Radiation Torque Research Articles

The YORP effect on 25 143 Itokawa

Context. The asteroid 25143 Itokawa is one of the candidates for the detection of the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect in the rotation period. Previous studies were carried out up to the 196 608 facets triangulation model and were not able to provide a good theoretical estimate of this effect, raising questions about the influence of the mesh resolution and the centre of mass location on the evolution the rotation period. Aims. The YORP effect on Itokawa is computed for different topography models up to the highest resolution Gaskell mesh of 3 145 728 triangular faces in an attempt to find the best possible YORP estimate. Other, lower resolution models are also studied and the question of the dependence of the rotation period drift on the density distribution inhomogeneities is reexamined. A comparison is made with 433 Eros models possessing a similar resolution. Methods. The Rubincam approximation (zero conductivity) is assumed in the numerical simulation of the YORP effect in rotation period. The mean thermal radiation torques are summed over triangular facets assuming Keplerian heliocentric motion and uniform rotation around a body-fixed axis. Results. There is no evidence of YORP convergence in Gaskell model family. Differently simplified meshes may converge quickly to their parent models, but this does not prove the quality of YORP computed from the latter. We confirm the high sensitivity of the YORP effect to the fine details of the surface for 25 143 Itokawa and 433 Eros. The sensitivity of the Itokawa YORP to the centre of mass shift is weaker than in earlier works, but instead the results prove to be sensitive to the spin axis orientation in the body frame. Conclusions. Either the sensitivity of the YORP effect is a physical phenomenon and all present predictions are questionable, or the present thermal models are too simplified.

Radiation torque on a sphere centered on an acoustic helicoidal (vortex) Bessel beam.

Circularly polarized electromagnetic waves carry axial angular momentum and analysis shows that the axial radiation torque on an illuminated sphere is proportional to the power absorbed by the sphere [P. L. Marston and J. H. Crichton, Phys. Rev. A. 30, 2508–2516 (1984)]. Hefner and Marston [J. Acoust. Soc. Am. 106, 3313–3316 (1999)] proposed that a helicoidal acoustic beam (an acoustic vortex) also carries axial angular momentum and noted that absorption of such a beam should also produce an axial radiation torque. In the present work the acoustic radiation torque on a sphere centered on an acoustic helicoidal Bessel beam is analyzed and the torque is predicted to be proportional to the ratio of the power absorbed as a result of the interaction of sound with the sphere to the acoustic frequency. The torque is also proportional to the topological charge of the beam. Depending on the beam helicity, the torque is parallel or anti-parallel to the beam axis. The analysis uses a relation between the scattering and the partial wave coefficients for a sphere in a helicoidal Bessel beam [P. L. Marston, J. Acoust. Soc. Am. 124, 2905–2910 (2008)]. [This research was supported in part by ONR and NASA.]

A light touch on nanotubes: femtonewton force sensing and nanometric spatial resolution

Light can exert a mechanical action onmatter. Although this simple concept has been known for centuries (Kepler’s explanation of comet tails is based on it), the advent of the laser age has led to tremendous experimental advances and understanding of this phenomenon. Optical tweezers, instruments based on a tightly focused laser beam, have been used to trap, manipulate, control, and assemble dielectric particles, single atoms, cells, metal, and semiconducting nanostructures, leading to a real optical revolution in physics, biology, and nanotechnology. When used as force transducer, optical tweezers can measure forces in the piconewton range. In this context, the concept of photonic force microscopy (PFM) has been developed by scanning a dielectric sphere over surfaces in a liquid environment and sensing the force interaction. While the lateral resolution in PFM applications is related to particle size, the extension of conventional optical trapping to nanoparticles is a difficult task, since the radiation force scales with the volume of the trapped particle. Recently, optical trapping of carbon nanotube bundles was realized in aqueous environments. The almost linear geometry of these nanostructures, which have a subwavelength cross section and very high aspect ratio, is of crucial importance for bridging the gap between the micro and nano-world. In our work we demonstrated that the nanotubes’ small transverse size is key to achieving nanometric resolution for PFM applications, while an axial dimension in the micron range ensures stable trapping and allows force sensing in the femtonewton regime. A critical element in force sensing with optical tweezers is Brownian motion—random fluctuations of particles in a fluid. Performing statistical analysis of an optically trapped particle’s fluctuations about equilibrium enables force measurements. The Figure 1. (a) Optical trapping geometry. A laser beam is expanded to over-fill the back aperture of a high numerical microscope objective. The laser light propagates along the z axis (oriented as k wavevector) while x is the polarization axis (oriented as E=electric field). The light is focused in a chamber containing the nanotube solution; here the cylinder represents a randomly oriented nanotube. (b) A laser trapped bundle oriented by radiation torque along the optical axis. (c) The same bundle un-trapped (laser is off) and randomly oriented by Brownian motion.

