Shape, size and multiplicity of main-belt asteroids I. Keck Adaptive Optics survey

2.1. Collected data

In 2001, we initiated a campaign to identify and study binary asteroids in various populations of asteroids from the main-belt to the trans-neptunian objects using telescopes equipped with AO systems (Marchis et al., 2004a). The data presented here were collected in 2003 and 2004 using the Keck II AO system (Wizinowich et al., 2000) and the near-infrared NIRC-2 camera (1024 × 1024 Aladdin-3 InSb array). All observations were recorded in the narrow field of view (with a 9.942 mas pixel scale) in Kp broad-band filter (λ₀ = 2.124 μm; Δλ = 0.351 μm). The AO system was used in Natural-Guide Star (NGS) mode, i.e., the asteroid itself was used as a reference for the AO wavefront sensor. With the improvements made to the system in 2003 (van Dam et al., 2004), the Keck AO system is able to provide full and stable correction in this mode for targets up to R = 13.5 magnitude under good atmospheric conditions (photometric sky and seeing < 0.8″ ), reaching a Strehl Ratio of ∼45% in Kp band.

Because of their small predicted angular size (<0.2″), the main-belt asteroids are excellent targets for an AO system. Fig. 1 illustrates the sensitivity limits of the wavefront sensor as function of distance to the Sun. Our selected targets are well-above this limit. By estimating the magnitude in visible and using the IMCCE ephemeris,¹ we find that a total of ∼300 main-belt asteroids (with perihelia > 2.15 AU and aphelia < 3.3 AU) should be accessible to the Keck AO system in its NGS mode. This survey focuses on observations covering 11% of this total. For each observing night, we selected from the IMCCE ephemeris all asteroids with an elongation angle larger than 120° and a predicted magnitude in the visible m_v < 13.8. A typical sample would include approximately 110 asteroid candidates. The total typical integration time per asteroid is ∼5 min. Considering the overhead of the telescope and the AO system, the number of targets observable on a 5 h half-night was ∼20 (Marchis et al., 2004a). Thirty eight observations of 31 main-belt asteroids are reported in Tables 1a and 1b on three half-nights (December 6, 2003, December 7, 2003, and October 25, 2004).

Two additional observations are included in this work: 192 Nausikaa, observed in September 2000 at its opposition using KCAM camera in H broad band filter (λ₀ = 1.63 μm; Δλ = 0.30 μm). One observation of 511 Davida recorded in kp band with NIRC-2 in December 2002 (Conrad et al., 2003) is also included in our analysis. Most of the targets were observed close to their opposition at an average distance of ∼1.9 AU. Their mean estimated size from Tedesco et al. (2002) varied from 43 to 326 km (Fig. 1).

Basic data processing (sky substraction, bad-pixel removal, and flat-field correction) was applied on the raw data using the eclipse data reduction package (Devillard, 1997). Successive frames taken over a time span less than 8 min, were combined into one single averaged image after applying an accurate shift-and-add transformation through the Jitter pipeline² offered in the same package. Data processing with this software on such high S/N data (∼1000) is relatively straightforward, since the centroid position on each frame is estimated by a Gaussian fit, then the final image is obtained stacking set of cross-correlated individual frames.

2.2. Image quality

AO systems enable real-time observations with an angular resolution close to the diffraction limit of the telescope. The quality of AO correction, however, can vary slightly in time due to variations in seeing conditions during a night and as a function of target brightness. To better characterize the quality of the Keck AO data during our observations, we recorded several observations of unresolved stars at similar magnitudes (between magnitude 9 and 12.8) several times during the nights, and used them as approximations to the point spread function (PSF) of the AO system. The quality of correction can be estimated either by measuring the full width half-maximum (FWHM) on the star, corresponding to the angular resolution of the image, or calculating the Strehl ratio (SR), which compares the observational PSF with the theoretical PSF provided by the telescope.³ The characteristics of these PSF stars is described in Table 2. It is important to note that the AO corrections are stable in this wavelength range and for these bright targets. The FWHM which is estimated to be ∼54 mas (for a SR ∼ 35%), is quite close to the diffraction limit of the telescope (43 mas at 2.1 μm) and corresponds to a spatial resolution of 75 km at 1.9 AU (the average distance of the targets in this survey).

