Asteroid rotation: III. 1978 Observations

Photoelectric observations of 32 asteroids observed from Table Mountain Observatory during the second half of 1978 are reported. Rotation periods were obtained for most objects. Absolute magnitudes and phase functions were not determined for any of these asteroids. The geometric mean rotation period of the 32 asteroids observed is 14.2 ± 1.6 hr, as compared to 9.38 ± 0.35 hr for 182 asteroids analyzed in Paper I (A. W. Harris and J. A. Burns, 1979, Icarus 40, 115–144). We attribute this difference to an observational selection effect which favors detection of fast rotation, as discussed in Paper I. If this is true, then the present sample contains the reverse bias, since it is complete in that a period (in some cases very approximate) was obtained for each object observed, but fast rotators are underrepresented due to prior discovery of their rotation properties.     

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.     

Tentative detection of the rotation of Eris

We report a multi-week sequence of B-band photometric measurements of the dwarf planet Eris using the Swift satellite. The use of an observatory in low-Earth orbit provides better temporal sampling than is available with a ground-based telescope. We find no compelling evidence for an unusually slow rotation period of multiple days, as has been suggested previously. A ∼1.08 day rotation period is marginally detected at a modest level of statistical confidence (∼97%). Analysis of the combination of the Swift data with the ground-based B-band measurements of Rabinowitz et al. [Rabinowitz, D.L., Schaefer, B.E., Tourtellotte, S.W., 2007. Astron. J. 133, 26-43] returns the same period (∼1.08 day) at a slightly higher statistical confidence (∼99%).     

Spin states and climates of eccentric exoplanets

The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.     

CCD and photon-counting photometric observations of asteroids carried out at Padova and Catania observatories

We present the results of observational campaigns of asteroids performed at Asiago Station of Padova Astronomical Observatory and at M.G. Fracastoro Station of Catania Astrophysical Observatory, as part of the large research programme on Solar System minor bodies undertaken since 1979 at the Physics and Astronomy Department of Catania University. Photometric observations of six Main-Belt asteroids (27 Euterpe, 173 Ino, 182 Elsa, 539 Pamina, 849 Ara, and 984 Gretia), one Hungaria (1727 Mette), and two Near-Earth Objects (3199 Nefertiti and 2004 UE) are reported. The first determination of the synodic rotational period of 2004 UE was obtained. For 182 Elsa and 1727 Mette the derived synodic period of 80.23±0.08 and , respectively, represents a significant improvement on the previously published values. For 182 Elsa the first determination of the H-G magnitude relation is also presented.     

Exoplanet's Figure and Its Interior

Along with the development of the observing technology, the observation and study on the exoplanets’ oblateness and apsidal precession have achieved significant progress. The oblateness of an exoplanet is determined by its interior density profile and rotation period. Between its Love number k₂ and core size exists obviously a negative correlation. So oblateness and k₂ can well constrain its interior structure. Starting from the Lane-Emden equation, the planet models based on different polytropic indices are built. Then the flattening factors are obtained by solving the Wavre's integro-differential equation. The result shows that the smaller the polytropic index, the faster the rotation, and the larger the oblateness. We have selected 469 exoplanets, which have simultaneously the observed or estimated values of radius, mass, and orbit period from the NASA (National Aeronautics and Space Administration) Exoplanet Archive, and calculated their flattening factors under the two assumptions: tidal locking and fixed rotation period of 10.55 hours. The result shows that the flattening factors are too small to be detected under the tidal locking assumption, and that 28% of exoplanets have the flattening factors larger than 0.1 under the fixed rotation period of 10.55 hours. The Love numbers under the different polytropic models are solved by the Zharkov's approach, and the relation between k₂ and core size is discussed.     

On the Long-Term Modulation of Solar Differential Rotation

Long-term modulation of solar differential rotation was studied with data from Mt. Wilson and our original observations during Solar Cycles 16 through 23. The results are that i) the global B-value (i.e. latitudinal gradient of differential rotation) is modulated with a period of about six or seven solar cycles, ii) the B-values of the northern and southern hemispheres are also modulated with a period similar to the global one, but iii) they show quasi-oscillatory behavior with a phase shift between them. We examined the yearly fluctuations of the B-values in every solar cycle with reference to the phase of the sunspot cycle and found that the B-values in the sunspot-minimum years show large and erratic variations, while those in the sunspot-maximum years show small fluctuations. Positive correlation between the former B-values and the latter was found. We discuss the independent long-term behavior of solar differential rotation between the northern and southern solar hemispheres and the implication for the solar dynamo.     

