For studies of the long-term evolution of small Solar System objects, it is fundamental to add the Yarkovsky and Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects in the dynamical model. Still, implementations of these effects in publicly available N-body codes are often lacking, or the effects are implemented using significantly simplified models. In this paper, we present an implementation of the coupled Yarkovsky/YORP effects in the mercury and OrbFit $N$-body codes. Along with these two effects, we also included the effects of non-destructive collisions and rotationally induced breakups to model the asteroid spin state properly. Given the stochastic nature of many incorporated effects, the software is suitable for statistical dynamical studies. Here we explained the scientific aspect of the implementation, while technical details will be made freely available along with the source codes.
Any population of asteroids, like asteroid families, will disperse in semi-major axis due to the Yarkovsky effect. The amount of drift is modulated by the asteroid spin state evolution which determines the balance between the diurnal and seasonal Yarkovsky force. The asteroid's spin state is, in turn, controlled in part by the YORP effect. The otherwise smooth evolution of an asteroid can be abruptly altered by collisions, which can cause impulsive changes in the spin state and can move the asteroid onto a different YORP track. In addition, collisions may also alter the YORP parameters by chan…
We propose an analytic model for the normal YORP and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider 3 such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction a…
We present an adaptation of the ATPM to simultaneously predict the Yarkovsky and YORP effects in the presence of global self-heating that occurs within the large concavities of irregularly shaped asteroids, which has been neglected or dismissed in all previous models. It is also combined with rough surface thermal-infrared beaming effects, which have been previously shown to enhance the Yarkovsky-orbital-drift and dampen on average the YORP-rotational-acceleration by orders of several tens of per cent. Tests on all published concave shape models of near-Earth asteroids, and also on one hundred…
<Abridged> The impact of a meteoroid onto an asteroid transfers linear and angular momentum to the larger body, which may affect its orbit and its rotational state. Here we show that the meteoroid environment of our Solar System can have an effect on small asteroids that is comparable to the Yarkovsky and Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects under certain conditions. The momentum content of the meteoroids themselves is expected to generate an effect much smaller than that of the Yarkovsky effect. However, momentum transport by ejecta may increase the net effective force by two …
It is now becoming widely accepted that photon recoil forces from the asymmetric reflection and thermal re-radiation of absorbed sunlight are, together with collisions and gravitational forces, primary mechanisms governing the dynamical and physical evolution of asteroids. The Yarkovsky effect causes orbital semi-major axis drift and the YORP effect causes changes in the rotation rate and pole orientation. We present an adaptation of the Advanced Thermophysical Model (ATPM) to simultaneously predict the Yarkovsky and YORP effects in the presence of thermal-infrared beaming caused by surface ro…
The Yarkovsky effect describes a small but significant force that affects the orbital motion of meteoroids and asteroids smaller than $30-40$ kilometers in diameter. It is caused by sunlight; when these bodies heat up in the Sun, they eventually re-radiate the energy away in the thermal waveband, which in turn creates a tiny thrust. This recoil acceleration is much weaker than solar and planetary gravitational forces, but it can produce measurable orbital changes over decades and substantial orbital effects over millions to billions of years. The same physical phenomenon also creates a thermal…
We explore the hypothesis that the population of Martian Trojans is the result of a balance between the production of new asteroids ("YORPlets") through the YORP effect and their eventual escape from the Trojan clouds through Yarkovsky-driven orbital evolution. Our principal observables are: (5261) Eureka, its family of 8 asteroids and the family-less Trojans (101429) 1998 VF31 & (121514) 1999 UJ7. We model the population evolution as a birth-death random process and assume it is in a steady state. We then simulate the discovery of Trojans to-date and find that family members of 101429 and 121…
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 $\mathrm{d} ω/ \mathrm{d} t$ as a free parameter of…
The Clarissa family is a small collisional family composed of primitive C-type asteroids. It is located in a dynamically stable zone of the inner asteroid belt. In this work we determine the formation age of the Clarissa family by modeling planetary perturbations as well as thermal drift of family members due to the Yarkovsky effect. Simulations were carried out using the Swift-rmvs4 integrator modified to account for the Yarkovsky and Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effects. We ran multiple simulations starting with different ejection velocity fields of fragments, varying proport…
Near-Earth asteroid (1862) Apollo has strong detections of both orbital semimajor axis drift and rotational acceleration. We produce a unified model that can accurately match both observed effects using a single set of thermophysical properties derived from ground-based observations, and we determine Apollo's long term evolution. We use light-curve shape inversion techniques and the ATPM on published light-curve, thermal-infrared, and radar observations to constrain Apollo's thermophysical properties. The derived properties are used to make detailed predictions of Apollo's Yarkovsky and YORP e…
The influence of optical scattering and thermal radiation models an the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is studied. Lambertian formulation is compared with Hapke scattering and emission laws and Lommel-Seeliger reflection. Although the form of reflectivity function strongly influences mean torques due to scattering or thermal radiation alone, their combined contribution to the rotation period YORP is not much different from the standard Lambertian values. For higher albedo values the differences between the Hapke and Lambert models become significant for the YORP in attitud…
