Marco Delbo CNRS - Observatoire De La Cote D’Azur, Nice, France

Interferometry of ASTEROIDS

Marco Delbo CNRS - Observatoire de la Cote d’Azur, Nice, France

Collaborators: A. Matter (Bonn, Germany), B. Carry (ESA), S. Ligori (Torino, Italy), P. Tanga (Nice, France), and G. Van Belle (Flagstaff, USA)

ESAC - Madrid - Aug 25, 2011 Outline

• Introduction: why to study asteroids and what do their physical properties tell us? • Main Belt Asteroids • Size, shape, density and internal structure • Interferometry of asteroids • Data analysis models, potential targets. • First results of VLTI-MIDI observations. • Future projects/perspectives. Asteroids of the main belt

Plotted here are the positions of the ﬁrst 5000 asteroids every 5 days. Asteroids of the main belt

Plotted here are the positions of the ﬁrst 5000 asteroids every 5 days. Near-Earth Asteroids (NEAs)

Some are from the main belt Some are dead comets

dynamical lifetime: 107y ∼ Size distribution of main belt asteroids

Bottke et al. 2005 Assumption of spherical shapes Size distribution of main belt asteroids

Bottke et al. 2005 Assumption of spherical shapes

D(km) θ(mas)= 0.72 ∆(AU) 1.5 D ∼ × ∆ θ(mas) D(km) at the center∼ of the Belt Size distribution of main belt asteroids

Bottke et al. 2005 Assumption of at the center of the MB spherical shapes for D=100km F (12µm) 20(Jy) ∼ D(km) F D2 θ(mas)= ∝ 0.72 ∆(AU) 1.5 D ∼ × ∆ θ(mas) D(km) at the center∼ of the Belt NEAs: size distribution Images of asteroids from spacecrafts DAWN in orbit around (4) Vesta Images of asteroids from spacecrafts Rosetta ﬂyby of 21 Lutetia

Covered with a regolith, estimated to be 600 m thick, The regolith softens the outlines of many of the larger craters. size: 132 × 101 × 76 km mass: 1.7 x 1018 kg [pre Rosetta estimate: (2.2-2.6) x 1018 kg] Images of asteroids from spacecrafts

66×48×46 km 18×10×9 km 54×24×15 km

Mission NEAR, 1998 (NASA) Mission Galileo, 1993 (NASA) images from the NEAR shoemaker mission (NASA)

(433) Eros: size = 23 km 2nd largest near-Earth asteroids Discovered in Nice in 1898 First detailed images of the surface of an asteroid (433 Eros) 25143 Itokawa (viewed by Hayabusa)

size: 535 × 294 × 209 m mass: (3.58±0.18)×1010 kg density:1.9±0.13 g/cm³ Asteroids and the origin of our solar system • Debris of the planet formation process • Small → little alteration → conserve pristine material Asteroids and the origin of our solar system • Debris of the planet formation process • Small → little alteration → conserve pristine material

• Asteroids suffered collisional evolution. • Sizes, shapes, and bulk densities tell us about their collisional histories

Simulation of disruption and reaccumulation by P. Michel Britt et al.: Asteroid Density, Porosity, and Structure 487 tural weakness that break apart during impacts to form what oid 4 Vesta has a bulk density consistent with basaltic mete- become meteorites. Macroporosoity defines the internal struc- orites overlying an olivine mantle and metal-rich core. The ture of an asteroid. Those with low macroporosity are solid, primitive C-type asteroid 1 Ceres has a bulk density similar coherent objects, while high macroporosities values indicate to primitive CI meteorites (for definitions of meteorite types loosely consolidated objects that may be collections of rub- see McSween, 1999). However, the smallest of these three ble held together by gravity (see Richardson et al., 2002). asteroids is an order of magnitude more massive than the next well-characterized asteroids and these less-massive 1.2. Current Measurements of asteroids exhibit some intriguing trends. In general, S-type Asteroid Bulk Density asteroids appear to have higher bulk densities than C-type asteroids, but the range in both groups is large. The M-type Spacecraft missions and advances in asteroid optical and asteroid 16 Psyche, which is interpreted to have a mineral- radar observations have revolutionized our knowledge of ogy analogous to Fe-Ni meteorites, shows a bulk density in asteroid bulk density. Shown in Table 1 and Fig. 1 is a sum- the range of hydrated clays. This indicates either very high mary of published mass and volume measurements. The porosity or a misidentification of the mineralogy. In the case methods of mass and volume determination are discussed of 16 Psyche, in addition to spectra and albedo consistent in section 2.0, but a glance at Table 1 shows that before the with metal, radar-albedo data strongly indicate a largely 1990s bulk-density measurements were limited to a handful metallic surface. of the largest asteroids. In the past 10 years, the accuracy and breadth of these measurements has exploded and pro- 2. THE DETERMINATION OF ASTEROID duced our first picture of the density structure of the aster- MASSES, VOLUMES, AND oid belt. The largest three asteroids, Ceres, Pallas, and Vesta, BULK DENSITIES have been studied for decades and have well-constrained values. These objects make up most of the mass of the aster- Though the number of asteroid density measurements oid belt. As shown in Fig. 1 in comparison with meteorite has begun to increase rapidly in the last few years, still only grain densities, these density values seem to make miner- a tiny fraction of the known asteroids have usable density alogical sense. Because common geologic materials can measurements. A short history of the efforts to determine vary by almost a factor of 4 in their grain density, asteroid the masses of asteroids has been provided by Hilton (2002). bulk-density measurements need to be interpreted in terms Asteroid masses have been reliably determined from asteroid- of the object’s mineralogy. The differentiated V-type aster- asteroid or asteroid-spacecraft perturbations. That is, the mass Densities of asteroids & meteorite analogs

1E + 22

1 Ceres (G)

2 Pallas (B) 4 Vesta (V)

1E + 20 87 Sylvia (P) 16 Psyche (M) 22 Kalliope (M) 45 Eugenia (C) 20 Massalia (S) 762 Pulcova (F) 11 Parthenope (S) 21 Hermione (C) 1E + 18 90 Antiope (C) Average S Average C

