The surface roughness of (433) Eros as measured by thermal-infrared beaming

In planetary science, surface roughness is regarded to be a measure of surface irregularity at small spatial scales, and causes the thermal-infrared beaming effect (i.e. re-radiation of absorbed sunlight back towards to the Sun). Typically, surface roughness exhibits a degeneracy with thermal inertia when thermophysical models are fitted to disc-integrated thermal-infrared observations of asteroids because of this effect. In this work, it is demonstrated how surface roughness can be constrained for near-Earth asteroid (433) Eros (i.e. the target of NASA's NEAR Shoemaker mission) when using the Advanced Thermophysical Model with thermal-infrared observations taken during an ‘almost pole-on’ illumination and viewing geometry. It is found that the surface roughness of (433) Eros is characterized by an rms slope of 38 ± 8° at the 0.5-cm spatial scale associated with its thermal-infrared beaming effect. This is slightly greater than the rms slope of 25 ± 5° implied by the NEAR Shoemaker laser ranging results when extrapolated to this spatial scale, and indicates that other surface shaping processes might operate, in addition to collisions and gravity, at spatial scales under one metre in order to make asteroid surfaces rougher. For other high-obliquity asteroids observed during ‘pole-on’ illumination conditions, the thermal-infrared beaming effect allows surface roughness to be constrained when the sub-solar latitude is greater than 60°, and if the asteroids are observed at phase angles of less than 40°. They will likely exhibit near-Earth asteroid thermal model beaming parameters that are lower than expected for a typical asteroid at all phase angles up to 100°

Observing the variation of asteroid thermal inertia with heliocentric distance

Thermal inertia is a useful property to characterise a planetary surface since it can be used as a qualitative measure of the regolith grain size. It is expected to vary with heliocentric distance because of its dependence on temperature. However, no previous investigation has conclusively observed a change in thermal inertia for any given planetary body. We have addressed this by using NEOWISE data and the Advanced Thermophysical Model to study the thermophysical properties of the near-Earth asteroids (1036) Ganymed, (1580) Betulia, and (276049) 2002 CE26 as they moved around their highly eccentric orbits. We confirm that the thermal inertia values of Ganymed and 2002 CE26 do vary with heliocentric distance, although the degree of variation observed depends on the spectral emissivity assumed in the thermophysical modelling. We also confirm that the thermal inertia of Betulia did not change for three different observations obtained at the same heliocentric distance. Depending on the spectral emissivity, the variations for Ganymed and 2002 CE26 are potentially more extreme than that implied by theoretical models of heat transfer within asteroidal regoliths, which might be explained by asteroids having thermal properties that also vary with depth. Accounting for this variation reduces a previously observed trend of decreasing asteroid thermal inertia with increasing size, and suggests that the surfaces of small and large asteroids could be much more similar than previously thought. Furthermore, this variation can affect Yarkovsky orbital drift predictions by a few tens of per cent

Constraints on the near-Earth asteroid obliquity distribution from the Yarkovsky effect

Aims. From lightcurve and radar data we know the spin axis of only 43 near-Earth asteroids. In this paper we attempt to constrain the spin axis obliquity distribution of near-Earth asteroids by leveraging the Yarkovsky effect and its dependence on an asteroid’s obliquity. Methods. By modeling the physical parameters driving the Yarkovsky effect, we solve an inverse problem where we test different simple parametric obliquity distributions. Each distribution results in a predicted Yarkovsky effect distribution that we compare with a X2 test to a dataset of 125 Yarkovsky estimates. Results. We find different obliquity distributions that are statistically satisfactory. In particular, among the considered models, the best-fit solution is a quadratic function, which only depends on two parameters, favors extreme obliquities, consistent with the expected outcomes from the YORP effect, has a 2:1 ratio between retrograde and direct rotators, which is in agreement with theoretical predictions, and is statistically consistent with the distribution of known spin axes of near-Earth asteroids

Physical characterisation of near-Earth asteroid (1620) Geographos: reconciling radar and thermal-infrared observations

