The Yarkovsky effect on near-earth asteroids with Gaia M. Delbo 1, S. Mouret 2, M. Havel 1, M. Carpino 3, P. Tanga 1, D. Hestroffer 3, F. Mignard 1, and A. Morbidelli 1 1 Observatoire de la Cote d Azurd 2 Institute de Mécanique Celeste et Calcul des Ephemerides (IMCCE), Paris 3 INAF-Osservatorio astronomico di Milano Earth-based support to Gaia Solar System science (Beaulieu sur Mer,, France - 27 & 28 October)
Yarkovsky effect The Yarkovsky effect is the weak non gravitational force felt by asteroids due to the emission of thermal photons. r f f( D, A, ε, ρ, ρ, κ, s, S ) f recoil force D diameter Aalbedo ε emissivity κ thermal conductivity ρρr b bulk density s surface density s spin vector S shape Vokrouhlicky, 1998. f The recoil force causes a variation of the semimajor axis of the orbit da dt Bottke et al., 2002, 2006 b s asteroid s s spin axis is perpendicular to the orbital plane. Recoil force IR emission Surface temperature 0K 200K 400K
Motivations for the study of the Yarkovsky effect The Yarkovsky effect is responsible for: Injection of Main Belt objects into resonances to maintain a steady state Near-Earth Object population. Dispersion of asteroid dynamical families. Long Cosmic Ray Exposure ages of meteorites vs. short (10 7 yr) dynamical lifetime in resonances. The largest source of uncertainty in the Earth impact probability prediction of potentially hazardous asteroids, such as 1950 DA and 99942 Apophis Bottke et al. 2006 Giorgini et al. 2003
Measurements of the Yarkovsky effect The main measurable feature of the Yarkovsky effect is the run-off of the asteroid orbital longitude (quadratic with time). 3 4 n a 2 Δ M = da dtδ t M = n = ; mean anomaly; mean motion Direct detection of the Yarkovsky effect: (6489) Golevka: radar astrometry (Chesley et al., 2003) 1992 BF: extended optical astrometry 1953-2006 (Chesley et al., 2006).
Gaia ESA Cornerstone mission: launch 2012 All sky survey V 20; V 10 9 stars: 250,000 asteroids Photometry: σ V =0.01 0.03 for V~[15-20] Astrometric accuracy: (~0.2mas @ V~15; V 2-3mas @ V~20 V for each CCD observation)
Variance-covariance covariance analysis O-C difference between the observed and the calculated positions. δu 0 corrections to initial positions & velocities; δc p corrections to physical parameters. A contains the partial derivatives of observed positions w.r.t. initial position & velocities,, & physical parameters. W: : weight of the error on the observed position It is possible to demonstrate (ask Serge) that the error on the determination of the physical parameters of asteroids δc p is equivalent to computing particular elements of the matrix (A t WA) 1 Mouret et al. in preparation
Our sample of asteroids: NEAs We simulated Gaia s astrometric measurements for the sample of known NEAs. With the Gaia Solar System Simulator (Mignard we simulate observations of NEAs. Mignard-Tanga) First lines of the output of our Gaia Solar System Simulator for the NEA 2000 WN10 Initial orbital condition: mid 2014 (half mission)
Physical parameters Known sizes and spin vectors (Eros ) Sizes and spin vector randomly distributed within the known size and spin vector NEA distributions. Thermal inertia (Г)( Size dependence of asteroids thermal inertia: Delbo et al. 2007
Mouret et al. in preparation Results
Caveats systematic errors not taken into account planetary perturbations; non Gaussian errors; the masses of main-belt perturbers high eccentricities of NEAs, non spherical shapes; Relativistic effects & solar quadrupole moment. small orbital semi-major axes & high eccentricities.
Conclusions and future work Detection of the Yarkovsky effect from Gaia s for 30 50 NEAs. There are some hundreds NEAs with good radar astrometry. Gaia s + radar will allow the detection of the Yarkovsky effect for ~60+ NEAs Delbo et al. in preparation If sizes of these objects are available (e.g. from radiometry, polarimetry,, radar) measurement of the Yarkovsky effect bulk density internal structure.
Future projects Radiometric sizes for 35,000 asteroids Spitzer Archive project (PI D. Trilling, Lowell; CoI M. Mueller EU possibly France) Thermal inertia value is needed for the NEAs for which we can measure the Yarkovsky effect Ground based thermal IR obs.. at different epochs are required.