2.3. Deconvolution

The typical PSF in adaptive optics is characterized by a peak of coherent light that defines the spatial resolution surrounded by a halo produced by the uncorrected residual phase. The direct effect of this halo is a blurring of the recorded image. As we measured an estimate of the AO system PSF, it is possible to apply an a posteriori deconvolution method to improve image sharpness. Deconvolution is an inversion process which aims to reconstruct a good approximation for the initial object given the PSF for the system. Many algorithms based on different mathematical approaches for both astronomical instrumentation as well as medical imaging have been developed in the last two decades (Starck et al., 2002). Part of our group is involved in the development of a deconvolution method dedicated to objects with well-defined edge, a common characteristic to spatially-resolved planetary science targets. Our new adaptive image deconvolution algorithm (AIDA) which is described and tested thoroughly in Hom et al. (2006) is based on a stochastic approach to the deconvolution problem. The algorithm, inspired by MISTRAL (Myopic Iterative STep-preserving Restoration ALgorithm), a deconvolution algorithm developed by Mugnier et al. (2004), includes several important improvements. This new algorithm aims to find the best image reconstruction, using information about the object and the PSF. It requires several star images to evaluate variations in the PSF. The main improvement of this approach over more classical methods is that it avoids both noise amplification and the creation of sharp-edged artifacts or “ringing effects,” and thus better restores the photometry (see simulations below). Additionally, we implemented in AIDA an automatic determination of the balance between the maximum-likelihood criterion and two regularization priors. The first one called L1—L2 permits the restoration of a sharp edge in the image limiting the formation of Gibbs artifacts close to the limb of the asteroid. The second is the myopic criterion which considers the variability of the PSF. How the algorithm weights each prior to achieve a good deconvolution is beyond the scope of this paper and is described in Hom et al. (2006). An inappropriate weighting of the L1—L2 prior, made manually by the user in MISTRAL, can result in strong Gibbs artifacts. For instance, this problem is apparent in deconvolved images of 511 Davida presented in Conrad et al. (2003).

To characterize the performance of the AIDA deconvolution for the study of shape and size of main-belt asteroids, we performed a series of simulations: artificial images of asteroids with various sizes (from 2 to 20 pixels), shapes (an ellipse whose axis ratio a/b = 1.0, 1.2,..., 2.0), and orientations were created. These perfect images were degraded by convolving them with one real set of observed PSFs from Table 2. Both Poisson and detector noises were added to the degraded image for which the peak S/N was ∼1200, hence mimicking the image quality in our observations. ∼The AIDA deconvolution was applied on these sets of images using its adaptive regularization weighting, and using a different set of PSFs to better quantify the effect of variability of the AO correction. Fig. 2 displays one set with various sizes, two orientations, and the same a/b ratio. The deconvolution process improves the sharpness of the image and restores the initial shape and orientation of the images for an asteroid larger than >5 pixels. For the largest asteroids, some deconvolved images still show a typical bright-edge artifact with a contrast <10–15%. A feature at lower contrast could be in fact an artifact of deconvolution. To measure the size, the apparent shape, and the orientation of an asteroid, we fit the image with an ellipse characterized by a major axis 2a, a minor axis 2b and the orientation (in degrees counter-clockwise from the sky east). We compared these parameters with the ones defined to build the initial image for the simulation.

We summarized in Fig. 3 a statistical study of the size recovery accuracy for the entire set of simulations. In this figure, we compared the ratio between the measured size before and after deconvolution with that of the initial image. For a size between 5 and 12 pixels (corresponding to 50–120 mas), the estimated size after deconvolution is better on average (with an accuracy of ∼5–10%) than before deconvolution (usually over-estimated by 10–30%). Beyond 12 pixel size, the difference between the size measurements on the basic-processed and deconvolved images is less evident although the accuracy on a deconvolved image is 3% better. Below 5 pixels, which corresponds to the angular resolution provided by the Keck AO system (see Section 2.2), the estimation of the real size of the asteroid is challenging even after deconvolution. To quantify the accuracy of our size estimates for the asteroids in our sample (see Section 3.1), we fit the ratio in Fig. 3 by an empirical function.

