YORP torque as the function of shape harmonics

TL;DR

This paper derives a second-order analytical approximation of the mean YORP torque for minor bodies, expressed explicitly through shape spherical harmonics, incorporating temperature effects and obliquity dependence with improved numerical properties.

Contribution

It introduces a new, simplified expression for insolation, accounts for nonzero conductivity, and provides explicit Legendre series for YORP torque components with enhanced numerical stability.

Findings

Explicit formulas for YORP torque components as Legendre series.

Inclusion of nonzero conductivity effects in YORP modeling.

Improved numerical properties allowing easy truncation of series.

Abstract

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).