The triaxial ellipsoid dimensions, rotational pole, and bulk density of ESA Rosetta target asteroid (21) Lutetia
Key Words.:Minor planets, asteroids: individual: Lutetia - Methods: observational - Techniques: high angular resolution - Instrumentation: adaptive optics
Context:Asteroid (21) Lutetia is the target of the ESA Rosetta mission flyby in 2010 July.
Aims:We seek the best size estimates of the asteroid, the direction of its spin axis, and its bulk density, assuming its shape is well described by a smooth featureless triaxial ellipsoid, and to evaluate the deviations from this assumption.
Methods:We derive these quantities from the outlines of the asteroid in 307 images of its resolved apparent disk obtained with adaptive optics (AO) at Keck II and VLT, and combine these with recent mass determinations to estimate a bulk density.
Results:Our best triaxial ellipsoid diameters for Lutetia, based on our AO images alone, are km, with uncertainties of km including estimated systematics, with a rotational pole within 5 of ECJ2000  = , or EQJ2000 [RA DEC] = . The AO model fit itself has internal precisions of km, but it is evident, both from this model derived from limited viewing aspects and the radius vector model given in a companion paper, that Lutetia has significant departures from an idealized ellipsoid. In particular, the long axis may be overestimated from the AO images alone by about 10 km. Therefore, we combine the best aspects of the radius vector and ellipsoid model into a hybrid ellipsoid model, as our final result, of km that can be used to estimate volumes, sizes, and projected areas. The adopted pole position is within 5 of  =  or [RA DEC] = .
Conclusions:Using two separately determined masses and the volume of our hybrid model, we estimate a density of or g cm. From the density evidence alone, we argue that this favors an enstatite-chondrite composition, although other compositions are formally allowed at the extremes (low-porosity CV/CO carbonaceous chondrite or high-porosity metallic). We discuss this in the context of other evidence.
The second target of the ESA Rosetta mission, asteroid (21) Lutetia, had a favorable opposition in 2008-09, reaching a minimum solar phase angle of on 2008 November 30, and a minimum distance from the Earth of 1.43 AU a week earlier. Based on previously determined sizes of Lutetia, with diameters ranging from 96 km from IRAS [2002-AJ-123-Tedesco; PDSSBN-Iras] to 116 km from radar 1999-Icarus-140-Magri; 2007-Icarus-186-Magri, Lutetia should have presented an apparent diameter of 0.10″, slightly more than twice the diffraction limit of the Keck Observatory 10 m telescope at infrared wavelengths (1-2 m). Continuing our campaign [2007-Icarus-191-Conrad; 2009-Icarus-202-Drummond; 2010-Icarus-205-Carry-a] to study asteroids resolved with the world’s large telescopes equipped with adaptive optics (AO), we have acquired more than 300 images of Lutetia, most from the 2008-09 season. An exceptionally good set of 81 images was obtained on 2008 December 2 with the Keck II telescope, which, despite the high sub-Earth latitude, yields a full triaxial ellipsoid solution from the changing apparent ellipses projected on the plane of the sky by the asteroid. Analyzing all available images (2000, 2007, and 2008-09 seasons) yields a result consistent with the December 2 set.
Table 1 gives the observing circumstances for all seven observation dates, where, in addition to the date, Right Ascension, Declination, and Ecliptic longitudes and latitudes of Lutetia, we give its Earth and Sun distance, the solar phase angle (), the position angle of the Sun measured east from north while looking at the asteroid (NTS), the filter and the number of images () used to form mean measurements at epochs, the scale in km/pix at the distance of the asteroid on the date, and the instrument and telescope configurations used for the observations as listed in Table 2. Multiplying the first scale in Table 1 by the scale in Table 2 will give a km/ scale at the distance of the asteroid, and multiplying this by the appropriate resolution element () from Table 2, which is the diffraction limit , where is the wavelength and is the telescope diameter, gives the last column of Table 1, the km per resolution element scale.
