P Berthier

J Descamps

M Pajuelo
email: myriam.pajuelo@obspm.fr

B Carry

F Vachier

M Marsset

J Berthier

P Descamps

W J Merline

P M Tamblyn

J Grice

A Conrad

A Storrs

B Timerson

D Dunham

S Preston

A Vigan

B Yang

P Vernazza

S Fauvaud

L Bernasconi

D Romeuf

R Behrend

C Dumas

J D Drummond

J.-L Margot

P Kervella

F Marchis

J H Girard

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

Keywords:

Introduction

Main belt asteroids are the remnants of the building blocks that accreted to form terrestrial planets, leftovers of the dynamical events that shaped our planetary system. Among them, large bodies (diameter larger than ≈ 100 km) are deemed primordial [START_REF] Morbidelli | Asteroids were born big[END_REF], and contain a relatively pristine record of their initial formation conditions Decades of photometric and spectroscopic surveys have provided an ever-improving picture of the distribution of material in the inner solar system (e.g. [START_REF] Gradie | Compositional structure of the asteroid belt[END_REF][START_REF] Burbine | Mantle material in the main belt: battered to bits?[END_REF]2002;Bus and Binzel, 2002a;[START_REF] Rivkin | Hydrated minerals on asteroids: the astronomical record[END_REF]2006;[START_REF] Vernazza | Compositional differences between meteorites and near-Earth asteroids[END_REF]2010;[START_REF] Vernazza | Multiple and fast: the accretion of ordinary chondrite parent bodies[END_REF][START_REF] Demeo | Solar system evolution from compositional mapping of the asteroid belt[END_REF], yet these studies have probed the composition of the surface only. As such, they do not necessarily lead us to the original location and time scales for the accretion of these blocks, which are key to understanding the important processes in the disk of gas and dust around the young Sun.

These issues can be addressed by studying the internal structure of asteroids: objects formed far from the Sun are expected to be composed of various mixtures of rock and ice, while objects closer to the Sun are expected to be volatile-free. Depending on their formation time scale, the amount of radiogenic heat varied, leading to complete, partial, or no differentiation. In that respect, density is clearly the most important remotely measurable property that can constrain internal structure [START_REF] Scheeres | Asteroid Interiors and Morphology[END_REF].

Determination of density requires measurement of mass and volume, and for that, large asteroids with satellites are prime targets [START_REF] Merline | Discovery of a moon orbiting the asteroid 45 eugenia[END_REF]2002;Marchis et al., 2008b;2008a;[START_REF] Carry | Integral-field spectroscopy of (90482) orcus-Vanth[END_REF][START_REF] Margot | Asteroid Systems: Binaries, Triples, and Pairs[END_REF]. The study of the orbits of satellites within asteroid binaries or multiple systems is currently the most precise method to estimate the mass of the primary asteroid. If the primary also happen to have an angular diameter large enough to be spatially resolved by large telescopes, this also allows an accurate determination of the primary's volume. In addition, the orbits of the satellites themselves offer a way to probe the gravity field, related to mass distribution inside the asteroid ( Berthier et al., 2014;[START_REF] Marchis | The puzzling mutual orbit of the binary trojan asteroid (624) hektor[END_REF].

Here we focus on the outer-main-belt asteroid (107) Camilla, orbiting in the Cybele region and discovered on November 17, 1868 from Madras, India by N. R. Pogson. Its first satellite, S/2001 (107) 1 (hereafter S1), was discovered in March 2001 by Storrs et al. (2001) , using the Hubble Space Telescope (HST), and its orbit first studied by Marchis et al. (2008a) using observations from large ground-based telescopes equipped with adaptive-optics (AO) systems. Its second satellite, S/2016 (107) 1 (hereafter S2), was discovered in 2016 by our team ( Marsset et al., 2016 ), using the European Southern Observatory (ESO) Very Large Telescope (VLT).

Camilla was originally classified as a C-type based on its visible colors and albedo [START_REF] Tedesco | Three-parameter asteroid taxonomy classifications[END_REF]. Later on, both Bus and Binzel (2002a) and [START_REF] Lazzaro | S 3 OS 2 : the visible spectroscopic survey of 820 asteroids[END_REF] classified it as X, based on visible spectra. More recently, based on a near-infrared spectrum from NASA IRTF Spex, [START_REF] Lindsay | Composition, mineralogy, and porosity of multiple asteroid systems from visible and nearinfrared spectral data[END_REF] classified Camilla as either Xe or L.

The physical properties of Camilla have been extensively studied, from its rotation period of 4.8 h (e.g., [START_REF] Weidenschilling | Photometric geodesy of main-belt asteroids. I -lightcurves of 26 large, rapid rotators[END_REF][START_REF] Di Martino | Photoelectric photometry of 17 asteroids[END_REF] to its spin and 3D shape model [START_REF] Torppa | Shapes and rotational properties of thirty asteroids from photometric data[END_REF][START_REF] Ďurech | Combining asteroid models derived by lightcurve inversion with asteroidal occultation silhouettes[END_REF][START_REF] Hanuš | Sizes of main-belt asteroids by combining shape models and Keck adaptive optics observations[END_REF]2017 ). Its diameter, however, was poorly constrained, with estimates ranging from 185 ± 9 km [START_REF] Marchis | Shape, size and multiplicity of main-belt asteroids[END_REF] to 256 ± 12 km ( Marchis et al., 2012 ). More recent studies combining images or stellar occultations with lightcurve-based 3D shape modeling, are yielding diameters in excess of 220 km (see Fig. B.2 and Table B.2 for the exhaustive list of diameter estimates). The mass estimates also spanned a wide range, from 2 . 25 +18 . 00 -2 . 25 to 39 ± 10 × 10 18 kg [START_REF] Zielenbach | Mass determination studies of 104 large asteroids[END_REF] B.1 for the exhaustive list of mass estimates). With these large spread of values, deriving an accurate density would require substantial improvements to these parameters.

Gathering all the available disk-resolved and high-contrast images from HST and AO-fed cameras, optical lightcurves, stellar occultations, and visible and near-infrared spectra ( Section 2 ), we present an extensive study of the dynamics of the system ( Section 3 ), of the surface properties of Camilla and its main satellite S1 ( Section 4 ), and of Camilla's spin and 3-D shape ( Section 5 ), all constraining its internal composition and structure ( Section 6 ).

Observations

Optical lightcurves

We gather the 24 lightcurves used by [START_REF] Torppa | Shapes and rotational properties of thirty asteroids from photometric data[END_REF] to create a convex 3-D shape model of Camilla1 , compiled from the Uppsala Asteroid Photometric Catalog 2 [START_REF] Lagerkvist | Asteroid Photometric Catalog V1[END_REF]. We also retrieve the three lightcurves reported by [START_REF] Polishook | Lightcurves for shape modeling obtained at the wise observatory[END_REF] .

In addition to these data, we acquired 29 lightcurves using 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. We also extracted 63 lightcurves from the data archive of the SuperWASP survey ( Pollacco et al.,20 06 ) for the period 20 06-20 09. This survey aims to find and characterize exoplanets by observations of their transits of the host star. Its large field of view (8 °× 8 °) provides a goldmine for asteroid lightcurves [START_REF] Parley | Serendipitous asteroid lightcurve survey using superwasp[END_REF][START_REF] Grice | The shapes of primordial asteroids[END_REF].

A total of 127 lightcurves observed between 1981 and 2016 ( Table A.1 ) are used in this work.

High-angular-resolution imaging

We compile here all the high-angular-resolution images of Camilla taken with the HST and large ground-based telescopes equipped with AO-fed cameras: Gemini North, ESO VLT, and W. M. Keck, of which only a subset had already been published ( Storrs et al., 2001;Marchis et al., 2008a ). All of these data sets were acquired by the authors of this paper. The data comprise 62 different epochs, with multiple images each, spanning 15 years, from March 2001 to August 2016.

The images from the VLT were acquired with both the first generation instrument NACO (NAOS-CONICA, [START_REF] Lenzen | NAOS-CON-ICA First on sky results in a variety of observing modes[END_REF][START_REF] Rousset | NAOS, The first AO system of the VLT: on-sky performance[END_REF] and SPHERE (Spectro-Polarimetric Highcontrast Exoplanet REsearch, Fusco et al., 2006;[START_REF] Beuzit | SPHERE: a 'Planet Finder' instrument for the VLT[END_REF], the second generation extreme-AO instrument designed for exoplanet detection and characterization. The images taken with SPHERE used its IRDIS differential imaging camera sub-system (In-fraRed Dual-band Imager and Spectrograph, [START_REF] Dohlen | The infra-red dual imaging and spectrograph for SPHERE: design and performance[END_REF]. Images taken at the Gemini North used NIRI camera (Near In-fraRed Imager, Hodapp et al., 2003 ), fed by the ALTAIR AO system ( Herriot et al.,20 0 0 ). Finally, observations at Keck were acquired with NIRC2 (Near-InfraRed Camera 2, van [START_REF] Van Dam | Performance of the Keck observatory adaptive-optics system[END_REF]Wizinowich et al., 20 0 0 ). We list in Table A.2 the details of each observation.

The basic data processing (sky subtraction, bad-pixel removal, and flat-field correction) was performed using in-house routines developed in Interactive Data Language (IDL) to reduce AO-imaging data (see [START_REF] Carry | Near-Infrared mapping and physical properties of the dwarf-planet ceres[END_REF] , for more details).

High-angular-resolution spectro-imaging

In 2015 and 2016, we also used the integral-field spectrograph (IFS) of the SPHERE instrument at the ESO VLT, aiming to measure the reflectance spectrum of Camilla's largest satellite S1, and the astrometry of the fainter satellite S2. The observations were made in the IRDIFS_EXT mode [START_REF] Zurlo | Performance of the VLT planet finder SPHERE. i. photometry and astrometry precision with IRDIS and IFS in laboratory[END_REF], in which both IRDIS ( Dohlen et al., 2008 ) and the IFS ( Claudi et al., 2008 ) data are acquired simultaneously. In this set-up, the IFS covers the wavelength range from 0.95 to 1.65 μm (YJH bands) at a spectral resolving power of ∼ 30 in a 1.7 × 1.7 field of view (FoV), while IRDIS operates in the dual-band imaging mode (DBI, [START_REF] Vigan | Photometric characterization of exoplanets using angular and spectral differential imaging[END_REF] with K 12 , a pair of filters in the K band ( λ K 1 = 2.110 μm and λ K 2 = 2.251 μm, ∼ 0.1 μm bandwidth), within a 4.5 FoV. All observations were performed in the pupil-tracking mode, where the pupil remains fixed while the field orientation varies during the observations. This mode provides the best PSF stability and helps in reducing and subtracting static speckle noise in the images.

