Elsevier

Icarus

Volume 205, Issue 2, February 2010, Pages 460-472
Icarus

Physical properties of (2) Pallas

https://doi.org/10.1016/j.icarus.2009.08.007 Get rights and content

Abstract

Ground-based high angular-resolution images of asteroid (2) Pallas at near-infrared wavelengths have been used to determine its physical properties (shape, dimensions, spatial orientation and albedo distribution).

We acquired and analyzed adaptive optics (AO) J/H/K-band observations from Keck II and the Very Large Telescope taken during four Pallas oppositions between 2003 and 2007, with spatial resolution spanning 32–88 km (image scales 13–20 km/pixel). We improve our determination of the size, shape, and pole by a novel method that combines our AO data with 51 visual light-curves spanning 34 years of observations as well as archived occultation data.

The shape model of Pallas derived here reproduces well both the projected shape of Pallas on the sky (average deviation of edge profile of 0.4 pixel) and light-curve behavior (average deviation of 0.019 mag) at all the epochs considered. We resolved the pole ambiguity and found the spin-vector coordinates to be within 5° of [longitude, latitude] = [30°, −16°] in the Ecliptic J2000.0 reference frame, indicating a high obliquity of about 84°, leading to high seasonal contrast. The best triaxial-ellipsoid fit returns ellipsoidal radii of a = 275 km, b = 258 km , and c = 238 km . From the mass of Pallas determined by gravitational perturbation on other minor bodies ( 1.2 ± 0.3 ) × 10 - 10 M , [Michalak, G., 2000. Astron. Astrophys. 360, 363–374], we derive a density of 3.4 ± 0.9 g cm - 3 significantly different from the density of C-type (1) Ceres of 2.2 ± 0.1 g cm - 3 [Carry, B., Dumas, C., Fulchignoni, M., Merline, W.J., Berthier, J., Hestroffer, D., Fusco, T., Tamblyn, P., 2008. Astron. Astrophys. 478 (4), 235–244]. Considering the spectral similarities of Pallas and Ceres at visible and near-infrared wavelengths, this may point to fundamental differences in the interior composition or structure of these two bodies.

We define a planetocentric longitude system for Pallas, following IAU guidelines. We also present the first albedo maps of Pallas covering ∼80% of the surface in K-band. These maps reveal features with diameters in the 70–180 km range and an albedo contrast of about 6% with respect to the mean surface albedo.

Introduction

A considerable amount of information regarding the primordial planetary processes that occurred during and immediately after the accretion of the early planetesimals is still present among the population of small Solar System bodies (Bottke et al., 2002).

Fundamental asteroid properties include composition (derived from spectroscopic analysis) and physical parameters (such as size, shape, mass, and spin orientation). While compositional investigations can provide crucial information on the conditions in the primordial solar nebula (Scott, 2007) and on asteroid thermal evolution (Jones et al., 1990), the study of asteroid physical properties can yield insights on asteroid cratering history (Davis, 1999), internal structure (Britt et al., 2002), and volatile fraction (Mousis et al., 2008) for example. These approaches complement one another—the density derived by observations of physical properties strongly constrains the composition (Merline et al., 2002), which is key to evaluation of evolution scenarios.

Spacecraft missions to asteroids, for example NEAR to (253) Mathilde and (433) Eros (Veverka et al., 1999), and Hayabusa to (25143) Itokawa (Fujiwara et al., 2006), greatly enhanced our understanding of asteroids. The high cost of space missions, however, precludes exploration of more than a few asteroids, leaving most asteroids to be studied from Earth-based telescopes.

Although several remote observation techniques can be used to determine the physical properties of asteroids, our technique relies primarily on disk-resolved observations. Indeed, knowing accurately the size is crucial for the determination of asteroid volume, and hence density. If enough chords are observed, occultations provide precise measurement of asteroid shape and size (Millis and Dunham, 1989), but at only one rotational phase (per occultation event). Moreover, because occultations of bright stars seldom occur, only a small fraction of all occultations are covered by a significant number of observers. Describing an asteroid’s 3D size and shape with this method thus requires decades. Assuming a tri-axial ellipsoidal shape is a common way to build upon limited observations of asteroid projected sizes (Drummond and Cocke, 1989). From the inversion of photometric light-curves, one can also derive asteroid shapes (Kaasalainen et al., 2002), with sizes then relying on albedo considerations. On the other hand, disk-resolved observations, either radar or high angular-resolution imagery, provide direct measurement of an asteroid’s size and shape when its apparent disk can be spatially resolved.

For about a decade now, we have had access to instrumentation with the angular-resolution required to spatially resolve large Main-Belt Asteroids at optical wavelengths. This can be done in the visible from space with the Hubble Space Telescope (HST) or in near-infrared from large telescopes equipped with adaptive optics (AO) such as Keck, the Very Large Telescope (VLT), and Gemini. Disk-resolved observations allow direct measurement of an asteroid’s absolute size (Saint-Pé et al., 1993a), and of its shape, if enough rotational-phase coverage is obtained (Taylor et al., 2007, Conrad et al., 2007). One can also derive the spin-vector coordinates from the time evolution of limb contours (Thomas et al., 2005) or from the apparent movement of an albedo feature (Carry et al., 2008). Ultimately, albedo maps may provide significant constraints on surface properties such as mineralogy or degree of space weathering (Binzel et al., 1997, Li et al., 2006, Carry et al., 2008).