The best data set, obtained at K on December 2, comprises images at 9 epochs, 9 images per epoch, where each image is a 0.4 second exposure. Figure 1 shows a single image from each of the 9 epochs, and clearly reveals the asteroid rotating over a quarter of its 8.2 h period.
Figure 2 illustrates the range of solar phase angles for our observations, showing that on more than half of the dates the phase angle was greater than , which, for irregular bodies, can lead to violations of the assumptions we adopt in Section 3. In this particular case, however, we have found the data are still quite useful and contribute substantially to our final results.
|(UT)||(RA° Dec°)||(Lon° Lat°)||(AU)||(AU)||(°)||(°)||(m/n)||(km/pix)||Table 2||(km/rex)|
|Aug 15, 2000||12.3||11.2||10.5||1.239||2.057||21.6||71.6||K(19/1)||15.10||A||39.8|
|Jun 6, 2007||246.0||247.8||10.1||1.295||2.305||3.3||286.4||Ks(35/7)||12.47||B||51.7|
|Oct 22, 2008||75.1||76.2||11.2||1.555||2.352||17.9||85.9||J(15/2)||11.21||C||29.3|
|Oct 22, 2008||75.1||76.2||11.2||1.555||2.352||17.9||85.9||H(15/2)||11.21||C||38.3|
|Oct 22, 2008||75.1||76.2||11.2||1.555||2.352||17.9||85.9||K(33/3)||11.21||C||49.6|
|Nov 21, 2008||69.4||70.9||10.5||1.430||2.406||4.7||88.5||K(4/1)||10.31||C||45.6|
|Dec 2, 2008||66.4||68.1||10.2||1.441||2.426||1.1||236.7||K(81/9)||10.39||C||46.0|
|Jan 23, 2009||59.6||61.9||11.8||1.895||2.518||20.1||258.5||K(30/2)||13.66||C||60.5|
|Feb 2, 2009||60.6||62.8||12.0||2.033||2.534||21.5||258.9||H(30/2)||14.66||C||81.1|
|Feb 2, 2009||60.6||62.8||12.0||2.033||2.534||21.5||258.9||K(45/3)||14.66||C||64.9|
|B||NACO||ESO VLT UT4||8.2||75.36||Ks||2.18||0.055|
Assuming that an asteroid can be modeled as a uniformly illuminated
triaxial ellipsoid rotating about its short axis, it is possible to
estimate its diameters
and find the direction of its spin axis
from the observation of a series of ellipses projected as it rotates. We can
thus treat any asteroid in the same manner as we treat asteroids that are well
described by the triaxial assumption, e.g., those that we have defined as
Standard Triaxial Ellipsoid Asteroids, or STEAs
[1985-Icarus-61-Drummond; 1998-Icarus-132-Drummond; 2009-Icarus-202-Drummond; 2007-Icarus-191-Conrad; 2008-Icarus-197-Drummond].
The key to turning the projected ellipses into a triaxial
ellipsoid is determining the ellipse parameters from AO images. We use
the method of Parametric Blind Deconvolution
[PBD, 1998-Icarus-132-Drummond; 2000-LGSAO-Drummond]
to find the long () and short
() projected (plane of sky) ellipse axes dimensions and the orientation or
position angle (PA) of the long axis. PBD allows us to find not only the
ellipse parameters but parameters for the Point Spread Function (PSF)
Having shown that a good model for the AO PSF is a Lorentzian
we simply treat a disk-resolved
image of an asteroid as the convolution of a flat-topped ellipse and a
Lorentzian, making a simultaneous fit for each in the Fourier plane
where the convolution becomes a simple product.
All 307 images were fit for the projected asteroid ellipse parameters and individual Lorentzian PSFs. The mean and standard deviations of the parameters were formed around epochs consisting of a series of 3 to 15 images obtained in one sitting at the telescope. We then solve the triaxial ellipsoid from a least square inversion of the ellipse parameters [1985-Icarus-61-Drummond; 2000-LGSAO-Drummond].
