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Open Access
Issue
A&A
Volume 623, March 2019
Article Number A132
Number of page(s) 36
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201833898
Published online 20 March 2019

© B. Carry et al. 2019

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1 Introduction

The C-complex encompasses 50% of the mass of the asteroid belt (or 14% if the four largest bodies, Ceres, Vesta, Pallas and Hygeia, are disregarded, DeMeo & Carry 2013, 2014). Within this complex, the Ch- and Cgh-types are defined by the presence of an absorption band around 0.7 μm, and a UV-dropoff (sharper for the Cgh). These have been estimated to represent between 30 and 65% by number (Rivkin 2012; Fornasier et al. 2014), and are associated with CM chondrites (namely the Ch- and Cgh-types, see Vilas et al. 1993; Burbine 1998; Bus & Binzel 2002; DeMeo et al. 2009; Lantz et al. 2013; Fornasier et al. 2014; Vernazza et al. 2016; Takir et al. 2013). In other words, CM-like bodies represent a significant fraction of the C-complex population and encompass about 10% of the mass of all main-belt asteroids. They are spread over the entire Main Belt, and are found at all diameters (e.g., Rivkin 2012; Fornasier et al. 2014).

Their absorption band at 0.7 μm has been associated with phyllosilicates (Vilas & Sykes 1996). This is supported by the presence of a phyllosilicate band near 2.8 μm (commonly called the 3 μm absorption, Rivkin et al. 2015), as well as a shallow band at 2.33 μm. The 2.8 μm band is very similar to that seen in the B-type asteroid (2) Pallas (Takir & Emery 2012; Rivkin et al. 2015) and interpreted as being due to serpentine (e.g., Takir et al. 2013). The 2.33 μm band is also associated with the serpentine group (i.e., hydrous magnesium-iron phyllosilicates, Beck et al. 2018).

The meteorites originating from these bodies, the CM chondrites, represent 1.6% of all falls (Scott 2007). Together with CI carbonaceous chondrites, they represent the most chemically primitive meteorites (i.e., closest to the solar composition, Scott 2007) while paradoxically having suffered extensive hydration (e.g., Alexander et al. 2013). This aqueous alteration took place at low temperature, and thermal alteration of CM parent bodies peaked around 120 ° C (e.g., Dufresne & Anders 1962; Zolensky et al. 1989, 1997; Guo & Eiler 2007), and went up to 150 ° C as revealed by the formation of dolomite carbonates (Lee et al. 2014). As such, they are thought to have formed from a mixture of ice and dust where water ice was subsequently brought to a liquid state via the radioactive decay of 26 Al contained in dust particles, leading to the aqueous alteration of a significant fraction of the dust (see, e.g., Krot et al. 2006).

Recently, Vernazza et al. (2016) made a spectral survey of 70 Ch/Cgh asteroids, which included large 200+ km deemed-primordial bodies, but also objects as small as 15 km diameter, presumed to be the collisional fragments of dynamical families created from large bodies. This allowed a probe of the internal composition of prior, larger parent bodies. These authors interpreted the spectral diversity, already reported elsewhere (e.g., Vilas 1994; Fornasier et al. 1999, 2014), as resulting mainly from a variation of the average regolith grain size rather than to different thermal histories (Fornasier et al. 2014; Rivkin et al. 2015), although differences in band depths and centers also argue for some heterogeneity in mineral abundances (Burbine 1998; Cloutis et al. 2011; Fornasier et al. 2014). This evidence points toward an overall homogeneous internal structure for the parent bodies of CM chondrites.

The thermal modeling of the early internal structure of CM parent bodies by Bland & Travis (2017) supports this conclusion. They showed that convection may have prevented strong thermal gradients and differentiation of material. Starting from the accretion of dust and ices beyond the snow line (Scott et al. 2018), the original non-lithified structure of CM parent bodies has allowed large-scale circulation of material. This model explains both the limited temperature experienced by CM parent bodies, and the small-scale heterogeneity (such as temperature and redox state observed at the hundred of micrometer level, see Fujiya et al. 2015) observed in CM chondrites (Guo & Eiler 2007; Bland & Travis 2017).