3.1. Shape and size

The AIDA deconvolution algorithm was applied to all basic-processed frames of asteroid listed in Tables 1a and 1b. To better estimate the PSF variability, in several cases (e.g., for December 6, 2003) we used as an initial set of PSF, a mixed set of PSF frames taken the day after or on the same day as the observations. Owing to the excellent stability of the AO correction as described in Section 2.2, this approximation has a minor impact on the final deconvolved image which is clearly improved as shown in Figs. 4a-4e. The deconvolution is not perfect and could be improved by slightly tuning the regularization parameters. However most of the work described here aims to estimate the size and shape of the asteroids. Our simulations ensured a good calibration of the systematic effects affecting the size estimate, caused by AIDA when it is ran with standard automatic parameters. Considering that this calibration could be affected by a manual adjustment of the parameters, and that the size and shape determination is the main goal of this study, we did not perform a manual optimization in each case, thereby favoring the accuracy of the size determination.

The size and shape were approximated using the same fitting technique described for the simulated images in Section 2.3. For comparison, we also fit an ellipse on the basic-processed images. The major-axes and orientations obtained for both, the basic-processed and the deconvolved images, are listed in Tables 3a and 3b. A brief comparison between the size measurements confirm that those obtained from the basic-processed data are over-estimated in comparison with the deconvolved ones. This effect is predominant for the asteroids with a major-axis between 5 and 10 pixels.

In Tables 4a and 4b, we report the best size and shape estimates in km for the 33 asteroids observed in this survey. The error bar reported for the major-axes of the ellipse has been derived from the empirical function obtained from our simulated images after deconvolution as described in Section 2.3. The uncertainty in the orientation was approximated by comparing the results from the fits on the basic-processed and deconvolved images. We are confident that we obtain a good estimate of the uncertainty on the orientation of the fit ellipse, since the Keck AO PSF is quite symmetrical with a FWHM_x/FWHM_y < 5%. Therefore, even after convolution by the PSF of the AO system, the asteroid elliptical shape keeps its asymmetry and the uncertainty on the orientation is mostly introduced by the fitting process.

3.2. Search for moonlet companions

4.1. Comparison of AO images with lightcurve inversion models

Several asteroids in this paper have been analyzed via light-curve inversions by Kaasalainen et al. (2002b), Michałowski et al. (2004) and Torppa et al. (2003). We compared the inversion model plane-of-sky predictions with the observed images. The model was produced with the same scattering model described in the corresponding inversion articles. In many cases, the AO images approached the same level of detail as the lightcurve models, and for 9 Metis and 130 Elektra the images may even reveal some features not resolvable by photometry. Slight albedo variations are not expected to affect the global shape model significantly. This is called Minkowski stability (Kaasalainen and Torppa, 2001): it can be shown that attributing photometric variations to shape is a considerably more stable process than attributing them to albedo. Also, photometric inversion provides a measure of probable albedo variegation, which so far has been significant (though still moderate) for only a few asteroids out of about one hundred. Spacecraft images appear to corroborate this. In a future paper (Kaasalainen and Marchis, in preparation), we will simultaneously combine the complementary data sources of adaptive optics images and photometry to make shape/albedo/rotation models that produce mutually consistent plane-of-sky images and lightcurves. Such multi-data inversions considerably reduce the modeling uncertainties (Kaasalainen and Lamberg, 2006).

Comparing the AO images with 3D-models allows us to discard the photometric mirror pole solution inevitable for asteroids moving close to the plane of the ecliptic. The plane-of-sky model image for the wrong pole is usually clearly different from the AO image in orientation and also shape. Thus even limited angular resolution AO images reveal the correct pole solution. The photometric inversion models agree well with the AO images, thus confirming the validity of both the lightcurve inversion method [much as space probe ground truths in Kaasalainen et al. (2001)] and the AO image reduction technique.