Acoustic radiation torque on an irregularly shaped scatterer in an arbitrary sound field

To eliminate the limitation of the conventional acoustic radiation torque theory, which is only applicable to a disklike scatterer in a plane sound field, a new theory is established to calculate the radiation torque on any irregularly shaped scatterer in any arbitrary sound field. First, with the aid of the conservation law of angular momentum, the acoustic radiation torque is expressed as the angular momentum flux through a spherical surface with the center at the scatterer's centroid. Second, the velocity potential of the scattered field is derived, taking into account the influences of the translational and rotational movements of the scatterer induced by the first order stress of the incident sound field. Finally, a general calculating formula of the acoustic radiation torque is achieved. For a disklike scatterer in a plane sound filed, results from the above formula are well identical with those conventional formulas. By studying the case of a semicircular cylinder scatterer in a standing-wave sound field, it is found that for an irregularly shaped scatterer its rotation velocity is normally nonzero and the radiation torque changes with the spatial attitude.

Scattering of a helicoidal Bessel beam by a sphere: The effect of an azimuthal phase gradient.

In prior work [P. L. Marston, J. Acoust. Soc. Am. 121, 753–758 (2007)] the partial wave series for the scattering by a sphere centered on an ordinary Bessel beam was derived. The present work extends the analysis of the far field scattering to the case of a helicoidal Bessel beam having an angular phase ramp equal to the azimuthal angle. Helicoidal beams possess an axial null and have an azimuthal phase gradient. Some of the resulting modifications of the scattering are illustrated for an empty steel shell in water. In agreement with symmetry arguments given previously [B. T. Hefner and P. L. Marston, J. Acoust. Soc. Am. 106, 3313–3316 (1999)] the backward scattering and forward scattering vanish. For some directions the scattering increases when shifting from ordinary to a helicoidal beam illumination. In addition to describing the scattering by acoustic beams, there are potential applications of this analysis to the description of acoustic radiation forces and torques. [Work supported in part by ONR and by NASA.]

The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

AbstractThis paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed.The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

Radiation torque exerted on a spheroid: Analytical solution

As a companion work to our previous study [F. Xu, et al., Phys. Rev. E. 75, 026613 (2007)] on radiation force prediction for a homogeneous spheroid, we provide in this paper the analytical solution to the radiation torque exerted by an arbitrarily shaped beam on a spheroid, which can be prolate or oblate, transparent or absorbing. Calculations based upon this theoretical development are performed for both linearly and circularly polarized incident beams, and the results are compared to those of a sphere. Stable orientations of spheroids inside a linearly and a circularly polarized Gaussian beam are predicted. We analyze two physical mechanisms, the polarization torque and the reaction force torque, which do not exist or have no contribution to the torque on a sphere but cause rotation of a spheroid. As verification, the dipole method is also developed for the torque calculation for spheroids of size much less than the wavelength, and geometrical optics is developed to qualitatively analyze the torque exerted on spheroids of large size.

