GAIA asteroid simulations:from point-like to ellipsoidal objects

Helsinki May 27-28, 2004

P. Tanga, F. Mignard (OCA)A. Cellino (OATo, Turin)

J. Berthier, D. Hestroffer (IMCCE, Paris)

Goal

Implementation of physical properties (shape, spin) in the existing detection simulation

Modeling of their effects on photometry and astrometry

Statistics not in contradiction with reality

Simplified calculations to preserve simulation speed

Assumptions

Asteroids can be modelled as 3D-ellipsoids (at 1st order)

Regular rotation (constant spin, pole)

Radius and average absolute magnitude coming from the existing catalogues are reliable

MethodsExploitation of existing databases:

Magnusson – Kryszczynska shape (b/a, c/a), (several records/object) period,

pole

Harris lightcurve parameters shape (b/a, c/a), period

Appropriate generation of missing data

Magnusson database, selection criteria:

If several records exist, the most recent is retainedIf several poles exists in that record, a solution is chosen at randomIf the spin period associated to that solution exists, it is selectedIf there are estimates of the b/a, c/a ratios, they are used to compute the volume-equivalent ellipsoid axes

Lightcurve parameters (Harris):

Rotation period selected when not available from MagnussonTumbling asteroid periods discarded

Generation of physical parameters - 1Poles : uniform random distribution on the skyRotational phases at t = 0 : uniform random distributionShapes :

size range (km) <∆m> ± σ

D > 200 0.188 ± 0.028

100 < D < 200 0.181 ± 0.011

50 < D < 100 0.206 ± 0.015

20 < D < 50 0.362 ± 0.057

D < 20 0.526 ± 0.059

b/a : ∆m ~ 2.5 log (a/b)

c/b = 1. - abs(η),

<η> = 0. ± 0.5

Tedesco & Zappalà 1985

Generation of physical parameters - 2

PeriodsLarge asteroids (D > 30 km). Well fitted by a single Maxwellian. 150 m < D < 40 km. Non-maxwellian with excess both at large and small bodies.

Distribution fitted by multiple (4) maxwellians

(Donnison 2002)

Ω⎟⎟⎠

⎞⎜⎜⎝

⎛ Ω−

Ω=<Ω ∑

=

dDfk

iikk

1

2

2/3

2

...1...1 2exp2),,(

σσπϖδϖσ

The physical parameters file

pole coordinatesrotation period

shape parameters

From model to lightcurvesFor each detection :

(H,G) system average magnitude at given phase angle

Physical ephemeris computation orientation on the sky

Analytic computation of geometric shading fluctuations around the average

Advantages : phase – magnitude relation preservedfast computation

An example21 Lutetia

(normalized for the Sun and Earth distance)

Limitations (at present)

Each object has its H, but G is unique and fixed

No complex shapes

No satellites

Phase angle – amplitude relation poorly modelled (scattering not taken into account properly)

No poles « polarization »

Future extensionsNEO

Different values of G

Effects on astrometry : simple model of photocenter displacement

Simple scattering effectsmodel of the amplitude-phase relationship

Satellites

…suggestions !