4.2. 9 Metis

Fig. 6 shows the basic-processed and deconvolved unsatu-rated images of 9 Metis. This S-type asteroid was observed twice on October 25, 2004 at 06 UT and 2 h later. The average size of 181 km is close to the 190 km size reported by Kristensen (1984). At 650 km from the center of the primary (corresponding to 2/100 × R_Hill the minimum detectable size for a companion was 5.4 km. At 1/4 × R_Hill the detectivity improved and a 4 km moonlet would have been unambiguously detected. We did not see the companion reported by Wang et al. (1981) located at ∼1100 km with a ∼60 km diameter. Considering the excellent sensitivity in our image, such a large companion could go unseen only if the orbit is nearly edge-on from Earth, and if the satellite is located in front or behind the primary. We calculated that the absence of a 60 km diameter companion around Metis is confident at 95%. The apparent size ratio (a/b) of the asteroid is 8% smaller than the one reported by lightcurve observations suggesting that we did not observe 9 Metis at its maximum apparent size. A 3D ellipsoid model proposed by Mitchell et al. (1995) by combination of radar, and lightcurve measurements indicates that 9 Metis can be approximated by an ellipsoid with 2a = 215 km, 2b 170 km, and 2c = 135 km. Fig. 6 shows a close-up view of both Metis observations. In fact, the asteroid is quite irregular in shape and displays albedo features with a contrast of up to 50%. Our simulations (Section 3.1) showed that the contrast in deconvolution artifacts for Metis-sixed objects was always <15%. Hence, these surface markings are consequently real. The most prominent one corresponding to a low albedo area (contrast ∼50%) is located at the astronomical north of the 08 UT image. The bright structure in the astronomical south-west with a contrast of 20% is visible on both images. These observations were recorded using a Kp broadband filter from 1.95 to 2.30 μm. In this wavelength range, mafic minerals show a very strong absorption in their reflectance (Gaffey et al., 1993) suggesting a heterogeneous distribution of this mineral on the surface of 9 Metis. Photo-polarimetric observations by Nakayama et al. (2000) also indicates a heterogeneous surface for Metis.

The variations in intensity may not be caused by albedo markings only. The lightcurve inversion model images displayed in Fig. 6 do not have any albedo features, yet they are bright and dark in several same areas as the AO images. In fact, surface scattering properties (different viewing and illumination directions, i.e., “subsolar brightening” of a dark surface of irregular shape) also contribute to the variation of light. The relative contributions of albedo, scattering, and shape will be better quantified in Kaasalainen and Marchis (in preparation). Because of 9 Metis’ irregular shape and the significant variation of brightening on its surface, it is possible that it is made up by the combination of accreted chunks. By combining this work with spectroscopic analysis, it should be possible to better characterize the surface composition.

The lightcurve pole solution of (λ = 181°, β = +23° in ECJ2000) from Torppa et al. (2003) is clearly the correct one, demonstrating that AO can remove the pole ambiguity, and the shape solution fits the image well. This solution is also in excellent agreement with the HST image taken by Storrs et al. (1999).

4.3. 52 Europa

52 Europa, a C-type asteroid, was observed once on December 7, 2003 at 07:50 UT. Fig. 7 shows how remarkably close this asteroid is to a perfect ellipse. No moonlet companion was detected around 52 Europa; at 2/100 × R_Hill, the minimum detectable moonlet size was 9.2 km. Its average measured size of 308 km is very close to the D_IRAS measurement of 302 km indicating that we are observing the asteroid at its maximum apparent size. The apparent shape of the asteroid can be well approximated by an ellipse with 2a = 349 ± 2 km and 2b = 267 ± 1 km leading to a/b = 1.30 ± 0.01. Surface features are not well detected since no specific PSF was taken for this target. Our deconvolution with AIDA shows a typical artifact of deconvolution (bright edge and bright peak in the middle of the asteroid) with a contrast <10% (Fig. 7). One dark structure with a contrast of 19% is detectable close to the north-east limb, but it remains quite marginal and additional observations and a more careful deconvolution analysis is needed to confirm the presence of surface markings on this asteroid. Comparing 52 Europa with 9 Metis, an S-type asteroid, it is clear that they are quite different in composition and shape, which is probably due to a difference in formation and evolution.

The lightcurve pole solution of (λ = 252°, β = +38° in ECJ2000) from Michałowski et al. (2004) is the correct one, resolving the pole ambiguity; the shape is also consistent with the image.

