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Register a new userAnalysis of the rotation period of asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger - search for the YORP effect
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The spin state of small asteroids can change on a long timescale by the Yarkovsky-OKeefe-Radzievskii-Paddack (YORP) effect, the net torque that arises from anisotropically scattered sunlight and proper thermal radiation from an irregularly-shaped asteroid. The secular change in the rotation period caused by the YORP effect can be detected by analysis of asteroid photometric lightcurves. We analyzed photometric lightcurves of near-Earth asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible deviations from the constant rotation caused by the YORP effect. We carried out new photometric observations of the three asteroids, combined the new lightcurves with archived data, and used the lightcurve inversion method to model the asteroid shape, pole direction, and rotation rate. The YORP effect was modeled as a linear change in the rotation rate in time domega /dt. Values of domega/ dt derived from observations were compared with the values predicted by theory. We derived physical models for all three asteroids. We had to model Eger as a nonconvex body because the convex model failed to fit the lightcurves observed at high phase angles. We probably detected the acceleration of the rotation rate of Eger domega / dt = (1.4 +/- 0.6) x 10^{-8} rad/d (3sigma error), which corresponds to a decrease in the rotation period by 4.2 ms/yr. The photometry of Cerberus and Ra-Shalom was consistent with a constant-period model, and no secular change in the spin rate was detected. We could only constrain maximum values of |domega / dt| < 8 x 10^{-9} rad/d for Cerberus, and |domega / dt| < 3 x 10^{-8} rad/d for Ra-Shalom.
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The rotation states of small asteroids are affected by a net torque arising from an anisotropic sunlight reflection and thermal radiation from the asteroids surfaces. On long timescales, this so-called YORP effect can change asteroid spin directions and their rotation periods. We analyzed lightcurves of four selected near-Earth asteroids with the aim of detecting secular changes in their rotation rates that are caused by YORP. We use the lightcurve inversion method to model the observed lightcurves and include the change in the rotation rate $mathrm{d} omega / mathrm{d} t$ as a free parameter of optimization. We collected more than 70 new lightcurves. For asteroids Toro and Cacus, we used thermal infrared data from the WISE spacecraft and estimated their size and thermal inertia. We also used the currently available optical and radar astrometry of Toro, Ra-Shalom, and Cacus to infer the Yarkovsky effect. We detected a YORP acceleration of $mathrm{d}omega / mathrm{d} t = (1.9 pm 0.3) times 10^{-8},mathrm{rad},mathrm{d}^{-2}$ for asteroid Cacus. For Toro, we have a tentative ($2sigma$) detection of YORP from a significant improvement of the lightcurve fit for a nonzero value of $mathrm{d}omega / mathrm{d} t = 3.0 times 10^{-9},mathrm{rad},mathrm{d}^{-2}$. For asteroid Eger, we confirmed the previously published YORP detection with more data and updated the YORP value to $(1.1 pm 0.5) times 10^{-8},mathrm{rad},mathrm{d}^{-2}$. We also updated the shape model of asteroid Ra-Shalom and put an upper limit for the change of the rotation rate to $|mathrm{d}omega / mathrm{d} t| lesssim 1.5 times 10^{-8},mathrm{rad},mathrm{d}^{-2}$. Ra-Shalom has a greater than $3sigma$ Yarkovsky detection with a theoretical value consistent with observations assuming its size and/or density is slightly larger than the nominally expected values.
The larger number of models of asteroid shapes and their rotational states derived by the lightcurve inversion give us better insight into both the nature of individual objects and the whole asteroid population. With a larger statistical sample we can study the physical properties of asteroid populations, such as main-belt asteroids or individual asteroid families, in more detail. Shape models can also be used in combination with other types of observational data (IR, adaptive optics images, stellar occultations), e.g., to determine sizes and thermal properties. We use all available photometric data of asteroids to derive their physical models by the lightcurve inversion method and compare the observed pole latitude distributions of all asteroids with known convex shape models with the simulated pole latitude distributions. We used classical dense photometric lightcurves from several sources and sparse-in-time photometry from the U.S. Naval Observatory in Flagstaff, Catalina Sky Survey, and La Palma surveys (IAU codes 689, 703, 950) in the lightcurve inversion method to determine asteroid convex models and their rotational states. We also extended a simple dynamical model for the spin evolution of asteroids used in our previous paper. We present 119 new asteroid models derived from combined dense and sparse-in-time photometry. We discuss the reliability of asteroid shape models derived only from Catalina Sky Survey data (IAU code 703) and present 20 such models. By using different values for a scaling parameter cYORP (corresponds to the magnitude of the YORP momentum) in the dynamical model for the spin evolution and by comparing synthetics and observed pole-latitude distributions, we were able to constrain the typical values of the cYORP parameter as between 0.05 and 0.6.
