Densities of asteroids: convex shape models and Gaia masses
This project focus on the volume determination by scaling the convex shape models in size. To determine the shape models, we need additional optical data for several asteroids. Density is then derived from the volume and the adopted mass.
This project is funded by CNES.
To determine a meaningful bulk density
of an asteroid, both accurate volume
estimates are necessary. The volume can be computed by scaling the size of the 3D shape model to fit the disk-resolved images or stellar occultation profiles, which are available in the literature or through collaborations. Here we provide a list of asteroids, for which (i) there are already mass estimates with reported uncertainties better than 20% or their mass will be most likely determined in the future from Gaia astrometric observations, and (ii) their 3D shape models are currently unknown. Additional optical lightcurves are necessary to determine the convex
(sometimes even non-convex) shape models
of these asteroids. We maintain here an up-to-date list of these objects to assure efficiency and to avoid any overlapping efforts.
What kind of data we need?
Standard dense-in-time lightcurves, typically several hours of observations. Even lightcurve from a single night is useful, however, combined lightcurves from several nights are welcome as well (especially if the rotation period is long).
Why these asteroids?
We choose the targeted asteroids based on these criteria:
- There are already mass estimates with reported uncertainties better than 20% or we will know their masses from Gaia astrometric observations.
- We have complementary data that can be used to scale the shape models in size (AO or occultation data). In some cases, observation campaign in order to obtain occultation data will be initiated.
- Shape models cannot be determined from currently available optical data.
Currently, the leading method is the convex inversion (Kaasalainen and Torppa, 2001; Kaasalainen et al., 2001), which makes use of only disk-integrated photometry and provides a convex shape model with the sidereal rotational period and the pole orientation. About 400 hudred shape models were derived by this method so far, most of them are stored in the Database of Asteroid Models from Inversion Techniques (DAMIT, http://astro.troja.mff.cuni.cz/projects/asteroids3D
). A more advanced KOALA method of Carry et al. (2012), which is build on the lightcurve inversion basis, allows a non-convex shape model determination. This method uses among the disk-integrated photometry also stellar occultation measurements and/or disk-resolved images (2D contours) obtained by the 8-10m class telescopes equipped with adaptive optics systems. Moreover, recent inversion method of Viikinkoski et al. (2015) called ADAM can handle, among the already mentioned types of data, also disk-resolved thermal data, interferometry and radar observations. In our work, we use the lightcurve inversion method or the ADAM algorithm if there are non-convex signatures in the disk-resolved data (AO, occultation).
Scaling the size
The most frequent method to determine the size (and volume) of an asteroid is fitting the thermal data observations (typically from IRAS, WISE, and AKARI satellites) by simple thermal models that assume a spherical shape model (e.g., the Near-Earth Asteroid Thermal Model, Harris, 1998). The reported size uncertainties for individual asteroids are usually very small (few percent), however, they are not realistic. Indeed, the uncertainties are dominated by the model systematics the spherical shape assumption is too crude and also the role of the geometry is neglected (e.g., the spin axis orientation). In the statistical sense, the sizes determined by thermal models are reliable, but could be easily off for individual objects by 1030%. This implies a volume uncertainty of 3090%! Obviously, more complex shape models (instead of spheres and ellipsoids) have to be used for more accurate size and volume determinations. Convex shape models allow us already a reasonable opportunity to determine the volume.
The disk-integrated photometric data itself are not sufficient to constrain the dimensions of these asteroids. However, there are three methods commonly used to determine the size of the shape model:
- scaling the asteroid shape projections by disk-resolved images obtained by adaptive optics systems;
- scaling the asteroid shape projections to fit the stellar occultation measurements; and
- fitting the thermal measurements by the thermophysical model.
The shape model can be either an input (typically computed by the convex inversion) or derived simultaneously with the size. To be specific, the method for comparing the AO contours with the asteroids projections was developed and already used for size determinations of ∼40 asteroids in Hanu et al. (2013). Conceptually similar method can be applied when constraining the asteroid sizes with stellar occultation measurements (see Durech et al. 2011).On the other hand, the KOALA method of Carry et al. (2012) allows a non-convex shape model determination and a simultaneous scaling in the size. Stellar occultation measurements and/or disk-resolved images (2D contours) obtained by the 8-10m class telescopes equipped with adaptive optics systems are used. Moreover, recent inversion method of Viikinkoski et al. (2015) called ADAM can handle, among the already mentioned types of data, also disk-resolved thermal data, interferometry and radar observations and provides a scaled, in principle non-convex, shape model as well.
With available thermal data (WISE, IRAS, AKARI), it is possible to constrain sizes of asteroids by the means of thermophysical modeling (see, e.g., Delbo 2004; Delbo et al. 2007). By this method, which uses the convex shape model as a fixed input, surface properties such as albedo, surface roughness or thermal inertia can be determined. The main limitation here is the fact that the WISE data for these relatively big asteroids exist, but they are often saturated, because of their brightness and the fixed exposure time of WISE. On top of that, although the other thermal data from IRAS or AKARI are often available, however, due to their worse quality, the solution (for example the size) is usually not well constrained.
We either adopt the masses from the literature (see, for example the review of Carry 2012) or we assume a list of asteroids for which the mass will be determined from Gaia astrometric observations. Recent mass determinations were reported from the astrometric observations, namely based on the planetary ephemeris or orbit deflection methods, and promise a significant improvement of the currently poor knowledge of the mass. Goffin (2014) published more than one hundred mass estimates with a typical uncertainty of 520% (planetary ephemeris). The astrometric observations of the Gaia satellite should also provide masses, namely for ∼150 asteroids (for ∼50 with an accuracy better than 10%, Mouret et al., 2007, 2008) by the orbit deflection method. The advantage of Gaia masses is in the uniqueness of the mission, which should result in a comprehensive sample with well-described biases (e.g., the current mass estimates are strongly biased towards the inner main belt).
Bulk density - the ultimate goal
The currently available mass and volume estimates allowed the determination of densities with accuracy formally better than 20% for less than hundred asteroids (Carry, 2012). A significant number of the density estimates with uncertainties better than 20% reported in Carry (2012) are determined from sizes based on spherical shape models (i.e., determined by thermal models), and thus the uncertainties are most likely strongly underestimated. This means that our knowledge of accurate densities (<20%) is probably limited too only a few dozens of asteroids, which sizes/volume were determined by more sophisticated techniques. Our project has the potential to greatly improve our current knowledge about accurate densities.
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- 27 Aug 2015