4.4. 87 Sylvia

87 Sylvia was observed on October 25, 2004 at 06:30 UT. Around this C-type asteroid orbits a moonlet companion discovered by Brown et al. (2001). We successfully detected this companion at 0.236 arcsec (peak intensity of 2.9 magnitude), corresponding to an apparent separation of 445 km, much closer than expected for the semi-major axis reported in Merline et al. (2002). Assuming the same albedo for the primary and secondary, the integrated flux ratio of Δm(integrated) = 5.4 indicates a typically-sized companion diameter of ∼20 ± 5 km. Sylvia’s primary was resolved with an average diameter (D = 282 km) that was 7% larger than the IRAS radiometric diameter (D_IRAS = 261 km). The primary displays an elliptical shape and does not seem to be binary as suggested by Prokof’eva and Demchik (1994) based on the light variation analysis with several optical filters. The best elliptical fit of Sylvia resulted in 2a = 348 ± 1 km and 2b = 217 ± 6 km and a ratio of a/b = 1.60, although lightcurve measurements suggest that a/b ∼ 1.77. No albedo structures were detected on this hemisphere of the asteroid. The pole solution (λ = 72°, β = +66° in ECJ2000) and shape from Kaasalainen et al. (2002b) is consistent with the image (see Fig. 8).

Marchis et al. (2005b) reported recently the discovery of a second moonlet [named (87) Sylvia II Remus] around 87 Sylvia using NACO, the adaptive optics system available on the ESO-VLT UT4 telescope. Because this satellite is closer and fainter, it is more difficult to detect on their AO observations. We carefully searched for it on the Keck observation after subtracting the azimuthally averaged profile. A secondary point-like structure appears, ∼2–3 magnitude fainter (peak intensity = 6.3) can be seen at 0.349″ east of the primary, corresponding to 660 km (see Fig. 15). This detection is marginal (the 2-σ detection limit at this distance is 5.1) but compatible in position with the semi-major axis reported in Marchis et al. (2005b) (a = 706 km).

4.5. 130 Elektra

On December 7, 2003 at 07:16 UT we observed 130 Elektra, a G-type asteroid. This C-type sub-class is characterized by a low albedo (A ∼ 0.05) and strong UV absorption (Tholen and Barucci, 1989). A moonlet companion orbiting around 130 Elektra was recently discovered by Merline et al. (2003). Itsorbital elements, however, are mysterious (Marchis et al., 2005a) and additional are taken by our group to refine them. The satellite companion was successfully detected on our Kp band image with a Δm(integrated) = 7.4 and with an angular separation of 0.79″ , corresponding to an apparent separation of 1040 km. Assuming the same surface albedo for Elektra and its moonlet, we derived a diameter for the secondary of ∼6 km.

Elektra’s primary shape is quite irregular as shown on our AO resolved observation displayed in Fig. 9. Its mean size (D = 191 km) is slightly larger than the one derived from radio-metric IRAS measurements. Its surface displays several albedo features with a contrast of ∼5–15%. A better characterization of 130 Elektra surface will soon be possible using AO systems combined with spectro-imager instruments.

The pole solution of (λ = 68°, β = -88° in ECJ2000), period 5.2247 h and shape from Ďurech et al. (in preparation) agrees well with this image and again removes the pole ambiguity.

4.6. 192 Nausikaa

On September 16, 2000, shortly after the final commissioning of the Keck AO system, 192 Nausikaa, an S-type asteroid, was observed by D. Le Mignant with the KCAM IR test camera. Two observations were recorded with a 16.8 mas pixel scale in the H band (1.6 μm). No moonlet companion was detected but the primary was clearly resolved with an average size of 86 km and an elliptical ratio of a/b = 1.51 (slightly smaller than the ratio estimated by lightcurve observations). Fig. 10 shows that this hemisphere of the asteroid surface does not display any obvious surface features at 1.6 μm.

As we later found out, a few pole solutions in Kaasalainen et al. (2002b) and Torppa et al. (2003) were offset due to an error in one of the version of the program used to read the Uppsala database (UAPC) (cf. Michałowski et al., 2004). Fortunately, this version was used only for a small part of the datasets, and the error affected only a fraction of them. 192 Nausikaa was one of the affected targets; an updated solution (λ 326°, β = +33° in ECJ2000) and sidereal period of 13.6217 h a pro-grade version of the pole in Kaasalainen et al. (2002b) is consistent with the images. The existing lightcurve set is underdetermined with only three oppositions, leading to a threefold pole degeneracy with a weak constraint on pole latitude and shape. The AO image clearly singled out the right pole (Fig. 10). The last observation epoch of the lightcurve set is from 1985, so the rotation phase of the model is apparently slightly offset from the one of the AO image.