To test this model, we sought to gather evidence for or against an originally differentiated internal structure within large Ch/Cgh asteroids. Our goal was to measure their bulk density, which, when compared with the density of CM chondrites, can reveal the presence, or absence, of denser material in their interior. Determination of a density requires both a mass and a volume. Masses for larger objects can be determined by their gravitational effects on other bodies, but the precision is often low, and is particularly problematic for objects of low mass (see Carry 2012, for a discussion on the precision and biases in mass determination). If any object is binary, however, the orbit of the satellite yields the primary mass directly. Therefore, binary asteroids are crucial to establish solid and accurate references on which a larger population can be analyzed.

The present article focuses on asteroid (41) Daphne as representative of the Ch spectral class, around which a satellite was discovered in 2008 (S/2008 (41) 1, which we call Peneius1 , Conrad et al. 2008). Daphne was observed within a survey we are currently conducting (ID 199.C-0074, PI P. Vernazza) to image a substantial fraction of main-belt asteroids larger than 100 km in diameter, sampling the main compositional classes (see Vernazza et al. 2018, for a description of the survey). We image these asteroids throughout their rotation at high angular-resolution with the SPHERE/ZIMPOL extreme adaptive-optics (AO) camera (Beuzit et al. 2008; Thalmann et al. 2008) mounted on the European Southern Observatory (ESO) Very Large Telescope (VLT). The high-quality correction delivered by the AO system of SPHERE (Fusco et al. 2006, 2014) compared to previous generations of AO cameras, and the use of shorter wavelength (visible R band compared to the near-infrared J∕H∕K bands typically used with previous cameras), provides a twofold to threefold improvement in angular resolution. This sharper resolution allows the detailed modeling of asteroid shapes and enhanced satellite detection capability, as recently illustrated on the main-belt asteroids (3) Juno, (6) Hebe, (16) Psyche, (89) Julia, (107) Camilla, and (130) Elektra (Viikinkoski et al. 2015, 2018; Marsset et al. 2016, 2017a,b; Yang et al. 2016; Hanuš et al. 2017a; Pajuelo et al. 2018; Vernazza et al. 2018).

The article is organized as follows: we first describe our observations in Sect. 2, followed by the determination of the 3D shape model (Sect. 3.1), the mutual orbit of Daphne and its satellite (Sect. 3.2), and the diameter and spectrum of the satellite itself (Sect. 3.3). Based on the density of (41) Daphne and a compilation of mass and diameter estimates from the literature, we then discuss the internal structure of CM parent bodies in Sect. 4.

2 Observations

Daphne was imaged with ZIMPOL once in May 2017 and three times in August 2018. We also compile 24 epochs of high-angular resolution and high-contrast images (Table B.1) from large ground-based telescopes equipped with adaptive-optics (AO) cameras: NIRC2 at Keck (van Dam et al. 2004) and NACO at ESO VLT (Rousset et al. 2003).

We process the ZIMPOL data with the ESO pipeline (see details in Vernazza et al. 2018). We then reduce all other imaging epochs with the same suite of IDL routines for consistency. The basic data reduction encompasses bad pixel mapping and removal by median interpolation, sky subtraction, and flat-field correction, following the steps described in Carry et al. (2008). We then use Mistral, a myopic deconvolution algorithm optimized for celestial targets with sharp boundaries (Fusco et al. 2002; Mugnier et al. 2004), to deconvolve the images and enhance their angular resolution for shape modeling purposes. The results of this approach have already been demonstrated elsewhere (e.g., Witasse et al. 2006; Drummond et al. 2014). In parallel, the diffused halo of light surrounding Daphne was removed by subtracting concentric annuli (as described thoroughly in Pajuelo et al. 2018) for satellite detection.

We complement this data set with an additional epoch of Daphne in May 2017 with the SPHERE integral-field spectrograph (IFS, Claudi et al. 2008) to acquire the near-infrared spectrum of its satellite Peneius. This epoch was obtained within the “Other Science” program (ID: 099.D-0098, PI J.-L. Beuzit) of the guaranteed-time observations (GTO) of the SPHERE consortium. The aim of this program is to illustrate SPHERE’s capabilities in science topics other than its primary goal: direct imaging of planets and disks. The IFS data were reduced using the SPHERE consortium pipeline, which includes bad pixel removal, sky subtraction, flat-field correction, and wavelength calibration.

Together with these images, we retrieve nine stellar occultations by Daphne compiled on the PDS by Dunham et al. (2017). We convert the locations of observers and disappearance timings into chords on the plane of the sky using the recipes by Berthier (1999). We detail the circumstances of observation of these occultations in Table B.2.