Even if images can provide a complete description of asteroid properties, their combination with other sources of data (like light-curves or occultations) can significantly improve asteroid 3D shape models (see the shape model of (22) Kalliope in (Descamps et al., 2008), for instance).

Pallas is a B-type asteroid (Bus and Binzel, 2002). As such, it is thought to have a composition similar to that of the Carbonaceous Chondrite (CC) meteorites (see Larson et al., 1983, for a review). Spectral analysis of the 3 μm band (Jones et al., 1990) exhibited by Pallas suggests that its surface has a significant anhydrous component mixed with hydrated CM-like silicates (CM is a subclass of CC meteorites). Although Pallas is generally linked to CC/CM material, its composition remains uncertain. Indeed, Pallas’ visible and near-infrared spectrum is almost flat with only a slight blue slope, with the only absorption band clearly detected being the 3 μm band.

Compositional/mineralogical studies for Pallas are further hampered by a poorly determined density. First, there is significant uncertainty in the mass, as most mass estimates do not overlap within the error bars (see Hilton, 2002, for a review). Second, although the size of Pallas has been estimated from two occultations (Wasserman et al., 1979, Dunham et al., 1990), at least three events are required to determine asteroid spin and tri-axial dimensions (Drummond and Cocke, 1989).

Until recently, the only published disk-resolved observations of Pallas were limited to some AO snapshots collected in 1991 by Saint-Pé et al. (1993b), but the lack of spatial resolution prevented conclusions about Pallas’ size, shape, or spatial orientation.

Recent observations of Pallas from Lick (Drummond and Christou, 2008) and Keck Observatories (Drummond et al., 2009) lead to new estimates for its triaxial-ellipsoid dimensions, but there was still a relatively large uncertainty on the short axis. These Keck observations are included as a subset of the data considered here. Also, observations of Pallas were recently obtained using the WFPC2 instrument on HST (see Schmidt et al., 2009).

Section snippets

Observations

Here we present high angular-resolution images of asteroid (2) Pallas, acquired at multiple epochs, using AO in the near-infrared with the Keck II telescope and the ESO Very Large Telescope (VLT).

During the 2003, 2006 and 2007 oppositions, we imaged Pallas in Kp-band (central wavelengths and bandwidths for all bands are given in Table 2) with a 9.942 ± 0.050 milliarcseconds per pixel image scale of NIRC2, the second generation near-infrared camera ( 1024 × 1024 InSb Aladdin-3) and the AO system

Data reduction

We reduced the data using standard techniques for near-infrared images. A bad pixel mask was made by combining the hot and dead pixels found from the dark and flat-field frames. The bad pixels in our calibration and science images were then corrected by replacing their values with the median of the neighboring pixels ( 7 × 7 pixel box). Our sky frames were obtained from the median of each series of dithered science images, and then subtracted from the corresponding science images to remove the sky

Size, shape and spin-vector coordinates

Disk-resolved observations (from space, ground-based AO, radar, or occultations) provide strong constraints on asteroid shape. The limb contour recorded is a direct measurement of the asteroid’s outline on the sky. Combination of such contours leads to the construction of an asteroid shape model and an associated pole solution (Conrad et al., 2007). To improve our shape model, we combined our AO data with the numerous light-curves available for Pallas (51 of them, which led Torppa et al. (2003)

Surface mapping

As highlighted in Greeley and Batson (1990), the best way to study planetary landmarks is to produce surface maps. It allows location and comparison of features between independent studies and allows correction of possible artifacts (e.g., from deconvolution). Here we do not describe the whole process of extracting surface maps from AO asteroid images, because it has been covered previously for Ceres (Carry et al., 2008). Instead, we report below the main improvements with respect to our

Conclusion

We report here the first study of an asteroid using a new approach combining light-curves and occultation data with high-angular-resolution images obtained with adaptive optics (AO), which we have termed KOALA for Knitted Occultation, Adaptive optics and Light-curve Analysis. This method allows us to derive the spin-vector coordinates, and to produce an absolute-sized shape model of the asteroid, providing an improved volume measurement. This method can be used on any body for which

Acknowledgments

We would like to thank Franck Marchis (SETI Institute) for the flat-field frames he provided for our August 2006 observations. Thanks to Team Keck for their support and Keck Director Dr. Armandroff for the use of NIRC2 data obtained on 2007 July 12 technical time. Partial support for this work was provided by NASA’s Planetary Astronomy Program (PIs Dumas and Merline), NASA’s OPR Program (PI Merline) and NSF’s Planetary Astronomy Program (PI Merline). M.K. was supported by the Academy of Finland

References (60)

  • M. Kaasalainen et al.