243 Ida (S) 253 Mathilde (C)

Phobos 1E + 16 Mass in Kilograms (log scale) Mass in Kilograms Ordinary Chondrite Densities Grain CI Grain Density CI Grain 433 Eros (S)

Deimos Density CV Grain CM Grain Density CM Grain 1E + 14 0.5 1 1.5 2 2.5 3 3.5 4

Density (g/cm3) Britt et al. 2002 Fig. 1. Bulk densities of measured asteroids with the grain densities of common meteorites for comparison. Also included in the plot are the asteroidlike moons of Mars, Phobos and Deimos, as well as estimates for the average C- and S-type asteroids (Standish, 2001). Several asteroids in Table 1 with large error bars have been left off the plot for clarity. Densities of asteroids & meteorite analogs

1E + 22

1 Ceres (G)

2 Pallas (B) 4 Vesta (V) 1E + 20 M 87 Sylvia (P) 16 Psyche (M) ρ = 22 Kalliope (M) 45 Eugenia (C) 20 Massalia (S) 762 Pulcova (F) V 11 Parthenope (S) 21 Hermione (C) 1E + 18 90 Antiope (C) Average S Average C 2243 Ida (S) 2 253σ Mathildeρ (C) σM σD Phobos 1E + 16 = +9 Mass in Kilograms (log scale) Mass in Kilograms Ordinary Chondrite Densities Grain

ρ M Density CI Grain D 433 Eros (S)

Deimos Density CV Grain CM Grain Density CM Grain 1E + 14 0.5 1 1.5 2 2.5 3 3.5 4

Density (g/cm3) Britt et al. 2002 Methods of physical characterization

Size

Volume

Shape

Mass

Density Methods of physical characterization

2 Size Radiometry in the thermal infrared (FIR∝D ) Stellar occultation timing Volume Visible photometry (lightcurves) Shape

Mass

Density Methods of physical characterization

2 Size Radiometry in the thermal infrared (FIR∝D ) Stellar occultation timing Volume Visible photometry (lightcurves) Shape Asteroid-asteroid perturbation Asteroid-planet (mars) perturbation Mass Asteroid-spacecraft perturbation

Density Methods of physical characterization

Density Adaptive optics, visible photometry Optical interferometers Keck

LBT

ESO-VLT Optical interferometers Keck

LBT

ESO-VLT Interferometry and physical characterization of asteroids

Size from 1 visibility

Volume

Shape

Mass

Density Interferometry and physical characterization of asteroids

Size from 1 visibility

Volume visibility as a function of time as the asteroid rotates Shape

Mass

Density PROGRAMME JEUNES Projet BACCI CHERCHEUSES ET JEUNES CHERCHEURS DOCUMENT SCIENTIFIQUE

EDITION 2010

3.3. DESCRIPTION DES TRAVAUX PAR TÂCHE / DETAILED DESCRIPTION OF THE WORK ORGANISED BY TASKS Task Sub Tasks (Work Packages) Manager Participants Time

0. Organization MDB MDB, 6 PT 1 1. Astronomical 1.A Interferometric data MDB MDB 18 observations and 1.B Thermal infrared data PT 6 data treatment. 1.C Visible lightcurves MM 2.4 1.D Spectroscopic data HC 3 DH 4 SL 10 AC 3 PD 16 CDDC 8 2. Data modeling 2.A Lightcurve inversion PT MDB 12 and determination 2.B global modeling PT 8 of physical 2.C physical modeling PM 7 Interferometryquantities and physical MM 1.6 HC 2 DH 8 characterization of asteroids SL 2 AC 6 PD 8 CDDC 16 Team members: MDB=Marco Delbo; PT= Paolo Tanga; PM=Patrick Michel; MM=Michael Mueller from (post-doc@UMR6202 1 visibility Cassiopée until 08/2011); HC=Humberto Campins; Size DH=Daniel Hestroffer; SL=Sebastiano Ligori; AC=Alberto Cellino; PD=post-doc recruited with ANR funds; CDDC=Non-permanent research position (CDD chercheur) financed through ANR; The time is given in terms of person/work/months.

Volume 3.3.1 TÂCHEvisibility 1 / TASK 1as ASTRONOMICAL a function OBSERVATIONS AND DATA TREATMENT Task 1 includesof time all activities as the devoted to the acquisition of the astronomical observations needed for the project: for each of our targets, we will obtain interferometric observations; photometric lightcurves in visible light; thermal infrared fluxes; spectroscopic observations in the visibleasteroid and near infrared. rotates In some cases, the data acquisition will require traveling to Shapethe observatories. In the following we give a technical description of the subtasks:

1.A InterferometricAsteroid data satellites: Aim: measure the scale of the orbit of the system with relativeP from accuracy lightcurves better than 10% (as and shown a Mass by Delbo et al. 2009) Providers:from MD, SL, thePD, CD visibilityDC, HC (for LBTI) at Deliverables: distance primary-secondary projected along the(some) interferometer epochs baseline at some epochs (the distance d of Fig. 4) Risks: objects aligned across the baseline; objects too faint to achieve the2 10% relative2 error on d; Description: DataP will be obtained4π mainly at the VLTI using the ATs 3 and= later the UTs during the PRIMA commissioninga time GM(in 2010 and likely in 2011) and GTO time allocated for ESO, the Torino Figure 4 Geometry of the orbit on the Density plane of the sky at the time of interferometric measurement. 16/37 Simple geometric models (1) uniform disk Visibility ﬁrst order Bessel function of ﬁrst kind

Interferometric visibility of a uniform disk of diameter !

as function of !, where u = B/" Simple geometric models (2) binary model

Visibility

Interferometric visibility of a binary of components of sizes !1 and !2 separated by a distance rho as function of lambda in meters

theta1=20; theta2=10; rho=200 mas Simple geometric models (2) binary model

Visibility

Interferometric visibility of a binary of components of sizes !1 and !2 separated by a distance rho as function of lambda in meters

theta1=20; theta1=20; theta2=10; theta2=10; rho=200 rho=100 mas mas Simple geometric models (2) binary model

Visibility

Interferometric visibility of a binary of components of sizes !1 and !2 separated by a distance rho as function of lambda in meters

theta1=20; theta1=20; theta1=20; theta2=10; theta2=10; theta2=10; rho=200 rho=100 rho=60 mas masmas Results from interferometry The VLTI of the ESO

• Coherent combination of the light from telescopes (distance between them B) of the VLT • Resolution !~"/B • MIDI "#[8,13]µm • AMBER "#[1.2,2.5]µm • VLTI B#[16,120]m

!MIDI#[15,100]mas

!AMBER#[3,25]mas Not sensitive enough for asteroids..