ANALYTIC THEORY FOR THE YARKOVSKY-O'KEEFE-RADZIEVSKI-PADDACK EFFECT ON OBLIQUITY

The Yarkovsky-O'Keefe-Radzievski-Paddack (YORP) effect is a thermal radiation torque that causes small objects to speed up or slow down their rotation and modify their spin vector orientation. This effect has important implications for spin dynamics of diameter D 50 km asteroids. In our previous work we developed an analytic theory for the component of the YORP torque that affects the spin rate. Here we extend these calculations to determine the effect of the YORP torque on obliquity. Our theory is limited to objects with near-spherical shapes. Two limiting cases are studied: (1) immediate emission of the thermal energy that occurs for surface thermal conductivity K = 0; (2) the effects of K ≠ 0 in the limit of small temporal variations of the surface temperature. We use the linearized heat transport equation to model (2). The results include explicit scaling of the YORP torque on obliquity with physical and dynamical parameters such as the thermal conductivity and spin rate. The dependence of torques on the obliquity is given as series of the Legendre polynomials. Comparisons show excellent agreement of the analytic results with the numerically calculated YORP torques for objects such as asteroids 1998 KY26 and (66391) 1999 KW4. We suggest that an important fraction of main belt asteroids may have specific obliquity values (generalized Slivan states) arising from the roots of the Legendre polynomials.

Radiation Torque and Force on Optically Trapped Linear Nanostructures

We study the optical trapping of highly elongated linear nanostructures in the focal region of a high-numerical aperture lens (optical tweezers). The radiation torque and trapping force on these nanostructures that are modeled as chains of identical spherical scatterers are calculated by means of multipole field expansions in the framework of the transition matrix approach. We investigate both orientational and trapping stability and calculate force constants and trap parameters in order to clarify the role of the linear geometry in the optical trapping mechanism. Furthermore, we calculate optical trapping of nanowires of different materials and compare our theoretical findings with available experimental results.

Rotational dynamics of a solar system body under solar radiation torques

The rotational dynamics of a small solar system body subject to solar radiation torques is investigated. A set of averaged evolutionary equations are derived as an analytic function of a set of spherical harmonic coefficients that describe the torque acting on the body due to solar radiation. The analysis also includes the effect of thermal inertia. The resulting equations are studied and a set of possible dynamical outcomes for the rotation rate and obliquity of a small body are found and characterized.

Entanglement of a Laguerre-Gaussian cavity mode with a rotating mirror

It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper we consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning, and orbital angular momentum carried by the cavity mode.

ACOUSTIC RADIATION FORCE AND TORQUE ON A SOLID ELLIPTIC CYLINDER

Exact expressions for the acoustic radiation torque and force components experienced by elastic cylinders of elliptic cross-section immersed in ideal fluids and placed in a progressive or standing wave field is developed. The classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop analytical expressions in the form of infinite series involving Mathieu and modified Mathieu functions. The complications arising due to the nonorthogonality of angular Mathieu functions corresponding with distinct wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided in an elegant manner by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. Numerical calculations of the radiation force and torque function amplitudes are performed in a wide range of frequencies and cross-sectional eccentricities for a stainless steel cylinder submerged in water. Particular attention is paid to assessment of the effects of cross-sectional ellipticity as well as incident field asymmetry on the acoustic radiation force/torque acting on the elliptical cylinder. Limiting case involving an elastic circular or elliptic cylinder in an ideal fluid is considered and fair agreements with well-known solutions are established.

Long-Term Attitude Drift of Spinning Spacecraft Under Solar Radiation Torques

Solar radiation pressure effects are exploited on-board satellites since about four decades. Control concepts have been developed using solar radiation forces with practical applications focusing on attitude control of communications satellites. The forces and torques induced by solar radiation pressure can substantially alter the orbital and attitude behavior of spacecraft especially in long duration missions. Furthermore, the effects are amplified for large structures such as solar sails. The present work analyzes the long term effect of the solar radiation torques on the evolution of the spin axis attitude pointing of any type of spacecraft (e.g., Earth-orbiting spacecraft, deep space probes, and solar sails). Analytic models are presented that can be applied to spacecraft of an arbitrary geometrical shape. Compact results are established that predict the annual drift of the spacecraft spin axis under solar radiation torques. The models presented will be useful for the design of spacecraft attitude control systems as well as for space mission planning.