The projected ellipse parameters
can also be extracted from
images deconvolved with an alternate algorithm such as
Mistral [2000-Msn-99-Conan; 2004-JOSAA-21-Mugnier].
Such contours provide a direct measurement of details of the
projected shape of the
asteroid, allowing the construction of the radius vector model that
we present in 2010-AA--Carry, providing a more refined
description of the shape of Lutetia.
However, only the PBD parameters were used in deriving
ellipsoid solutions here.
While observations from one night can produce triaxial ellipsoid results [2007-Icarus-191-Conrad; 2008-Icarus-197-Drummond; 2009-Icarus-202-Drummond] it is possible to combine observations from different nights over multiple oppositions to make a global fit if a sidereal period is known with enough accuracy (Drummond et al. in preparation). This can resolve the natural two-fold ambiguity in the location of a rotational pole from a single night of data (see Section 4.2), and in some cases reduce the uncertainty in the triaxial ellipsoid dimensions if the asteroid is observed over a span of sub-Earth latitudes. For instance, when observations are restricted to high sub-Earth latitudes, even a few images at an equatorial aspect will supply a much better view of the axis than a long series at near polar aspects. In other words, different viewing geometries generally lead to a better solution.
Unfortunately, during the last two oppositions, in 2007 and 2008-09, Lutetia’s positions were apart on the celestial sphere. In fact, the position of Lutetia for the Very Large Telescope (VLT) observations on 2007 Jun 6 was exactly from its position on 2008 December 2 (see Table 1), which meant that regardless of the location of the rotational pole, the two sets of observations were obtained at the same sub-Earth latitude, but of opposite signs. Thus, with the now-known pole, our observations of Lutetia over the 2008-09 opposition were at the same (but southerly) deep sub-Earth latitudes as the VLT observations in the previous (but northerly) deep sub-Earth latitude opposition in 2007, affording the same view of the strongly fore-shortened axes, but from the opposite hemisphere. The single set of images in 2000 was also obtained at deep southerly latitudes. Thus, we have no equatorial view of Lutetia and, therefore, its shortest () dimension remains less well determined than the other two.
4.1 Ellipsoid Fits
We made two separate fits to our data, one using only our best data set from December 2, and the other combining all of our data taken over the 8.5 year span using a sidereal period of 8.168 27 h from 2010-AA--Carry to link them together. The results of these two fits give highly consistent values for the equatorial dimensions, but not for . When fitting all of the data, a higher value is preferred, but we restrict to the usual physical constraint of . Because the entire data set, taken as an ensemble, has higher noise, we consider the as a limiting case (a biaxial ellipsoid), and adopt the value of c derived from the Dec 2 data alone as our preferred value. Both solutions are listed in Table 3, where is the sub-Earth latitude, is the position angle of the line of nodes measured east from north, and is rotational phase zero, the time of maximum projected area when the axis lies unprojected in the plane of the sky. The uncertainties shown in Table 3 are the internal precisions of the model fit, and do not include systematics. We have assigned overall uncertainties to our ellipsoid model, including systematics, of km in the dimensions, and 5 in the pole position.
|Triaxial (Dec 2008)||Biaxial (All)|
|c (km)||93 8||c=b|
|[RA°; Dec°]||[44;+9]||[34; +16]|
|Triaxial (2008 Dec only)||0.4||0.9||1.1||3|
Figure 3 shows the triaxial ellipsoid fit to the December data. Figure 4 shows the residuals from the prediction using the December triaxial ellipsoid model for all of the data, and Figure 5 shows the overall residuals to the biaxial fit. The difference between Figs 4 and 5 is subtle, showing that Lutetia is close to a prolate ellipsoid. Trends in some of the residuals, such as the curling set of position angles at the right of the top plot in Fig 4, and at the left of the similar plot in Fig 5, indicate departures from our assumptions of a smooth featureless ellipsoid rotating about its short axis, and motivate the more detailed shape model that we present in 2010-AA--Carry. The rms weighted (by the observational uncertainty of each measurement) residuals for and , the projected ellipse major and minor axes lengths, and the weighted residuals for the position angle (PA) of the long axis, are given in Table 4, and are to be associated with Figs 3-5. These can be interpreted as uncertainties (but without possible systematics) for any predicted future projected ellipse parameters.