!PRIMA#[3,25]mas K<9 (guide star) dual field (reference star and asteroid need to be within ~30”) The VLTI of the ESO

• Coherent combination of the light from telescopes (distance between them B) of the VLT • Resolution !~"/B • MIDI "#[8,13]µm • AMBER "#[1.2,2.5]µm • VLTI B#[16,120]m

!MIDI#[15,100]mas

!AMBER#[3,25]mas Not sensitive enough for asteroids..

!PRIMA#[3,25]mas K<9 (guide star) dual field (reference star and asteroid need to be within ~30”)

So far results for MIDI only First successful observations of asteroids with MIDI-VLTI Obtained fringes on • 951 Gaspra (a testbed) • 234 Barbara (complex shape) • long rotation period (26.5 hr, Schober 1981; Harris & Young 1983) suggestive of a possible binary system. • interferometric observations by Delbo et al 2009 • 41 Daphne (complex shape) • Matter et al 2011 (almost in press) Results for Gaspra: size

Uniform disk ﬁt to visibility d =11 ± 2 km.

d=13 ± 2 or 11 ± 2 km expected value from Thomas et al. (1994) in-situ observations depending of the spin- pole solution adopted Results for Barbara: size and shape Results for Barbara: size and shape No. 2, 2009No. 2, 2009 MIDI-VLTI OBSERVATIONS MIDI-VLTI OF ASTEROIDS OBSERVATIONS OF ASTEROIDS 1233 1233 Results for Barbara: Tablesize 3 and shapeTable 3 Gaspra with the asteroid’sGaspra projected with the size asteroid’s known from projected Galileo size known from Galileo Results From Geometric ModelsResults Fits From to Measured Geometric Visibilities Models Fits to Measuredspacecraft Visibilities observationsspacecraft is discussed observations in Section 5 is. discussed in Section 5. Asteroid D (km)Asteroid θ (mas)D (km) Notesθ (mas) Notes d 4.2. (234) Barbara 4.2. (234) Barbara Gaspra 11 Gaspra1172EWSmask 11 1172EWSmask ± ± ± ± Barbara 44.6 Barbara0.3 51.0 44.60.40.3 poor 51.0 fit 0.4The visibility poor fit of (234) BarbaraThe visibility extracted of (234) from MIDIBarbara observa- extracted from MIDI observa- ± ± ± ± Barbara(1) 37.1 Barbara(1)0.5 43.0 37.10.50.5 primary 43.0 0.5 primary ± ± ± ± tions are shown in Figuretions3.Errorbars,obtainedusingtheEWS are shown in Figure 3.Errorbars,obtainedusingtheEWS Barbara(2) 21.0 Barbara(2)0.2 24.2 21.00.20.2 satellite 24.2 0.2 satellite ± ± ± ± data reduction software,data represent reduction the standard software, deviation represent of the the standard deviation of the a (km) ρ (mas)a (km) ρ (mas) visibility. As for the casevisibility. of (951) As Gaspra, for the a case least-squares of (951) Gaspra, fit of a least-squares fit of (1)–(2) 24.2 (1)–(2)0.2 28.1 24.20.20.2 separation 28.1 0.2 separation ± ± ± ± Equation (2)wasperformedtothedatapointswiththeangularEquation (2)wasperformedtothedatapointswiththeangular diameter θ of the uniformdiameter disk asθ theof the only uniform free parameter. disk as the We only free parameter. We Note. Uncertainties are 1σ . Note. Uncertainties are 1σ . obtained θ 51.0 0.4obtained mas, whichθ 51.0 corresponds0.4 mas, to D which44.6 corresponds to D 44.6 ˜ ˜ Table 4 Table 4 0.3 km at= the distance± 0.3 of the km asteroid. at= the distance± However, of the Figure= asteroid.3 However, Figure= 3 Results from Thermal ModelResults Fits from Thermal Model Fits clearly± shows that a uniformclearly± disk shows model that provides a uniform a poor disk modelfit to provides a poor fit to Asteroid D (km) Asteroidp D (km)ηθp(mas) Modelηθthe(mas) measurements. Model Modelthe visibilities measurements. calculated Model by visibilities means of calculated by means of ˜ V ˜ D V D Gaspra 13.8 1.0 0.24Gaspra0.14 1.06 13.8 0.171.0 0.24 22.0 0.141.6 NEATM 1.06 0.17 22.0the NEATM,1.6 NEATM the STM, andthe NEATM, the FRM thermal the STM, models and the also FRM give thermal a models also give a ± ± ±± ±± ± ± Gaspra 11.6 0.4 0.34Gaspra0.13 11.6 (0.756)0.4 0.34 18.4 0.130.6 STM (0.756) 18.4poor fit0.6 of the STM actual measurements.poor fit of the This actual is likely measurements. an indication This is likely an indication ± ± ± ±± ± Gaspra 24.0 0.3 0.08Gaspra0.04 24.0 0.3 0.0838.1 0.040.5 FRM 38.1that the0.5 spatial FRM distributionthat of the the spatial source’s distribution infrared of flux the differs source’s infrared flux differs ± ± ···± ±± ··· ± Barbara 51 20.17Barbara0.09 1.17 51 0.0520.17 58 0.092NEATM 1.17 0.05from 58 that2NEATM of a uniform singlefrom that body. of a uniform single body. ± ± ±± ±± ± ± Barbara 40 10.27Barbara0.09 40(0.756)10.27 46 0.091 STM (0.756) 46An1 application STM of theAn binary application disk model of the to the binary measured disk model to the measured ± ± ± ±± ± Barbara 89 10.06Barbara0.03 89 10.06102 0.031FRM 102 1FRM ± ± ···± ±± ··· visibility,± however, givesvisibility, much better however, results. gives In much this case, better we results. In this case, we found a remarkably goodfound match a remarkably between the good model match and between the the model and the Notes. Uncertainties are at 1Notes.σ level.UncertaintiesD is the diameter are at of 1σ alevel. sphereD withis the the diameterobservations, of a sphere with as the shown inobservations, Figure 3.Best-fitvaluesofthemodel as shown in Figure 3.Best-fitvaluesofthemodel same projected area visible tosame the observer; projectedpV areais the visible geometric to the albedo observer; in visiblepV is the geometric albedo in visible parameters θ1, θ2,andρparametersare 43.0 θ0.5,1, θ2 24.2,andρ0.2,are 43.0 and 28.10.5, 24.2 0.2, and 28.1 light; η is the beaming parameter.light; Anη is uncertainty the beaming of parameter. 0.5 mag was An assumed uncertainty on of 0.50.2 mag mas, was assumed respectively. on When0.2 mas, we take respectively.± into account± When the we distance take± into± to account± the distance± to the adopted value of the absolutethe adopted magnitude valueH of(from the absolute the MPC). magnitude Values ofHη(from the MPC). Values of η in brackets are default values.inθ bracketsis the angular are default extension values. ofθ Disin the mas angular at the extensionthe of asteroidD in mas at at the the time ofthe our asteroid observations at the time we derive of our diametersobservations we derive diameters D D of D 37.1 0.5 km andof DD 37.121.0 0.50.2 km km and forD the primary21.0 0.2 km for the primary distance of the asteroid. distance of the asteroid. ˜ 1 ˜ 1˜ 2 ˜ 2 and the= secondary± componentsand the= of= secondary the binary±± components system. The of= center- the binary± system. The center- to-center distance projectedto-center on the distance interferometer projected baseline on the interferometer was baseline was the values of the diametersthe values and the of the albedos diameters obtained and from the albedos obtained from of a 24.2 0.2 km. of a 24.2 0.2 km. models fits to the infraredmodels fluxes). fits to We the calculated infrared fluxes).the