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Modeling the YORP Effect

Modeling the YORP Effect. “Radiative Spin-up and Spin-down of Small Asteroids” – D. Rubincam And “ YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam’s Approximation” - D. Vokrouhlicky and D. Capek Presented by David Riethmiller 26 September 2007.

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Modeling the YORP Effect

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  1. Modeling the YORP Effect “Radiative Spin-up and Spin-down of Small Asteroids” – D. Rubincam And “YORP-Induced Long-Term Evolution of the Spin State of Small Asteroids and Meteoroids: Rubincam’s Approximation” - D. Vokrouhlicky and D. Capek Presented by David Riethmiller 26 September 2007

  2. Yarkovsky – O’Keefe – Radzievskii – Paddock Effect • Asteroids rotate with some angular velocity • YORP is a radiation “recoil” effect that puts a net torque on the asteroid • We are interested in how the asteroid’s spin rate evolves with time, due to the YORP effect.

  3. Yarkovsky – O’Keefe – Radzievskii – Paddock Effect

  4. θ Directed Radiation • Observed radiant intensity proportional to cos(θ) • Consequence: area element viewed from any angle measures same radiance

  5. Surface Modeling • Surface of asteroid modeled as triangular facets, based on Gaussian Random Sphere method • Each facet absorbs sunlight and reradiates immediately

  6. N rs How to Use the Model • Power deposited on surface element dA: • rs = unit vector from asteroid to sun • N = unit vector normal to surface element • S = insolation • FS = incident solar flux

  7. More How to Use It • Assume each surface element in radiative steady state with respect to insolation • (all energy absorbed gets re-radiated immediately • Surface elements act as blackbodies • Lambert’s Law gives the “recoil” force per unit area on dA:

  8. The Important Part • If r is the vector from the asteroid center of mass to the area element, the torque on each area element is given by:

  9. Obliquity • Unlikely that the net torque will maintain the asteroid’s spin axis orientation • How will torque components change the orientation over time?

  10. Obliquity Evolution: Type I Stable ε at 90° (Eros)

  11. Obliquity Evolution: Type II Stable ε at 0 and 180 (Deimos)

  12. Obliquity Evolution: Type III Stable ε at ~35 and 150 (Geographos)

  13. Obliquity Evolution: Type IV Stable ε at 90 and 180 (Golevka)

  14. Conclusions • YORP is a radiation “recoil” effect that puts a net torque on an asteroid. • This net torque changes the spin axis orientation (obliquity) and rotation period of the asteroid over time. • Asteroid shape influences its evolution type, characterized by points of stable obliquity. Got ‘roids?

  15. Extra Slide 1: Spherical Harmonic Surface Modeling • The models used are spherical harmonic expansions on known asteroid shapes: • Plm(cos θ) = Legendre polynomial of degree l and order m • θ = co-latitude • λ = east longitude • Almi = shape coefficients derived from inner products of spherical harmonics with numerical shapes

  16. Extra Slide 2: Gaussian Random Spheres • Original model called for spherical harmonic expansion on known asteroid shapes • Improved model uses Gaussian Random Spheres • The radii of a large sample of objects satisfy log-normal statistics with a variance σ and a characteristic dimensional factor a, and the the radius r in the direction given by spherical angles θ and φ may be expressed as:

  17. Extra Slide 3: Long-Term Obliquity Evolution

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