The axial ratios derived from our model are and . From a
4.2 Rotational Pole
There is a natural two-fold ambiguity in the location of the rotational pole with our method that is symmetric with respect to the position of the asteroid if observed on one night. Thus, there are two possible poles for the December triaxial ellipsoid solution. However, if the asteroid can be observed at significantly different positions, then the rotational pole can be disambiguated. The single 2000 observation helps break the ambiguity since the residuals are some 18% higher for the rejected pole than for the accepted region when considering all of the data. Otherwise, the 2008-09 observations and the 2007 data from the same positions, would not have provided enough diversity to break the ambiguity.
The poles from various lightcurve techniques can have two- or
[see 1989-AsteroidsII-2-Magnusson, for a good summary],
which can be broken when paired with our results.
Figure 6 shows the
positions of about half of the poles (see footnote 1) found from
lightcurve methods (the other half lie on the opposite hemisphere), as well as ours. We assert that the correct region for the pole location is
where our poles near coincide with the span of lightcurve poles in this hemisphere. Furthermore, the lightcurve inversion (LCI; see
5 Comparison with Lightcurve Inversion Model
Figure 7 shows our PBD images of Lutetia from 2008 December 2. Each image is the mean of 9 shifted and added images at each epoch, and then linearly deconvolved of the Lorentzian PSF found in its fit. Notice the tapered end.
For comparison, the lightcurve inversion model (see footnote 2) based on the work of 2003-Icarus-164-Torppa is shown in Fig 8 for the same times. The model appears to match the overall shape and orientation in the images, verifying the pole and sidereal period, but it does appear fatter and less tapered than the images of the asteroid. In a following article we combine our AO images with lightcurve data using a method known as KOALA (Knitted Occultation, Adaptive-optics, and Lightcurve Analysis [2010-AA--Carry]) to produce an improvement over the previous LCI model. Not only does it yield better matches to the AO images, but it provides an absolute kilometer scale, and it can reproduce Lutetia’s lightcurve history.
Although a triaxial ellipsoid fit of the new KOALA model yields diameters of , the model is very non-ellipsoid in appearance, and while the diameter is in agreement between the AO-only and the KOALA model, both the KOALA and dimensions are km smaller than from our triaxial ellipsoid results here. The AO-only triaxial ellipsoid solution comes from only a quarter of a rotation, when the minimum area is projected (over what would be a lightcurve minimum). During the time of the 2008 Dec 2 AO observations, the axis was seen unprojected in the plane of the sky, but both the and axes were not. It is the extrapolation, as it were, in rotation to the maximum projected area, when the axis could be seen unprojected, that leads to an dimension larger than found from KOALA. The KOALA technique, by combining lightcurves that cover all rotational phases and sub-Earth latitudes with the AO images (at restricted rotational phases and latitudes), finds that there is a large depression on the side of Lutetia away from the 2008 Dec 2 observations that was not completely sampled by our imaging, resulting in the smaller KOALA model axis dimension. This depression of km explains the difference between the two dimensions.
On the other hand, since KOALA only uses amplitudes from lightcurves, and since amplitudes are a strong function of but a weak function of , the KOALA model dimension is only weakly determined when the AO images at high sub-Earth latitudes only reveal a strongly foreshortened axis. (See [2010-AA--Carry] for a discussion on the limits of the KOALA inversion in the particular case of Lutetia.) Therefore, Lutetia’s dimension is best determined from the 2008 December 2 AO data set.