Fourier We calculated= the Fourier± = ± transform of the model thermaltransform infrared of the emission model thermal and evaluated infrared emission and evaluated 5. DISCUSSION 5. DISCUSSION this function at (u Bthiscos functionθB ,v atB (sinu θB ).B Thecos θ valuesB ,v ofB sin θB ). The values of = = = = B and θB are reportedB inand TableθB2arefor reported each VLTI in Table observation.2 for each VLTIFor observation. (951) Gaspra we haveFor (951) a priori Gaspra information we have on a its priori size, information on its size, The predicted interferometricThe predicted visibilities interferometric corresponding visibilities to the correspondingshape, and to spin the vectorshape, state and from spin spacecraft vector state observations from spacecraft observations different thermal radiometrydifferent solutions thermal are radiometry overplotted solutions along are overplotted(Thomas et along al. 1994). This(Thomas is the et main al. 1994 reason). This why is we the decided main reason why we decided with the measured valueswith in Figures the measured2 and values3 as the in three Figures dotted2 and 3 asto the observe three thisdotted object, into order observe to obtain this object, a reliable in order estimate to obtain of a reliable estimate of lines labeled NEATM, STM,lines labeled and FRM. NEATM, STM, and FRM. the resulting accuracy inthe the resulting size determination accuracy in fromthe size thermal determination from thermal In a second step, weIn used a second the simple step, geometric we used models the simple geometricmodels and models by means ofmodels the uniform and by disk means model of the fit uniform to MIDI disk model fit to MIDI described in Section 2 todescribed analyze measured in Section visibilities.2 to analyze measured visibilities.interferometric observations.interferometric We caution observations. here that a single We caution uni- here that a single uniform disk model may provideform disk a poor model description may provide of the a poor spatial description of the spatial 4.1. (951) Gaspra 4.1. (951) Gaspra distribution of the infrareddistribution emission of of the asteroids infrared in emission some cases, of asteroids in some cases, Fringes were detectedFringes for all interferometric were detected for observations all interferometricas clearly observations demonstratedas by clearly our observations demonstrated of (234) by our Barbara. observations of (234) Barbara. reported in Tables 1 andreported2.However,bycarefulanalysisofthe in Tables 1 and 2.However,bycarefulanalysisoftheIn order to estimate theIn reliability order to of estimate our size the determinations reliability of our size determinations acquisition images, weacquisition discovered images, a failure we in discovered the acquisition a failure inof the (951) acquisition Gaspra, we comparedof (951) Gaspra, the sizes we derived compared from the our sizes derived from our of the source during theof first the MIDI source measurement during the first (the MIDI one taken measurementMIDI (the measurements one taken withMIDI that measurements published by with Thomas that published et al. by Thomas et al. at UT 03:21:43). So, weat limited UT 03:21:43). our analysis So, we to the limited second our and analysis( to1994 the). second As a and first step,(1994 we). computed As a first the step, orientation we computed of the the orientation of the the third observations, only.the third In order observations, to increase only. the In signal order to to increaseshape the of signal the asteroid to atshape the epochof the of asteroid the VLTI at the observation epoch of the VLTI observation noise ratio of the visibilitynoise measurements, ratio of the visibility we computed measurements, the weusing computed an asteroid the physicalusing ephemerides an asteroid service physical of ephemerides the Institut service of the Institut de Mecanique´ Celeste etde de M Calculecanique´ des Celeste Ephemerides et de Calcul (IMCCE) des Ephemerides (IMCCE) average visibility extractedaverage using visibility the EWS extracted mask between using the the EWS mask between4 the 4 second and third measurementsecond and(i.e., third those measurement obtained at 04:29:28 (i.e., those obtainedin Paris. at 04:29:28The shape modelin Paris. of theThe asteroid, shape model derived of from the asteroid, the derived from the and 05:04:27 UT). Figureand2 shows 05:04:27 the UT). obtained Figure data2 shows points. the The obtainedGalileo data points. spacecraft The observations,Galileo spacecraft is that of Thomas observations, et al. ( is1994 that). of Thomas et al. (1994). error bars correspond toerror half bars of the correspond difference to between half of the the two differenceTwo between spin thevector two modelsTwo are spin available, vector namely models a are first available, one with namely a first one with αp 9.5, δp 26.7(Thomasetal.αp 9.5, δp 199426)andasecondone.7(Thomasetal.1994)andasecondone measurements. measurements. = ◦ = ◦ = ◦ = ◦ 6 1 6 1 with λp 20◦, βp 19with◦ (Kaasalainenλp 20◦, β etp al. 192001◦ (Kaasalainen), where αp et al. 2001), where αp We note that for B/λ !We3.8 note10 thatrad for−B/,correspondingtoλ ! 3.8 10 rad− ,correspondingto= = = = × × and δp are J2000 equatorialand δp coordinateare J2000 of equatorial the asteroid’s coordinate pole, of the asteroid’s pole, λ " 11 µm, Figure 2 showsλ " 11 thatµ them, Figure visibility2 shows oscillates that around the visibility oscillates around 1, which we interpret as1, due which to the we lack interpret of spatial as due resolution to the lack at of spatialwhereas resolutionλp and atβp are itswhereas J2000λ eclipticp and β longitudep are its J2000 and latitude. ecliptic longitude and latitude. these wavelengths. these wavelengths. Figure 4 shows the orientationFigure 4 ofshows (951) the Gaspra, orientation assuming of (951) the Gaspra, assuming the We performed a least-squaresWe performed fit of Equation a least-squares (2) (uniform fit of Equationspin ( model2) (uniform 1, at the timespin of model the second 1, at and the time the third of the visibility second and the third visibility disk model) to the datadisk points model) of Figure to the2 datausing pointsθ as the of Figure only 2 usingmeasurement.θ as the only Note thatmeasurement. the asteroid was Note observed that the almost asteroid pole- was observed almost pole- free parameter and usingfreeB parameter41.64 m. and We using obtainB θ 4117.64 m. Weon. obtain Figureθ 517shows a comparisonon. Figure 5 ofshows the object a comparison shape model of the object shape model = = = ± adopted and= one± imageadopted taken by and the one Galileo image mission. taken by the Galileo mission. 