On possible binarity of Leatitia asteroid 39

The 39 Laetitia asteroid was observed by the digital television complex at the Crimean Astrophysical Observatory in 2000 in three spectral bands close to B, V and R simultaneously. An analysis of the variations in the absolute magnitude shows that there is a known period of rotation P = 0.^d214093. In variations of color indices B-V and V-R, this period is absent. Frequency analysis of color indices B-V and V-R makes it possible to reveal the true periods of rotation for components as follows: P ₁ = 0.^d237 and P ₂ = 0.^d177. The theoretical and observed period of librations agrees in value. Based on the two detected periods of rotation for asteroid components according to color indices B-V and V-R, a period of the libration of the satellite according to integral magnitude, we conclude that this asteroid is a binary one.     

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.     

LASCO observations of the coronal rotation and morphology of tracers seen at solar maximum and comparison with solar minimum

We present data obtained from the Large Angle Spectrometric Coronagraph (LASCO) aboard the Solar and Heliospheric Observatory spacecraft (SOHO). We compare the rotation of the white-light corona as seen during a period approaching the maximum of the solar 11-year activity cycle with that observed in a previous study made at solar minimum (Lewis et al., 1999). We find no fundamental difference in the rotation characteristics and again find the white-light corona to be radially rigid. The rotation has been observed at altitudes from 2.5 R _⊙ to beyond 15 R _⊙ and as predicted in the previous study, the greater level of complexity in the coronal structures and their relatively rapid evolution has not allowed periods to be determined as accurately as at solar minimum. Our best estimate of the mean synodic rotation period during the period of study (7 March 1999 to 6 March 2000) is 27.5±0.3 days. This is consistent with the relatively small scale structures associated with the surface activity imposing their rotation signature on an otherwise axisymmetric background corona. The short-lived nature of the small scale coronal morphologies at this epoch has made a thorough analysis of the latitudinal variation difficult, although we again find some evidence for the white light corona's increased latitudinal rigidity when compared to the underlying photosphere. However, we again note how projection effects create difficulties in confirming the exact degree of rigidity in the corona at these altitudes and a very simple coronal model is used to highlight how the appearance of lower latitude features in projection can contaminate the coronal signal observed at other latitudes. We also note evidence for a sudden and apparently fundamental change to the global coronal morphology on the approach to solar maximum and suggest this may represent the time beyond which the classical solar dipole ceases to dominate the coronal field.     

Variations in the Solar Coronal Rotation with Altitude – Revisited

Here we report an in-depth reanalysis of an article by Vats et al. (Astrophys. J. 548, L87, 2001) that was based on measurements of differential rotation with altitude as a function of observing frequencies (as lower and higher frequencies indicate higher and lower heights, respectively) in the solar corona. The radial differential rotation of the solar corona is estimated from daily measurements of the disc-integrated solar radio flux at 11 frequencies: 275, 405, 670, 810, 925, 1080, 1215, 1350, 1620, 1755, and 2800 MHz. We use the same data as were used in Vats et al. (2001), but instead of the twelfth maxima of autocorrelograms used there, we use the first secondary maximum to derive the synodic rotation period. We estimate synodic rotation by Gaussian fit of the first secondary maximum. Vats et al. (2001) reported that the sidereal rotation period increases with increasing frequency. The variation found by them was from 23.6 to 24.15 days in this frequency range, with a difference of only 0.55 days. The present study finds that the sidereal rotation period increases with decreasing frequency. The variation range is from 24.4 to 22.5 days, and the difference is about three times larger (1.9 days). However, both studies give a similar rotation period at 925 MHz. In Vats et al. (2001) the Pearson’s factor with trend line was 0.86, whereas present analysis obtained a \({\sim}\,0.97\) Pearson’s factor with the trend line. Our study shows that the solar corona rotates more slowly at higher altitudes, which contradicts the findings reported in Vats et al. (2001).     