A numerical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect for objects defined in terms of a triangular mesh is described. The algorithm requires that each surface triangle can be handled independently, which implies the use of a 1D thermal model. Insolation of each triangle is determined by an optimized ray-triangle intersection search. Surface temperature is modeled with a spectral approach; imposing a quasi-periodic solution we replace heat conduction equation by the Helmholtz equation. Nonlinear boundary conditions are handled by an iterative, FFT based solver. The result…
The Yarkovsky--O'Keefe--Radzievskii--Paddack (YORP) effect governs the spin evolution of small asteroids. The axial component of YORP, which alters the rotation rate of the asteroid, is mostly independent of its thermal inertia, while the obliquity component is very sensitive to the thermal model of the asteroid. Here we develop a semi-analytic theory for the obliquity component of YORP. We integrate an approximate thermal model over the surface of an asteroid, and find an analytic expression for the obliquity component in terms of two YORP coefficients. This approach allows us to investigate …
We present the first self-consistent simulations of the coupled spin-shape evolution of small gravitational aggregates under the influence of the YORP effect. Because of YORP's sensitivity to surface topography, even small centrifugally driven reconfigurations of aggregates can alter the YORP torque dramatically, resulting in spin evolution that can differ qualitatively from the rigid-body prediction. One third of our simulations follow a simple evolution described as a modified YORP cycle. Two-thirds exhibit one or more of three distinct behaviors---stochastic YORP, self-governed YORP, and st…
Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered on Eureka. We explored two cases: cluster dispersal through planetary gravity alone over 1 Gyr, and a 1 Gyr evolution due to both gravity and the Yarkovsky effect. We find that the dispersal of the cluster in eccentricity is primarily due to dynamical chaos, while the inclinations and libration amplitudes are primarily changed by the Yarkovsky ef…
The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect plays an important role in the rotational properties and evolution of asteroids. While the YORP effect induced by the macroscopic shape of the asteroid and by the presence of surface boulders has been well studied, no investigation has been performed yet regarding how craters with given properties influence this effect. We introduce and estimate the crater-induced YORP effect (CYORP), which arises from the concave structure of the crater, to investigate the magnitude of the resulting torques as a function of varying properties of the crat…
Understanding the fate of planetary systems through white dwarfs which accrete debris crucially relies on tracing the orbital and physical properties of exo-asteroids during the giant branch phase of stellar evolution. Giant branch luminosities exceed the Sun's by over three orders of magnitude, leading to significantly enhanced Yarkovsky and YORP effects on minor planets. Here, we place bounds on Yarkovsky-induced differential migration between asteroids and planets during giant branch mass loss by modelling one exo-Neptune with inner and outer exo-Kuiper belts. In our bounding models, the as…
In addition to collisions and gravitational forces, it is now becoming widely acknowledged that photon recoil forces and torques from the asymmetric reflection and thermal re-radiation of sunlight are primary mechanisms that govern the rotational evolution of an asteroid. The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect causes changes in the rotation rate and pole direction of an irregularly shaped asteroid. We present a simple Monte Carlo method to estimate the range of YORP-rotational-accelerations acting on a near-Earth asteroid (NEA) without knowledge of its detailed shape, and to e…
The Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect is a net torque caused by solar radiation directly reflected and thermally re-emitted from the surface of small asteroids and is considered to be crucial in their dynamical evolution. By long-term photometric observations of selected near-Earth asteroids, it's hoped to enlarge asteroid samples with a detected YORP effect to facilitate the development of a theoretical framework. Archived light-curve data are collected and photometric observations are made for (1685) Toro and (85989) 1999 JD6, which enables measurement of their YORP effect …
The Karin cluster is a young asteroid family thought to have formed only $\simeq 5.75$~My ago. The young age can be demonstrated by numerically integrating the orbits of Karin cluster members backward in time and showing the convergence of the perihelion and nodal longitudes (as well as other orbital elements). Previous work has pointed out that the convergence is not ideal if the backward integration only accounts for the gravitational perturbations from the Solar System planets. It improves when the thermal radiation force known as the Yarkovsky effect it is accounted for. This argument can …
Exploring rotational properties and the YORP effect in asteroid families
University of Padova（帕多瓦大学）；University of Tokyo（东京大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学，蔚蓝海岸天文台，法国国家科学研究中心，拉格朗日实验室）
The spin state of small asteroids can change on a long timescale by the Yarkovsky-O'Keefe-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. W…
The rotation state of small asteroids is affected by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, which is a net torque caused by solar radiation directly reflected and thermally reemitted from the surface. Due to this effect, the rotation period slowly changes, which can be most easily measured in light curves because the shift in the rotation phase accumulates over time quadratically. We collected archived light curves and carried out new photometric observations for asteroids (10115) 1992 SK, (1620) Geographos, and (1685) Toro. We applied the method of light curve inversion to f…
A rotating frequency analysis in a previous paper, showed that two samples of C and S-type asteroids belonging to the Main Belt, but not to any families, present two different values for the transition diameter to a Maxwellian distribution of the rotation frequency, respectively 48 and 33 km. In this paper, after a more detailed statistical analysis, aiming to verify that the result is physically relevant, we found a better estimate for the transition diameter, respectively $D_C = 44 \pm 2$ km and $D_S = 30 \pm 1$ km. The ratio between these estimated transition diameters, $D_C/D_S = 1.5 \pm 0…