2mas,whichcorrespondsto2mas,whichcorrespondstoD 11 1kmatthedistanceD 11 1kmatthedistance ˜ = ± ˜ = ± of the asteroid. (see Tableof the3 for asteroid. a summary (see Table of our3 for results). a summary4 ofInternet our service results). available at4 http://www.imcce.frInternet service availableEphemerides at http://www.imcce.fr Ephemerides The comparison of our VLTIThe comparison/MIDI size of determination our VLTI/MIDI of (951) size determinationEphemeris for of physical (951) observationEphemeris of the for solar physical bodies.→ observation of the→ solar bodies.→ → No. 2, 2009No. 2, 2009 MIDI-VLTI OBSERVATIONS MIDI-VLTI OF ASTEROIDS OBSERVATIONS OF ASTEROIDS 1233 1233 Results for Barbara: Tablesize 3 and shapeTable 3 Gaspra with the asteroid’sGaspra projected with the size asteroid’s known from projected Galileo size known from Galileo Results From Geometric ModelsResults Fits From to Measured Geometric Visibilities Models Fits to Measuredspacecraft Visibilities observationsspacecraft is discussed observations in Section 5 is. discussed in Section 5. Asteroid D (km)Asteroid θ (mas)D (km) Notesθ (mas) Notes d 4.2. (234) Barbara 4.2. (234) Barbara Gaspra 11 Gaspra1172EWSmask 11 1172EWSmask ± ± ± ± Barbara 44.6 Barbara0.3 51.0 44.60.40.3 poor 51.0 fit 0.4The visibility poor fit of (234) BarbaraThe visibility extracted of (234) from MIDIBarbara observa- extracted from MIDI observa- ± ± ± ± Barbara(1) 37.1 Barbara(1)0.5 43.0 37.10.50.5 primary 43.0 0.5 primary ± ± ± ± tions are shown in Figuretions3.Errorbars,obtainedusingtheEWS are shown in Figure 3.Errorbars,obtainedusingtheEWS Barbara(2) 21.0 Barbara(2)0.2 24.2 21.00.20.2 satellite 24.2 0.2 satellite ± ± ± ± data reduction software,data represent reduction the standard software, deviation represent of the the standard deviation of the a (km) ρ (mas)a (km) ρ (mas) visibility. As for the casevisibility. of (951) As Gaspra, for the a case least-squares of (951) Gaspra, fit of a least-squares fit of (1)–(2) 24.2 (1)–(2)0.2 28.1 24.20.20.2 separation 28.1 0.2 separation ± ± ± ± Equation (2)wasperformedtothedatapointswiththeangularEquation (2)wasperformedtothedatapointswiththeangular diameter θ of the uniformdiameter disk asθ theof the only uniform free parameter. disk as the We only free parameter. We Note. Uncertainties are 1σ . Note. Uncertainties are 1σ . obtained θ 51.0 0.4obtained mas, whichθ 51.0 corresponds0.4 mas, to D which44.6 corresponds to D 44.6 ˜ ˜ Table 4 Table 4 0.3 km at= the distance± 0.3 of the km asteroid. at= the distance± However, of the Figure= asteroid.3 However, Figure= 3 Results from Thermal ModelResults Fits from37km Thermal Model Fits clearly± shows that a uniformclearly± disk shows model that provides a uniform a poor disk modelfit to provides a poor fit to Asteroid D (km) Asteroidp D (km)ηθp(mas) Modelηθthe(mas) measurements. Model Modelthe visibilities measurements. calculated Model by visibilities means of calculated by means of ˜ V ˜ D V D Gaspra 13.8 1.0 0.24Gaspra0.14 1.06 13.8 0.171.0 0.24 22.0 0.141.6 NEATM 1.06 0.17 22.0the NEATM,1.6 NEATM the STM, andthe NEATM, the FRM thermal the STM, models and the also FRM give thermal a models also give a ± ± ±± ±± ± ± Gaspra 11.6 0.4 0.34Gaspra0.13 11.6 (0.756)0.4 0.34 18.4 0.130.6 STM (0.756) 18.4poor fit0.6 of the STM actual measurements.poor fit of the This actual is likely measurements. an indication This is likely an indication ± ± ± ±± ± proposedGaspra geometric 24.0 0.3 model 0.08Gaspra0.04 24.0 0.3 0.0838.1 0.040.5 FRM 38.1that the0.5 spatial FRM distributionthat of the the spatial source’s distribution infrared of flux the differs source’s infrared flux differs ± ± ···± ±± ··· ± Barbara 51 20.17Barbara0.09 1.17 51 0.0520.17 58 0.092NEATM 1.17 0.05from 58 that2NEATM of a uniform singlefrom that body. of a uniform single body. ± ± ±± ±± ± ± Barbara 40 10.27Barbara0.09 40(0.756)10.27 46 0.09153km STM (0.756) 46An1 application STM of theAn binary application disk model of the to the binary measured disk model to the measured ± ± ± ±± ± Barbara 89 10.06Barbara0.03 89 10.06102 0.031FRM 102 1FRM ± ± ···± ±± ··· visibility,± however, givesvisibility, much better however, results. gives In much this case, better we results. In this case, we found a remarkably goodfound match a remarkably between the good model match and between the the model and the Notes. Uncertainties are at 1Notes.σ level.UncertaintiesD is the diameter are at of 1σ alevel. sphereD withis the the diameterobservations, of a sphere with as the shown inobservations, Figure 3.Best-fitvaluesofthemodel as shown in Figure 3.Best-fitvaluesofthemodel same projected area visible tosame the observer; projectedpV areais the visible geometric to the albedo observer; in visiblepV is the geometric albedo in visible parameters θ1, θ2,andρparametersare 43.0 θ0.5,1, θ2 24.2,andρ0.2,are 43.0 and 28.10.5, 24.2 0.2, and 28.1 light; η is the beaming parameter.light; Anη is uncertainty the beaming of parameter. 0.5 mag was An assumed uncertainty on of 0.50.2 mag mas, was assumed respectively. on When0.2 mas, we take respectively.± into account± When the we distance take± into± to account± the distance± to the adopted value of the absolutethe adopted magnitude valueH of(from the absolute the MPC). magnitude Values ofHη(from the MPC). Values of η in brackets are default values.inθ bracketsis the angular are default extension values. ofθ Disin the mas angular at the extensionthe of asteroidD in mas at at the the time ofthe our asteroid observations at the time we derive of our diametersobservations we derive diameters D D of D 37.1 0.5 km andof DD 37.121.0 0.50.2 km km and forD the primary21.0 0.2 km for the primary distance of the asteroid. distance of the asteroid. ˜ 1 ˜ 1˜ 2 ˜ 2 and the= secondary± componentsand the= of= secondary the binary±± components system. The of= center- the binary± system. The center- to-center distance projectedto-center on the distance interferometer projected baseline on the interferometer was baseline was the values of the diametersthe values and the of the albedos diameters obtained and from the albedos obtained from of a 24.2 0.2 km. of a 24.2 0.2 km. models fits to the infraredmodels fluxes). fits to We the calculated infrared fluxes).the Fourier We calculated= the Fourier± = ± transform of the model thermaltransform infrared of the emission model thermal and evaluated infrared emission and evaluated 5. DISCUSSION 5. DISCUSSION this function at (u Bthiscos functionθB ,v atB (sinu θB ).B Thecos θ valuesB ,v ofB sin θB ). The values of = = = = B and θB are reportedB inand TableθB2arefor reported each VLTI in Table observation.2 for each VLTIFor observation. (951) Gaspra we haveFor (951) a priori Gaspra information we have on a its priori size, information on its size, The predicted interferometricThe predicted