Pairs of asteroids sharing similar heliocentric orbits, but not bound together, were found recently. Backward integrations of their orbits indicated that they separated gently with low relative velocities, but did not provide additional insight into their formation mechanism. A previously hypothesized rotational fission process may explain their formation-critical predictions are that the mass ratios are less than about 0.2 and, as the mass ratio approaches this upper limit, the spin period of the larger body becomes long. Here we report photometric observations of a sample of asteroid pairs, revealing that the primaries of pairs with mass ratios much less than 0.2 rotate rapidly, near their critical fission frequency. As the mass ratio approaches 0.2, the primary period grows long. This occurs as the total energy of the system approaches zero, requiring the asteroid pair to extract an increasing fraction of energy from the primary's spin in order to escape. We do not find asteroid pairs with mass ratios larger than 0.2. Rotationally fissioned systems beyond this limit have insufficient energy to disrupt. We conclude that asteroid pairs are formed by the rotational fission of a parent asteroid into a proto-binary system, which subsequently disrupts under its own internal system dynamics soon after formation.

Context. In the past decade, more than one hundred asteroid models were derived using the lightcurve inversion method. Measured by the number of derived models, lightcurve inversion has become the leading method for asteroid shape determination. Aims. Tens of thousands of sparse-in-time lightcurves from astrometric projects are publicly available. We investigate these data and use them in the lightcurve inversion method to derive new asteroid models. By having a greater number of models with known physical properties, we can gain a better insight into the nature of individual objects and into the whole asteroid population. Methods. We use sparse photometry from selected observatories from the AstDyS database (Asteroids -Dynamic Site), either alone or in combination with dense lightcurves, to determine new asteroid models by the lightcurve inversion method. We investigate various correlations between several asteroid parameters and characteristics such as the rotational state and diameter or family membership. We focus on the distribution of ecliptic latitudes of pole directions. We create a synthetic uniform distribution of latitudes, compute the method bias, and compare the results with the distribution of known models. We also construct a model for the long-term evolution of spins. Results. We present 80 new asteroid models derived from combined data sets where sparse photometry is taken from the AstDyS database and dense lightcurves are from the Uppsala Asteroid Photometric Catalogue (UAPC) and from several individual observers. For 18 asteroids, we present updated shape solutions based on new photometric data. For another 30 asteroids we present their partial models, i.e., an accurate period value and an estimate of the ecliptic latitude of the pole. The addition of new models increases the total number of models derived by the lightcurve inversion method to ∼200. We also present a simple statistical analysis of physical properties of asteroids where we look for possible correlations between various physical parameters with an emphasis on the spin vector. We present the observed and de-biased distributions of ecliptic latitudes with respect to different size ranges of asteroids as well as a simple theoretical model of the latitude distribution and then compare its predictions with the observed distributions. From this analysis we find that the latitude distribution of small asteroids (D < 30 km) is clustered towards ecliptic poles and can be explained by the YORP thermal effect while the latitude distribution of larger asteroids (D > 60 km) exhibits an evident excess of prograde rotators, probably of primordial origin.

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Photometric observations of asteroids show that some of them are in non-principal axis rotation state (free precession), called tumbling. Collisions between asteroids have been proposed as a possible asteroid rotation excitation mechanism. We simulated subcatastrophic collisions between asteroids of various physical and material parameters to find out whether they could be responsible for the excited rotation. For every simulated target body after the collision, we computed its rotational lightcurve and we found that tumbling was photometrically detectable for the rotational axis misalignment angle β greater than about 15 • . We found that subcatastrophic collisions are a plausible cause of non-principal axis rotation for small slowly rotating asteroids. The determining parameter is the ratio of the projectile orbital angular momentum to the target rotational angular momentum and we derived an approximate relation between this ratio and the angle β. We also compared the limiting energy for the onset of tumbling with the shattering energy. Slowly rotating asteroids of diameter 100 m and larger can be rotationally excited by collisions with energies below the shattering limit.

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