Context. The Yarkovsky (orbital drift) and YORP (spin state change) effects play important roles in the dynamical and physical evolution of asteroids. Thermophysical modelling of these observed effects, and of thermal-infrared observations, allows a detailed physical characterisation of an individual asteroid to be performed. Aims. We perform a detailed physical characterisation of near-Earth asteroid (1620) Geographos, a potential meteor stream source and former spacecraft target, using the same techniques as previously used for (1862) Apollo. Methods. We use the advanced thermophysical model (ATPM) on published light-curve, radar, and thermal-infrared observations to constrain the thermophysical properties of Geographos. The derived properties are used to make detailed predictions of the Yarkovsky orbital drift and YORP rotational acceleration, which are then compared against published measurements to determine Geographos’s bulk density. Results. We find that Geographos has a thermal inertia of 340-100+140 J m-2 k-1s-1/2, a roughness fraction of ≥50%, and a bulk density of 2100-450+550 kg m-3 when using the light-curve-derived shape model with the radar-derived maximum equatorial diameter of 5.04 ± 0.07 km. It is also found that the radar observations had overestimated the z-axis in Geographos’s shape model because of their near-equatorial view. This results in a poor fit to the thermal-infrared observations if its effective diameter is kept fixed in the model fitting. Conclusions. The thermal inertia derived for Geographos is slightly higher than the typical values for a near-Earth asteroid of its size, and its derived bulk density suggests a rubble-pile interior structure. Large uncertainties in shape model z-axes are likely to explain why radar and thermal-infrared observations sometimes give inconsistent diameter determinations for other asteroids

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

Space missions and ground-based observations have shown that some asteroids are loose collections of rubble rather than solid bodies. The physical behaviour of such ‘rubble-pile’ asteroids has been traditionally described using only gravitational and frictional forces within a granular material. Cohesive forces in the form of small van der Waals forces between constituent grains have recently been predicted to be important for small rubble piles (ten kilometres across or less), and could potentially explain fast rotation rates in the small-asteroid population. The strongest evidence so far has come from an analysis of the rotational breakup of the main-belt comet P/2013 R3, although that was indirect and poorly constrained by observations. Here we report that the kilometre-sized asteroid (29075) 1950 DA is a rubble pile that is rotating faster than is allowed by gravity and friction. We find that cohesive forces are required to prevent surface mass shedding and structural failure, and that the strengths of the forces are comparable to, though somewhat less than, the forces found between the grains of lunar regolith

A thermophysical analysis of the (1862) Apollo Yarkovsky and YORP effects

Context. The Yarkovsky effect, which causes orbital drift, and the YORP effect, which causes changes in rotation rate and pole orientation, play important roles in the dynamical and physical evolution of asteroids. Near-Earth asteroid (1862) Apollo has strong detections of both orbital semimajor axis drift and rotational acceleration. Aims. To produce a unified model that can accurately match both observed effects using a single set of thermophysical properties derived from ground-based observations, and to determine Apollo’s long term evolution. Methods. We use light-curve shape inversion techniques and the Advanced Thermophysical Model (ATPM) on published light-curve, thermal-infrared, and radar observations to constrain Apollo’s thermophysical properties. The derived properties are used to make detailed predictions of Apollo’s Yarkovsky and YORP effects, which are then compared with published measurements of orbital drift and rotational acceleration. The ATPM explicitly incorporates 1D heat conduction, shadowing, multiple scattering of sunlight, global self-heating, and rough surface thermal-infrared beaming in the model predictions. Results. We find that ATPM can accurately reproduce the light-curve, thermal-infrared, and radar observations of Apollo, and simultaneously match the observed orbital drift and rotational acceleration using: a shape model with axis ratios of 1.94:1.65:1.00, an effective diameter of 1.55 ± 0.07 km, a geometric albedo of 0.20 ± 0.02, a thermal inertia of 140 +140-100 J m-2 K-1 s-1/2, a highly rough surface, and a bulk density of 2850 +480-680 kg m-3. Using these properties we predict that Apollo’s obliquity is increasing towards the 180 degree YORP asymptotic state at a rate of 1.5 +0.3-0.5 degrees per 105 yr. Conclusions. The derived thermal inertia suggests that Apollo has loose regolith material resting on its surface, which is consistent with Apollo undergoing a recent resurfacing event based on its observed Q-type spectrum. The inferred bulk density is consistent with those determined for other S-type asteroids, and suggests that Apollo has a fractured interior. The YORP effect is acting on a much faster timescale than the Yarkovsky effect and will dominate Apollo’s long term evolution. The ATPM can readily be applied to other asteroids with similar observational data sets

Granular convection in microgravity

We investigate the role of gravity on convection in a dense granular shear flow. Using a microgravity-modified Taylor-Couette shear cell under the conditions of parabolic flight microgravity, we demonstrate experimentally that secondary, convective-like flows in a sheared granular material are close to zero in microgravity, and enhanced under high gravity conditions, though the primary flow fields are unaffected by gravity. We suggest that gravity tunes the frictional particle-particle and particle-wall interactions, which have been proposed to drive the secondary flow. In addition, the degree of plastic deformation increases with increasing gravitational forces, supporting the notion that friction is the ultimate cause