visibilities interferometric corresponding visibilities to the correspondingshape, and to spin the vectorshape, state and from spin spacecraft vector state observations from spacecraft observations different thermal radiometrydifferent solutions thermal are radiometry overplotted solutions along are overplotted(Thomas et along al. 1994). This(Thomas is the et main al. 1994 reason). This why is we the decided main reason why we decided with the measured valueswith in Figures the measured2 and values3 as the in three Figures dotted2 and 3 asto the observe three thisdotted object, into order observe to obtain this object, a reliable in order estimate to obtain of a reliable estimate of lines labeled NEATM, STM,lines labeled and FRM. NEATM, STM, and FRM. the resulting accuracy inthe the resulting size determination accuracy in fromthe size thermal determination from thermal In a second step, weIn used a second the simple step, geometric we used models the simple geometricmodels and models by means ofmodels the uniform and by disk means model of the fit uniform to MIDI disk model fit to MIDI described in Section 2 todescribed analyze measured in Section visibilities.2 to analyze measured visibilities.interferometric observations.interferometric We caution observations. here that a single We caution uni- here that a single uniform disk model may provideform disk a poor model description may provide of the a poor spatial description of the spatial 4.1. (951) Gaspra 4.1. (951) Gaspra distribution of the infrareddistribution emission of of the asteroids infrared in emission some cases, of asteroids in some cases, Fringes were detectedFringes for all interferometric were detected for observations all interferometricas clearly observations demonstratedas by clearly our observations demonstrated of (234) by our Barbara. observations of (234) Barbara. reported in Tables 1 andreported2.However,bycarefulanalysisofthe in Tables 1 and 2.However,bycarefulanalysisoftheIn order to estimate theIn reliability order to of estimate our size the determinations reliability of our size determinations acquisition images, weacquisition discovered images, a failure we in discovered the acquisition a failure inof the (951) acquisition Gaspra, we comparedof (951) Gaspra, the sizes we derived compared from the our sizes derived from our of the source during theof first the MIDI source measurement during the first (the MIDI one taken measurementMIDI (the measurements one taken withMIDI that measurements published by with Thomas that published et al. by Thomas et al. at UT 03:21:43). So, weat limited UT 03:21:43). our analysis So, we to the limited second our and analysis( to1994 the). second As a and first step,(1994 we). computed As a first the step, orientation we computed of the the orientation of the the third observations, only.the third In order observations, to increase only. the In signal order to to increaseshape the of signal the asteroid to atshape the epochof the of asteroid the VLTI at the observation epoch of the VLTI observation noise ratio of the visibilitynoise measurements, ratio of the visibility we computed measurements, the weusing computed an asteroid the physicalusing ephemerides an asteroid service physical of ephemerides the Institut service of the Institut de Mecanique´ Celeste etde de M Calculecanique´ des Celeste Ephemerides et de Calcul (IMCCE) des Ephemerides (IMCCE) average visibility extractedaverage using visibility the EWS extracted mask between using the the EWS mask between4 the 4 second and third measurementsecond and(i.e., third those measurement obtained at 04:29:28 (i.e., those obtainedin Paris. at 04:29:28The shape modelin Paris. of theThe asteroid, shape model derived of from the asteroid, the derived from the and 05:04:27 UT). Figureand2 shows 05:04:27 the UT). obtained Figure data2 shows points. the The obtainedGalileo data points. spacecraft The observations,Galileo spacecraft is that of Thomas observations, et al. ( is1994 that). of Thomas et al. (1994). error bars correspond toerror half bars of the correspond difference to between half of the the two differenceTwo between spin thevector two modelsTwo are spin available, vector namely models a are first available, one with namely a first one with αp 9.5, δp 26.7(Thomasetal.αp 9.5, δp 199426)andasecondone.7(Thomasetal.1994)andasecondone measurements. measurements. = ◦ = ◦ = ◦ = ◦ 6 1 6 1 with λp 20◦, βp 19with◦ (Kaasalainenλp 20◦, β etp al. 192001◦ (Kaasalainen), where αp et al. 2001), where αp We note that for B/λ !We3.8 note10 thatrad for−B/,correspondingtoλ ! 3.8 10 rad− ,correspondingto= = = = × × and δp are J2000 equatorialand δp coordinateare J2000 of equatorial the asteroid’s coordinate pole, of the asteroid’s pole, λ " 11 µm, Figure 2 showsλ " 11 thatµ them, Figure visibility2 shows oscillates that around the visibility oscillates around 1, which we interpret as1, due which to the we lack interpret of spatial as due resolution to the lack at of spatialwhereas resolutionλp and atβp are itswhereas J2000λ eclipticp and β longitudep are its J2000 and latitude. ecliptic longitude and latitude. these wavelengths. these wavelengths. Figure 4 shows the orientationFigure 4 ofshows (951) the Gaspra, orientation assuming of (951) the Gaspra, assuming the We performed a least-squaresWe performed fit of Equation a least-squares (2) (uniform fit of Equationspin ( model2) (uniform 1, at the timespin of model the second 1, at and the time the third of the visibility second and the third visibility disk model) to the datadisk points model) of Figure to the2 datausing pointsθ as the of Figure only 2 usingmeasurement.θ as the only Note thatmeasurement. the asteroid was Note observed that the almost asteroid pole- was observed almost pole- free parameter and usingfreeB parameter41.64 m. and We using obtainB θ 4117.64 m. Weon. obtain Figureθ 517shows a comparisonon. Figure 5 ofshows the object a comparison shape model of the object shape model = = = ± adopted and= one± imageadopted taken by and the one Galileo image mission. taken by the Galileo mission. 2mas,whichcorrespondsto2mas,whichcorrespondstoD 11 1kmatthedistanceD 11 1kmatthedistance ˜ = ± ˜ = ± of the asteroid. (see Tableof the3 for asteroid. a summary (see Table of our3 for results). a summary4 ofInternet our service results). available at4 http://www.imcce.frInternet service availableEphemerides at http://www.imcce.fr Ephemerides The comparison of our VLTIThe comparison/MIDI size of determination our VLTI/MIDI of (951) size determinationEphemeris for of physical (951) observationEphemeris of the for solar physical bodies.→ observation of the→ solar bodies.→ → Barbara follow up: photometric lightcurves 2009 occultation events

