Equilibrium figures of inhomogeneous synchronous binary asteroids

The present paper deals with the application of the classical theory of equilibrium figures of two rotating liquid masses to the case where bodies exhibit a radially stratified internal density distribution so that they can be considered as inhomogeneous bodies. The derived ellipsoidal shape solutions are applied to five real systems of equal-sized synchronous asteroids. Furthermore, internal inhomogeneity puts strong constraints on the surface grain density. A satisfactory model fit is achieved with internal densities of asteroids steadily increasing outwards. In particular, from such an approach we derived grain densities of the considered systems in agreement with their mineralogical composition inferred from reflectance spectroscopy. According to this new approach, 4492 Debussy, presently of unknown spectral type, is predicted to appear as a C-type object with a grain density on the order of 2 g/cm³.     

Angular momentum of binary asteroids: Implications for their possible origin

We describe in this work a thorough study of the physical and orbital characteristics of extensively observed main-belt and trojan binaries, mainly taken from the LAOSA (Large Adaptive Optics Survey of Asteroids [Marchis, F., Baek, M., Berthier, J., Descamps, P., Hestroffer, D., Kaasalainen, M., Vachier, F., 2006c. In: Workshop on Spacecraft Reconnaissance of Asteroid and Comet Interiors. Abstract #3042]) database, along with a selection of bifurcated objects. Dimensionless quantities, such as the specific angular momentum and the scaled primary spin rate, are computed and discussed for each system. They suggest that these asteroidal systems might be the outcome of rotational fission or mass shedding of a parent body presumably subjected to an external torque. One of the most striking features of separated binaries composed of a large primary (Rp>100 km) with a much smaller secondary (Rs<20 km) is that they all have total angular momentum of ∼0.27. This value is quite close to the Maclaurin-Jacobi bifurcation (0.308) of a spinning fluid body. Alternatively, contact binaries and tidally locked double asteroids, made of components of similar size, have an angular momentum larger than 0.48. They compare successfully with the fission equilibrium sequence of a rotating fluid mass. In conclusion, we find that total angular momentum is a useful proxy to assess the internal structure of such systems.     

The cool surfaces of binary near-Earth asteroids

Here we show results from thermal-infrared observations of km-sized binary near-Earth asteroids (NEAs). We combine previously published thermal properties for NEAs with newly derived values for three binary NEAs. The η value derived from the near-Earth asteroid thermal model (NEATM) for each object is then used to estimate an average thermal inertia for the population of binary NEAs and compared against similar estimates for the population of non-binaries. We find that these objects have, in general, surface temperatures cooler than the average values for non-binary NEAs as suggested by elevated η values. We discuss how this may be evidence of higher-than-average surface thermal inertia. This latter physical parameter is a sensitive indicator of the presence or absence of regolith: bodies covered with fine regolith, such as the Earth’s moon, have low thermal inertia, whereas a surface with little or no regolith displays high thermal inertia. Our results are suggestive of a binary formation mechanism capable of altering surface properties, possibly removing regolith: an obvious candidate is the YORP effect.We present also newly determined sizes and geometric visible albedos derived from thermal-infrared observations of three binary NEAs: (5381) Sekhmet, (153591) 2001 SN₂₆₃, and (164121) 2003 YT₁. The diameters of these asteroids are 1.41 ± 0.21 km, 1.56 ± 0.31 km, and 2.63 ± 0.40 km, respectively. Their albedos are 0.23 ± 0.13, 0.24 ± 0.16, and 0.048 ± 0.015, respectively.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.     

Rotational lightcurves of asteroids belonging to families

Complete lightcurves of 17 asteroids belonging to the Themis, Eos, and Maria families have been obtained, as well as single-night photometric observations of eight objects belonging to the same families. Using also data previously available in the literature, we perform a preliminary statistical analysis aimed at detecting possible correlations between rotational periods, overall lightcurve amplitudes, and objetcs' sizes. No evident correlation was found, with the possible exception of a weak anticorrelation between size and spin period. The implications of this possible anticorrelation are discussed.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.     