We also compile 29 optical lightcurves, from the historical works of Scaltriti & Zappala (1977), Barucci (1983), Barucci et al. (1985), and Weidenschilling et al. (1987, 1990), used by Kaasalainen et al. (2002) and Hanuš et al. (2017b) to reconstruct the 3D shape of Daphne. We complement this data set with twelve lightcurves obtained by amateur astronomers, two lightcurves obtained with the 60 cm André Peyrot telescope mounted at Les Makes observatory on Réunion Island (operated as a partnership among Les Makes Observatory and the IMCCE, Paris Observatory), one lightcurve obtained with the Antarctic Search for Transiting ExoPlanet (ASTEP) telescope (Daban et al. 2010) during its commissioning at the Observatoire de la Côte d’Azur in Nice (Matter et al. 2011), and extract three serendipitously observed lightcurves from the SuperWASP image archive (Grice et al. 2017). The details of these lightcurves are provided in Table B.3.

3 Properties of Daphne and its satellite

3.1 Spin and 3D shape

We determine the spin properties (rotation period and spin-vector coordinates) and reconstruct the 3D shape of Daphne with the open-source2 ADAM algorithm (Viikinkoski et al. 2015). ADAM uses the Levenberg-Marquardt optimization algorithm to find the spin and 3D shape that best reproduce the lightcurves, stellar occultation chords, and disk-resolved images simultaneously by comparing the observations with synthetic data generated by the model at each step.

The best-fit solution displayed in Fig. 1, the details of which are listed in Table 1, has a sidereal rotation period Ps of 5.98798 h and spin-vector ecliptic coordinates of (199°, −33°), very similar to the results from convex shape modeling from lightcurves only by Kaasalainen et al. (2002) and multi-data shape reconstruction from a slightly different data set with ADAM by Hanuš et al. (2017b). The shape model is of an irregular body with several large flat areas, putative impact basins, and has a spherical-volume-equivalent diameter of 187 ± 21.5 km (3 σ uncertainty). We present all the data compared with the predictions from the shape model in Appendix B.

An almost similar shape model and spin solution had been previously reported by Carry (2009) with the multi-data KOALA shape reconstruction algorithm (based on the same algorithm as ADAM but with different implementation, Carry et al. 2010a; Kaasalainen 2011). Because KOALA has been validated by comparing the shape model of (21) Lutetia (Carry et al. 2010b; Drummond et al. 2010) with the images returned by the ESA Rosetta mission during its flyby of the asteroid (Sierks et al. 2011; Carry et al. 2012), the agreement between the two models provides solid evidence for the reliability of both ADAM and of the shape model of Daphne.

While there is a significant spread of diameter estimates in the literature (average diameter of 192 ± 38 km), all the estimates based on direct measurements, i.e. stellar occultations, disk-resolved imaging, mid-infrared interferometry, are narrowly clustered around our value: 188 ± 14 km (3 σ deviation, see Table A.1). In particular, the mid-infrared interferometric observations by Matter et al. (2011) provide an independent confirmation, being based on a totally different data set. These authors analyzed their interferometric visibilities using the convex shape model of Kaasalainen et al. (2002) and the non-convex shape model of Carry (2009), almost identical to the model presented here. The associated diameters differ by 15 km, showing how the determination of diameter is sensitive to the shape of the object. Their best-fit diameter associated with the non-convex model was 185.5 ± 10.5 km (3 σ), supporting the present value.

We define the prime meridian of Daphne to be along its longest axis, on which a hill, which we call the nose, is present at the equator (elevation of 11 km above the reference ellipsoid, see the map in Fig. 2). Several flat regions (hereafter A, B, C) can be identified in the images and on the shape model, as well as a clear depression (D). The three flat areas are located near both poles, and on the opposite side of the nose. These flat areas and the depression are large compared with the diameter of Daphne andmay be indicative of large impact basins not modeled because concavities could not be detected with the available data (Ďurech & Kaasalainen 2003; Devogèle et al. 2015). The central location and overall dimensions of these features, including the ratio of their surface-equivalent diameter to the diameter of Daphne, are listed in Table 2.

thumbnail Fig. 1

Views of the shape model of Daphne. The X, Y and Z axes are aligned along the principal axes of inertia.
Table 1

Spin solution (coordinates in ecliptic and equatorial J2000 reference frames) and shape model parameters (the overall shape is reported as the a > b > c diameters of a triaxial ellipsoid fit to the shape model).

thumbnail Fig. 2

Topography of Daphne, measured in kilometers with respect to its reference ellipsoid (Table 1). The putative depression is marked by the letter D, while the three flat areas are labeled A, B, and C. They may appear as circular depressions here (in particular B) because the topography is measured with respect to an ellipsoid.
Table 2

Dimensions (semi-axes and , surface area , and fraction f of Daphne’s diameter) and planetocentric coordinates (λc, βc ) of the four notable topographic features of Daphne.