Stellar occultation 1 note also the

Oct 5, 2009 Stellar occultation 2 double coord Ecliptic longitude, heliocentric: 77° ; geocentric: 103° Phase angle: 25° Nov 21, 2009 Ecliptic longitude, heliocentric: 89° ; geocentric: 107° (chord n. 2 is not precisely dated) Phase angle: 18° Source: http://www.euraster.net/results/ 2009/20091105-Barbara-crd_temp.gif Source: http://www.asteroidoccultation.com/observations/Results/ Size from the MIDI-VLTI observations conﬁrmed KOALA shape model of Barbara from occultations and photometry

Tanga, Carry, Delbo et al, in preparation KOALA shape model of Barbara from occultations and photometry

Carry’s KOALA model

Tanga, Carry, Delbo et al, in preparation KOALA vs VLTI models projected on the sky at the time of VLTI observations

KOALA model VLTI model from Tanga et al. adapted from from Delbo et al. 2009 80

N 60

20 Secondary

0 E km

-20 Proj. baseline Primary

-40

-60

-80 -80 -60 -40 -20 0 20 40 60 80 km KOALA vs VLTI models projected on the sky at the time of VLTI observations

KOALA model VLTI model from Tanga et al. adapted from from Delbo et al. 2009 80

N 60

20 Secondary

0 E km

-20 Proj. baseline Primary

-40

-60

-80 -80 -60 -40 -20 0 20 40 60 80 km

41 Daphne Matter et al. et Matter Icarus, press in

Figure 4:

40 41 Daphne: nature of the surface

Given a priori information a b o u t t h e s h a p e , w e constrained the thermal inertia.