Analytic Theory of the YORP Effect for Near-Spherical Objects

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 KY26 and on more elongated and/or irregular objects like (1862) Apollo and (25143) Itokawa.

Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre–Gaussian beam

We present the analyses of radiation force and torque on a spherical particle illuminated by Laguerre–Gaussian beam. Since Laguerre–Gaussian beam has angular momentum, the particle can be rotated by illumination of Laguerre–Gaussian beam. Radiation forces and torques for a silver sphere and a silicon sphere near the silver substrate are analyzed. We found that the maximum torque on silicon sphere is about five times higher than the maximum torque on silver sphere and fine control of the focused spot is required to push the particle to the substrate.

Acceleration of the rotation of asteroid 1862 Apollo by radiation torques

The anisotropic reflection and thermal re-emission of sunlight from an asteroid's surface acts as a propulsion engine. The net propulsion force (Yarkovsky effect) changes the orbital dynamics of the body at a rate that depends on its physical properties; for irregularly shaped bodies, the propulsion causes a net torque (the Yarkovsky-O'Keefe-Radzievskii-Paddack or YORP effect) that can change the object's rotation period and the direction of its rotation axis. The Yarkovsky effect has been observed directly, and there is also indirect evidence of its role in the orbital evolution of asteroids over long time intervals. So far, however, only indirect evidence exists for the YORP effect through the clustering of the directions of rotation axes in asteroid families. Here we report a change in the rotation rate of the asteroid 1862 Apollo, which is best explained by the YORP mechanism. The change is fairly large and clearly visible in photometric lightcurves, amounting to one extra rotation cycle in just 40 years even though Apollo's size is well over one kilometre. This confirms the prediction that the YORP effect plays a significant part in the dynamical evolution of asteroids.

Radiation torque on nonspherical particles in the transition matrix formalism: erratum

An erratum is presented to correct the errors in two equations in Sect. 3 of [Opt. Express 14, 9508--9521 (2006)].

On the rotational stability of nonspherical particles driven by the radiation torque

We calculate the radiation torque exerted by a monochromatic plane wave, either unpolarized or linearly polarized, on aggregates of spheres and investigate the stability of the resulting rotational motion. In fact, neglecting any braking momenta we calculate the component of the electromagnetic torque orthogonal to the principal axis of maximum moment of inertia through the center of mass (transverse torque), as a function of the direction of propagation of the incident field. The aggregates we study are composed of homogeneous spheres, possibly of different materials. The electromagnetic torque is calculated through the transition matrix approach along the lines of the theory reported in our recent paper [F. Borghese, P. Denti, R. Saija and M. A. Iati, Opt. Express 14, 9508 (2006)]. When the transverse component of the electromagnetic torque is small or vanishes the rotational motion driven by the component along the principal axis of inertia may be nearly stable.

Radiation torque on nonspherical particles in the transition matrix formalism: erratum

An erratum is presented to correct the errors in two equations in Sect. 3 of [Opt. Express 14, 9508--9521 (2006)].

Three-dimensional smoothed particle hydrodynamics simulations of radiation-driven warped accretion discs

We present three-dimensional smoothed particle hydrodynamics calculations of warped accretion discs in X-ray binary systems. Geometrically thin, optically thick accretion discs are illuminated by a central radiation source. This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc, resulting in a torque that acts on the disc to induce a twist or warp. Initially planar discs are unstable to warping driven by the radiation torque and, in general, the warps also precess in a retrograde direction relative to the orbital flow. We simulate a number of X-ray binary systems which have different mass ratios, using a number of different luminosities for each. Radiation-driven warping occurs for all systems simulated. For mass ratios q∼ 0.1 a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane (cf. X 1916-053). For less extreme mass ratios, the entire disc tilts out of the orbital plane (cf. Her X-1). For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction, we obtain both positive and negative superhumps simultaneously in the dissipation light curve (cf. V603 Aql).