Photometric survey of binary near-Earth asteroids

Photometric data on 17 binary near-Earth asteroids (15 of them are certain detections, two are probables) were analysed and characteristic properties of the near-Earth asteroid (NEA) binary population were inferred. We have found that binary systems with a secondary-to-primary mean diameter ratio Ds/Dp?0.18 concentrate among NEAs smaller than 2 km in diameter; the abundance of such binaries decreases significantly among larger NEAs. Secondaries show an upper size limit of Ds=0.5-1 km. Systems with Ds/Dp?0.5 are abundant but larger satellites are significantly less common. Primaries have spheroidal shapes and they rotate rapidly, with periods concentrating between 2.2 to 2.8 h and with a tail of the distribution up to ∼4 h. The fast rotators are close to the critical spin for rubble piles with bulk densities about 2 g/cm³. Orbital periods show an apparent cut-off at Porb∼11 h; closer systems with shorter orbital periods have not been discovered, which is consistent with the Roche limit for strengthless bodies. Secondaries are more elongated on average than primaries. Most, but not all, of their rotations appear to be synchronized with the orbital motion; nonsynchronous secondary rotations may occur especially among wider systems with Porb>20 h. The specific total angular momentum of most of the binary systems is similar to within ±20% and close to the angular momentum of a sphere with the same total mass and density, rotating at the disruption limit; this suggests that the binaries were created by mechanism(s) related to rotation near the critical limit and that they neither gained nor lost significant amounts of angular momentum during or since formation. A comparison with six small asynchronous binaries detected in the main belt of asteroids suggests that the population extends beyond the region of terrestrial planets, but with characteristics shifted to larger sizes and longer periods. The estimated mean proportion of binaries with Ds/Dp?0.18 among NEAs larger than 0.3 km is 15±4%. Among fastest rotating NEAs larger than 0.3 km with periods between 2.2 and 2.8 h, the mean proportion of such binaries is (66⁺¹⁰₋₁₂)%.     

New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses

In 2007, the M-type binary Asteroid 22 Kalliope reached one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, was aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. A dedicated international campaign of photometric observations, based on amateur-professional collaboration, was organized and coordinated by the IMCCE in order to catch several of these events. The set of the compiled observations is released in this work. We developed a relevant model of these events, including a topographic shape model of Kalliope refined in the present work, the orbit solution of Linus as well as the photometric effect of the shadow of one component falling on the other. By fitting this model to the only two full recorded events, we derived a new estimation of the equivalent diameter of Kalliope of 166.2±2.8 km, 8% smaller than its IRAS diameter. As to the diameter of Linus, considered as purely spherical, it is estimated to 28±2 km. This substantial “shortening” of Kalliope, gives a bulk density of 3.35±0.33 g/cm³, significantly higher than past determinations but more consistent with its taxonomic type. Some constraints can be inferred on the composition.     

(U)BVRI photometry of Trojan L5 asteroids

(U)BVRI photometry of 27 mainly small (≈30 km) Trojans show that the previously reported size-spectral slope trend among Trojans and Hildas must be modified. The small-slope small-bodies gap present in previous works does not exist. This has also been noted by other recent reported observations. While the largest asteroids have slopes less than about 10% kÅ⁻¹ the smallest asteroids have both small and large slopes. The maximum slope is about 15% kÅ⁻¹ for all outer main belt groups (Cybeles, Hildas and Trojans). Combining observations from different authors reveal that these three groups have small asteroids (below 50 km) in the same slope range, while the large Trojans (≈100 km) have in general significantly steeper slopes than Hildas and Cybeles of similar size. The size-slope trend would favor organic materials as mainly responsible for the reflectance properties of the surfaces.     

Photometry and models of eight near-Earth asteroids

We present new observations and models of the shapes and rotational states of the eight near-Earth Asteroids (1580) Betulia, (1627) Ivar, (1980) Tezcatlipoca, (2100) Ra-Shalom, (3199) Nefertiti, (3908) Nyx, (4957) Brucemurray, and (5587) 1990 SB. We also outline some of their solar phase curves, corrected to common reference geometry with the models. Some of the targets may feature sizable global nonconvexities, but the observable solar phase angles were not sufficiently high for confirming these. None is likely to have a very densely cratered surface. We discuss the role of the intermediate topographic scale range in photometry, and surmise that this scale range is less important than large or small scale lengths.     

Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

Shapes and rotational properties of thirty asteroids from photometric data

We have analyzed photometric lightcurves of 30 asteroids, and present here the obtained shapes, rotational periods and pole directions. We also present new photometric observations of five asteroids. The shape models indicate the existence of many features of varying degrees of irregularity. Even large main-belt asteroids display such features, so the resulting poles and periods are more consistent than those obtained by simple ellipsoid-like models. In some cases the new rotational parameters are rather different from those obtained previously, and in a few cases there were no proper previous estimates at all.     

