Analytic Theory of the YORP Effect for Near-Spherical Objects

Abstract

The YORP effect is produced when the surface of a small object in interplanetary space is heated by sunlight and reradiates the absorbed energy in thermal wavelengths. The absorbed, reflected, and emitted photons produce tiny torques on the small body that can change its spin rate and obliquity over planetary timescales. Previous theories of the YORP effect relied on numerical or seminumerical evaluation of the radiation torques. Here we develop an alternative approach and calculate the YORP torques analytically. Our theory is limited to near-spherical objects. While unsuitable for a precise determination of torques on elongated and /or highly irregular objects, the analytic theory helps to explain several general properties of the YORP torques that were identified in previous numerical works. For example, we demonstrate that the component of the YORP torque that affects the spin rate,¯s, can vanish for obliquity values % 55 (and % 125 ). As discussed by Vokrouhlický and coworkers, this property of¯s is important for establishing the so-called Slivan states, which arise as evolutionary end states of spin vectors of small solar system bodies such as asteroids. We show that¯s (averaged over spin and orbit periods) is a second-order quantity in the small parameter that describes the deviation of the shape from an ideal sphere. We calculate¯s explicitly as polynomials of cos . These expressions show that the YORP torque arises from coupled deformations of the body's shape in topographic longitude and latitude. Moreover, by introducing a small phase lag to mimic the delay between the absorption and reemission of photons we demonstrate that¯s is insensitive to the exact value of the surface thermal conductivity. These and other analytic results described here provide a baseline for understanding the YORP effect on bodies with more complicated surface shapes and properties other than the ones considered here. We discuss applications of the analytic theory on near-spherical asteroids like 1998 KY 26 and on more elongated and/or irregular objects like (1862) Apollo and (25143) Itokawa.

New photometric observations of asteroids (1862) Apollo and (25143) Itokawa – an analysis of YORP effect

“…Even with the finest model we used, the predicted YORP value did not converge exactly, thus leaving some uncertainty in the result. We note that this is in agreement with the theoretical prediction of Nesvorný & Vokrouhlický (2007 whose analytical calculations show that the YORP value may depend on very small-scale irregularities of the asteroid's shape. Moreover, not only the resolution but also the representation of the shape for a given resolution plays an important role -even models with the same resolution give different results (see Table 3).…”

YORP effect on real objects

“…Moreover, these results confirm the extreme sensitivity of the YORP effect to the details of the shape (in agreement with the discussion of Nesvorný & Vokrouhlický 2007). All the YORP results obtained so far, including the ones presented below, should always be seen and considered under this perspective.…”

“…Recently, Nesvorný & Vokrouhlický (2007, 2008 have developed the first completely analytic theory of the phenomenon that is able, under the assumption of a near-spherical shape, to predict some of the key aspects of the YORP effect. In general, no easy intuitive readout of the results is possible.…”

“…In general, no easy intuitive readout of the results is possible. However, a rough taxonomy of the behavior of bodies with regard to the YORP effect has been introduced in Vokrouhlický &Čapek (2002); four main classes of objects have been defined, and the above-quoted papers by Nesvorný & Vokrouhlický (2007, 2008 provided a first analytical interpretation of their origin.…”

Multiple origins of asteroid pairs

“…If a common origin hypothesis is accepted than these pairs provide powerful tools to test many theories including space weathering, mutual body tides and binary evolution. 56 S. A. Jacobson Vokrouhlický andČapek 2002;Breiter et al 2007;Nesvorný and Vokrouhlický 2007;Scheeres 2007b), and the rotational acceleration is:…”