inertia and diameter is presented. For some asteroids thermophysical modeling allowed us to discriminate between the two still possible spin vector solutions derived from optical lightcurve inversion. This is important for (720) Bohlinia: our preferred solution was predicted to be the correct one by Vokrouhlický et al. [2003. The vector alignments of asteroid spins by thermal torques. Nature 425, 147-151] just on theoretical grounds.     

Differential rotation and giant cell circulation of solar Ca+-network

We report new results obtained from high precision computer controlled tracings of ca. 400 bright Ca⁺-mottles made during summer 1975 in continuation of our 1974 program (Schröter and Wöhl, 1975). In particular, we looked in 1975 for the existence of a giant circulation pattern in the equatorial zone. We find for the differential rotation: = 13.93 – 2.90 sin² B (deg/day, sidereal) when combining the new measurements with those obtained in 1974. Observations from 26th April until June 19th give strong evidence that at that time four giant circulation cells, crossing the solar equator, (i.e. a nonaxisymmetric velocity field pattern with respect to the solar equator) did exist. This yields two more rapid and two slower rotating sectors with v = ±80 m s^–1. These giant cells transport angular momentum towards the equator.     

Obliquity evolution of extrasolar terrestrial planets

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio (m/Mp) and initial obliquity (γ₀), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins (sinγ₀∼1) are more likely to be produced than straight ones (sinγ₀∼0). The ratio m/Mp is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet-satellite systems have focused on a particular case of the Earth-Moon systems in which m/Mp?0.0125 and γ₀∼10° or the two-body planar problem in which γ₀=0° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m/Mp (from 0.0025 to 0.05) and γ₀ (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth-Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼10-20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m/Mp-γ₀ space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet-satellite systems and discussions of surface environments of the planets.