For the pre-processing of both the IFS and IRDIS data, we used the preliminary release (v0.14.0-2) of the SPHERE Data Reduction and Handling (DRH) software ( Pavlov et al., 2008 ), as well as additional in-house tools written in IDL, including parts of the public pipeline presented in [START_REF] Vigan | Highcontrast imaging of sirius a with vlt/sphere: looking for giant planets down to one astronomical unit[END_REF] . See our recent works on (3) Juno and (6) Hebe for more details [START_REF] Viikinkoski | VLT/SPHERE-And ALMA-based shape reconstruction of asteroid (3) juno. Astron[END_REF][START_REF] Marsset | 3D Shape of asteroid (6) hebe from VLT/SPHERE imaging: implications for the origin of ordinary h chondrites[END_REF]. We used the DRH for the creation of some of the basic calibrations: master sky frames, master flat-field, IRDIFS spectra positions, initial wavelength calibration and flat field. Before creating the data cubes, we used IDL routines to subtract the background from each science frame and correct for the bad pixels identified using the master dark and master flat-field DRH products. This step was introduced as a substitute for the bad pixel correction provided by the DRH. Bad pixels were first identified using a sigma-clipping routine, and then corrected using a bicubic pixel interpolation with the MASKINTERP IDL routine. The resulting frames were then injected into the DRH recipe to create the data cubes by interpolating the data spectrally and spatially.

Stellar occultations

Eleven stellar occultations by Camilla have been observed in the last decade, mostly by amateur astronomers (see [START_REF] Mousis | Instrumental methods for professional and amateur collaborations in planetary astronomy[END_REF]Dunham et al., 2016a ). The timings of disappearance and reappearance of the stars, together with the location of each observing station are compiled by Dunham et al. (2016b) , and publicly available on the Planetary Data System (PDS 3 ). We converted the disappearance and reappearance timings ( Table A.3 ) of the occulted stars into segments (called chords) on the plane of the sky, 3 http://sbn.psi.edu/pds/resource/occ.html using the location of the observers on Earth and the apparent motion of Camilla following the recipes by [START_REF] Berthier | Principe de réduction des occultations stellaires[END_REF] . Four stellar occultations had multiple chords; other events had only one or two positive chords, and contributed less to constraining the size and apparent shape of Camilla. In none of these eleven stellar occultations was there any evidence for a companion. We list in Table A.4 the details of the seven events that we used.

Near-infrared spectroscopy

On November 1, 2010, we observed Camilla over 0.8-2.5 μm with the near-infrared spectrograph SpeX [START_REF] Rayner | Spex: A Medium-Resolution 0.8-5.5 micron spectrograph and imager for the NASA infrared telescope facility[END_REF], on the 3-meter NASA IRTF located on Mauna Kea, Hawaii, using the low resolution Prism mode ( R = 100). We used the standard nodding procedure for the observations, using alternately two separated locations on the slit (e.g., [START_REF] Nedelcu | Near infra-red spectroscopy of the asteroid 21 Lutetia. II. Rotationally resolved spectroscopy of the surface[END_REF] to estimate the sky background. We used Spextool (SPectral EXtraction TOOL), an IDL-based data reduction package written by [START_REF] Cushing | Spextool: a spectral extraction package for SpeX, a 0.8-5.5 micron cross-Dispersed spectrograph[END_REF] to reduce SpeX data.

Dynamical properties

Data processing

The main challenges in measuring the position and apparent flux of the satellite of an asteroid results from their sub-arcsecond angular separation and high contrast (several magnitudes), combined with imperfect AO correction. A typical image of a binary asteroid ( Fig. 1 ) displays a central peak (the asteroid itself, angularly resolved or not) encompassed by a halo (its diffused light), within which speckle patterns appear. The faintness of these speckles, produced by interference of the incoming light, make them very similar in appearance to a small moon with a contrast up to several thousands, and they can be misleading. Speckles, however, vary (position and flux) on short timescales, depending on the ambient conditions and AO performances (e.g., seeing, airmass, brightness of the AO reference source). These fluctuations can be used to distinguish genuine satellites from speckles.

As for the direct imaging of exoplanets, it is crucial to substract the halo that surrounds the primary (in a similar way to the digital coronography of [START_REF] Assafin | Instrumental and digital coronagraphy for the observation of the uranus satellites' upcoming mutual events[END_REF]. Because asteroids are also marginally resolved, their light is not fully coherent, and the speckle pattern is not as stable in time, nor simple, as in the case of a star. The tool we developed considers concentric annuli around the center of light of the primary to evaluate its halo. Although the principle is straightforward, great caution was taken in the implementation, especially in the computation of the intersection of the annulus with the pixels to allow the use of annuli with a sub-pixel width. The contribution of each pixel to different annuli is thus solved first, and the median flux of each annulus is computed, and subtracted from each pixel accordingly.

The position and flux of the satellite, relative to the primary, is then measured by fitting a 2-D Gaussian function to the halosubtracted image. The satellites are distinguished from speckles by comparing different images, taken both close in time and over a range of times. To estimate the uncertainties on the position and apparent flux of both the primary and the satellites, we use different integration apertures for each object. The sizes of the apertures are determined by fitting a 2-D Gaussian to each, with diameters typically being 5 to 150 pixels for the primary, and 3 to 15 pixels for the satellites. The reported positions and apparent magnitudes ( Tables A.5 and A.6 ) are the average of all fits (after removal of outlier values), and the reported uncertainties are the standard deviations.

Orbit determination with Genoid

We use our algorithm Genoid (GENetic Orbit IDentification, [START_REF] Vachier | Determination of binary asteroid orbits with a genetic-based algorithm[END_REF] to determine the orbit of the satellites.

Genoid is a genetic-based algorithm that relies on a metaheuristic method to find the best-fit (i.e., minimum χ 2 ) suite of dynamical parameters (mass, semi-major axis, eccentricity, inclination, longitude of the node, argument of pericenter, and time of passage to pericenter) by refining, generation after generation, a grid of test values (called individuals ).

The first generation is drawn randomly over a very wide range for each parameter, thus avoiding a miss of the global minimum from inadequate initial conditions. For each individual (i.e., set of dynamical parameters), the χ 2 residuals between the observed and predicted positions is computed as

χ 2 = N i =1 X o,i -X c,i σ x,i 2 + Y o,i -Y c,i σ y,i 2 (1)
where N is the number of observations, and X i and Y i are the relative positions between the satellite and Camilla along the right ascension and declination respectively. The indices o and c stand for observed and computed positions, and σ are the measurement uncertainties.

A new generation of individuals is drawn by mixing randomly the parameters of individuals with the lowest χ 2 from the former generation. This way, the entire parameter space is scanned, with the density of evaluation points increasing toward low χ 2 regions along the process. At each generation, we also use the best individual as initial condition to search for the local minimum by gradient descent. The combination of genetic grid-search and gradient descent thus ensures finding the best solution.

We then assess the confidence interval of the dynamical parameters by considering all the individuals providing predictions within 1, 2, and 3 σ of the observations. The range spanned by these individuals provide the confidence interval at the corresponding σ level for each parameter.

The reliability of Genoid has been assessed during a stellar occultation by (87) Sylvia and its satellites Romulus and Remus on January 6, 2013: Genoid had been used to predict the position of Romulus before the event, directing observers to locations specifically to target the satellite. Four different observers detected an occultation by Romulus at only 13.5 km off the predicted track (the cross-track uncertainty was 65 km, [START_REF] Berthier | Physical and dynamical properties of the main belt triple asteroid (87) sylvia[END_REF].

Orbit of S1: S/2001 (107) 1

We measured 80 astrometric positions of the satellite S1 relative to Camilla over a span of 15 years, corresponding to 5642 days or 1520 revolutions. The orbit we derive with Genoid fits all 80 observed positions of the satellite with a root mean square (RMS) residual of 7.8 milli-arcseconds (mas) only, which corresponds to a sub-pixel accuracy.

S1 orbits Camilla on a circular, prograde, equatorial orbit, in 3.71 days with a semi-major axis of 1248 km. We detail all the parameters of its orbit in Table 1 , with their confidence interval taken at 3 σ . The distribution of residuals between the observed and predicted positions, normalized by the uncertainty on the measured positions, are plotted in Fig. 2 . The orbit we determine here is qualitatively similar to the one given by Marchis et al. (2008a) , while much better constrained: we fit 80 astrometric positions over 15 years with an RMS residual of 7.8 mas, compared to their fit of 23 positions over less than 3 years with an RMS residual of 22 mas. The much longer time span of observations provides a much more stringent constraint on the period (3.712 34 ± 0.0 0 0 04 day) of S1, compared to the value of 3.722 ± 0.009 day reported by Marchis et al. (2008a) .

As a result, we determine a much more precise mass for Camilla of (1.12 ± 0.01) × 10 19 kg (3 σ uncertainty), about 1% of the mass of Ceres [START_REF] Carry | Density of asteroids[END_REF]. We list in Table B.1 the reported values of the mass of Camilla found in the literature. Our mass value agrees well with the average value (1.10 ± 0.69) × 10 19 kg we show in Table B.1 , although the mass estimates derived from orbital deflection and solar system ephemerides have a large scatter (see [START_REF] Carry | Density of asteroids[END_REF] , for a discussion on the precision and bias of mass determination methods). Our determination significantly reduces the uncertainty in the prior value of (1.12 ± 0.09) × 10 19 kg, that also used the orbit of S1 ( Marchis et al., 2008a ).

Table 1 Orbital elements of the satellites of Camilla, S1 and S2, expressed in EQJ20 0 0, obtained with Genoid : orbital period P , semi-major axis a , eccentricity e , inclination i , longitude of the ascending node , argument of pericenter ω, time of pericenter t p . The number of observations and RMS between predicted and observed positions are also provided. Finally, we report the derived primary mass M , the ecliptic J20 0 0 coordinates of the orbital pole ( λp , βp ), the equatorial J20 0 0 coordinates of the orbital pole ( αp , δp ), and the orbital incli- nation ( ) with respect to the equator of Camilla. Uncertainties are given at 3-σ .

