Rotational properties of ten main belt asteroids: Analysis of the results obtained by photoelectric photometry

V photoelectric lightcurves of ten main belt asteroids (11 Partenope, 20 Massalia, 31 Euphrosyne, 41 Daphne, 55 Pandora, 71 Niobe, 79 Eurynome, 129 Antigone, 344 Desiderata, and 387 Aquitania), obtained during the 1981–1983 oppositions, are reported. The rotation period of 11 Partenope is P = 7.83 hr and that of 344 Desiderata P = 10.53 hr. The shape and the pole coordinates of 20 Massalia, 31 Euphrosyne, and 129 Antigone were also derived and those of 41 Daphne confirmed. The lightcurves of the remaining objects are presented: a preliminary discussion of their possible rotational properties and their morphological features is given.     

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.     

The pole of (51) Nemausa

The complex lightcurves make (51) Nemausa a good case for the study of general methods for pole determination. From six lightcurves the pole is determined to 20^h24^m; +53° (1950); the rotation is retrograde with period 7^h.782936 ± 0^h.000005. Presence of nongeometric scattering is proved by a significant 0.008 mag amplitude. Formulae and photometric elements are given for predictions of the shapes of lightcurves in future oppositions. The precision of the Fourier coefficients may be reduced below the present ±0.003 mag level by avoiding the systematic errors in the observations due to phase factor variations and discontinuities when changing comparison stars.     

Pole orientation of 16 psyche by two independent methods

Nineteen new lightcurves of 16 Psyche are presented along with a pole orientation derived using two independent methods, namely, photometric astrometry (PA) and magnitude-amplitude-shape-aspect (MASA). The pole orientations found using these two methods agree to within 4°. The results from applying photometric astrometry were prograde rotation, a sidereal period of $\text{0}\text{d}\text{dot}\text{1748143 ± 0}\text{d}\text{dot}\text{0000003}$, and a pole at longitude 223° and latitude +37°, with an uncertainty of 10°; and, from applying magnitude-amplitude-shape-aspect a pole at 220 ± 1°, +40 ± 4°, and a modeled triaxial ellipsoid shape (a > b > c) with a/b = 1.33 ± 0.02 and b/c = 1.33 ± 0.07. The discrepancy between the high pole latitude found here and the low latitudes reported by others is discussed.     

Photoelectric photometry of 21 asteroids

Photoelectric lightcurves of 21 asteroids are presented. The observations were carried out from 1978 to 1982 at the Astronomical Observatory of Torino (at the Astrophysical Observatory of Catania for 137 Meliboea). For 10 objects a reliable rotation period has been obtained, while for two others a rough estimate is given. In several cases the analysis of the observed amplitudes versus the ecliptic longitudes indicates the most favorable future oppositions for period and/or pole determination. For some asteroids transformations to UBV Standard System were performed.     

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.     

Photometric lightcurves and pole determination of 433 Eros

Fourteen photometric lightcurves of 433 Eros were made at the Astronomical Observatory of Torino during the 1974–75 close passage. The absolute magnitude of the primary maximum (10^m78), the phase coefficient (0.023 mag/degree), the synodic and sidereal period of rotation (0^d.21956 and 0^d.21959, respectively) and the ecliptic coordinates of the pole (λ = 17°, β = 10°) were deduced.     

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.     

Figure of the double Asteroid 90 Antiope from adaptive optics and lightcurve observations

A long-term adaptive optics (AO) campaign of observing the double Asteroid (90) Antiope has been carried out in 2003-2005 using 8-10-m class telescopes, allowing prediction of the circumstances of mutual events occurring during the July 2005 opposition [Marchis, F., Descamps, P., Hestroffer, D., Berthier, J., de Pater, I., 2004. Bull. Am. Astron. Soc. 36, 1180]. This is the first opportunity to use complementary lightcurve and AO observations to extensively study the (90) Antiope system, an interesting visualized binary doublet system located in the main belt. The orbital parameters derived from the AO observations have served as input quantities for the derivation of a whole set of other physical parameters (namely shapes, surface scattering, bulk density, and internal properties) from analysis of collected lightcurves. To completely model the observed lightcurves, we employed Roche figures to construct an overall shape solution. The combination of these complementary observations has enabled us to derive a reliable physical and orbital solution for the system. Our model is consistent with a system of slightly non-spherical components, having a size ratio of 0.95 (with Ravg=42.9±0.5 km, separation=171±1 km), and exhibiting equilibrium figures for homogeneous rotating bodies. A comparison with grazing occultation event lightcurves suggests that the real shapes of the components do not depart from Roche equilibrium figures by more than 10%. The J2000 ecliptic coordinates of the pole of the system are λn=200°±2° and αn=38°±2°. The orbital period was refined to P=16.5051±0.0001 h, and the density is found to be slightly lower than previous determinations, with a value of 1.25±0.05 g/cm³, leading to a significant macro-porosity of 30%. Possible scenarios for the origin of the system are also discussed.     

