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 NEO-WISE 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 1 sigma spread of YORP rotational acceleration expected to be acting on a particular NEA (d omega/dt in rad yr(-2)) can be estimated from its semimajor axis (a in au), eccentricity (e) and diameter (D in km) by using vertical bar d omega/dt vertical bar = 1.20(-0.86)(+1.66) x 10(-2)(a(2)root 1 - e(2)D(2))(-1) and/or by using vertical bar d omega/dt vertical bar = 1.00(-0.81)(+3.07) x 10(-2)(a(2)root 1 - e(2)D(2))(-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 (T-CAM_50 in yr) can be estimated by using T-CAM_50 = 12.5(a(2)root 1 - e(2)D(2))(1/2) and/or by using T-CAM_50 = 13.7(a(2)root 1 - e(2)D(2))(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 similar to 3.4 and similar to 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.