S1 S2

Observing We measured 11 astrometric positions of the satellite S2 relative to Camilla during 2015 and 2016, corresponding to 428 days or 311 revolutions. These observations correspond to three wellseparated epochs: 2015-May-29, 2016-Jul-12, and 2016-Jul-30, providing the minimum needed to constrain the orbit. Thus, although the orbit we determine with Genoid fits all 11 observed positions of S2 with an RMS residual of only 5.0 mas and yields reliable values for the major orbital elements, details of all orbital parameters will require further observations. S2 orbits Camilla in 1.38 days with a semi-major axis of 644 km. We detail all the parameters of its orbit in Table 1 and present the distribution of residuals between the observed and predicted positions in Fig. 3 . Unlike S1, its orbit seems neither equatorial nor circular. While cognizant of the larger uncertainties, we favor an orbit inclined to the equator of Camilla by an angle of 32 ± 28 °( Fig. 4 ), and a more eccentric orbit (e = 0.18 +0 . 23 -0 . 18 ). Although a circular orbit, co-planar with S1 is marginally within the range of uncertainty, such a solution results in significantly higher residuals. This configuration of an outer satellite on a circular and equatorial orbit with an inner satellite on an inclined and more eccentric orbit has already been reported for other triple systems: (45) Eugenia, (87) Sylvia, and (130) Elektra ( Marchis et al., 2010;[START_REF] Fang | Orbits, masses, and evolution of main belt triple (87) sylvia[END_REF][START_REF] Berthier | Physical and dynamical properties of the main belt triple asteroid (87) sylvia[END_REF][START_REF] Yang | Extreme ao observations of two triple asteroid systems with sphere[END_REF][START_REF] Drummond | The orbit and size of (87) Sylvia's Romulus from the 2015 apparition[END_REF].

Surface properties

Data processing

We measured the near-infrared spectra of Camilla and its largest satellite S1 using the SPHERE/IRDIFS data. Telluric features were removed, and the reflectance spectra were obtained by observing the nearby solar type star HD139380.

Similarly to previous sections, the bright halo of Camilla 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 centered on Camilla. To estimate the uncertainty and potential bias on photometry introduced by this method, we performed a number of simulations in which we injected fake companions on the 39 spectral images of the spectroimaging cube, at separation ( ≈ 300 mas) and random position angles from the primary. The simulated sources were modeled as the PSF, from the calibration star images, scaled in brightness.

The halo from Camilla 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. Based on a total statistics of 500 simulated companions, we find that the median loss of flux at each wavelength is 11 ± 10%. A spectral gradient is also introduced by our technique, but it is smaller than 0.06 ± 0.07% • μm -1 . The spectra of Camilla and S1, normalized at 1.1 μm, are shown in Fig. 5 .

Spectrum of Camilla

We combine the near-infrared spectrum we acquired at NASA IRTF ( Section 2.5 ) with the visible spectrum from SMASS ( Bus and Binzel,20 02a; 20 02b ) and analyze them with the M4AST 4 (Model-4 http://m4ast.imcce.fr/ ing for Asteroids, [START_REF] Popescu | Modeling of asteroid spectra -M4AST[END_REF] suite of Web tools to determine asteroid taxonomic classification, mineralogy, and most-likely meteorite analog. From this longer wavelength range, we found Camilla to be an Xk-type asteroid (using Bus-DeMeo taxonomic scheme, Fig. 5, [START_REF] Demeo | An extension of the bus asteroid taxonomy into the near-infrared[END_REF]. The low albedo of Camilla (0.059 ± 0.005, taken as the average of the estimates by [START_REF] Morrison | TRIAD Radiometric Diameters and Albedos[END_REF][START_REF] Tedesco | The supplemental IRAS minor planet survey[END_REF][START_REF] Ryan | Rectified asteroid albedos and diameters from IRAS and MSX photometry catalogs[END_REF][START_REF] Usui | Asteroid catalog using akari: AKARI/IRC mid-Infrared asteroid survey[END_REF][START_REF] Masiero | Main belt asteroids with WISE/NEOWISE. i. preliminary albedos and diameters[END_REF], hints at a P-type classification, using the [START_REF] Tedesco | Three-parameter asteroid taxonomy classifications[END_REF] scheme.

Although the best spectral match is formally found for an Enstatite Chondrite EH5 meteorite (Queen Alexandra Range, Antarctica origin, maximum size of 10 μm), the low albedo of Camilla argues for a different type of analog material. The composition of P-type asteroids is indeed difficult, if not impossible, to infer from their visible and near-infrared spectra owing to the lack of absorption bands.

Recently, [START_REF] Vernazza | Interplanetary dust particles as samples of icy asteroids[END_REF] have shown that anhydrous chondritic porous interplanetary dust particules (IDPs) were likely to originate from D-and P-types asteroids, based on spectroscopic observations in the mid-infrared of outer-belt D-and P-type asteroids, including Camilla. The mixture of olivine-rich and pyroxenerich IDPs they used was compatible with the visible and nearinfrared spectrum of Camilla. As such, the surface of Camilla, and more generally of D-and P-types, is very similar to that of comets, as already reported by [START_REF] Emery | Thermal emission spectroscopy (5.2 38 μm) of three trojan asteroids with the spitzer space telescope: detection of fine-grained silicates[END_REF] from the spectroscopy of Jupiter Trojans in the mid-infrared, revealing the presence of anhydrous silicates.

Spectrum of S1

As visible in Fig. 5 , the spectrum of S1 is similar to that of Camilla. No significant difference in slope nor absorption band can be detected. This implies that the two components are spectraly identical from 0.95 to 1.65 μm, within the precision of our measurements. Such a similarity between the components of multiple systems have already been reported for several other main-belt asteroids: (22) Kalliope [START_REF] Laver | Componentresolved near-infrared spectra of the (22) kalliope system[END_REF], (90) Antiope ( Polishook et al., 2009;[START_REF] Marchis | The origin of (90) antiope from component-resolved near-infrared spectroscopy[END_REF], ( 130) Elektra ( Yang et al., 2016 ), and (379) Huenna ( DeMeo et al., 2011 ).

Such spectral similarity, together with the main characteristics of the orbit (prograde, equatorial, circular) supports an origin of these satellites, here for S1 in particular, by impact and reaccumulation of material in orbit (see [START_REF] Margot | Asteroid Systems: Binaries, Triples, and Pairs[END_REF] , for a review). Formation by rotational fission is unlikely owing to the rotation period of Camilla (4.84 h).

Physical properties

Data processing

We used the optical lightcurves without modification, only converting their heterogeneous formats from many observers to the usual lightcurve inversion format ( Ďurech et al., 2010 ). For the occultation observations, the location of observers, together with their timings of the disappearance and the reappearance of the star, were converted into chords on the plane of the sky, using the recipes from [START_REF] Berthier | Principe de réduction des occultations stellaires[END_REF] . Finally, the 2-D profile of the apparent disk of Camilla was measured on the AO images, deconvolved using the Mistral algorithm ( Fusco, 20 0 0;[START_REF] Mugnier | MISTRAL: A myopic edge-Preserving image restoration method, with application to astronomical adaptive-Optics-Corrected long-Exposure images[END_REF], the reliability of which has been demonstrated elsewhere [START_REF] Witasse | Overview of the coordinated ground-based observations of titan during the huygens mission[END_REF], using the wavelet transform described in [START_REF] Carry | Near-Infrared mapping and physical properties of the dwarf-planet ceres[END_REF]Carry et al. ( , 2010b) ) .

3-D Shape modeling with KOALA

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 ).

The KOALA algorithm minimizes the total

χ 2 = χ 2 LC + w AO χ 2 AO + w Occ χ 2
Occ that is composed of the individual contributions from light curves (LC), profiles from disk-resolved images (AO), and occultation chords (Occ). Adaptive optics and occultation data are weighted with respect to the lightcurves with parameters w AO and w Occ , respectively. Within each type of data, all the epochs are weighted uniformly. The optimum values of these weights can be objectively obtained following the approach of [START_REF] Kaasalainen | Maximum compatibility estimates and shape reconstruction with boundary curves and volumes of generalized projections[END_REF] .

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 [START_REF] Sierks | Images of asteroid (21) Lutetia: a remnant planetesimal from the early solar system[END_REF]. Before the encounter, the spin and 3-D shape of Lutetia had been deter-mined with KOALA , using lightcurves and AO images ( Carry et al., 2010b;[START_REF] Drummond | Physical properties of the ESA rosetta target asteroid (21) Lutetia. i. The triaxial ellipsoid dimensions, rotational pole, and bulk density[END_REF]. A comparison of the pre-flyby solution with the OSIRIS images showed that the spin vectorwas accurate to within 2 °and the diameter to within 2%. The RMS residual in the surface topography between the KOALA predictions and the OSIRIS images was only 2 km, for a 98 km-diameter asteroid ( Carry et al., 2012 ).

Spin and 3-D shape of Camilla

We used 127 optical lightcurves, 34 profiles from disk-resolved imaging, and 7 stellar occultation events to reconstruct the spin axis and 3-D shape of Camilla. The model fits well the entire data set, with mean residuals of only 0.03 mag for the lightcurves ( Figs. 6 andC.1 ), 0.29 pixel for the images ( Fig. 7 ), and 0.35 s for the stellar occultations ( Fig. 8 ). There are small local departures of the shape model from the stellar occultation chords that can be due to local topography not modeled with our low-resolution shape model.

The rotation period and coordinates of the spin axis ( Table 2 ) agree very well with previous results from lightcurve-only inversion and convex shape modeling [START_REF] Torppa | Shapes and rotational properties of thirty asteroids from photometric data[END_REF][START_REF] Ďurech | Combining asteroid models derived by lightcurve inversion with asteroidal occultation silhouettes[END_REF]Hanuš et al., 2016 ), as well as models obtained by combining lightcurves and smaller subsets of the present AO data (respectively 3 and 21 epochs, see [START_REF] Hanuš | Sizes of main-belt asteroids by combining shape models and Keck adaptive optics observations[END_REF]2017 ). The shape of Camilla is far from a sphere, with a strong ellipsoidal elongation along the equator (a/b axes ratio of 1.37 ± 0.12, see Table 2 ). Departures from the ellipsoid are, however, limited, and mainly consist in two large circular basins, reminiscent of impact craters ( Fig. 9 ).

The spherical-volume-equivalent diameter of Camilla is found to be 254 ± 36 km (3 σ ), in excellent agreement with the recent determination by [START_REF] Hanuš | Volumes and bulk densities of forty asteroids from ADAM shape modeling[END_REF] based on a similar data set. Both estimates are high compared to diameter estimates from infrared observations with IRAS, AKARI, or WISE [START_REF] Tedesco | IRAS Minor Planet Survey[END_REF][START_REF] Ryan | Rectified asteroid albedos and diameters from IRAS and MSX photometry catalogs[END_REF][START_REF] Usui | Asteroid catalog using akari: AKARI/IRC mid-Infrared asteroid survey[END_REF][START_REF] Masiero | Main belt asteroids with WISE/NEOWISE. i. preliminary albedos and diameters[END_REF] , see Table B.2). However, diameter determinations by mid-IR radiometry are based on disk-integrated fluxes. In the case of 2017) and developed here with lightcurves, disk-resolved images, and stellar occultation timings, providing direct size measurements, indeed argues for Camilla being larger than previously thought. The corresponding volume is 8.5 ± 1.2 • 10 6 km 3 . The uncertainty on the volume matches closely that of the diameter ( δV / V ≈ δD / D ) in the case of 3-D shape modeling, as shown by [START_REF] Kaasalainen | Shape reconstruction of irregular bodies with multiple complementary data sources[END_REF] , because it derives from the uncertainty on the radius of each vertex, which are correlated (unlike in the case of scaling a sphere).

