YORP torque as the function of shape harmonics

The second order analytical approximation of the mean YORP torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane parallel model of the temperature distribution derived from the insolation function allows to take into account a nonzero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity, and precession are given in a form of Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of Legendre polynomials or associated functions, with first two terms playing the principal role. The present version fixes the errors discovered in the text that appeared in Monthly Notices RAS (388, pp. 297-944).Comment: 19 pages, 3 figures, published Mon. Not. R.A.S with minor errors that are corrected in the present versio

The Influence of Rough Surface Thermal-Infrared Beaming on the Yarkovsky and YORP Effects

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 roughness, which has been neglected or dismissed in all previous models. Tests on Gaussian random sphere shaped asteroids, and on the real shapes of asteroids (1620) Geographos and (6489) Golevka, show that rough surface thermal-infrared beaming enhances the Yarkovsky orbital drift by typically tens of percent but it can be as much as a factor of two. The YORP rotational acceleration is on average dampened by up to a third typically but can be as much as one half. We find that the Yarkovsky orbital drift is only sensitive to the average degree, and not to the spatial distribution, of roughness across an asteroid surface. However, the YORP rotational acceleration is sensitive to the surface roughness spatial distribution, and can add significant uncertainties to the predictions for asteroids with relatively weak YORP effects. To accurately predict either effect the degree and spatial distribution of roughness across an asteroid surface must be known.Comment: 49 pages, 21 figures, 4 tables. Accepted by MNRA

Stress field and spin axis relaxation for inelastic triaxial ellipsoids

A compact formula for the stress tensor inside a self-gravitating, triaxial ellipsoid in an arbitrary rotation state is given. It contains no singularity in the incompressible medium limit. The stress tensor and the quality factor model are used to derive a solution for the energy dissipation resulting in the damping (short axis mode) or excitation (long axis) of wobbling. In the limit of an ellipsoid of revolution, we compare our solution with earlier ones and show that, with appropriate corrections, the differences in damping times estimates are much smaller than it has been claimed. This version implements corrections of misprints found in the MNRAS published text.Comment: 14 pages, 6 figures, published in Monthly Notices RAS (containing misprints

Note on the generalized Hansen and Laplace coefficients

Recently, Breiter et al (2004) reported the computation of Hansen coefficients $X_k^{\gamma,m}$ for non integer values of $\gamma$. In fact, the Hansen coefficients are closely related to the Laplace $b_{s}^{(m)}$, and generalized Laplace coefficients $b_{s,r}^{(m)}$ (Laskar and Robutel, 1995) that do not require $s,r$ to be integers. In particular, the coefficients X_0^{\g,m} have very simple expressions in terms of the usual Laplace coefficients b_{\g+2}^{(m)}, and all their properties derive easily from the known properties of the Laplace coefficients.Comment: 9/11/200

Yarkovsky-O’Keefe-Radzievskii-Paddack effect on tumbling objects

A semi-analytical model of the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect on an asteroid spin in a non-principal axis rotation state is developed. The model describes the spin-state evolution in Deprit–Elipe variables, first-order averaged with respect to rotation and Keplerian orbital motion. Assuming zero conductivity, the YORP torque is represented by spherical harmonic series with vectorial coefficients, allowing us to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló & Scheeres. The integrals do not exist when higher degree terms of the illumination function are included, and then the asymptotic states known from Vokrouhlický et al. appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not previously detected. Non-averaged numerical integration by the Taylor series method for an exemplary shape of 3103 Eger is in good agreement with the semi-analytical theory

Orbital similarity functions - application to asteroid pairs

The paper expands the idea of Vokrouhlický and Nesvorný who used a modified Zappalà et al. metric with osculating elements in search for pairs of asteroids suspected of having a common origin. Using six different orbital similarity functions, we find that five of them display a similar excess of close pairs in the catalogue of osculating elements. The excess is even higher when mean orbital elements are used. Similarly, when the mean elements are applied, there is a better agreement between the closest pairs found in the same catalogue using different metrics. The common subset of 62 pairs from five lists of 100 closest pairs according to different distance functions is provided. Investigating an artificial sample of asteroid orbital pairs with a known initial orbital velocity difference we find that the Drummond metric best preserves orbital proximity over long time intervals

The role of spatial frequency information for ERP components sensitive to faces and emotional facial expression

To investigate the impact of spatial frequency on emotional facial expression analysis, ERPs were recorded in response to low spatial frequency (LSF), high spatial frequency (HSF), and unfiltered broad spatial frequency (BSF) faces with fearful or neutral expressions, houses, and chairs. In line with previous findings, BSF fearful facial expressions elicited a greater frontal positivity than BSF neutral facial expressions, starting at about 150 ms after stimulus onset. In contrast, this emotional expression effect was absent for HSF and LSF faces. Given that some brain regions involved in emotion processing, such as amygdala and connected structures, are selectively tuned to LSF visual inputs, these data suggest that ERP effects of emotional facial expression do not directly reflect activity in these regions. It is argued that higher order neocortical brain systems are involved in the generation of emotion-specific waveform modulations. The face-sensitive N170 component was neither affected by emotional facial expression nor by spatial frequency information

The strength and detectability of the YORP effect in near-Earth asteroids: a statistical approach

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 estimate its detectability using light-curve observations. The method requires knowledge of an asteroid's orbital properties and size, and assumes that the future observational circumstances of an asteroid have already been thought through. It is verified by application to the observational circumstances of the seven YORP-investigated asteroids, and is then applied to 540 NEAs with NEOWISE and/or other diameter measurements, and to all NEAs using Minor Planet Center Orbit absolute magnitudes. The YORP detectability is found to be a strong function of the combined asteroid orbital and diameter properties, and is independent of the rotation period for NEAs that do not have very fast or slow rotation rates. The median and 1σ spread of YORP rotational acceleration expected to be acting on a particular NEA (dω/dt in rad yr−2) can be estimated from its semimajor axis (a in au), eccentricity (e) and diameter (D in km) by using |dω/dt|=1.20+1.66−0.86 ×10−2 (a2 √1−e2D2)−1 and/or by using |dω/dt|=1.00+3.07−0.81 ×10−2 (a2√1−e2D2)−1 if the diameter is instead estimated from the absolute magnitude by assuming a geometric albedo of 0.1. The length of a light-curve observational campaign required to achieve a 50 per cent probability of detecting the YORP effect in a particular NEA (TCAM_50 in yr) can be estimated by using TCAM_50=12.5(a2√1−e2D2)1/2 and/or by using TCAM_50 =13.7(a2√1−e2D2)1/2 for an absolute-magnitude-estimated diameter. To achieve a 95 per cent YORP-detection probability, these last two relations need to be multiplied by factors of ~3.4 and ~4.5, respectively. This method and approximate relations will be useful for astronomers who plan to look for YORP rotational acceleration in specific NEAs, and for all-sky surveys that may serendipitously observe NEA light curves