2 Pallas: 1982 and 3 lightcurves and a new pole solution

Photoelectric lightcurves of asteroid 2 Pallas obtained in March 1982 and May 1983 display amplitudes of 0.04 and 0.10 magnitude respectively. The latter lightcurve shows that Pallas was at a V(1,0) magnitude of 4.51 ± 0.02 when it occulted 1 Vulpeculae on May 29 1983. A least-squares best fit to an amplitude-aspect relation for all available lightcurve observations of Pallas between 1951 and 1983 yields two solutions for its pole position: λ = 200, β = 40 and λ = 220, β = 15, where the uncertainty regions corresponds to an overall estimate of ± degrees. Use of phase angle bisector coordinates (A. W. Harris, J. W. Young, F. Scaltriti, and V. Zappalà (1984) Icarus57, 251–258) gave lower residuals than geocentric coordinates. The (220,15) pole position is favored since it is in very good agreement with an independent pole solution obtained by photometric astrometry (J. V. Lambert 1983 personal communication). This pole position implies that the latitude of the sub-Earth point at the time of the occultation was 22 degrees.     

Photoelectric lightcurves of the asteroid 1862 Apollo

Photoelectric lightcurves of the asteroid 1862 Apollo were obtained in November–December 1980 and in April–May 1982. The period of rotation is unambiguously determined to be 3.0655 ± 0.0008 hr. The 1980 observations span a range of solar phase angle from 30° to 90°, and the 1982 observations, 0.°2 to 90°. The Lumme-Bowell-Harris phase relation can be fit to the absolute magnitudes at maximum light with an RMS scatter of 0.06 magnitude over the entire range of phase angle. The constants of the solution are absolute V magnitude at zero phase angle and at maximum light, 16.23 ± 0.02; slope parameter, 0.23 ± 0.01. These constant corresponds to values in the linear phase coefficient system of V(1, 0) = 16.50 ± 0.02 and a phase coefficient of β_v = 0.0305 ± 0.0012 mag/degree in the phase range 10°–20°. The slope of the phase curve is typical for a moderate albedo asteroid. The absolute magnitudes observed in 1980 and 1982 fall along a common phase curve. That is, Apollo was not intrinsically brighter at one apparition than the other. This is not surprising, since the two apparitions were almost exactly opposite one another in the sky. A pole position was calculated from the observed deviation of the lightcurve from constant periodicity (synodic-sidereal difference) during both apparitions. The computed 1950 ecliptic coordinates of the pole are: longitude = 56°, latitude = −26°. This is the “north” pole with respect to right-handed (counter-clockwise) rotation. The formal uncertainty of the solution for the pole position is less than 10°, but realistically may be several times that, or even completely wrong. The sidereal period of rotation asscociated with this pole solution is 3.065436 ± 0.000012 hr.     

Radar and photometric observations and shape modeling of contact binary near-Earth Asteroid (8567) 1996 HW1

We observed near-Earth Asteroid (8567) 1996 HW1 at the Arecibo Observatory on six dates in September 2008, obtaining radar images and spectra. By combining these data with an extensive set of new lightcurves taken during 2008-2009 and with previously published lightcurves from 2005, we were able to reconstruct the object’s shape and spin state. 1996 HW1 is an elongated, bifurcated object with maximum diameters of 3.8 × 1.6 × 1.5 km and a contact-binary shape. It is the most bifurcated near-Earth asteroid yet studied and one of the most elongated as well. The sidereal rotation period is 8.76243 ± 0.00004 h and the pole direction is within 5° of ecliptic longitude and latitude (281°, −31°). Radar astrometry has reduced the orbital element uncertainties by 27% relative to the a priori orbit solution that was based on a half-century of optical data. Simple dynamical arguments are used to demonstrate that this asteroid could have originated as a binary system that tidally decayed and merged.     

Photoelectric photometry of 14 asteroids

Results of observations of 14 asteroids are reported; all of them, except 181 Eucharis, have been previously observed at least once. V photoelectric lightcurves were obtained from September 1982 to June 1983 at the Astronomical Observatory of Torino and at the Astrophysical Observatory of Catania. Part of this program aims to obtain complete lightcurves and, when possible, phasecurve information and to determine amplitudes and V magnitudes at different longitudes for a selected group of asteriods, in order to enlarge the set of known rotational axis directions.     