To make the best possible model for use in evaluating sizes, cross-sectional areas, volumes, and densities, we combine what we consider the best aspects of both models into a hybrid triaxial ellipsoid/KOALA model that has dimensions of km, taking the diameter from KOALA and the diameter from the AO triaxial ellipsoid fit. The original KOALA model radius vector components are merely expanded by 93/80. We estimate the uncertainties on these dimensions, including possible systematics, to be km. Our best final average diameter is, then, km. The rotational pole for these hybrids should be the KOALA pole at [RA Dec]=, since it is primarily based on lightcurves obtained over 47 years as opposed to the triaxial ellipsoid pole in Table 3 from nine epochs on 2008 December 2, although they are less than 8 apart. The uncertainty for this pole is about in each coordinate.
6 Taxonomy and Density
Lutetia was well observed in the 1970s, yielding visible and near-infrared
reflectance spectra [1975-ApJ-195-McCord],
radiometric albedos and
diameter estimates [1977-Icarus-31-Morrison],
and polarimetric albedos and
diameter estimates [1976-AJ-81-Zellner],
which have been confirmed by
similar observations reported during the last decade
[see review by 2010-AA-Belskaya].
Based on these data, 1975-Icarus-25-Chapman
placed only three asteroids, (16) Psyche, (21) Lutetia,
and (22) Kalliope, into a distinct taxonomic
group to which 1976-AJ-81-Zellner
assigned the letter “M”.
The M type was
defined in terms of spectral and albedo properties by
1978-Icarus-35-Bowell, who assigned a diameter of 112 km to
Lutetia (estimates by
1977-Icarus-31-Morrison and 1976-AJ-81-Zellner had
been diameters of 108–109 and 110 km, respectively).
It was later found by radar that some, but not all, M-types were metallic. 1995-Icarus-117-Rivkin recognized that there were two sub-types of M-type asteroids. The standard M types showed high radar reflectivity and relatively neutral colors, both apparently due to metal. The other type (also showing similar colors, but now thought to be due to metal flakes embedded in a colorless stony matrix) had a 3 micron band, ascribed to hydrated minerals and which was deemed to be unlikely on a chiefly metallic body. 1995-Icarus-117-Rivkin called this new “wet” subclass M(W) and assigned Lutetia to this subclass [2000-Icarus-145-Rivkin]. 1973-Icarus-19-Chapman first suggested that what we now term an M-type spectrum might be associated with enstatite chondrites (ECs) and 2000-Icarus-145-Rivkin suggested a hydrated EC as a plausible composition for Lutetia. Recently, 2009-Icarus-202-Vernazza and (partly) 2007-AA-470-Nedelcu showed that ECs are a good match for the visible/near-infrared spectra of Lutetia.
The measured visual albedo for Lutetia has typically ranged over 15–22%, much higher than for the more common (CI/CM) carbonaceous chondrites (CC) and overlapping the lower range for S-types (in recent literature, the early dedicated observations of Lutetia have been supplanted by reference to five rather inconsistent IRAS scans, which imply a still higher albedo and smaller effective diameter for Lutetia, well under 100 km, to which we assign less significance, especially because they are inconsistent with the mean size derived here). The radiometry by 2006-AA-447-Mueller, reduced using two different thermal models, also yields albedos too high for most CC meteorites. A recent determination of visual albedo, using Hubble Space Telescope observations [2009-arXiv-Weaver] and the size/shape/pole results from the present paper and 2010-AA--Carry, indicate a value near 16%. This value, consistent with EC albedos (as well as metallic), is generally higher than most CCs, although some types of CCs, namely CO/CVs, have higher albedos, typically about 10%, with some COs getting as high as 15–17% [2009-Icarus-202-Clark].
