GAIA Observations of Asteroids: Sizes, Taxonomy, Shapes and Spin Properties Alberto Cellino (INAF, Torino Observatory), and the GAIA Solar System Working Group
The impact of GAIA on Asteroid Science will be extremely important!
Some important problems in current asteroid science: The determination of asteroid masses and densities The direct measurement of asteroid sizes and shapes The determination of spin properties for a large sample A possible size-dependence of asteroid albedos The distribution of taxonomic classes within the Main Belt GAIA will play a decisive role in the solution of the above problems.
HST Speckle Interferometry The size distribution of Main Belt asteroids is a major constraint for models of the collisional evolution of the asteroid belt. Moreover, sizes and shapes are needed to derive average densities when masses are known. However, asteroid size data are generally not known from direct size measurements! GAIA will directly measure asteroid sizes
Asteroid signals are being simulated by means of suitable numerical algorithms.
The basic idea observed signal width inferred angular size
Modeling the measurement of a 20th mag object, taking into account all effects determining the final asteroid signals (photon noise, etc.) width dispersion Dispersion of compatible sizes
Results of simulations of Size measurement accuracy, taking into account nominal instrumental configuration of GAIA (Astrometric fields) (Source: A. Dell Oro)
N N N Resulting statistics of the fraction of the population with size measured N times with an accuracy better than 10%, as a function of size (in km). Based on Mignard s simulations of GAIA asteroid detections over five years (Source: A. Dell Oro)
Summarizing: The minimum angular size that can be measured with an accuracy of 10% is ~ 20 mas at magnitude G ~ 12, and ~ 120 mas at magnitude G ~ 20 Based on simulations of GAIA detections, most Main belt asteroids larger than 20 30 km will be measured with an accuracy equal or better than 10%, at least once during the operational lifetime of GAIA. This corresponds to more than 1,000 objects. This will be a tremendous improvement in our knowledge of the asteroid size distribution!
IRAS albedo distributions D > 50 km D < 50 km
Asteroid taxonomy has been traditionally based on spectrophotometric properties, in the wavelength range covering UBVRI colors. The distribution of different taxonomic classes as a function of heliocentric distance is related to the general composition gradient of our Solar System
GAIA will observe in 4-5 (BBP) + 11-12 (MBP) colors
There are about 213,000 asteroids with mean apparent magnitude < 20 (Source: C.-I. Lagerkvist)
Disk-integrated photometry by GAIA: Expected photometric behavior of the asteroids b/a = 0.7 c/a = 0.5 Example: Orbit of 39 Laetitia Varying (mag) with respect to first observation for different choices of the pole and shape parameters, as a function of time λ p = 30 β p = 60
Simulated GAIA observations Orbit of 39 Laetitia λ p = 30 β p = 60 b/a = 0.7 c/a = 0.5 P = 7 h.527 φ 0 = 0.4 (mag) with respect to first observation
The general idea We want to develop automatic algorithms capable of finding a simultaneous solution for : Pole coordinates (λp, βp ) Sidereal Rotation Period (P) General shape Different approaches are being tested by the GAIA SSWG to attack this problem
First Approach: The objects are assumed to be triaxial ellipsoids, and a genetic algorithm is used to solve for the unknown spin period, spin axis direction, axial ratioes, rotational phase at t=0, and phase-magnitude linear coefficient.
Alternative approach, based on photometry-inversion techniques by M. Kaasalainen, which do not assume any a priori shape. Asteroid shapes and spins from sparse photometry (Kaasalainen 2004, A&A 422, L39) Best sidereal period peaks strongly in the initial trial period scan => fast and completely automatic procedure Typically get pole within 2 to 15 degrees, basic shape dimension ratios within 15 %; photometric calibration within 0.05 mag is sufficient, so no problem for GAIA s expected 0.01 mag
Preliminary genetic algorithm solutions for HIPPARCOS data of 216 Kleopatra (only 21 photometric measurements!) Pole Period b/a c/a k s APR fitk => (50, +28) 5.38531 0.25 0.11 0.024 -- fitksamp => (49, +28) 5.38531 0.37 0.15 0.023 0.013 The real Kleopatra Pole Period (72, +27) 5.385
To be pessimistic, GAIA should photometrically measure with an accuracy of 0.01 mag in G, all the asteroids having H 12.5 (assuming V - H = 6, e V lim = 18.5) The number of these objects is uncertain (not all of them have yet been discovered), but it should be of the order of 10,000 or slightly less. Taking into account that: (a) GAIA can measure with 0.01 mag accuracy many objects fainter than H = 12.5; (b) the inversion algorithms seem to work well even when the photometric errors are more than twice as large, we conclude that we expect to find solutions (poles, Periods and axial ratios) for no less than 10,000 asteroids.
General application: Spin properties as a new, important constraint to modern models of the collisional evolution of Main Belt asteroids. Specific applications: (1) test of the existence of possible preferential alignments of the spin axes of family members. (2) Tests of the effectiveness of the Yarkovsky effect.
Expected Post-GAIA scenario in Asteroid science: Masses and average densities of ~100 objects Sizes directly measured for ~1,000 objects Spin properties and general shapes of thousands of objects; spin as a constraint to collisional evolution models Assessment of size albedo relation, possibly interpreted in terms of space weathering New taxonomy of a very big sample of the population. Implications on the original gradient in composition of the Solar System, and on dynamical diffusion and collisional mechanisms. New spectroscopic families.