3.2 Dynamics of the system

On each image, we measure the relative position of the satellite with respect to center of light of the primary by adjusting a 2D gaussian on the primary using the unmodified images and another on the satellite using the halo-removed images (Fig. 3). We use the meta-heuristic algorithm Genoid (Vachier et al. 2012) to find the set of orbital parameters that best fitthe observations. The orbital parameter space is usually 6D for a simple Keplerian motion: orbital period, excentricity, inclination, longitude of the ascending node, argument of periapsis, and time of passage to the periapsis. More dimensions are required if the gravitational potential is not central, such as in accounting for a gravitational quadrupole J2 . Genoid explores this parameter space in successive generations of orbital solutions, randomly merging the parameters of the best solutions to create newer generations. In combination with this broad exploration of the parameter space, Genoid uses gradient descent at each generation to find the minimum closest to each best-trial solution.

The reliability of this approach has been assessed during a stellar occultation by (87) Sylvia in 2013. We had used Genoid to predict the position of its largest satellite Romulus before the event, placing observers on the occultation path of the satellite. Four different observers detected an occultation by Romulus at only 13.5 km off the predicted position (Berthier et al. 2014).

The best-fit orbit adjusts the 30 positions with a root-mean square (rms) residual of 8.3 mas only, i.e., smaller than the pixel size of most observations (21 out of 30 taken with NACO/VLT and NIRC2/Keck, see Table C.1). The observations, covering 3783 days or 3326 revolutions, provide solid constraints on the orbital period (1.137 446 ± 0.000 009 day). The satellite orbits Daphne on a Keplerian, equatorial, and prograde orbit, slightly eccentric (Table 3), at a distance of only 7.4 primary radii. We searched for a signature of the gravitational quadrupole J2 but the poor time coverage of the astrometry with a gap of nine years between the positions in 2008 and those in 2017 and 2018 precluded any firm conclusion. A regular follow-up of the position of Peneius is required to conclude on the J2 of Daphne. These orbital characteristics argue in favor of a formation of the satellite by impact excavation, and re-accumulation of material in orbit, followed by tidal circularization (Weidenschilling et al. 1989; Merline et al. 2002; Durda et al. 2004; Margot et al. 2015).

thumbnail Fig. 3

Example images of Daphne and its satellite. Each panel represents a different epoch. The image is displayed in the inner circle, showing the irregular shape of Daphne. The outer region shows the images after halo removal, showing the satellite (highlighted by a small circle). On each panel the telescope, instrument, filter, and UTC date are reported.
Table 3

Orbital elements of Peneius, the satellite of Daphne, expressed in EQJ2000, obtained with Genoid.

3.3 Spectrum and diameter of the satellite

We recorded the near-infrared spectra of Daphne and its satellite with SPHERE/IFS. Telluric features were removed by observing the nearby star HD 102085 (G3V). Similarly to previous sections, the bright halo of Daphne that contaminated the spectrum of the moon was removed. This was achieved by measuring the background at the location of the moon for each pixel as the median value of the area defined as a 40 ×1-pixel arc centeredon Daphne. To estimate the uncertainty and potential bias on photometry (at each wavelength) introduced by this method, we performed a number of simulations (similarly to our study of the satellite of Camilla, see Pajuelo et al. 2018).

We added synthetic companions on the 39 spectral images of the spectro-imaging cube, at a similar separation to the satellite ( ≈300 mas) and random position angles from the primary. The simulated sources were modeled as the point-spread function from the calibration star images scaled in brightness. The halo from Daphne was then removed from these simulated images using the method described above, and the flux of the simulated companion measured by adjusting a 2D-Gaussian profile (see Sect. 3.2). Based on a total statistics of 100 simulated companions, we find that the median loss of flux at each wavelength is 13 ± 9% and that the spectral slope is affected (−0.50%/100 nm on average).