On the differential rotation of the polar caps of neutron stars

The model of a magnetized rotating neutron star with an electric current in the region of its fluid polar magnetic caps is considered. The presence of an electric current leads to differential rotation of the magnetic caps. The rotation structure is determined by the electric current density distribution over the surface. In the simplest axisymmetric configuration, the current flows in one direction near the polar cap center and in the opposite direction in the outer ring (the total current is zero for the neutron star charge conservation). In this case, two rings with opposite directions of rotation appear on the neutron star surface, with the inner ring always lagging behind the star’s main rotation. The differential rotation velocity is directly proportional to the electric current density gradient along the polar cap radius. At a width of the region of change in the electric current from 1 to 10² cm and a period ～1 s and a magnetic field B ～ 10¹² G typical of radio pulsars, the linear differential rotation velocity is ～10^?2–10^?4 cm s^?1 (corresponding to a revolution time of ～0.1–10 yr).     

Physical properties of asteroid 433 Eros

Newly available photometric, polarimetric, spectroscopic, thermal-radiometric, radar, and occultation results are synthesized in order to derive a coherent model for Eros. The geometric albedo is 0.19±0.01 at the visual wavelength, and the overall dimensions are approximately 13 × 15 × 36km. The rotation is about the short axis, in the direct sense, with a sidereal period of 5^h16^m13^s.4. The pole of rotation lies within a few degrees of ecliptic coordinates λ = 16° and β = + 11°.Eros is uniformly coated with a particulate surface layer several millimeters thick. It has an iron-bearing silicate composition, similar to that of a minority of main-belt asteroids, and probably identifiable with H-type ordinary chondrites.     

Coordinated observations of asteroids 1219 Britta and 1972 Yi Xing

Identified as possible flyby targets for the Galileo spacecraft, Asteroids 1219 Britta and 1972 Yi Xing became the focus of a coordinated observing program. Although a subsequent change in the launch date removed these asteroids from consideration for the Galileo mission, the ground-based observing program yielded a substantial amount of information on these previously unobserved asteroids. Britta's sideral rotation period is found to be 5.57497 ± 0.00013 hr and its rotation is retrograde. The lightcurve amplitude ranged from 0.60 to 0.70 mag, depending on phase angle. Britta can be classified as an S-type asteroids based on its measured spectra and albedo. The absolute magnitude and slope parameter derived from the lightcurve maxima are H₀ = 11.67 ± 0.03 and G₀ = 0.03 ± 0.04. A 0.002 mag deg⁻¹ phase reddening in B·V was also measured. 1972 Yi Xing was less well observed but a unique synodic period of 14.183 ± 0.003 hr was determined. The observed lightcurve amplitude was 0.18 mag. Five-color measurements are consistent with an S-type classification. For an assumed slope parameter G = 0.25, Yi Xing's (lightcurve maximum) absolute magnitude H₀ = 13.32 ± 0.01.     

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.     

Decametric radio measurement of Jupiter's rotation period

A total of 26 measurements of Jupiter's 12-year average rotation period were made at frequencies of 18, 20, and 22.2 MHz at observatories in Florida and Chile. An improved method was employed in which histograms of occurrence probability vs central meridian longitude obtained at the same frequency and observatory during apparitions about 12 years (one Jovian year) apart were cross correlated. The longitude shift giving maximum cross correlation was used to correct the initially assumed rotation period value. The mean of the measurements is 9 hr 55 min 29.689 sec, with a standard deviation of the mean of 0.005 sec. This is about 0.02 sec, or 4 standard deviations, less than the System III (1965) value. The measurements indicate that the rotation period was not changing (linearly) at a rate in excess of 0.03 sec/yr. If the synoptic monitoring program is continued through the next maximum of the jovicentric declination of the Earth (D_E), we will probably be able to detect a rate of change in rotation period as small as 0.002 sec/yr. This accuracy might be sufficient to reveal a secular drift in Jupiter's magnetic field.     