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

The influence of global self-heating on the Yarkovsky and YORP effects

In addition to collisions and gravitational forces, there is a growing amount of evidence that photon recoil forces from the asymmetric reflection and thermal re-radiation of absorbed sunlight are primary mechanisms that are fundamental to the physical and dynamical evolution of small asteroids. The Yarkovsky effect causes orbital drift, and the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect causes changes in the rotation rate and pole orientation. We present an adaptation of the Advanced Thermophysical Model to simultaneously predict the Yarkovsky and YORP effects in the presence of global self-heating that occurs within the large concavities of irregularly shaped asteroids, which has been neglected or dismissed in all previous models. It is also combined with rough surface thermal-infrared beaming effects, which have been previously shown to enhance the Yarkovsky orbital drift and dampen on average the YORP rotational acceleration by orders of several tens of per cent. Tests on all published concave shape models of near-Earth asteroids, and also on 100 Gaussian random spheres, show that the Yarkovsky effect is sensitive to shadowing and global self-heating effects at the few per cent level or less. For simplicity, Yarkovsky models can neglect these effects if the level of accuracy desired is of this order. Unlike the Yarkovsky effect, the YORP effect can be very sensitive to shadowing and global self-heating effects. Its sensitivity increases with decreasing relative strength of the YORP rotational acceleration, and does not appear to depend greatly on the degree of asteroid concavity. Global self-heating tends to produce a vertical offset in an asteroid's YORP-rotational-acceleration versus obliquity curve which is in opposite direction to that produced by shadowing effects. It also ensures that at least one critical obliquity angle exists at which zero YORP rotational acceleration occurs. Global self-heating must be included for accurate predictions of the YORP effect if an asteroid exhibits a large shadowing effect. If global self-heating effects are not included, then it is found in ~75 per cent of cases that better predictions are produced when shadowing is also not included. Furthermore, global self-heating has implications for reducing the sensitivity of the YORP effect predictions to detailed variations in an asteroid's shape model

The nucleus of Comet 67P/Churyumov-Gerasimenko: a new shape model and thermophysical analysis

Context. Comet 67P/Churyumov-Gerasimenko is the target of the European Space Agency Rosetta spacecraft rendez-vous mission. Detailed physical characteristation of the comet before arrival is important for mission planning as well as providing a test bed for ground-based observing and data-analysis methods. Aims. To conduct a long-term observational programme to characterize the physical properties of the nucleus of the comet, via ground-based optical photometry, and to combine our new data with all available nucleus data from the literature. Methods. We applied aperture photometry techniques on our imaging data and combined the extracted rotational lightcurves with data from the literature. Optical lightcurve inversion techniques were applied to constrain the spin state of the nucleus and its broad shape. We performed a detailed surface thermal analysis with the shape model and optical photometry by incorporating both into the new Advanced Thermophysical Model (ATPM), along with all available Spitzer 8–24 μm thermal-IR flux measurements from the literature. Results. A convex triangular-facet shape model was determined with axial ratios b/a = 1.239 and c/a = 0.819. These values can vary by as much as 7% in each axis and still result in a statistically significant fit to the observational data. Our best spin state solution has Psid = 12.76137 ± 0.00006 h, and a rotational pole orientated at Ecliptic coordinates λ = 78◦(±10◦), β = +58◦(±10◦). The nucleus phase darkening behaviour was measured and best characterized using the IAU HG system. Best fit parameters are: G = 0.11 ± 0.12 and HR(1,1,0) = 15.31 ± 0.07. Our shape model combined with the ATPM can satisfactorily reconcile all optical and thermal-IR data, with the fit to the Spitzer 24 μm data taken in February 2004 being exceptionally good. We derive a range of mutually-consistent physical parameters for each thermal-IR data set, including effective radius, geometric albedo, surface thermal inertia and roughness fraction. Conclusions. The overall nucleus dimensions are well constrained and strongly imply a broad nucleus shape more akin to comet 9P/Tempel 1, rather than the highly elongated or “bi-lobed” nuclei seen for comets 103P/Hartley 2 or 8P/Tuttle. The derived low thermal inertia of −2 K−1 s−1/2 is comparable with that measured for other comets scaled to similar heliocentric distances, and implies a surface regolith finer than lunar surface material