The measured slope for each individual simulation, however, is not reliable, the standard deviation of all simulations being of 2.73%/100 nm. The value for each depends on the location (position angle) of the simulated satellite. Furthermore, the signal-to-noise ratio (S/N) of the simulations range from virtually zero to four, with an average of 1.8 only. The spectrum of the satellite, therefore, is not reliable, being noisy and likely affected by strong slope effects.

From the integrated fluxes measured with the 2D gaussian functions on Daphne and its satellite at each epoch (Fig. C.2 and Table C.1), we derived their magnitude difference to be 9.49 ± 0.32. Combined with our determination of a diameter of 187 ± 21.5 km, we derive a diameter of 2.4 km for the satellite, under the assumption of a similar albedo for both. This assumption is supported by the multiple reports of spectral similarities between the components of multiple asteroid systems: (22) Kalliope (Laver et al. 2009), (90) Antiope (Polishook et al. 2009), (107) Camilla (Pajuelo et al. 2018), (130) Elektra (Yang et al. 2016), and (379) Huenna (DeMeo et al. 2011).

4 Implications on the internal structure

Using the volume determined from ADAM (Sect. 3.1) and the mass from Genoid (Sect. 3.2), we derive a bulk density of 1.77 ± 0.26 (g cm−3, 3 σ uncertainty). This value is smaller but marginally consistent with the typical density of the CM carbonaceous chondrites, at 2.13 ± 0.57 g cm−3 (3 σ, Consolmagno et al. 2008). Comparing these two density values implies a macroporosity of 17 ± 3%.

As visible in Fig. 4, Ch and Cgh asteroids over two orders of magnitude in mass follow the same trend and have a density smaller than that of CM meteorites, although there is definitively some scatter due to large uncertainties and biases in the determination of their density (see Appendix D for the complete list of estimates, and Carry 2012, for a discussion on the reliability of mass, diameter, and density estimates). The distribution of all density estimates weighted by their respective uncertainty is Gaussian with an average value of 1.40 g cm−3. This value changes to 1.58 ± 0.97 g cm−3 (3 σ) by considering only the estimates with less than 20% relative uncertainty (represented by the blue curves in Fig. 4). This highlights the importance of the study of binary systems that can be angularly resolved to accurately determine both the volume and the mass, hence the density.

There are three large (150+ km) binary Ch-type asteroids: (41) Daphne, (121) Hermione, and (130) Elektra. The density of Hermione was estimated to 1.4 g cm−3 by Descamps et al. (2009) and 1.26 ± 0.90 g cm−3 by Viikinkoski et al. (2017). The density of Elektra was reported as 1.60 ± 0.39 g cm−3 by Hanuš et al. (2017a), based on the mass estimate by Marchis et al. (2008a) while the mass recently derived by Yang et al. (2016) leads to 1.50 ± 0.36 g cm−3. These values are somewhat smaller than the density of the three other large Ch-types: (13) Egeria at 1.99 ± 0.69 g cm−3, (19) Fortuna at 1.96 ± 0.28 g cm−3, and (48) Doris at 1.63 ± 0.74 g cm−3 (see Appendix D). The density of these six targets is systematically smaller than CM meteorites.

Over the wide range of mass spanned by the Ch/Cgh asteroids studied here (Fig. 4), the density appears roughly constant although there is a larger spread toward smaller diameters. This larger spread is likely due to larger uncertainties on the density estimates (the gravitational signature of asteroids become harder to detect toward smaller sizes, see Carry 2012). Indeed, the report by Carry (2012) of a correlation between density and mass (or diameter) due to an increasing macroporosity toward smaller diameters mainly happens for objects smaller than 100 km. This density of Ch/Cgh asteroids systematically lower than that of CM meteorites has two implications.

First, the density of the largest Ch/Cgh asteroids argues against the presence of material denser than CM-like material in their interior, i.e., differentiation. If denser material was present, their macroporosity would have to be large to maintain their bulk density, contrarily to what is observed for 100–200+ km bodies (Carry 2012). Together with the observed compositional homogeneity of Ch/Cgh asteroids (Vernazza et al. 2016), it supports the idea of an originally undeifferentiated internal structure of CM parent bodies. Because collisional fragments sample the interior of their parent bodies, this spectral homogeneity only modulated by grain sizes together with the density smaller than the surface analog material can be interpreted as evidence for a homogeneous internal structure, without differentiation, of the CM parent bodies. The thermal modeling in “giant mud balls” (non-lithified structure) proposed by Bland & Travis (2017) then provides an explanation for the observed peak temperature of 120 ° C (e.g., Guo & Eiler 2007).