The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation when it moves in elliptic orbit through Space. According to the results of Efroimsky, Frouard (2016), various perturbations (collisions, close encounters, YORP effect) destabilize the rotation of a small body (asteroid), deviating it from the initial-current spin state. This yields evolution of the spin towards rotation about maximal-inertia axis due to the process of nutation relaxation or to the proper spin state corresponding to minimal energy with a fixed angular momentum. We consider in our research the aforementioned spin state of asteroid but additionally under non-vanishing influence of the effects of non-gravitational nature (YORP effect), which is destabilizing the asteroid rotation during its motion far from giant planets. Meanwhile, new solutions for asteroid rotation dynamics in case of negligible (time-dependent) applied torques have been obtained in our development. New method for solving Euler equations for rigid body rotation is suggested; an elegant example for evolution of spin towards the rotation about maximal-inertia axis is calculated.
The YORP effect is a small thermal-radiation torque experienced by small asteroids, and is considered to be crucial in their physical and dynamical evolution. It is important to understand this effect by providing measurements of YORP for a range of asteroid types to facilitate the development of a theoretical framework. We are conducting a long-term observational study on a selection of near-Earth asteroids to support this. We focus here on (68346) 2001 KZ66, for which we obtained both optical and radar observations spanning a decade. This allowed us to perform a comprehensive analysis of the asteroids rotational evolution. Furthermore, radar observations from the Arecibo Observatory enabled us to generate a detailed shape model. We determined that (68346) is a retrograde rotator with its pole near the southern ecliptic pole, within a $ 15^circ$ radius of longitude $ 170^circ$ and latitude $ -85^circ$. By combining our radar-derived shape model with the optical light curves we developed a refined solution to fit all available data, which required a YORP strength of $ (8.43pm0.69)times10^{-8} rm~rad ~day^{-2} $. (68346) has a distinct bifurcated shape comprising a large ellipsoidal component joined by a sharp neckline to a smaller non-ellipsoidal component. This object likely formed from either the gentle merging of a binary system, or from the deformation of a rubble pile due to YORP spin-up. The shape exists in a stable configuration close to its minimum in topographic variation, where regolith is unlikely to migrate from areas of higher potential.
The available set of spin and shape modelled asteroids is strongly biased against slowly rotating targets and those with low lightcurve amplitudes. As a consequence of these selection effects, the current picture of asteroid spin axis distribution, rotation rates, or radiometric properties, might be affected too. To counteract these selection effects, we are running a photometric campaign of a large sample of main belt asteroids omitted in most previous studies. We determined synodic rotation periods and verified previous determinations. When a dataset for a given target was sufficiently large and varied, we performed spin and shape modelling with two different methods. We used the convex inversion method and the non-convex SAGE algorithm, applied on the same datasets of dense lightcurves. Unlike convex inversion, the SAGE method allows for the existence of valleys and indentations on the shapes based only on lightcurves. We obtained detailed spin and shape models for the first five targets of our sample: (159) Aemilia, (227) Philosophia, (329) Svea, (478) Tergeste, and (487) Venetia. When compared to stellar occultation chords, our models obtained an absolute size scale and major topographic features of the shape models were also confirmed. When applied to thermophysical modelling, they provided a very good fit to the infrared data and allowed their size, albedo, and thermal inertia to be determined. Convex and non-convex shape models provide comparable fits to lightcurves. However, some non-convex models fit notably better to stellar occultation chords and to infrared data in sophisticated thermophysical modelling (TPM). In some cases TPM showed strong preference for one of the spin and shape solutions. Also, we confirmed that slowly rotating asteroids tend to have higher-than-average values of thermal inertia.
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