4 juin - 7 juin 2013


S06 Astrom├ętrie de haute pr├ęcision et applications

Orbits of binary asteroids using a Markov chain Monte Carlo technique

D. A. Oszkiewicz, D. Hestroffer, P. David

We present a novel method of orbit computation for resolved binary asteroids. The method combines the Thiele-Innes-van den Bos method with a Markov chain Monte Carlo technique (MCMC). The classical Thiele-van den Bos method has been

commonly used in multiple applications before, including orbits of binary stars and asteroids; conversely this novel method can be used for the analysis of binary stars, and of other gravitationally bound binaries. The method requires a minimum of three observations (observing times and relative positions - Cartesian or polar) made at the same

tangent plane - or close enough for enabling a first approximation. Further, the use of the MCMC technique for statistical inversion yields the whole bundle of orbits possible, including the most probable one.

In this new method, we make use of the Metropolis-Hastings algorithm to sample the parameters of the Thiele-van den Bos

method, that is the orbital period (or equivalently the double areal constant)

together with three randomly selected observations from the same tangent

plane. The observations are sampled within their observational errors (with an assumed distribution) and

the orbital period is the only parameter that has to be tuned during the

sampling procedure. We run multiple chains to ensure that the parameter

phase space is well sampled and that the solutions have converged. After

the sampling is completed we perform convergence diagnostics. The main

advantage of the novel approach is that the orbital period does not need to be known in advance and the entire region of possible

orbital solutions is sampled resulting in a maximum likelihood solution and

the confidence regions. We have tested the new method on several known

binary asteroids and conclude a good agreement with the results obtained

with other methods. The new method has been implemented into the Gaia

DPAC data reduction pipeline and will be used in the long-term processing of the Gaia

data in particular to confirm the binary nature of a suspected system, and for deriving the mass determination of the binary system.