Second, the density of Ch/Cgh asteroids being systematically smaller than CM chondrite indicates the presence of large voids, or less dense material, in their interior. Given the extensive hydration suffered by CM chondrites (e.g., Alexander et al. 2013) and the detection of water ice on/near the surface of asteroids well-within the snowline (e.g., Campins et al. 2010; Küppers et al. 2014), one cannot reject the hypothesis of the presence of water ice in Ch/Cgh asteroids. However, considering that all these objects have experienced numerous collisions over the history of the solar system, some macroporosity, i.e. voids, can be expected.

thumbnail Fig. 4

Mass vs. diameter distribution for 76 Ch/Cgh asteroids (grey circles). Those more precise than 50 and 20% are plotted as dark grey and black circles, respectively. Unreliable density estimates (below 0.5 g cm−3) are not displayed. The three binary asteroids, (41) Daphne, (121) Hermione, (130) Elektra, are labeled. The solid and dashed blue curves represent the average density (1.58 g cm−3) and 1 σ–2 σ (± 0.33 g cm−3) dispersion of the sample. The solid orange curve stands for the average density of CM chondrites at 2.13 ± 0.57 g cm−3 (3 σ).

5 Conclusion

We have acquired high-angular resolution images and spectro-images of the binary Ch-type asteroid (41) Daphne from large ground-based telescopes, including the new generation extreme adaptive-optics SPHERE camera mounted on the ESO VLT. We determined the orbit of its small satellite Peneius from 30 observations of its position around Daphne, with an rms of 8.3 mas only. Combining our disk-resolved images with optical lightcurves and stellar occultations, we determined the 3D shape of (41) Daphne.

The derived density of 1.77 ± 0.26 g cm−3 provides a solid reference to interpret the density of Ch/Cgh asteroids. The density is available for 76 of them and is found systematically smaller than that of the associated CM carbonaceous chondrites (2.13 ± 0.57 g cm−3, 3 σ), including for the largest asteroids. This provides robust evidence for a primordial homogeneous internal structure of these asteroids, in agreement with the observation of compositionnal homogeneity among Ch/Cgh asteroids of very different diameters by Vernazza et al. (2016) and the modeling of their early thermal history by Bland & Travis (2017).

Acknowledgements

Some of the work presented here is based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programs 281.C-5011 (PI Dumas), 099.D-0098, (SPHERE GTO), and 199.C-0074(A) (PI Vernazza). Some of the data presented herein were obtained 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. This research has made use of the Keck Observatory Archive (KOA), which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute (NExScI), under contract with the National Aeronautics and Space Administration. We thank the AGORA association which administrates the 60 cm telescope at Les Makes observatory, under a financial agreement with Paris Observatory. Thanks to A. Peyrot, J.-P. Teng for local support, and A. Klotz for helping with the robotizing. Some of these observations were acquired under grants from the National Science Foundation and NASA to W.J.M. (PI). B.C., A.D., J.G. and P.V. were supported by CNRS/INSU/PNP. J.H. and J.D. were supported by the grant 18-09470S of the Czech Science Foundation. The research leading to these results has received funding from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement no 687378. This paper makes use of data from the DR1 of the WASP data (Butters et al. 2010) as provided by the WASP consortium, and the computing and storage facilities at the CERIT Scientific Cloud, reg. no. CZ.1.05/3.2.00/08.0144 which is operated by Masaryk University, Czech Republic. TRAPPIST-South is funded by the Belgian Fund for Scientific Research (Fond National de la Recherche Scientifique, FNRS) under the grant FRFC 2.5.594.09.F, with the participation of the Swiss FNS. TRAPPIST-North is a project funded by the University of Liège, and performed in collaboration with Cadi Ayyad University of Marrakesh. E.J. and M.G. are Belgian FNRS Senior Research Associates. 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 to all the amateurs worldwide who regularly observe asteroid lightcurves and stellar occultations. Some co-authors of this study are amateurs who observed Daphne, and provided crucial data. The authors acknowledge the use of the Virtual Observatory tools Miriade 3 (Berthier et al. 2008), TOPCAT 4 , and STILTS 5 (Taylor 2005). This research used the SSOIS 6 facility of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency (Gwyn et al. 2012). Part of the data utilized in this publication were obtained and made available by the MIT-UH-IRTF Joint Campaign for NEO Reconnaissance, using SpeX spectrograph (Rayner et al. 2003). The IRTF is operated by the University of Hawaii under Cooperative Agreement no. NCC 5-538 with the National Aeronautics and Space Administration, Office of Space Science, Planetary Astronomy Program. The MIT component of this work is supported by NASA grant 09-NEOO009-0001, and by the National Science Foundation under Grant Nos. 0506716 and 0907766. We wish to acknowledge Professor Robert Groves, Director of Basic Languages (Classics) of the University of Arizona, for his assistance in selecting the name for Daphne’s satellite.