Diameter of S1

We list in Table A.5 and display in Fig. 11 the 65 measured brightness differences with an uncertainty lower than 1 magnitude between Camilla and its largest satellite S1. We found a normal distribution of measurement, as expected from photon noise, and measure an average magnitude difference of m = 6.51 ± 0.27, similar to the value of 6.31 ± 0.68 reported by Marchis et al. (2008a) on 22 epochs.

Using the diameter of 254 ± 36 km for Camilla ( Section 5.3 ) and assuming S1 has the same albedo as Camilla itself (supported by their spectral similarity, see Section 4.3 ), this magnitude difference implies a size of 12.7 ± 3.5 km for S1, smaller than previously reported.

Diameter of S2

We list in Table A.6 and display in Fig. 12 the 11 measured brightness differences between Camilla and its smaller satellite S2. We measure an average magnitude difference of m = 9.0 ± 0.3 (already reported upon discovery, see [START_REF] Marsset | IAU Circular[END_REF].

Using the diameter of 254 ± 36 km for Camilla ( Section 5.3 ) and assuming S2 has the same albedo as Camilla itself as we did for S1, this magnitude difference implies a size of 4.0 ± 1.2 km for S2.

Discussion

Internal structure

Using the mass derived from the study of the dynamics of the satellites and the volume from the 3-D shape modeling, we infer a density of 1,280 ± 130 kg • m -3 (3 σ uncertainty), in agreement with previous reports by Marchis et al. (2008a) and [START_REF] Hanuš | Volumes and bulk densities of forty asteroids from ADAM shape modeling[END_REF] . This highlights how critically the density relies on accurate volume estimates: the summary of previous diameter determinations ( Table B.2 ), mainly based on indirect techniques, leads to a density of 1,750 ± 1,400 kg • m -3 (3 σ uncertainty, [START_REF] Carry | Density of asteroids[END_REF].

The low density found here is comparable to that of (87) Sylvia, a P-type of similar size, also orbiting in the Cybele region ( Berthier et al., 2014 ), and the D-/P-type Jupiter Trojans (617) Patroclus and (624) Hektor [START_REF] Mueller | Eclipsing binary trojan asteroid patroclus: thermal inertia from spitzer observations[END_REF][START_REF] Marchis | The puzzling mutual orbit of the binary trojan asteroid (624) hektor[END_REF][START_REF] Buie | Size and shape from stellar occultation observations of the double jupiter trojan patroclus and menoetius[END_REF]. As mentioned above (Section 4.2 ), the most-likely analog material for this type of asteroids are IDPs ( Vernazza et al., 2015 ). There is no measurement of IDP density in the laboratory. However, a density of 30 0 0 • m -3 for the silicate phase was reported by the StarDust mission ( Brownlee et al., 2006 ). Because these silicates are mixed with organic carbonaceous particles ( ≈ 2200 • m -3 ), the density of the bulk material is likely of ≈ 2600 • m -3 ( Greenberg, 2000;[START_REF] Pätzold | A homogeneous nucleus for comet 67p/Churyumov-Gerasimenko from its gravity field[END_REF]. A macroporosity of 50 ± 9% would thus be required to explain the density of Camilla, i.e., half of its volume would be occupied by voids. Because the pressure inside Camilla reaches 10 5 Pa less than 15 km from its surface (90% of the radius), it is unlikely that its structure can sustain such large voids. While silicate grains crush at 10 7 Pa, larger structures will not resist pressure significantly smaller, as the compressive strength decreases as the power -1/2 of the size [START_REF] Lundborg | The strength-size relation of granite[END_REF][START_REF] Britt | Asteroid density, porosity, and structure[END_REF].

An alternate explanation to the low density of Camilla may be that it contains large amounts of water ice. An absorption band due to hydration at 3 μm was indeed reported by [START_REF] Takir | Outer main belt asteroids: identification and distribution of four 3-μm spectral groups[END_REF] , whose shape is similar to those of the nearby (24) Themis and (65) Cybele and interpreted as water frost coating on surface grains [START_REF] Campins | Water ice and organics on the surface of the asteroid 24 themis[END_REF][START_REF] Licandro | 65) Cybele: detection of small silicate grains, water-ice, and organics[END_REF]. Because water ice sublimates on airless surfaces at the heliocentric distance of Themis, Camilla, and Cybele, the ice on the surface must be replenishment from sub-surface reservoir(s) [START_REF] Rivkin | Detection of ice and organics on an asteroidal surface[END_REF] We thus investigate the possible range of dust-to-ice mass ratios as function of macroporosity in Camilla ( Fig. 13 ). As expected, the porosity decreases with higher ice content and reaches 10 -30% for dust-to-ice mass ratios of 1-6. Therefore, the volume occupied by dust, ice, and voids would be 33 ± 10%, 47 ± 19%, and 20 ± 10% respectively, the latter being preferentially found in the outer-most volume of the asteroid body.

To test this, we compute the gravitational potential quadrupole J 2 = 0.042 ± 0.004 of the 3-D shape model ( Section 5.3 ) under the assumption of a homogeneous interior using the method of [START_REF] Dobrovolskis | Inertia of any polyhedron[END_REF] . Because the orbit of S1 fits 80 astrometric positions over 15 years to measurement accuracy under the assumption of a null J 2 ( Section 3.3 ), the mass distribution in Camilla must be more concentrated at the center, with a denser core , than suggested by its shape. Similar internal structure has already been suggested for (87) Sylvia and (624) Hektor by [START_REF] Berthier | Physical and dynamical properties of the main belt triple asteroid (87) sylvia[END_REF] and [START_REF] Marchis | The puzzling mutual orbit of the binary trojan asteroid (624) hektor[END_REF] . Considering a core of pure silicate, and an outer shell of porous ice matching the masses above, the core radius would be 87 ± 8 km or 68 ± 7% of the radius of Camilla. Additional observations of S2 to determine precisely its orbit are now required to test further the internal structure of Camilla.

Future characterization of Camilla triple system

Owing to the large magnitude difference between Camilla and its satellites (6.5 and 9 mag.), constraining the size and orbit of the satellites by photometric observations of mutual event (eclipses and occultations, see, e.g., [START_REF] Scheirich | Modeling of lightcurves of binary asteroids[END_REF][START_REF] Carry | The small binary asteroid (939) isberga[END_REF] is not feasible. Observation of S2 will therefore rely on direct imaging such as presented here, or stellar occultations which can moreover provide a direct measurement of the diameter of the satellites. To this effect, we list in Table D.1 a selection of stellar occultations that will occur in the next three years.

Similarly to our work on (87) Sylvia which led to the observation of a stellar occultation by its satellite Romulus ( Berthier et al., 2014 ), we will continuously update the occultation path of Camilla and of its satellites, for these events. The precision of such predictions will benefit from each successive data release of the ESA Gaia astrometry catalogs [START_REF] Tanga | Asteroid occultations today and tomorrow: toward the GAIA era[END_REF]Gaia Collaboration et al., 2016;[START_REF] Spoto | Ground-based astrometry calibrated by gaia DR1: new perspectives in asteroid orbit determination[END_REF], that will reduce the uncertainty on the path of Camilla itself to a few kilometers. The uncertainty on the occultation path of the satellites will then mostly derive from the uncertainty on their orbital parameters, and we provide them in Table D.1 . The orbit of S2 being little constrained, the uncertainty on its position for upcoming occultations is very large. Initial improvement must thus rely on direct imaging of the system.

Summary

In the present study, we have acquired and compiled optical lightcurves, stellar occultations, visible and near-infrared spectra, and high-contrast and high-angular-resolution images and spectroimages from the Hubble Space Telescope and large ground-based telescopes (Keck, Gemini, VLT) equipped with adaptive-optics-fed cameras.

Using 80 positions spanning 15 years, we study the dynamics of the largest satellite, S1, and determine its orbit around Camilla to be circular, equatorial, and prograde. The residuals between our dynamical solution and the observations are 7.8 mas, corresponding to a sub-pixel accuracy. Using 11 positions of the second, smaller, satellite S2 that we discovered in 2015, we determine a preliminary orbit, marginally inclined from that of S1 and more eccentric. Predictions of the relative position of the satellite with respect to Camilla, critical for planning stellar occultations for instance, are available to the community through our VO service

Miriade5 ( Berthier et al., 2008 ).

From the visible and near-infrared spectrum of Camilla, we classify it as an Xk-type asteroid, in the Bus-DeMeo taxonomy [START_REF] Demeo | An extension of the bus asteroid taxonomy into the near-infrared[END_REF]. Considering its low albedo, it would be classified as a P-type in older taxonomic schemes such as Tedesco's [START_REF] Tedesco | Three-parameter asteroid taxonomy classifications[END_REF]. Using VLT/SPHERE integral-field spectrograph, we measure the near-infrared spectrum of the largest satellite, S1, and compare it with Camilla. No significant differences are found. This, together with its orbital parameters, argue for a formation of the satellite by excavation from impact, re-accumulation of ejecta in orbit, and circularization by tides.

Using optical lightcurves, profiles from disk-resolved imaging, and stellar occultation events, we determine the spin-vector coordinates and 3-D shape of Camilla. The model fits well each data set, and we find a spherical-volume-equivalent diameter of 254 ± 36 km. By combining the mass from the dynamics with the volume of the shape model, we find a density of 1,280 ± 130 kg • m -3 . Considering Camilla's most likely analog material are IDPs, this implies a macroporosity of 50 ± 9%, likely too high to be sustained. By considering a mixture of ice and silicate, the macroporosity could be in the range 10-30% for a dust-to-ice mass ratio of 1-6, the denser material being concentrated toward the center as suggested by the dynamics of the system.

Appendix A. Details on the observing data sets

We provide here the details for each lightcurve ( Table A.1 ), disk-resolved image ( Table A.2 ), and stellar occultation ( Table A.4 ), as well as the astrometry and photometry of S1 ( Table A.5 ) and S2 ( Table A.6 ). Date, mid-observing time (UTC), heliocentric distance ( ) and range to observer ( r ), phase angle ( α), apparent size ( ), longitude ( λ) and latitude ( β) of the subsolar and subobserver points (SSP, SEP). B.2 for details.