    Optimization methods for asteroid lightcurve inversion – II. The complete inverse problem

    Icarus

    (2001)
  • A. Kryszczyńska et al.

    New findings on asteroid spin-vector distributions

    Icarus

    (2007)
  • H.P. Larson et al.

    The composition of Asteroid 2 Pallas and its relation to primitive meteorites

    Icarus

    (1983)
  • J.-Y. Li et al.

    Photometric analysis of 1 Ceres and surface mapping from HST observations

    Icarus

    (2006)
  • F. Marchis et al.

    High-resolution Keck adaptive optics imaging of violent volcanic activity on Io

    Icarus

    (2002)
  • F. Marchis et al.

    Shape, size and multiplicity of main-belt asteroids

    Icarus

    (2006)
  • O. Saint-Pé et al.

    Ceres surface properties by high-resolution imaging from Earth

    Icarus

    (1993)
  • O. Saint-Pé et al.

    Demonstration of adaptive optics for resolved imagery of Solar System objects – Preliminary results on Pallas and Titan

    Icarus

    (1993)
  • E.M. Standish et al.

    A determination of the masses of Ceres, Pallas and Vesta from their perturbations upon the orbit of Mars

    Icarus

    (1989)
  • J. Torppa et al.

    Shapes and rotational properties of thirty asteroids from photometric data

    Icarus

    (2003)
  • Berthier, J. 1998. Définitions relatives aux éphémérides pour l’observation physique des corps du système solaire....
  • Berthier, J., 1999. Principe de réduction des occultations stellaires. Notes scientifiques et techniques du Bureau des...
  • W.F. Bottke et al.

    An overview of the asteroids: The asteroids III perspective

    Asteroids III

    (2002)
  • D.T. Britt et al.

    Asteroid density, porosity, and structure

    Asteroids III

    (2002)
  • B. Carry et al.

    Near-infrared mapping and physical properties of the dwarf-planet Ceres

    Astron. Astrophys.

    (2008)
  • Conrad, A., and 10 colleagues, 2007. Direct measurement of the size, shape, and pole of 511 Davida with Keck AO in a...
  • Descamps, P., and 18 colleagues, 2008. New determination of the size and bulk density of the binary asteroid 22...
  • Dunham, D.W., and 45 colleagues, 1990. The size and shape of (2) Pallas from the 1983 occultation of 1 Vulpeculae....
  • Dunham, D.W., Herald, D., 2008. Asteroid Occultations V6.0. EAR-A-3-RDR-OCCULTATIONS-V6.0. NASA Planetary Data...
  • A. Fienga et al.

    INPOP06: A new numerical planetary ephemeris

    Astron. Astrophys.

    (2008)
  • Cited by (76)

    • The impact of asteroid shapes and topographies on their reflectance spectroscopy

      2022, Icarus
      Citation Excerpt :

      Adaptive optics (AO) systems correct the atmospheric perturbations and increase the spatial resolution of the ground-based telescopes. The sizes and shapes of asteroids can be resolved using AO, though the surface topography is still unresolved (Marchis et al., 2006; Carry et al., 2010; Viikinkoski et al., 2017). The highest spatial resolution on the surface of the small bodies is achieved during in-situ observations by spacecrafts orbitting their targets.

    • Modeling the evolution of the parent body of acapulcoites and lodranites: A case study for partially differentiated asteroids

      2018, Icarus
      Citation Excerpt :

      As mentioned earlier, the CR chondrites plot in the oxygen three-isotope diagram in a field that is quite close to the AL field - on the other hand, we frankly acknowledge that some element patterns (e.g., stronger depletion of moderately volatile lithophile elements) rather contradict such a link, which should be kept in mind. The mean radius of 253–281 km (Carry et al., 2010; Schmidt et al., 2009) of Pallas is close to the radius of our best fit parent body. The latest density estimate of 3400 ± 900 kg m−3 for Pallas provided by Carry et al. (2010) also compares quite well with the average density in our model.

    • Physical, spectral, and dynamical properties of asteroid (107) Camilla and its satellites

      2018, Icarus
      Citation Excerpt :

      Finally, the 2-D profile of the apparent disk of Camilla was measured on the AO images, deconvolved using the Mistral algorithm (Fusco, 2000; Mugnier et al., 2004), the reliability of which has been demonstrated elsewhere (Witasse et al., 2006), using the wavelet transform described in Carry et al. (2008, 2010b). We used the multi-data inversion algorithm Knitted Occultation, Adaptive-optics, and Lightcurve Analysis (KOALA), which determines the set of rotation period, spin-vector coordinates, and 3-D shape that provide the best fit to all observations simultaneously (Carry et al., 2010a). This method has been spectacularly validated by the images taken by the OSIRIS camera on-board the ESA Rosetta mission during its flyby of the asteroid (21) Lutetia (Sierks et al., 2011).

    View all citing articles on Scopus

    Based on observations collected at the European Southern Observatory (ESO), Paranal, Chile – 074.C-0502 & 075.C-0329 and at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation.

    1

    Present address: Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland.

    View full text