Appendix A Compilation of diameter and mass estimates

Table A.1

The diameter estimates () of (41) Daphne collected in the literature.

Table A.2

The mass estimates () of (41) Daphne collected in the literature.

Appendix B Shape modeling: data and model predictions

thumbnail Fig. B.1

Comparison of the shape model (top image of each row), oriented and projected on the plane of the sky at the epoch of each disk-resolved observation (bottom image of each row). The brighter ring present in some images (e.g., second row, last column) is an artifact from deconvolution.
thumbnail Fig. B.2

The eight stellar occultations by Daphne, compared with the shape model (profile in black and facets in light gray) projected on the plane of the sky at the time of the occultation. Negative chords are represented by dotted lines, visual timings by dashed lines, and electronic timings by solid lines. Disappearance and reappearances timings are marked by filled circles, and their uncertainty by gray rectangles.
thumbnail Fig. B.3

The optical lightcurves of Daphne (grey spheres), compared with the synthetic lightcurves generated with the shape model (black lines). On each panel, the observing date, number of points, duration of the lightcurve (in hours), and rms residuals between the observations and the synthetic lightcurves are displayed. Measurement uncertainties are seldom provided by the observers but can be estimated from the spread of measurements.
thumbnail Fig. B.3

continued.
Table B.1

Date, telescope, camera, number of epochs (), heliocentric distance (Δ), range to observer (r), phase angle (α), angular diameter (Θ), and program ID and Principal Investigator (PI) for each night of AO imaging observations.

Table B.2

Date, number of positive and negative chords (#p and #n ), and average uncertainty in seconds (σs) and kilometers (σkm) for each stellar occultation.

Table B.3

Date, duration (, in hours), number of points (), phase angle (α), filter, residual (against the shape model), and observers, for each lightcurve.

Appendix C Magnitude and position of the satellite

thumbnail Fig. C.1

Distribution of residuals for the satellite between the observed (index o) and predicted(index c) positions, normalized by the uncertainty on the measured positions (σ), and color-coded by observing epoch. X stands for right ascension and Y for declination. The three large gray circles represent the 1, 2, and 3 σ limits (typically 10 mas at 1 σ). Top panel: histogram of residuals along X. Right panel: residuals along Y. The light gray Gaussian in the background has a standard deviation of one.
thumbnail Fig. C.2

Distribution of the magnitude differences between Daphne and its satellite. The open bars represent all measurements, and the blue bars those more precise than 0.75 magnitude. The dashed black line represents the normal distribution fit to our results, with a mean and standard deviation of 9.49 ± 0.32.
Table C.1

Astrometry of the satellite of Daphne.

Appendix D Mass and diameter of Ch and Cgh asteroids

Table D.1

Dynamical class (IMB, MMB, and OMB stand for inner, middle, and outer belt respectively), taxonomic class, mass (), diameter (), and density (ρ) of Ch/Cgh asteroids used in this work, compiled following the recipes described in Carry (2012).

Table D.2

The diameter estimates () for all the Ch/Cgh asteroids available in the literature.

Table D.3

The mass () for all the Ch/Cgh asteroids available in the literature.

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1

Pronounced “peh-NEH-oss.”

All Tables

Table 1

Spin solution (coordinates in ecliptic and equatorial J2000 reference frames) and shape model parameters (the overall shape is reported as the a > b > c diameters of a triaxial ellipsoid fit to the shape model).

In the text
Table 2

Dimensions (semi-axes and , surface area , and fraction f of Daphne’s diameter) and planetocentric coordinates (λc, βc ) of the four notable topographic features of Daphne.

In the text
Table 3

Orbital elements of Peneius, the satellite of Daphne, expressed in EQJ2000, obtained with Genoid.

In the text
Table A.1

The diameter estimates () of (41) Daphne collected in the literature.