Date UTC r α SEP λ SEP β SSP λ SSP β (AU) (AU) ( °) ( ) ( °) ( °) ( °) ( °) 1

Table B.1

The mass estimates ( M ) of (107) Camilla collected from the literature. For each, the 3 σ uncertainty, method, selection flag, and bibliographic reference are reported.

  (see Fig. B.1 and Table

Fig. 1 .

 1 Fig. 1. Examples of AO images from Gemini, Keck, and ESO VLT. The first two panels (1 & 2, August 13, 2003, from Keck) show a typical AO image, before and after halo subtraction: Camilla dominates the background and makes the satellites hard to detect. The remaining panels show halo-subtracted images from different dates, with small circles indicating the positions of the bright satellite S1 and the fainter S2 (frames 9 and 10 only). On these panels, the images before subtraction are also shown in the central circle to highlight the elongated shape of Camilla.

Fig. 2 .

 2 Fig. 2. Distribution of residuals for S1 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. The top panel shows the histogram of residuals along X, and the right panel the residuals along Y. The light gray Gaussian in the background has a standard deviation of one.

Fig. 3 .

 3 Fig. 3. Similar to Fig. 2 , but for S2.

Fig. 4 .

 4 Fig. 4. Coordinates and 1 -2 -3 σ contours of Camilla's spin axis (blue) and the orbital poles of S1 (gray) and S2 (red) in ecliptic coordinates. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 .

 5 Fig. 5. Visible and near-infrared spectrum of Camilla from IRTF (green and black dots) and SPHERE (red squares, offset by +0.1), and its moon S1 from SPHERE (blue triangles, offset by -0 .15). Gray areas represent the wavelength ranges affected by water vapour in the atmosphere. All spectra were normalized to unity at one micron. Overplot to the IRTF spectra is the Bus-DeMeo Xk class. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .

 6 Fig. 6. Examples of optical lightcurves of Camilla. For each epoch, the upper panel presents the observed photometry (grey spheres) compared with synthetic lightcurves generated with the shape model (black lines). The lower panel shows the residuals between the observed and synthetic flux. The observing date, number of points, duration of the lightcurve (in hours), phase angle ( α), and RMS residuals between the observations and the synthetic lightcurves are displayed. In most cases, measurement uncertainties are not provided by the observers but can be estimated from the spread of measurements. See Fig. C.1 for the entire data set.

Fig. 7 .

 7 Fig. 7. All 34 profiles of Camilla from disk-resolved images, compared with the projection of the shape model on the plane of the sky. On each panel, corresponding to a different epoch, the grey shaded areas correspond to the 1-2-3 σ confidence intervals of each profile, while the shape model is represented by the wired mesh.

Fig. 8 .

 8 Fig.8. The seven stellar occultations by Camilla, compared with the shape model projected on the plane of the sky for the times of the occultations. The observer of northern chord in the first occultation, presenting a clear mismatch with the shape model, reported the presence of thin cirrus that may explain the discrepancy.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Topographic map of Camilla, with respect to its reference ellipsoid ( Table2). The main features are the two deep and circular basins located at (87 °, -23 °) and (278 °+33 °).

Fig. 11 .

 11 Fig. 11. Distribution of the magnitude differences between Camilla and its largest satellite S1, compared with previous report from Marchis et al. (2008a) . The dashed black line represents the normal distribution fit to our results, with a mean and standard deviation of 6.51 ± 0.27.

Fig. 12 .

 12 Fig. 12. Distribution of the magnitude differences between Camilla and its second satellite S2. The dashed black line represents the normal distribution fit to our results, with a mean and standard deviation of 9.0 ± 0.3.

Fig. 13 .

 13 Fig. 13. Top: Dust density as function of its volumetric fraction for different porosities (10, 30, 50%). The expected range from pure organics to pure silicates is represented in shaded gray. Expected range is highlighted in gold. Bottom: Dust-to-ice mass ratios as function of the volumetric fraction of dust.

Fig. B. 2 .

 2 Fig. B.2. Diameter estimates of (107) Camilla gathered from the literature, see TableB.2 for details.

Fig. C. 1 .

 1 Fig. C.1.The optical lightcurves of Camilla (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 from the shape model are displayed. In many cases, measurement uncertainties are not provided by the observers but can be estimated from the spread of measurements.

Fig. C. 1 .

 1 Fig. C.1. Suite of all lightcurve plots, as described in Fig. 6 . (Continued).

Fig

  Fig. C.1. Continued

Table A .1

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

	Table A.2
		Table A.1 ( continued )
			Date		L	N p	α	Filter	RMS	IAU	Observers
					(h)		( °)			(mag)
		63	2008-06-23	4.2	83	16.4	clear	0.036	950	SuperWASP -J. Grice
		64	2008-06-24	4.1	81	16.5	clear	0.032	950	SuperWASP -J. Grice
		65	2008-06-27	1.7	63	16.6	C		0.019	181	Polishook (2009)
		66	2008-06-28	2.0	82	16.6	C		0.018	181	Polishook (2009)
		Date 67 68	L 2010-07-09 2010-07-10	N p 2.7 3.3	86 α 89	10.7 Filter 10.5	C C	RMS	0.019 IAU 0.019	615 Observers J. Montier & S. Heterier 517 F. Reignier
		69	(h) 2010-07-10	3.9	( °) 57	10.5	(mag) clear	0.063	950	SuperWASP -J. Grice
	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58	1981-02-01 70 2010-07-11 4.0 1981-02-02 6.2 71 2010-07-11 1981-02-04 7.7 72 2010-07-11 1981-02-05 5.6 73 2010-07-13 1982-01-09 2.4 74 2010-07-14 1982-01-15 4.4 75 2010-07-14 1982-05-20 4.5 76 2010-07-16 1982-06-23 4.6 77 2010-07-18 1982-06-24 2.1 78 2010-07-19 1982-06-25 2.9 79 2010-07-20 1983-03-27 2.0 80 2010-07-23 1983-03-29 4.3 81 2010-07-23 1983-05-24 4.8 82 2010-08-01 1983-07-03 4.7 83 2010-08-03 1984-06-07 2.2 84 2010-08-30 1984-06-10 4.6 85 2010-08-31 1984-07-05 3.0 86 2010-09-02 1984-08-16 5.5 87 2010-09-03 1985-10-20 4.6 88 2010-09-04 1987-02-06 2.7 89 2010-09-05 1987-02-07 4.7 90 2010-09-08 1988-04-25 4.7 91 2010-09-08 1988-04-26 3.6 92 2010-09-09 1988-04-29 2.9 93 2010-09-11 2004-09-19 6.8 94 2010-09-30 2004-11-05 5.6 95 2010-10-01 2008-03-07 2.0 96 2015-04-20 2008-03-13 5.2 97 2015-04-21 2008-03-17 3.0 98 2015-04-23 2008-03-18 5.3 99 2015-04-24 2008-03-29 3.3 100 2015-05-09 2008-03-29 4.0 101 2015-05-11 2008-03-30 4.5 102 2015-05-12 2008-04-01 5.0 103 2015-05-13 2008-04-13 4.8 104 2015-05-17 2008-04-13 0.7 105 2015-05-18 2008-04-16 4.9 106 2015-05-19 2008-04-16 4.1 107 2015-05-20 2008-04-22 4.2 108 2015-05-21 2008-04-22 5.3 109 2015-05-22 2008-04-23 3.9 110 2015-05-23 2008-04-23 3.3 111 2015-05-24 2008-04-24 3.2 112 2015-05-26 2008-04-24 3.7 113 2015-06-03 2008-04-27 2.4 114 2015-06-03 2008-04-28 3.3 115 2015-06-04 2008-04-29 5.2 116 2015-06-05 2008-05-04 1.4 117 2015-06-05 2008-05-09 3.8 118 2015-06-09 2008-05-10 3.2 119 2015-06-10 2008-05-10 4.6 120 2015-06-11 2008-05-12 3.6 121 2015-06-17 2008-05-12 3.9 122 2015-06-20 2008-05-13 4.5 123 2015-06-22 2008-05-19 2.4 124 2015-06-23 2008-05-20 3.8 125 2015-06-25 2008-05-31 1.5 126 2015-06-26 2008-06-05 1.1 127 2015-07-06	5 3.1 9 4.1 10 4.1 14 4.0 11 4.3 8 4.4 19 3.3 6 2.7 8 3.3 15 3.1 10 2.4 5 5.0 35 5.3 23 2.7 11 5.1 10 5.3 15 1.6 32 5.2 21 5.1 20 3.4 17 5.2 15 0.9 20 1.8 16 5.1 15 1.9 37 4.0 20 3.6 76 5.7 53 5.5 105 6.6 29 1.4 40 4.9 22 5.8 61 5.2 69 3.8 14 5.8 65 5.1 128 6.0 58 5.8 77 5.4 44 6.3 36 1.0 44 1.9 51 3.6 32 5.5 52 4.2 61 5.0 19 4.9 47 3.2 93 3.0 109 1.4 66 5.4 81 28.2 67 5.8 119 2.2 69 4.7 44 3.8 13 3.8	2.9 140 2.8 85 2.7 86 2.8 87 16.4 93 16.6 96 10.6 91 15.8 91 15.9 106 16.0 104 15.5 54 15.4 97 7.6 112 6.1 47 14.8 109 14.5 114 10.7 22 2.3 111 3.0 111 13.6 71 13.8 73 13.1 32 13.3 23 13.9 103 2.0 54 13.7 84 11.5 70 10.7 108 9.4 87 8.7 118 5.5 24 5.5 84 5.2 44 4.6 85 2.2 58 2.2 89 2.2 61 2.4 91 3.7 106 3.7 98 4.0 102 4.0 14 4.2 36 4.2 68 5.1 251 5.4 76 5.7 75 7.1 274 7.7 59 8.5 38 8.8 27 9.0 98 9.3 376 9.6 104 10.8 40 11.3 88 13.5 70 14.3 71	V 10.3 V 10.2 V 10.0 V 9.8 V 9.6 V 9.4 V 8.9 V 8.4 V 8.2 V 7.9 V 7.4 V 7.2 V 4.8 V 4.3 V 4.7 V 5.0 V 5.5 V 5.8 V 6.0 V 6.3 V 7.1 V 7.3 V 7.6 V 7.8 C 12.0 C 12.1 clear 8.2 clear 7.9 clear 7.4 clear 7.2 clear 3.9 clear 3.6 clear 3.6 clear 3.5 clear 3.5 clear 3.6 clear 3.7 clear 3.8 clear 4.0 clear 4.1 clear 4.3 clear 4.5 clear 4.9 clear 6.8 clear 6.8 clear 7.0 clear 7.3 clear 7.3 clear 8.3 clear 8.5 clear 8.7 clear 10.1 clear 10.7 clear 11.2 clear 11.4 clear 11.8 C 12.0 clear 13.7	0.012 0.023 clear C 0.018 clear 0.016 clear 0.021 clear 0.047 clear 0.028 clear 0.030 clear 0.037 clear 0.020 clear 0.048 clear 0.070 clear 0.027 clear 0.021 clear 0.026 clear 0.019 clear 0.047 clear 0.024 clear 0.019 clear 0.018 clear 0.019 clear 0.023 clear 0.027 clear 0.032 clear 0.013 clear 0.025 clear 0.060 R 0.029 R 0.028 R 0.036 R 0.028 R 0.033 R 0.021 R 0.025 R 0.041 R 0.011 R 0.033 R 0.027 R 0.040 R 0.029 R 0.030 R 0.023 R 0.019 R 0.020 R 0.021 V 0.033 R 0.029 R 0.025 V 0.028 R 0.026 R 0.028 R 0.022 R 0.048 R 0.036 R 0.048 R 0.048 R 0.030 R 0.043 R	654 0.020 654 0.024 654 0.031 654 0.087 695 0.040 695 0.143 695 0.028 695 0.036 695 0.043 695 0.035 695 0.035 695 0.052 695 0.037 695 0.035 695 0.038 695 0.029 695 0.023 809 0.030 695 0.030 695 0.070 695 0.029 695 0.031 695 0.024 695 0.033 A14 0.042 A14 0.052 950 0.028 950 0.027 950 0.025 950 0.023 950 0.024 950 0.021 950 0.029 950 0.022 950 0.025 950 0.018 950 0.024 950 0.021 950 0.021 950 0.021 950 0.021 950 0.024 950 0.021 950 0.022 950 0.026 950 0.025 950 0.019 950 0.026 950 0.024 950 0.021 950 0.024 950 0.024 950 0.023 950 0.052 950 0.036 950 0.026 181 0.029 950 0.029	615 Harris and Young (1989) J. Montier & S. Heterier 950 SuperWASP -J. Grice Harris and Young (1989) 950 SuperWASP -J. Grice Harris and Young (1989) 950 SuperWASP -J. Grice Harris and Young (1989) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice di Martino et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1987) 950 SuperWASP -J. Grice Weidenschilling et al. (1990) 950 SuperWASP -J. Grice Weidenschilling et al. (1990) 950 SuperWASP -J. Grice Weidenschilling et al. (1990) 950 SuperWASP -J. Grice Weidenschilling et al. (1990) 950 SuperWASP -J. Grice Weidenschilling et al. (1990) 950 SuperWASP -J. Grice L. Bernasconi 950 SuperWASP -J. Grice L. Bernasconi 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 517 D. Romeuf SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 517 D. Romeuf SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 586 S. Fauvaud SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier SuperWASP -J. Grice 181 F. Vachier Polishook (2009) SuperWASP -J. Grice 181 F. Vachier
	59	2008-06-06	4.5	19	14.7	clear		0.032	950	SuperWASP -J. Grice
	60	2008-06-06	1.2	20	14.9	clear		0.049	950	SuperWASP -J. Grice
	61	2008-06-10	4.8	83	15.0	clear		0.044	950	SuperWASP -J. Grice
	62	2008-06-10	2.4	46	16.3	clear		0.039	950	SuperWASP -J. Grice
										( continued on next page )