Photometric observations of 107P/Wilson-Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson-Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson-Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L₁:L₂:L₃ = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson-Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L₁:L₂:L₃ = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson-Harrington is C-type. No clear rotational color variations are confirmed on the surface.     

Submillimeter photometry and lightcurves of Ceres and other large asteroids

Photometry and thermal lightcurves of six large asteroids (1-Ceres, 2-Pallas, 3-Juno, 12-Victoria, 85-Io and 511-Davida) have been observed at 870 μm (345 GHz) using the MPIfR 19-Channel Bolometer of the Heinrich-Hertz Submillimeter Telescope. Only Ceres displayed a lightcurve with an amplitude (∼50%, peak to peak) that was significantly greater than the uncertainty in the observations. When thermal fluxes and brightness temperatures are corrected for heliocentric distance and albedo, there is a significant relation with the sub-solar latitude of the asteroid, or the local season of the asteroid. No such trend can be found between observations with solar phase angle. These results are evidence that most of the submillimeter thermal radiation is emitted from below the diurnal thermal wave. Comparing the observed trend with model output suggests that the submillimeter radiation from all the asteroids we observed is best modeled by surface material with low thermal inertia (<15 J m⁻² s^−0.5 K⁻¹, consistent with mid-infrared observations of large main-belt asteroids) and a refractive index closer to unity relative to densities inferred from radar experiments, implying a veneer of material over the asteroid surface with a density less than 1000 kg m⁻³. More data with better signal-to-noise and aspect coverage could improve these models and constrain physical properties of asteroid surface materials. This would also allow asteroids to be used as calibration sources with accurately known and stable, broadband fluxes at long wavelengths.     

New insights on the binary Asteroid 121 Hermione

We report on the results of a 6-month photometric study of the main-belt binary C-type Asteroid 121 Hermione, performed during its 2007 opposition. We took advantage of the rare observational opportunity afforded by one of the annual equinoxes of Hermione occurring close to its opposition in June 2007. The equinox provides an edge-on aspect for an Earth-based observer, which is well suited to a thorough study of Hermione’s physical characteristics. The catalog of observations carried out with small telescopes is presented in this work, together with new adaptive optics (AO) imaging obtained between 2005 and 2008 with the Yepun 8-m VLT telescope and the 10-m Keck telescope. The most striking result is confirmation that Hermione is a bifurcated and elongated body, as suggested by Marchis, et al. [Marchis, F., Hestroffer, D., Descamps, P., Berthier, J., Laver, C., de Pater, I., 2005. Icarus 178, 450-464]. A new effective diameter of 187 ± 6 km was calculated from the combination of AO, photometric and thermal observations. The new diameter is some 10% smaller than the hitherto accepted radiometric diameter based on IRAS data. The reason for the discrepancy is that IRAS viewed the system almost pole-on. New thermal observations with the Spitzer Space Telescope agree with the diameter derived from AO and lightcurve observations. On the basis of the new AO astrometric observations of the small 32-km diameter satellite we have refined the orbit solution and derived a new value of the bulk density of Hermione of 1.4 + 0.5/−0.2 g cm⁻³. We infer a macroscopic porosity of ∼33 + 5/−20%.     

Binary asteroid population: 1. Angular momentum content

We compiled a list of estimated parameters of binary systems among asteroids from near-Earth to trojan orbits. In this paper, we describe the construction of the list, and we present results of our study of angular momentum content in binary asteroids. The most abundant binary population is that of close binary systems among near-Earth, Mars-crossing, and main belt asteroids that have a primary diameter of about 10 km or smaller. They have a total angular momentum very close to, but not generally exceeding, the critical limit for a single body in a gravity regime. This suggests that they formed from parent bodies spinning at the critical rate (at the gravity spin limit for asteroids in the size range) by some sort of fission or mass shedding. The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is a candidate to be the dominant source of spin-up to instability. Gravitational interactions during close approaches to the terrestrial planets cannot be a primary mechanism of formation of the binaries, but it may affect properties of the NEA part of the binary population.     

A giant crater on 90 Antiope?