In the text
Table A.2

The mass estimates () of (41) Daphne collected in the literature.

In the text
Table B.1

Date, telescope, camera, number of epochs (), heliocentric distance (Δ), range to observer (r), phase angle (α), angular diameter (Θ), and program ID and Principal Investigator (PI) for each night of AO imaging observations.

In the text
Table B.2

Date, number of positive and negative chords (#p and #n ), and average uncertainty in seconds (σs) and kilometers (σkm) for each stellar occultation.

In the text
Table B.3

Date, duration (, in hours), number of points (), phase angle (α), filter, residual (against the shape model), and observers, for each lightcurve.

In the text
Table C.1

Astrometry of the satellite of Daphne.

In the text
Table D.1

Dynamical class (IMB, MMB, and OMB stand for inner, middle, and outer belt respectively), taxonomic class, mass (), diameter (), and density (ρ) of Ch/Cgh asteroids used in this work, compiled following the recipes described in Carry (2012).

In the text
Table D.2

The diameter estimates () for all the Ch/Cgh asteroids available in the literature.

In the text
Table D.3

The mass () for all the Ch/Cgh asteroids available in the literature.

In the text

All Figures

thumbnail Fig. 1

Views of the shape model of Daphne. The X, Y and Z axes are aligned along the principal axes of inertia.
In the text
thumbnail Fig. 2

Topography of Daphne, measured in kilometers with respect to its reference ellipsoid (Table 1). The putative depression is marked by the letter D, while the three flat areas are labeled A, B, and C. They may appear as circular depressions here (in particular B) because the topography is measured with respect to an ellipsoid.
In the text
thumbnail Fig. 3

Example images of Daphne and its satellite. Each panel represents a different epoch. The image is displayed in the inner circle, showing the irregular shape of Daphne. The outer region shows the images after halo removal, showing the satellite (highlighted by a small circle). On each panel the telescope, instrument, filter, and UTC date are reported.
In the text
thumbnail Fig. 4

Mass vs. diameter distribution for 76 Ch/Cgh asteroids (grey circles). Those more precise than 50 and 20% are plotted as dark grey and black circles, respectively. Unreliable density estimates (below 0.5 g cm−3) are not displayed. The three binary asteroids, (41) Daphne, (121) Hermione, (130) Elektra, are labeled. The solid and dashed blue curves represent the average density (1.58 g cm−3) and 1 σ–2 σ (± 0.33 g cm−3) dispersion of the sample. The solid orange curve stands for the average density of CM chondrites at 2.13 ± 0.57 g cm−3 (3 σ).
In the text
thumbnail Fig. B.1

Comparison of the shape model (top image of each row), oriented and projected on the plane of the sky at the epoch of each disk-resolved observation (bottom image of each row). The brighter ring present in some images (e.g., second row, last column) is an artifact from deconvolution.
In the text
thumbnail Fig. B.2

The eight stellar occultations by Daphne, compared with the shape model (profile in black and facets in light gray) projected on the plane of the sky at the time of the occultation. Negative chords are represented by dotted lines, visual timings by dashed lines, and electronic timings by solid lines. Disappearance and reappearances timings are marked by filled circles, and their uncertainty by gray rectangles.
In the text
thumbnail Fig. B.3

The optical lightcurves of Daphne (grey spheres), compared with the synthetic lightcurves generated with the shape model (black lines). On each panel, the observing date, number of points, duration of the lightcurve (in hours), and rms residuals between the observations and the synthetic lightcurves are displayed. Measurement uncertainties are seldom provided by the observers but can be estimated from the spread of measurements.
In the text
thumbnail Fig. B.3

continued.
In the text
thumbnail Fig. C.1

Distribution of residuals for the satellite between the observed (index o) and predicted(index c) positions, normalized by the uncertainty on the measured positions (σ), and color-coded by observing epoch. X stands for right ascension and Y for declination. The three large gray circles represent the 1, 2, and 3 σ limits (typically 10 mas at 1 σ). Top panel: histogram of residuals along X. Right panel: residuals along Y. The light gray Gaussian in the background has a standard deviation of one.
In the text
thumbnail Fig. C.2

Distribution of the magnitude differences between Daphne and its satellite. The open bars represent all measurements, and the blue bars those more precise than 0.75 magnitude. The dashed black line represents the normal distribution fit to our results, with a mean and standard deviation of 9.49 ± 0.32.
In the text

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