Previous determinations of mass and diameter

  Date, number of positive and negative chords (# p and # n ), average uncertainty in seconds ( σ s ) and kilometers ( σ k ), and RMS residuals with seconds, kilometers, and expressed in amount of standard deviation. Astrometry of S1. Date, mid-observing time (UTC), telescope, camera, filter, astrometry ( X is aligned with Right Ascension, and Y with Declination, and o and c indices stand for observed and computed positions), and photometry (magnitude difference M with uncertainty δM ). PIs of these observations were: * A. Storrs, a J.-L. Margot, b W. J. Merline, c L. Sromovsky, d F. Marchis, e P. Rojo, and f M. Marsset. Astrometry of S2. Date, mid-observing time (UTC), telescope, camera, filter, astrometry ( X is aligned with Right Ascension, and Y with Declination, and o and c indices stand for observed and computed positions), and photometry (magnitude difference M with uncertainty δM ). The PI of these observations was M. Marsset.

	Appendix B.
	Table A.5 ( continued )
	Table A.3 ( continued ) Date UTC	Tel.	Cam.	Filter	X o		Y o	X o-c		Y o-c	σ		M	δM
						(mas)		(mas)	(mas)	(mas)	(mas)	(mag)	(mag)
	2003-08-15 2003-08-17 Observer 2 2010-10-31 05:58:48.4 2010-10-31 06:03:23.2 3 2009-06-07 4 2010-06-28 2011-09-27 05:04:41.0 2015 May 06 08:35:22 10:50:07 Gemini Gemini 11:25:55 10:19:28 VLT Dan Caton Table A.5 2011-09-29 05:21:18.0 VLT 5 2004-09-01 05:17:22 Steve Messner 2011-11-08 03:21:35.3 VLT 6 2004-09-08 06:41:20 Roger Venable 2011-11-10 01:22:04.0 VLT 7 2004-09-13 03:42:51 Roger Venable 2015-05-29 04:38:46.4 VLT 8 2004-09-13 05:47:28 Roger Venable 2015-05-29 04:38:46.4 VLT 9 2004-09-14 04:09:30 10 2004-09-14 07:06:44 11 2004-09-14 07:14:31 Chris Anderson Chuck McPartlin 2015 August 23 Location 3.75 3.75 NIRI b NIRI b 3.68 3.74 NACO d Boone, NC NACO d 3.66 Bevier, MO NACO e 3.65 Elgin, SC NACO e 3.65 New Holland, SC 2.87 2.88 Kp Kp 2.71 3.04 H H 2.67 H 2.65 H 2.65 SPHERE f Ks 3.65 2.65 Hepzibah, GA SPHERE f YJH 3.65 2.65 3.65 2.65 3.65 2.65 Twin Falls, ID Santa Barbara, CA Date UTC Tel. Cam. Filter 2015-05-29 04:51:27.2 VLT SPHERE f YJH 2015-05-29 04:51:27.2 VLT SPHERE f Ks 2015-05-29 05:07:36.3 VLT SPHERE f Ks 12 2004-09-15 04:18:34 3.65 2.65 Steve Preston Carnation, WA 2001-03-01 05:48:13.0 HST ACS * F439W 2015-05-29 05:07:36.3 VLT SPHERE f YJH 13 2004-09-15 04:26:55 3.65 2.65 Andrea Dobson/Larry North Walla Walla, WA 2001-03-01 06:00:12.9 HST ACS * F791W 2015-05-29 05:15:13.1 VLT SPHERE f YJH 14 2004-09-16 04:48:18 3.65 2.65 Tony George Umatilla, OR 2002-05-08 10:46:01.0 Keck NIRC2 a Kp 2015-05-29 05:15:13.1 VLT SPHERE f Ks 15 2004-10-07 02:12:52 3.64 2.72 Chad Ellington Tumwater, WA 2003-06-06 14:03:06.0 Keck NIRC2 b Ks 2015-05-29 05:25:55.5 VLT SPHERE f Ks 16 2004-10-08 02:22:37 3.64 2.73 Chris Anderson Twin Falls, ID 2003-06-06 14:08:23.2 Keck NIRC2 b Ks 2015-05-29 05:28:59.5 VLT SPHERE f YJH 17 2011-11-08 03:21:35 3.50 2.59 David Becker Grasmere, ID 2003-06-06 14:13:30.2 Keck NIRC2 b Ks 2015-05-29 05:28:59.5 VLT SPHERE f Ks 18 2011-11-10 01:22:04 3.50 2.61 William Gimple Greenville, CA 2003-07-15 07:32:50.4 VLT NACO b H 2015-05-29 05:32:04.0 VLT SPHERE f Ks 19 2015-05-29 04:38:45 3.58 2.61 Charles Arrowsmith Quincy, CA 2003-07-15 07:37:26.2 VLT NACO b H 2015-05-29 05:32:04.0 VLT SPHERE f YJH 20 2015-05-29 04:51:26 3.58 2.61 Tom Beard Reno, NV 2003-08-14 10:35:08.0 Keck NIRC2 a H 2016-07-02 08:47:22.2 VLT SPHERE f YJH 21 2015-05-29 05:07:36 3.58 2.61 Jerry Bardecker Gardnerville, NV 2003-08-15 08:35:22.2 Keck NIRC2 c Kp 2016-07-12 05:04:19.4 VLT SPHERE f YJH 22 2015-05-29 05:15:12 3.58 2.61 Ted Swift Davis, CA 2003-08-15 08:39:27.2 Keck NIRC2 c Kp 2016-07-12 05:11:41.7 VLT SPHERE f YJH 23 2015-05-29 05:25:54 3.58 2.61 2016 July 21 2003-08-17 10:50:08.0 Keck NIRC2 b Kp 2016-07-12 05:19:03.9 VLT SPHERE f YJH 24 2015-05-29 05:28:58 3.58 2.61 Derek Breit Morgan Hill, CA 2003-08-17 10:53:39.3 Keck NIRC2 b Kp 2016-07-28 05:50:56.0 VLT SPHERE f YJH 25 2015-05-29 05:32:04 3.58 2.61 Bob Dunford Naperville, IL 2004-09-01 05:07:38.3 VLT NACO d Ks 2016-07-28 05:57:12.3 VLT SPHERE f YJH 26 2016-07-12 05:06:10 3.72 2.72 Brad Timerson Newark, NY 2004-09-01 05:17:22.2 VLT NACO d H 2016-07-28 06:03:30.1 VLT SPHERE f YJH 27 2016-07-12 05:13:32 3.72 2.72 Kevin Green Westport, CT 2004-09-01 08:06:43.4 VLT NACO d Ks 2016-07-30 01:37:12.1 VLT SPHERE f YJH 28 2016-07-12 05:20:55 3.72 2.72 Steve Conard Gamber, MD 2004-09-03 06:51:57.5 VLT NACO d Ks 2016-07-30 01:44:17.2 VLT SPHERE f YJH 29 2016-07-28 05:52:47 3.72 2.74 Gary Frishkorn Sykesville, MD 2004-09-05 04:28:20.2 VLT NACO d Ks 2016-07-30 01:51:22.2 VLT SPHERE f YJH 30 2016-07-28 05:59:03 3.72 2.74 Andy Scheck Scaggsville, MD 2004-09-08 06:41:20.1 VLT NACO d Ks 2016-08-11 00:18:43.4 VLT SPHERE f YJH 31 2016-07-28 06:05:21 3.72 2.74 David Dunham/Joan Dunham Greenbelt, MD 2004-09-11 04:34:26.2 VLT NACO d Ks 2016-08-11 02:41:34.1 VLT SPHERE f YJH 32 2016-07-30 01:39:02 3.72 2.75 Paul Maley Clifton, TX 2004-09-13 03:42:52.5 VLT NACO d Ks 2016-08-11 02:48:41.5 VLT SPHERE f YJH 33 2016-07-30 01:46:07 3.72 2.75 Ned Smith Trenton, GA 2004-09-13 05:47:28.2 VLT NACO d Ks 2016-08-11 02:55:50.8 VLT SPHERE f YJH 34 2016-07-30 01:53:12 3.72 2.75 Ernie Iverson Lufkin, TX 2004-09-14 04:09:30.3 VLT NACO d Ks 2004-09-15 04:18:34.3 VLT NACO d Ks 2004-09-15 04:26:56.5 VLT NACO d H	8.5 9.0 Latitude 0.119 0.117 ( °) -271 -8 Longitude 46.0 271.7 ( °) 27 -290 -2 10 5.0 0.124 267.1 12.6 0.116 231.4 -287 236 5 36.2514 -81.4122 440 -217 -3 3.7 0.118 120.4 39.7722 -92.5243 -438 -61 -6 1.5 0.119 129.5 34.1476 -80.7502 386 93 5 0.2 0.142 71.4 33.7397 -81.5201 -188 240 3 0.2 0.126 277.1 33.3394 -82.1542 -184 237 6 0.4 0.138 54.6 0.5 0.139 195.0 0.5 0.133 185.4 42.5839 -114.4703 34.4568 -119.7951 X o Y o X o-c -176 239 4 (mas) (mas) (mas) -180 241 1 -166 245 3 0.7 0.140 59.6 47.6437 -121.9224 -573 -84 -22 -164 241 5 0.7 0.134 49.2 46.0044 -118.8928 -565 -70 -20 -157 242 6 1.1 0.134 38.9 45.9221 -119.2983 472 -189 -4 -158 245 5 7.4 0.141 212.4 46.9763 -122.9111 402 -214 -5 -152 245 3 7.6 0.136 216.6 42.5839 -114.4703 406 -213 1 -148 243 4 7.7 0.131 283.0 42.6733 -115.8981 402 -218 -1 -150 247 3 8.2 0.134 103.6 40.1377 -120.8667 -540 216 8 -148 245 2 5.4 0.120 350.8 39.9477 -120.9691 -536 222 10 -146 243 4 5.4 0.118 335.1 39.3729 -119.8312 -183 227 5 -279 -90 -5 5.5 0.120 315.0 38.8899 -119.6723 554 -62 5 601 -129 -9 5.5 0.122 305.6 38.5522 -121.7856 550 -66 0 601 -130 -10 5.5 0.125 292.4 -568 146 8 601 -129 -10 5.5 0.126 288.6 37.1133 -121.7028 -567 144 9 -208 -138 7 5.5 0.127 284.7 41.759 -88.1167 504 -164 4 -212 -137 8 3.4 0.140 233.1 43.0066 -77.1185 510 -165 5 -216 -135 7 3.4 0.142 224.0 41.1714 -73.3278 576 -169 8 192 