Radar observations of Lutetia (1999-Icarus-140-Magri; 2007-Icarus-186-Magri, confirmed by 2008-Icarus-195-Shepard) showed that Lutetia has a moderate radar albedo (0.19–0.24), comfortably in the mid-range of ECs, but considerably lower than metallic M-types and higher than most CCs. The uncertainty range in these values overlaps with some CO/CV carbonaceous chondrites compositions at the low extreme and with some metallic compositions at the high end. Hence, CO/CV carbonaceous chondrites cannot be ruled out based on albedo considerations alone.
Indeed, numerous researchers in the last few years (2004-AA-425-Lazzarin; 2009-AA-498-Lazzarin; lazzarin-2010; 2005-AA-430-Barucci; 2006-AA-454-Birlan; 2008-AA-477-Barucci; 2010-AA-513-Perna, see summary by 2010-AA-Belskaya) have argued that Lutetia shows certain spectral characteristics (e.g., in the thermal IR) that resemble CO and CV types and do not resemble a metallic meteorite. However, in these studies, the comparisons with EC meteorites was less thorough, partly because mid-infrared comparison data are not extensive. From rotationally resolved visible/near-infrared spectra of Lutetia, 2007-AA-470-Nedelcu claimed a better match with CC in one hemisphere and with EC in the other, although this has yet to be confirmed. If Lutetia were highly heterogenous, that might explain some of the conflicting measurements.
2010-Icarus-207-Vernazza, however, have shown that mid-infrared emission of asteroids of similar composition can be very different due to differences in surface particle size. Mineralogical interpretations from this wavelength range are thus subject to caution and must be supported by VNIR reflectance spectra. Also, although some CO meteorites show albedos approaching that of Lutetia, the lack of a 1 micron olivine band in Lutetia’s reflectance spectrum [see Fig. 3 of 2005-AA-430-Barucci] argues against CO composition since most, but not all, COs have a 1 micron band. Since the strength of this band generally shows a positive correlation with albedo, Lutetia’s high albedo suggests that a strong 1 micron band should be present if its composition were CO. The lack of a drop-off in Lutetia’s spectral reflectance below 0.55 micron and its high albedo make it inconsistent with CV meteorites [see 1976-JGR-81-Gaffey, for instance]. Finally, M and W-type asteroids (parts of the X class [2009-Icarus-202-DeMeo] if albedo is not known) have colors in the visible that are inconsistent with C-types.
Colors, spectra, polarization, and albedos give us a picture of the relatively thin surface layers of an asteroid. Effects such as space weathering, repeated impacts that churn the regolith, recent impacts that may locally expose fresh material, particles sizes, or even differentiation processes may hinder our ability to ascertain the bulk composition of an object. Bulk density, on the other hand, gives us a picture of the entire asteroid body and ought to be a powerful constraint on bulk composition (subject to uncertainties about porosity and interior structure, mentioned below). Our new size estimates, when combined with recent mass determinations from other workers, now allow us to make estimates of the bulk density for Lutetia. Table 5 lists the volumes from three of the models addressed in this work, the triaxial ellipsoid model, the KOALA radius vector model, and our best estimate hybrid model. When coupled with two mass estimates, by 2008-DPS-40-Baer or 2009-AA-507-Fienga (which themselves differ by 25%), we find the given bulk densities.
Grain densities for stony meteorites range from 2.3 g.cm for CI/CM carbonaceous chondrites [2008-LPI-39-Consolmagno] to 3.0–3.6 g.cm for CO/CV [1999-Icarus-142-Flynn] to 3.6 g.cm for EC [2009-LPI-40-Macke]. Our best model yields densities of 4.3 or 3.5 g.cm, which are among the higher densities yet tabulated for asteroids. The maximal extent of uncertainties on our preferred model range from about 2.3 to 5.1 g.cm. Conservatively, if we were to consider meteorite grain densities, this range excludes iron-nickel, CI, and CM. Enstatite chondrites are favored, but CO/CV are also allowed. Perhaps more realistically, meteorite bulk densities should be considered instead. These are significantly lower – e.g., CO/CV appear to be, on average, about 0.6 g.cm lower [2009-LPI-40-Macke].
