How occultations improve asteroid shape models

Transcription

1 How occultations improve asteroid shape models Josef Ďurech Astronomical Institute, Charles University in Prague ESOP, August 30, 2014

2 Contents 1 Lightcurves Direct problem Inverse problem Reliability of the models 2 Occultations Scaling the convex models by occultations Detailed nonconvex models

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4 What do we know known asteroids numbered well known orbit 100 new discovered every day we know the orbit in the solar system and the size (from the brightness, 10 m to 1000 km) for 5000 we known the rotation period (1 min to 100 d) for 500 we know the global shape (from the lightcurve inversion mainly) for 20 we know the detailed shape (from space probes, radar,...) Physical properties are known for a small fraction of the population we want to know more.

5 Contents 1 Lightcurves Direct problem Inverse problem Reliability of the models 2 Occultations Scaling the convex models by occultations Detailed nonconvex models

6 Brief history related to asteroid lightcurves 1801 the first asteroid discovered 1898 the first brightness variation detected (lightcurve) 1906 Russell published a paper on lightcurve inversion, opposition geometry, geometrical scattering, reflectivity/shape ambiguity 80 s triaxial ellipsoids 1992 Kaasalainen et al. provided the first general analysis of the inverse problem 2001 Kaasalainen et al. published a robust inversion scheme present lightcurve inversion has become a standard tool for revealing asteroid shapes, confirmed by many independent techniques

7 Asteroid lightcurves Direct problem The apparent brightness depends on the distance from the Earth and the Sun (known) geometry Sun asteroid Earth (known) and unknown parameters shape rotation state spin axis direction, period of rotation 1987/1/ /7/20.0 surface properties (albedo, light-scattering behaviour) Relative intensity 1.5 Periodic change 1 of brightness 1caused by rotation 1 lightcurve. Periods from 1 min to 100 d, typically hours /2/ Relative intensity /7/ Phase of rotation /2/ Phase of rotation /4/ Phase of rotation

8 Shape vs. albedo (reflectance) Lightcurves can be caused by irregular shape albedo variance over the surface combination of both Fortunately, asteroids are mostly uniformly gray brightness changes are caused by shape.

9 Asteroid lightcurves Inverse problem From a set of lightcurves (tens) observed under different geometries (over years) we can reconstruct the shape, the spin axis direction, the period, and other parameters lightcurve inversion, Kaasalainen et al. (2001) If we have enough observations covering various viewing/illumination geometries, we get unique convex model. We assume that the reflectivity is uniform over the surface no spots, no chessboard pattern, etc. (usually a valid assumption). Because of the limited observing geometry (plane of the ecliptic), there are usually two pole solutions (λ, β) and (λ ± 180, β) and the corresponding shapes are mirror images of each other. Because the albedo is not known, all models derived from photometry only are scale-free no information about the size.

10 Stability of the solution The distribution of reflectivity over the surface is sensitive to the noise in data, amount of data, light-scattering model, etc. ill-posed problem. 3D shape is stable Minkowski stability (defined and proved mathematically). 56 lightcurves 53 lightcurves

11 Nonconvex models It is possible to model the shape as a nonconvex body, but the solution is not stable and it is not clear, which details on the model are real. Differences between non-/convex models are apparent only for high Sun-asteroid-Earth phase angles and for highly nonconvex bodies. Convex models are almost always sufficient in practice. (1627) Ivar

12 Comparison with the reality Good approximation, convex models are good for global shape characteristics, spin axis ±5, accurate rotation period ±0.01 s. (25143) Itokawa

13 Laboratory model of an asteroid Convex model is not sensitive to the scattering law which is good, we do not know it. Kaasalainen at al. (2005)

14 Lightcurve inversion models models of 500 asteroids 381 available at Database of Asteroid Models from Inversion Techniques (DAMIT) more models soon inversion of sparse-in-time photometry from all-sky surveys, distributed computing project thousands of models in the near future, much more with the data from Gaia, Pan-STARRS, LSST,...

15 Contents 1 Lightcurves Direct problem Inverse problem Reliability of the models 2 Occultations Scaling the convex models by occultations Detailed nonconvex models

16 Occultations of stars by asteroids

17 How to combine occultations with shape models? convex models from lightcurves shape, pole, and period known sky-plane orientation can be computed for past/future occultations scaling the model by fitting the chords solving the pole ambiguity one pole clearly better that the other

18 How to combine occultations with shape models? convex models from lightcurves shape, pole, and period known sky-plane orientation can be computed for past/future occultations scaling the model by fitting the chords solving the pole ambiguity one pole clearly better that the other nonconvex models by multi-data inversion lightcurves and occultation profile used simultaneously in one optimization algorithm model tries to fit both lightcurve and occultation data nonconvex details better volume estimation density if mass is known

19 Occultations and convex models scaling

20 Occultations and convex models many events

21 Occ. and convex models pole ambiguity resolved wrong pole correct pole

22 Occ. and conv. models pole ambiguity unresolved pole #1 pole #2

23 Multi-data inversion photometry the most important data source, available for almost all known asteroids lightcurve inversion robust method with results confirmed by ground-truths model: accurate rotation period, pole directions, global convex shape about 500 models now

24 Multi-data inversion photometry the most important data source, available for almost all known asteroids lightcurve inversion robust method with results confirmed by ground-truths model: accurate rotation period, pole directions, global convex shape about 500 models now other data general nonconvex shapes adaptive optics images details, size occultation silhouettes details, size thermal infrared observations albedo, size, thermal properties radar flyby data from spacecraft part of a 3D shape

25 Nonconvex details from lightcurves and occultations convex model scaled to fit occ. chords

26 Nonconvex details from lightcurves and occultations convex model scaled to fit occ. chords nonconvex model derived from by simultaneous inversion of lightcurves and occultation data

27 Occultation by binary asteroid (90) Antiope

28 Model vs. observations lightcurves Relative intensity Relative intensity /12/ /6/ Phase of rotation /11/ /1/ Phase of rotation /3/ /3/ Phase of rotation

29 Shape model of (90) Antiope

30 Model vs. observations occultation #1 Model projection vs. occultation data from 2011/07/ s 150 y [km] x [km]

31 Model vs. observations occultation #2 Model projection vs. occultation data from 2008/01/ s y [km] x [km]

32 Conclusions + Future Mass production of convex models from photometry much more data from ongoing and future surveys Gaia space mission of ESA Pan-STARRS (Hawaii) LSST (Large Synoptic Survey Telescope) scaling of convex models + removing pole ambiguity detailed models from combined (LC + Occ) data inversion models stored in Database of Asteroid Models from Inversion Techniques (DAMIT) possibility to plot sky-plane projections for any model for a given time distributed computing project Asteroids@home thousand of new models