141 -1 3.4 0.137 214.8 39.4692 -76.9516 -623 166 -21 194 135 -4 4.8 0.139 74.3 39.2316 -76.9929 624 -163 6 199 135 -4 4.8 0.139 66.5 39.1497 -76.8871 211 -120 4 579 -159 -9 4.8 0.140 58.7 38.9866 -76.8694 -539 87 -5 559 -189 -6 5.2 0.128 61.0 31.6814 -97.6744 470 -75 1 560 -189 -3 5.2 0.129 52.3 34.893 -85.4711 386 -46 -15 556 -194 -5 5.2 0.130 43.5 31.3213 -94.84 4 4 -500 153 -9 -321 35 0 Average 1 -315 36 0 Standard deviation 8	12.8 13.0 Disappearance 54.7 280.9 (UT) -8 21.90 12.0 Reappearance 6.67 (UT) -3 21.90 6.87 12.0 15.9 264.3 20.1 -1.9 221.2 12 13.24 6.39 5:23:07.46 5:23:19.46 -8 13.24 7.04 5.7 -8.5 117.3 5:24:02.71 5:24:20.96 0 13.24 6.66 -6.3 -7.6 128.3 5:22:54.75 5:23:09.05 17 13.24 7.35 -6.7 -7.0 71.6 Miss Miss 0 12.26 6.29 -6.9 -7.0 277.2 Miss Miss -3 7.40 6.28 -6.9 -6.9 55.0 -7.0 -6.9 195.5 -7.0 -6.9 185.9 Miss Miss Miss Miss Y o-c σ M -1 7.40 6.30 δM 0.05 0.06 1.09 1.18 0.06 0.17 0.06 0.07 0.13 (mas) (mas) (mag) 0 12.26 6.26 0.09 (mag) 2 12.26 6.26 0.06 -7.0 -6.8 60.3 4:17:35.07 4:17:42.89 1 10.00 0.00 0.00 -1 7.40 6.35 0.09 -7.0 -6.8 49.9 4:17:49.06 4:17:59.13 13 10.00 0.00 0.00 0 7.40 6.43 0.30 -7.0 -6.6 39.9 4:17:47.72 4:17:58.54 15 9.94 6.34 1.50 2 12.26 6.35 0.17 -7.1 -4.3 218.7 4:17:31.85 4:17:44.46 -8 9.94 6.53 1.18 1 12.26 6.36 0.16 -8.1 -4.2 223.2 4:18:14.41 4:18:27.46 -8 9.94 7.18 0.45 0 7.40 6.49 0.16 -8.1 -13.0 289.4 4:18:10.17 4:18:23.25 -12 9.94 6.31 0.23 2 12.26 6.34 0.08 -17.7 -12.9 110.5 Miss Miss 7 27.00 6.56 0.02 0 12.26 6.42 0.09 -17.8 18.1 354.8 Miss Miss 12 27.00 6.34 0.14 -1 7.40 6.51 0.17 22.0 18.1 339.1 Miss Miss -4 9.94 5.04 3.68 -4 7.40 6.68 0.28 22.0 18.1 319.1 Miss Miss -1 9.94 6.67 0.18 1 7.40 6.55 0.19 22.0 18.1 309.6 Miss Miss -5 9.94 6.62 0.31 1 7.40 6.51 0.06 22.0 18.1 296.4 2 9.94 6.55 1.21 4 7.40 6.49 0.03 22.0 18.1 292.6 Miss Miss 0 9.94 6.39 0.66 -5 7.40 6.96 0.24 22.0 18.1 288.8 Miss Miss 1 13.24 6.06 0.31 -6 7.40 7.10 0.06 22.0 10.4 233.3 Miss Miss 0 13.24 6.34 0.24 -5 7.40 7.07 0.19 13.8 10.4 224.1 Miss Miss -1 13.24 6.98 0.43 0 7.40 6.90 0.20 13.8 10.4 215.0 Miss Miss 2 13.24 6.76 0.70 -4 7.40 6.78 0.23 13.8 11.8 79.0 7:41:59.05 7:42:04.22 0 13.24 6.73 0.09 -2 7.40 6.65 0.44 13.2 11.8 71.3 7:41:57.87 7:42:06.68 -8 13.24 6.95 0.59 6 7.40 6.18 0.07 13.2 11.8 63.5 7:41:56.97 no report -9 13.24 7.09 1.15 5 7.40 6.54 0.23 13.2 11.9 66.3 7:43:26.99 7:43:40.62 0 13.24 7.23 1.22 6 7.40 6.43 0.08 13.1 11.9 57.5 7:42:28.72 7:42:42.92 6 13.24 6.08 1.51 2 7.40 6.43 0.07 13.1 11.9 48.7 13.1 7:43:15.48 7:43:27.47 -1 13.24 6.59 0.14 4 13.24 6.28 0 18 6.50 0.46 1.20 6 13.24 7.30 0.69 7 7 0.28 0.61
	2004-10-07	02:02:03.0	VLT	NACO d	Ks	-540	123	4	-4	13.24		8.49	1.55
	2004-10-08	02:22:38.3	VLT	NACO d	Ks	356	-106	3	0		13.24		8.22	2.62
	2004-10-08	04:47:21.2	VLT	NACO d	Ks	435	-125	3	-1	13.24		7.07	1.05
	2004-10-20	00:39:22.2	VLT	NACO d	Ks	553	-136	8	0		13.24		6.55	0.19
	2004-11-02	07:36:13.0	Gemini	NIRI b	Kp	-344	88		-2	0		21.90		6.49	0.62
	2004-11-02	07:38:36.9	Gemini	NIRI b	Kp	-340	90		0	2		21.90		6.40	0.29
	2004-11-05	08:09:18.1	Gemini	NIRI b	Kp	-538	138	-6	1		21.90		5.95	0.16
	Table A.3 2005-12-21	09:05:51.5	Gemini	NIRI d	Ks	684	0		8	-6	21.90		6.53	0.02
	Timing and location of each observer for the stellar occultations used in this work. 2006-01-01 10:17:12.1 Gemini NIRI d Ks 651 -35 6	-7	21.90		6.71	0.17
	Observer 2006-01-09 2006-01-16 Table A.6	05:20:11.1 05:16:51.5	Location Gemini NIRI d Gemini NIRI d	Ks Ks	Latitude 557 619	Longitude 116 17 -17 22	Disappearance 1 21.90 31 21.90	Reappearance 5.86 0.34 5.85 0.28
	2009-06-07	10:29:14.1	Keck	NIRC2 b	H	( °) 510	54	( °)	0	(UT) -1	9.94	(UT) 6.56	0.44
	2004 September 5 Cave Creek Desert, AZ 10:32:18.1 Randy Peterson 2009-06-07 Keck NIRC2 b H Table A.4 2009-06-07 10:54:08.0 Keck NIRC2 b Kp Paul Maley/Syd Leach Fountain Hills, AZ Scott Donnell Eastonville, CO 2009-06-07 11:23:04.0 Keck NIRC2 b Kp 2009-06-07 11:25:56.5 Keck NIRC2 b Kp Date UTC Tel. Cam. Filter 2009-08-16 06:47:02.0 Keck NIRC2 d FeII 2010 September 16 Kerry Coughlin LaPaz, Baja, Mexico Roc Fleishmann Todos Santos, Baja, Mexico Date UT # p # n 2010-08-15 08:07:02.0 Gemini NIRI d Kp 2015-05-29 04:38:46.4 VLT SPHERE YJH (h) 2010-08-15 08:16:53.5 Gemini NIRI d Kp 2015-05-29 04:51:27.2 VLT SPHERE YJH 2010-08-28 08:49:11.1 Gemini NIRI d Kp 2015-05-29 05:07:36.3 VLT SPHERE YJH 2015 January 01 Andy Scheck Scaggsville, MD 1 2004-09-05 08:54 3 0 2010-08-28 08:54:01.0 Gemini NIRI d Kp 2015-05-29 05:15:13.1 VLT SPHERE YJH Bob Dunford Naperville, IL 2 2010-09-16 04:01 1 1 2010-09-02 06:45:32.3 Gemini NIRI d Kp 2015-05-29 05:32:04.0 VLT SPHERE YJH Chad Ellington Owings, MD 3 2015-01-01 11:26 1 2 4 2015-02-12 11:58 2 0 2016-07-12 05:04:19.4 VLT SPHERE YJH 2016-07-12 05:11:41.7 VLT SPHERE YJH 2015 February 12 Derek Breit Morgan Hill, CA 5 2015-05-06 05:23 3 4 2016-07-12 05:19:03.9 VLT SPHERE YJH Derek Breit (double star) Morgan Hill, CA 6 2015-08-23 04:17 6 5 2016-07-30 01:37:12.1 VLT SPHERE YJH Ted Blank Payson, AZ 7 2016-07-21 07:42 5 5 2016-07-30 01:44:17.2 VLT SPHERE YJH Chuck McPartlin Santa Barbara, CA 0 Average -3 2 2016-07-30 01:51:22.2 VLT SPHERE YJH	33.813 511 516 33.6278 39.0725 530 530 X o (mas) -36 24.1387 23.4484 σ s -421 87 (s) -412 102 379 111 40.3511 0.73 378 121 41.759 0.05 -588 135 38.6906 0.22 0.20 -271 -275 37.1133 0.33 -272 37.1133 0.15 -295 34.2257 0.56 -295 34.4567 0.32 -288	-112.0 0 02 0 -4 -111.8333 -104.5778 -2 -3 X o-c (mas) 55 55 44 39 Y o (mas) 239 6 -110.3296 -110.2261 σ k RMS s 182 0 140 -3 (km) (s) 181 4 141 1 -189 0 137 -2 -77.0 17.831 0.860 -186 0 142 1 -88.1167 0.267 0.066 157 -3 136 2 -76.6354 2.445 0.017 6.728 1.230 115 10 113 2 -121.7028 3.831 0.389 119 0 -121.7028 4.994 0.072 104 -2 -111.2988 5.060 0.579 103 -6 -119.795 5.880 0.459 102 -3	8:54:49.1 0 7 8:54:50.96 8:54:01.5 5 0 Y o-c (mas) 0 Miss 4:01:03.91 RMS k 14 10 (km) 13 7 -14 -1 11:26:31.76 32.358 -12 1 Miss 0.995 9 -9 Miss 0.975 22.304 0 -5 11:58:13.97 9.94 9.94 9.94 9.94 σ (mas) 9.94 21.90 7.40 RMS σ 8:55:03.9 6.49 6.23 8:55:02.70 8:54:12.0 6.56 6.66 M (mag) 6.99 Miss 4:01:12.46 5.84 8.95 21.90 6.40 7.40 8.65 ( σ ) 21.90 6.05 7.40 8.43 3.277 21.90 6.52 7.40 8.66 11:26:34.77 1.318 21.90 6.02 7.40 8.83 Miss Miss 0.077 8.171 7.40 9.16 ( continued on next page ) 0.50 0.44 1.07 δM 0.17 (mag) 1.19 0.08 1.40 0.05 0.25 0.28 1.53 0.47 0.60 0.10 1.59 0.82 7.40 9.53 1.23 13.324 13.219 -2 7.40 9.34 0.95 11:58:23.98 11:58:11.03 8.039 2.362 5 7.40 9.32 0.33 11:58:25.48 11:58:56.82 18.920 3.067 0 7.40 9.23 0.20 11:58:58.55 Miss Miss 13.845 4.499 -3 7.40 9.53 1.69
	Tony George	Scottsdale, AZ		33.7157 Average	-111.8494 0	Miss 0	10	Miss 9.05	0.96
	Sam Herchak	Mesa, AZ		33.3967 Standard deviation 4 -111.6985	Miss 5	0	Miss 0.32	0.56
											( continued on next page )