Lightcurves and the axis of rotation of 433 Eros

Ten lightcurves and UBV photometry of 433 Eros were obtained between August 1972 and May 1975. The absolute magnitude of the lightcurve maximum is 10.75 and the phase coefficient is 0.025 mag/deg. There may be a small difference in B-V color between the northern and southern hemispheres. The pole of the axis of rotation is directed toward λ₀ = 16°, β₀ = 12°, ecliptic longitude and latitude, respectively, and the rotation is direct with a sidereal period of 0.^d219599 or 5^h16^m13^s4 ± 0.^s2. The dimensions derived from the polarimetric albedo and the lightcurve amplitudes are 12km × 12km × 31km for a smooth cylinder with hemispherical ends.     

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.     

2 Pallas pole revisited

2 Pallas pole was revisited and using a set of old and new photoelectric observations of zero amplitudes the pole coordinates were determined. The synodic period of Schrollet al. (1976) was checked, and a good agreement found for both coordinates of the pole and synodic period with those determined by Schrollet al. (1976).     

Photometric observations and modelling of the asteroid 85 Io in conjunction with data from an occultation event during the 1995–96 apparition

The asteroid 85 Io has been observed using CCD and photoelectric photometry on 18 nights during its 1995–96 and 1997 apparitions. We present the observed lightcurves, determined colour indices and modelling of the asteroid spin vector and shape. The colour indices (U-B = 0.35±0.02, B-V = 0.66±0.02, V-R = 0.34±0.02, R-I = 0.36±0.02) are as expected for a C-type asteroid. The allowed spin vector solutions have the pole co-ordinates λ₀ = 285±4°, β₀ = −52±9° or λ₀ = 108±10°, β₀ = −46±10° and λ₀ = 290±10°, β₀ = −16±10° with a retrograde sense of rotation and a sidereal period P_sid = 0^d.286463±0^d.000001. During the 1995–96 apparition the International Occultation Time Association (IOTA) observed an occultation event by 85 Io. The observations and modelling presented here were analysed together with the occultation data to develop improved constraints on the size of the asteroid. The derived value of 164 km is about 5% larger than the IRAS diameter. © 1999 Elsevier Science Ltd. All rights reserved.     

The lightcurve and phase function of the asteroid 304 Olga

Photoelectric lightcurves of 304 Olga were obtained at Table Mountain Observatory in 1978 near opposition. From these observations, and several observations made from Lowell Observatory a month later, we obtain a rotation period of 18.36 ± 0.02 hr and lightcurve amplitude of 0^m·20. The range of solar phase angle covered by the observations is from 2°·0 to 22°. The resulting phase function is well fit by the Bowell and Lumme model (1979, in Asteroids, T. Gehrels, Ed., pp. 132–169, Univ. of Arizona Press, Tucson), with Q = 0.02. This low value of Q is suggestive of a low-albedo object.     

Speckle interferometry of asteroids: III. 511 Davida and its photometry

511 Davida was observed with the technique of speckle interferometry at Steward Observatory's 2.3-m telescope on May 3, 1982. Assuming Davida to be a featureless triaxial ellipsoid, based on five 7-min observations its triaxial ellipsoid dimensions and standard deviations were found to be (465 ± 90) × (358 ± 58) × (258 ± 356) km. This shape is close to an equilibrium figure (a gravitationally shaped “rubble pile?”) suggesting a density of 1.4 ± 0.4 g/cm³. Simultaneously with the triaxial solution for the size and shape of Davida, we found its north rotational pole to lie within 29° of RA = 19^h08^m, Dec = +15° (λ = 291°, β = +37°). If Davida is assumed to be a prolate biaxial ellipsoid, then its dimensions were found to be (512 ± 100) × (334 ± 39) km, with a north pole within 16° of RA = 10^h52^m, Dec = +16° (λ = 322°, β = +32°). We derive and apply to Davida a new simultaneous amplitude-magnitude (SAM)-aspect method, finding, from photometric data only, axial ratios of a/b = 1.25 ± .02, b/c = 1.14 ± .03, and a rotational pole within 4° of λ = 307°, β = +32°. We also derive a (weighted) linearized form of the amplitude-aspect relation to obtain axial ratios and a pole. However, amplitudes must be known to better than .01 if the b/c or a/c ratios are desired to better than 10%. Combining the speckle and SAM results, we find for the Gehrels and Tedesco phase function a geometric albedo of .033 ± .009 and for the Lumme and Bowell function .041 ± .011, for a unified model of 437 × 350 × 307 km. Differences between the photometric and speckle axial ratios and poles are probably due to the effects of albedo structure over the asteroid; details on individual lightcurves support this conclusion.