Determination of zonal wind speeds at heights near 530 km from the orbit of Explorer 24 (1964-76A)

The orbit of Explorer 24 (1964–1976A) has been determined at 18 epochs during the five month period prior to its decay in October 1968, using the RAE orbit refinement computer program PROP6. As a balloon, the satellite was strongly influenced by atmospheric perturbations, despite its high perigee altitude near 490 km. It therefore provided an opportunity of determining atmospheric rotation rates at high altitude. The rotation rate, Λ rev day^?1, was estimated from the observed variation in orbital inclination, after the removal of perturbations including those due to solar radiation pressure.The mean rotation rates, averaged over local time, are Λ = 0.98 for 18 May to 18 August 1968 at 542 km; Λ = 1.06 for 18 May to 13 October 1968 at 533 km.For morning conditions, Λ = 0.9 for 22 June to 20 July 1968 at 540 km; Λ = 0.8 during September 1968 at 513 km.For evening conditions, Λ = 1.1 for 18 May to 15 June 1968, and for 26 July to 7 September 1968, at 540 km and 536 km respectively; Λ = 1.3 for 28 September to 13 October 1968 at 484 km.Further, the maximum W to E zonal wind has been estimated to occur at 20.5 h local time, during the period of the analysis.     

The lithium-rotation correlation for WTTS in Taurus–Auriga

Surface lithium abundance and rotation velocity can serve as powerful and mutually complementary diagnostics of interior structure of stars. So far, the processes responsible for the lithium depletion during pre-main sequence evolution are still poorly understood. We investigate whether a correlation exists between equivalent widths of Li (EW(Li)) and rotation period (P_rot) for weak-line T Tauri stars (WTTSs). We find that rapidly rotating stars have lower EW(Li) and the fast burning of Li begins at the phase when star’s P_rot evolves towards 3 days among 0.9M_⊙ to 1.4M_⊙ WTTSs in Taurus–Auriga. Our results support the conclusion by Piau and Turch-Chiéze about a model for lithium depletion with age of the star and by Bouvier et al. in relation to rotation evolution. The turn over of the curve for the correlation between EW(Li) and P_rot is at the phase of zero-age main sequence (ZAMS). The EW(Li) decreases with decreasing P_rot before the star reaches the ZAMS, while it decreases with increasing P_rot (decreasing rotation velocity) for young low-mass main sequence stars. This result could be explained as an age effect of Li depletion and the rapid rotation does not inhibit Li destruction among low-mass PMS stars.     

Asteroid rotation: I. Tabulation and analysis of rates,pole positions and shapes

Data are presented for the 182 asteroids whose rotational properties are available in the literature. Plots are provided for the asteroid rotational frequency f and lightcurve amplitude Δm versus asteroid size; the latter is determined using standard methods if data are available but otherwise is estimated from asteroid albedos, selected depending on taxonomic type or orbital position. A linear least-squares fit to all the data shows that f increases with decreasing size, confirming McAdoo and Burns' (1973) result; this is demonstrated to be primarily caused by relatively more small non-C than C asteroids in our sample, coupled with a slower mean rotation rate for C asteroids (P ≈ 11 hr) than non-C asteroids (P ≈ 9 hr). In terms of the collisional theory of Harris (1979a), this means that the C's are less dense than the other minor planets. Any slight tendency for smaller asteroids to spin faster, even within a taxonomic type, could be due to selection effects; our data are not extensive enough to determine whether the very smallest (? 10-km diameter) spin especially fast. The minor planets of our survey become more irregular at smaller sizes, disputing the conclusions of Bowell (1977b), Degewij (1977), and Degewij et al. (1978), based on other, perhaps more complete, data; selection effects may account for this disagreement. Shapes do not appear to depend on taxonomic type. The dispersion of asteroid rotation rates from the mean is found to be in excellent agreement with a three-dimensional Maxwellian distribution, such as would be developed in a collisionally evolved system. The rotation axes, therefore, appear to be randomly oriented in space. Rotation pole positions are also tabulated and calculated to likely be constant in space over the extent of past observation. Observers are encouraged to measure the rotational properties of faint objects and asteroids of unusual taxonomic types, and to carry out long-time studies of asteroids which over short periods do not seem to vary.     

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.