Mutual event observations between the two components of 90 Antiope were carried out in 2007-2008. The pole position was refined to λ₀ = 199.5 ± 0.5° and β₀ = 39.8 ± 5° in J2000 ecliptic coordinates, leaving intact the physical solution for the components, assimilated to two perfect Roche ellipsoids, and derived after the 2005 mutual event season (Descamps, P., Marchis, F., Michalowski, T., Vachier, F., Colas, F., Berthier, J., Assafin, M., Dunckel, P.B., Polinska, M., Pych, W., Hestroffer, D., Miller, K., Vieira-Martins, R., Birlan, M., Teng-Chuen-Yu, J.-P., Peyrot, A., Payet, B., Dorseuil, J., Léonie, Y., Dijoux, T., 2007. Figure of the double Asteroid 90 Antiope from AO and lightcurves observations. Icarus 187, 482-499). Furthermore, a large-scale geological depression, located on one of the components, was introduced to better match the observed lightcurves. This vast geological feature of about 68 km in diameter, which could be postulated as a bowl-shaped impact crater, is indeed responsible of the photometric asymmetries seen on the “shoulders” of the lightcurves. The bulk density was then recomputed to 1.28 ± 0.04 g cm⁻³ to take into account this large-scale non-convexity. This giant crater could be the aftermath of a tremendous collision of a 100-km sized proto-Antiope with another Themis family member. This statement is supported by the fact that Antiope is sufficiently porous (∼50%) to survive such an impact without being wholly destroyed. This violent shock would have then imparted enough angular momentum for fissioning of proto-Antiope into two equisized bodies. We calculated that the impactor must have a diameter greater than ∼17 km, for an impact velocity ranging between 1 and 4 km/s. With such a projectile, this event has a substantial 50% probability to have occurred over the age of the Themis family.     

Triplicity and physical characteristics of Asteroid (216) Kleopatra

To take full advantage of the September 2008 opposition passage of the M-type Asteroid (216) Kleopatra, we have used near-infrared adaptive optics (AO) imaging with the W.M. Keck II telescope to capture unprecedented high resolution images of this unusual asteroid. Our AO observations with the W.M. Keck II telescope, combined with Spitzer/IRS spectroscopic observations and past stellar occultations, confirm the value of its IRAS radiometric radius of 67.5 km as well as its dog-bone shape suggested by earlier radar observations. Our Keck AO observations revealed the presence of two small satellites in orbit about Kleopatra (see Marchis, F. et al. [2008a]. (3749) Balam. In: Green, D.W.E. (Ed.), IAU Circ. 8928; Marchis, F., Descamps, P., Berthier, J., Emery, J.P. [2008b]. S/2008 ((216)) 1 and S/2008 ((216)) 2. In: Green, D.W.E. (Ed.), IAU Circ. 8980). Accurate measurements of the satellite orbits over a full month enabled us to determine the total mass of the system to be 4.64 ± 0.02 × 10¹⁸ kg. This translates into a bulk density of 3.6 ± 0.4 g/cm³, which implies a macroscopic porosity for Kleopatra of ∼30-50%, typical of a rubble-pile asteroid. From these physical characteristics we measured its specific angular momentum, very close to that of a spinning equilibrium dumbbell.     

3782 Celle: Discovery of a binary system within the Vesta family of asteroids

Photometric observations of the minor planet (3782) Celle, which has been associated both dynamically and spectroscopically with the Vesta asteroid family, were obtained using the 1.8-m Vatican Advanced Technology Telescope during September 2001 and December 2002-January 2003. Analysis of these data reveals a normal rotational lightcurve (, amplitude =0.10-0.15 mag). During the 2002-2003 run, anomalous attenuation events were observed lasting for about 2.6-3.5 h that varied in amplitude from 0.15-0.3 mag. The attenuations were of two distinct types that can clearly be identified as primary and secondary occultation/eclipses similar to those that have been previously observed in known minor planet binary systems (Pravec et al., 2000). We therefore interpret our data as clear evidence that (3782) Celle is actually an asynchronous binary system with an orbital period of (Ryan et al., 2003). A preliminary model, based on spherical components, yields a primary-to-secondary diameter ratio of 0.43±0.01 and a combined bulk density of for the two components. Because these objects are likely to be composed of basaltic fragments, this density is indicative of a moderate to a highly fractured internal structure for at least one, if not both, of the binary components. Since the Vesta family is believed to have been created via a cratering event, this finding has important implications for understanding possible ejecta re-accumulation and satellite formation in subcatastrophic collisions.