4.7. 423 Diotima

423 Diotima, a C-type asteroid, was observed on December 6, 2003. This asteroid is the largest member of a collisional family (Karachkina and Prokofeva, 2003) and is suspected to have a satellite companion due to a lightcurve anomaly observed in 1982 by Schober (1983). With a mean angular size estimated to be 125 mas, the Keck AO system easily resolved the primary. Its estimated size is very close to the IRAS diameter measurement (208 km), probably because the asteroid shape is nearly spherical with a size ratio of a/b = 1.08. No albedo features were visible on the AO image and no companions with a diameter >7.8 km (>5.9 km) were seen to orbit Diotima’s primary at 2/100 × R_Hill (1/4 × R_Hill) and between (see Fig. 5b for details). Fig. 11 displays a close-up of the primary and a comparison with the shape model of (Kaasalainen and Marchis, in preparation) using a pole solution of (λ 353°, β = +2° in ECJ2000) and a period 4.77538 h. The apparent shape of the Keck AO image and the model agree quite well, and thus remove the pole ambiguity.

4.8. 511 Davida

511 Davida is the largest asteroid observed in this survey with an average observed diameter of 316 km. We describe one set of processed observations extracted from a set of data covering a full rotation acquired by the Keck Science team (Conrad et al., 2003). Davida was observed at its maximum apparent size. The measured size and ratio a/b are slightly smaller than the IRAS average diameter and the maximum ratio determined by the lightcurve measurements. Fig. 12 shows that no obvious surface markings are visible on the Kp-band image of this hemisphere. Most of the markings shown have a contrast of <5% and may simply be artifacts of deconvolution. A more accurate analysis (e.g., tuning the regularization parameters of deconvolution) on a larger set of images involving a cross-correlation of features could be used to confirm the existence of any albedo markings.

The pole solution in Torppa et al. (2003) is offset; the updated lightcurve solution (λ = 297°, β = +26° in ECJ2000), with a period of 5.129363 h, and shape are in an excellent agreement with the AO image.

4.9. 104 Klymene

104 Klymene intrigued us during the first observation taken on December 6, 2003. The AO image revealed a bi-lobed shape for the asteroid. A second observation taken one day later did not help to confirm this unusual shape because of the rotation of the asteroid (Fig. 13). Based on the deconvolved image, we fit the apparent shape of 104 Klymene by an ellipse with a major-axis (2a) of 163 ± 3 km and a minor-axis (2b) of 103 ± 5 km corresponding to an average size of 133 km and a/b = 1.58. Lightcurve measurements reported a maximum of 0.3 magnitude corresponding to a max(a/b) of 1.32. However, (104) Klymene lightcurve measurements are quite limited with a few measurements taken in September to November 1991 and analyzed by Shevchenko et al. (1992). It is possible that the asteroid was never observed at its maximum apparent size.

The apparent bifurcated shape of 104 Klymene could be approximated by two overlapping spheres with R₁ = 55 km and R² = 60 km and with a separation of 70 km. This shape is quite similar to the one proposed for 121 Hermione, another bi-lobed main-belt asteroid that was also observed with the Keck AO telescope (Marchis et al., 2005c). Bifurcated shapes in the near-Earth asteroid population are quite common and have been seen through radar observations [see review in Ostro et al. (2002)]. In the main-belt, the dumbbell-shape of 216 Kleopatra was accurately studied by radar (Ostro et al., 2000), AO (Hestroffer et al., 2002), and interferometric observations (Tanga et al., 2001). These exotic shapes are probably the result of collisional events. No moonlet companion with a diameter > 4.3 km (2.9 km) was seen around Klymene’s primary at 2/100 × R_Hill (1/4 × R_Hill). Additional observations under excellent seeing conditions and in various filters are necessary to confirm its shape and refine the structure of 104 Klymene.

4.10. Other asteroids

The mean size and axis ratio for each asteroid is detailed in Table 5. A comparison with the radiometric IRAS diameter and the lightcurve measurements (extracted from the Minor Planet Lightcurve Parameters updated by A.W. Harris and B.D. Warner) was added.