One must also be careful in trying to put too much emphasis on comparison of asteroid densities with meteorite densities. Most asteroids are thought to have significant macroporosity [e.g., they may be rubble piles like (25143) Itokawa 2006-Science-312-Fujiwara], so the asteroid density is likely to be substantially lower than the component material density [see 2006-LPI-37-Britt]. If so, then metallic meteorites are still ruled out, but only marginally at the upper end of the uncertainty range. CO/CV are similarly ruled out at the lower end of the uncertainty range, but not by much. The meteorite density values can only be guidelines. This provides some constraint on the possible bulk composition, but without reliable, smaller uncertainties in mass estimates, we must also rely on other observed quantities, such as albedo and spectra. A better mass estimate from Rosetta will reduce the density uncertainty considerably.
In summary, our consideration of density and other evidence favors EC composition for Lutetia, and although CO/CV composition is not ruled out definitively, we consider it a lower probability. Among all the known meteorite classes, hydrated enstatite chondrites seem to fit the most number of measured parameters. These chondrites are represented among known meteorites only by the hydrated EC clasts in the unusual meteorite Kaidun. Finally, we emphasize that Lutetia may well be composed of material that is either rare or not yet represented in our meteorite collections. One example that might work is a low-albedo carbonaceous matrix material to suppress the olivine bands, embedded with abundant high-albedo clasts (such as an Allende-like composition, but with a much higher abundance of CAIs).
|Vol||Density (g cm)|
|with mass of g from 2008-DPS-40-Baer|
|with mass of g from 2009-AA-507-Fienga|
We used adaptive optics images of (21) Lutetia from various large telescope facilities, and at various epochs, to make a triaxial ellipsoid shape model. In a companion paper, we combine these AO images with lightcurves covering several decades to produce a radius vector model. There are advantages and disadvantages to these two methods. Here, we have combined the best properties of each to yield a hybrid shape model, approximated by an ellipsoid of size km (with uncertainties km) that can be easily used to compute sizes, volumes, projected areas, and densities. When coupled with recent mass estimates, this hybrid model suggests a density of g cm or g cm. This is within the range expected for EC-like compositions, although the uncertainties formally permit other compositions.
The Rosetta mission presents a unique opportunity for us to perform the ultimate calibration of our PBD and triaxial ellipsoid approach to determine sizes and rotational poles. Furthermore, it will offer a chance to compare and contrast our triaxial ellipsoid model to the KOALA model for Lutetia.
We thank E. Dotta, D. Perna, and S. Fornasier for obtain- ing and sharing their VLT data, and for spirited discussions concerning Lutetia’s taxonomy which we feel materially improved the content of this paper. This study was supported, in part, by the NASA Planetary Astronomy and NSF Planetary Astronomy Programs (Merline PI), and used the services provided by the JPL/NASA Horizons web site, as well as NASA’s Astrophysics Data System. We are grateful for telescope time made available to us by S. Kulkarni and M. Busch (Cal Tech) for a portion of this dataset. We also thank our collaborators on Team Keck, the Keck science staff, for making possible some of these observations. In addition, the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.
- thanks: Based on observations collected at the W. M. Keck Observatory and the European Southern Observatory Very Large Telescope (program ID: 079.c-0493, PI: E. Dotto). The W. M. Keck Observatory 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.
- offprints: Jack.Drummond@Kirtland.af.mil
- http://vesta.astro.amu.edu.pl/Science/Asteroids/ is a web site gathering sidereal periods, rotational poles, and axial ratios maintained by A. Kryszczyńska. See 2007-Icarus-192-Kryszczynska.