Fig. B.1. Mass estimates of (107) Camilla gathered from the literature, see Table B.1 for details.

  The diameter estimates ( D) of (107) Camilla collected from the literature. For each, the 3 σ uncertainty, method, selection flag, and bibliographic reference are reported. The methods are im : Disk-Resolved Imaging, adam / koala : Multidata 3-D Modeling, lcimg : 3-D Model scaled with Imaging, lcocc : 3-D Model scaled with Occultation, neatm : Near-Earth Asteroid Thermal Model, stm : Standard Thermal Model, tpm : Thermophysical Model. Spherical-equivalent diameter ( D e ) of the shape model of Camilla projected on the plane of the sky as seen from IRAS, AKARI, and WISE[START_REF] Tedesco | IRAS Minor Planet Survey[END_REF] ;[START_REF] Usui | Asteroid catalog using akari: AKARI/IRC mid-Infrared asteroid survey[END_REF] ;[START_REF] Masiero | Main belt asteroids with WISE/NEOWISE. i. preliminary albedos and diameters[END_REF] . Owing to the elongated shape of Camilla, the 2-D diameter often underestimates the spherical-volume equivalent diameter.

	Table B.2
	#	D	δD	Method	Sel.	Reference
		(km)	(km)
	1 2	213.00 222.62	63.90 51.30	stm stm	√ √	Morrison and Zellner (2007) Tedesco et al. (2004)
	3 4 5 6 7 8	185.00 249.00 246.00 208.85 221.10 214.00	27.00 54.00 39.00 32.37 43.11 84.00	im neatm im stm neatm lcocc	✗ √ √ √ √ √	Marchis et al. (2006) Marchis et al. (2008a) Marchis et al. (2008a) Ryan and Woodward (2010) Ryan and Woodward (2010) Ďurech et al. (2011)
	9 10 11 12 13 14 15	200.37 219.37 256.00 245.00 227.00 254.00 254.00	10.53 17.82 35.00 75.00 72.00 18.00 36.00	stm neatm neatm tpm lcimg adam koala	✗ √ √ √ √ √ √	Usui et al. (2011) Masiero et al. (2011) Marchis et al. (2012) Marchis et al. (2012) Hanuš et al. (2013) Hanuš et al. (2017) This work
		234.72	53.11	Average
		Table B.3
				Epoch (UTC)		D e
	#	Mass ( M )		Method	Sel.	Reference
		(kg)
	1	(1.12 ± 0.09) × 10 19	bim	√	Marchis et al. (2008a)
	2 3 4 5 6 7 8 9 10 11	(36.20 ± 27.72) × 10 18 3 . 88 +32 . 70 -3.88 × 10 18 (39.00 ± 31.80) × 10 18 (17.60 ± 26.07) × 10 18 2 . 25 +54 . 00 -2.25 × 10 18 (27.10 ± 20.88) × 10 18 (6.79 ± 9.00) × 10 18 (11.10 ± 5.37) × 10 18 (16.10 ± 13.26) × 10 18 (1.12 ± 0.01) × 10 19	ephem defl defl defl defl ephem ephem defl ephem bin	✗ √ ✗ √ √ ✗ √ √ √ √	Fienga et al. (2010) Zielenbach (2011) Zielenbach (2011) Zielenbach (2011) Zielenbach (2011) Fienga et al. (2011) Fienga et al. (2013) Goffin (2014) Viswanathan et al. (2017) This work
		(1.12 ± 0.09) × 10 19	Average

The methods are bin : Binary, defl: Deflection, ephem : Ephemeris. ...".

Available on DAMIT( Ďurech et al.,

): http://astro.troja.mff.cuni.cz/projects/ asteroids3D/ 2 http://asteroid.astro.helsinki.fi/apc/asteroids/

http://vo.imcce.fr/

http://vo.imcce.fr/

https://mp3c.oca.eu

http://www.star.bristol.ac.uk/-pl2X-sim-mbt/topcat/

http://www.star.bristol.ac.uk/-pl2X-sim-mbt/stilts/

Acknowledgments

Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programmes 071.C-0 6 69 (PI Merline), 073.C-00 62 & 074.C-0052 (PI Marchis), 088.C-0528 (PI Rojo), 095.C-0217 & 297.C-5034 (PI Marsset).

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.

Some of these observations were acquired under grants from the National Science Foundation and NASA to Merline (PI).

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.

Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Founda-tion (United States), the National Research Council (Canada), CONI-CYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil).

We wish to acknowledge the support of NASA Contract NAS5-26555 and STScI grant .

Visiting Astronomer at the Infrared Telescope Facility, which is operated by the University of Hawaii under contract NNH14CK55B 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.

Thanks to all the amateurs worldwide who regularly observe asteroid lightcurves and stellar occultations. Many co-authors of this study are amateurs who observed Camilla, and provided crucial data.

We thank J. Ďurech for providing his implementation of Dobrovolskis (1996) method.

The authors acknowledge the use of the Virtual Observatory tools Miriade 6 ( Berthier et al., 2008 ), MP 3 C 7 ( Delbo et al., 2017 ), TOPCAT 8 , and STILTS 9 ( Taylor, 2005 ). This research used the facilities 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 ).

R Based on observations obtained at: (1) the Hubble Space Telescope, operated by NASA and ESA; (2) the Gemini Observatory and acquired through the Gemini Observatory Archive, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil); (3) the European Southern Observatory, Paranal, Chile -071.C-0669 (PI Merline), 073.C-0062 and 074.C-0052 (PI Marchis), 087.C-0014 (PI Marchis), 088.C-0528 (PI Rojo), 095.C-0217 and 297.C-5034 (PI Marsset) -and (4) 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.

Appendix D. Future occultations Table D.1

Selection of stellar occultations by (107) Camilla scheduled for the next 3 years. For each, we report the mean epoch of the event, the identifier of the UCAC-2 star and its magnitude ( m ), the expected drop in magnitude ( m ), the expected maximum duration of the event ( t ), the uncertainty (3 σ ) on the position of both satellites S1 and S2 at the date, projected on Earth, and the main area of visibility (location) .

Mean epoch