Extreme sensitivity of the YORP effect to small-scale topography

Abstract

Radiation recoil (YORP) torques are shown to be extremely sensitive to small-scale surface topography, using numerical simulations. Starting from a set of "base objects" representative of the near-Earth object population, random realizations of three types of small-scale topography are added: Gaussian surface fluctuations, craters, and boulders. For each, the expected relative errors in the spin and obliquity components of the YORP torque caused by the observationally unresolved small-scale topography are computed. Gaussian power, at angular scales below an observational limit, produces expected errors of order 100% if observations constrain the surface to a spherical harmonic order l 10. For errors under 10%, the surface must be constrained to at least l = 20. A single crater with diameter roughly half the object's mean radius, placed at random locations, results in expected errors of several tens of percent. The errors scale with crater diameter D as D 2 for D > 0.3 and as D 3 for D < 0.3 mean radii. Objects that are identical except for the location of a single large crater can differ by factors of several in YORP torque, while being photometrically indistinguishable at the level of hundredths of a magnitude. Boulders placed randomly on identical base objects create torque errors roughly 3 times larger than do craters of the same diameter, with errors scaling as the square of the boulder diameter. A single boulder comparable to Yoshinodai on 25143 Itokawa, moved by as little as twice its own diameter, can alter the magnitude of the torque by factors of several, and change the sign of its spin component at all obliquities. Most of the total torque error produced by multiple unresolved craters is contributed by the handful of largest craters; but both large and small boulders contribute comparably to the total boulder-induced error. A YORP torque prediction derived from groundbased data can be expected to be in error by of order 100% due to unresolved topography. Small surface changes caused by slow spin-up or spin-down may have significant stochastic effects on the spin evolution of small bodies. For rotation periods between roughly 2 and 10 hours, these unpredictable changes may reverse the sign of the YORP torque. Objects in this spin regime may random-walk up and down in spin rate before the rubble-pile limit is exceeded and fissioning or loss of surface objects occurs. Similar behavior may be expected at rotation rates approaching the limiting values for tensile-strength dominated objects.

Averaged rotational dynamics of an asteroid in tumbling rotation under the YORP torque

“…As pointed out in [Statler 2009], small changes in the surface of the body, and so in the illumination model, yield significant effects on the rotation. A better analytical model for the illumination of the body, including selfshadowing and finite thermal inertia, is necessary to describe the rotational dynamics under the YORP torque in a more accurate way.…”

“…It is possible that these differences are due to the fact that they also included gravitational torques due to the Sun and to the different model they used for the illumination function, which is more realistic in the numerical simulations and it can easily destroy the integrability of our simplified model. It is worth to notice that in [Statler 2009] it is shown, using full numerical simulations, the sensitivity of the YORP effect to small changes in the shape of the body.…”

Physical characterisation of near-Earth asteroid (1620) Geographos

“…Especially when previous studies have shown that the YORP effect can be highly sensitive to unresolved shape features and surface roughness (Statler 2009;Rozitis & Green 2012), the shape model resolution (Breiter et al 2009), and internal bulk density distribution (Scheeres & Gaskell 2008;Lowry et al 2014). However, Geographos has a relatively high YORPcoefficient of 0.01 (see Rossi et al 2009or Rozitis & Green 2013b for a definition), and Rozitis & Green (2013a) showed that asteroids with high values are less sensitive to the inclusion of concavities in their global shape model.…”

The YORP effect on 25 143 Itokawa

“…All known recipes for computing the YORP torques can be roughly divided in two main groups: most of them use a discrete mesh, summing the contributions from each triangular face (Vokrouhlický &Čapek 2002;Čapek & Vokrouhlický 2004;Scheeres 2007;Statler 2009), whereas others use a continuous shape model described in terms of spherical harmonics (Breiter & Michalska 2008;Mysen 2008;Nesvorný & Vokrouhlický 2008). The latter group cannot be applied to Itokawa, because its irregular shape, not being starlike, cannot be expressed in terms of spherical harmonics.…”