2 0.5 1 Γ < 50 Jm− s− K− Γ √κ ∝ Smooth surface

Conclusion: insulatingFigure 7:layer of mature and thick regolith; craters smoothed out by regolith landslides? From observations in the thermal IR at one epoch only Matter et al. 2011

43 Large MBAs NEA MBA<100km 1000 steins Itokawa (Muller, Mueller) 99JU3 by Campins et al. 2010 Delbo and Tanga 2009

YORP: by Mueller 2007

100 Lamy et al 2009 Thermal inertia (SI) TG Muller et al 1998

0.1 1 10 100 1000 Asteroid diameter (km) Large MBAs NEA MBA<100km 1000 steins Itokawa (Muller, Mueller) 99JU3 by Campins et al. 2010 Delbo and Tanga 2009

YORP: by Mueller 2007

100 Lamy et al 2009

thermal inertia Thermal inertia (SI) of our Moon TG Muller et al 1998

0.1 1 10 100 1000 Asteroid diameter (km) Large MBAs NEA MBA<100km 1000 steins Itokawa (Muller, Mueller) 99JU3 by Campins et al. 2010 Delbo and Tanga 2009

YORP: by Mueller 2007

100 Lamy et al 2009

thermal inertia Thermal inertia (SI) of our Moon TG Muller et al 1998 Transition size from primordial asteroids, never disrupted and asteroids reaccumulated 10 (Bottke et al. 2005)

0.1 1 10 100 1000 Asteroid diameter (km) 2500 bare rock value (Jakosky 1986) Large MBAs NEA MBA<100km 1000 steins Itokawa (Muller, Mueller) 99JU3 by Campins et al. 2010 Delbo and Tanga 2009

YORP: by Mueller 2007

100 Lamy et al 2009

thermal inertia Thermal inertia (SI) of our Moon TG Muller et al 1998 Transition size from primordial asteroids, never disrupted and asteroids reaccumulated 10 (Bottke et al. 2005)

0.1 1 10 100 1000 Asteroid diameter (km) 2500 bare rock value (Jakosky 1986) Large MBAs NEA MBA<100km 1000 steins Itokawa (Muller, Mueller) 99JU3 by Campins et al. 2010 Delbo and Tanga 2009

YORP: by Mueller 2007

100 Lamy et al 2009

thermal inertia Thermal inertia (SI) of our Moon TG Muller et al 1998 Transition size from primordial asteroids, never disrupted and asteroids reaccumulated 10 (Bottke et al. 2005)

0.1 1 10 100 1000 Asteroid diameter (km) 0.0035 0.02 0.1 1.0 10 escape velocity (m/s) Future projects Asteroids with satellites

1000

discovered by AOs

discovered by 100 photometry: transits and eclipses Apparent separation at opposition (mas)

8 10 12 14 16 18 Apparent magnitude at opposition (V) Asteroids with satellites

1000 AOs@8m discovered by AOs

discovered by 100 photometry: transits and eclipses Apparent separation at opposition (mas)

8 10 12 14 16 18 Apparent magnitude at opposition (V) Asteroids with satellites

1000 AOs@8m discovered by AOs

100 discovered by Linc-LBTI photometry: transits and eclipses Apparent separation at opposition (mas)

8 10 12 14 16 18 Apparent magnitude at opposition (V) Asteroids with satellites

1000 AOs@8m discovered by AOs

100 discovered by Linc-LBTI photometry: transits and eclipses Apparent separation at opposition (mas)

10 VLTI-ATs

8 10 12 14 16 18 Apparent magnitude at opposition (V) Asteroids with satellites

1000 AOs@8m discovered by AOs

100 discovered by Linc-LBTI photometry: transits and eclipses Apparent separation at opposition (mas)

10 VLTI-UTs VLTI-ATs

8 10 12 14 16 18 Apparent magnitude at opposition (V) Comets: 8P Tuttle 8. Attachments (Figures) January 07 2008 Rn=7.6 km Geometry of observation from the VLTI on January 17, 2008 Rn=5.0 km

UT3-UT4 10 UT1-UT2

UT2-UT3 Disk integrated flux (Jy) terminator 1 8 9 10 11 12 13 Wavelength (um) January 07 2008 1.0 UT1-UT2 Rn=7.6 km UT1-UT2 Rn=5.0 km UT2-UT3 Rn=7.6 km UT2-UT3 Rn=5.0 km UT3-UT4 Rn=7.6 km UT3-UT4 Rn=5.0 km 0.8 SUN N 0.6

0.4 Visibility

W 0.2

0.0 8 9 10 11 12 13 Wavelength (um)

January 17 2008 January 25 2008 Rn=7.6 km Rn=7.6 km Rn=5.0 km Rn=5.0 km

10 10 Disk integrated flux (Jy) Disk integrated flux (Jy) 1 1 8 9 10 11 12 13 8 9 10 11 12 13 Wavelength (um) Wavelength (um) January 17 2008 January 25 2008 1.0 UT1-UT2 Rn=7.6 km UT1-UT2 Rn=5.0 km 1.0 UT1-UT2 Rn=7.6 km UT1-UT2 Rn=5.0 km UT2-UT3 Rn=7.6 km UT2-UT3 Rn=5.0 km UT2-UT3 Rn=7.6 km UT2-UT3 Rn=5.0 km UT3-UT4 Rn=7.6 km UT3-UT4 Rn=5.0 km UT3-UT4 Rn=7.6 km UT3-UT4 Rn=5.0 km 0.8 0.8

0.6 0.6

0.4 0.4 Visibility Visibility

0.2 0.2

0.0 0.0 8 9 10 11 12 13 8 9 10 11 12 13 Wavelength (um) Wavelength (um)

Fig. 1: top-left: geometry of observation on Jan 17, 2008. Colors represent the normalized intensity of the emitted flux at 10 µm ranging from white (max) to dark red (min). On top of the comet nucleus the direction of the three projected baselines UT1-UT2, UT2-UT3, and UT3-UT4 are drawn with the red, green and blue colors respectively. Plots: Expected total thermal infrared flux and visibilities for the three baselines using the same color codes. Continuous lines represent the values obtained assuming a nucleus radius Rn=7.6 km (the nominal value), whereas the dashed lines assumes Rn=5 km. Note how the continuous curves can be easily distinguished from the dashed ones of the same colors indicating the strong sensitivity of MIDI measurements to the size of the nucleus. Fluxes and visbilities were calculated using the thermophsical model of Delbo et al. 2004, 2007 assuming an albedo of 4% and zero surface thermal inertia as suggested by the results of Groussin et al. (2007). In this latter work Co-I O. 2 0.5 1 Groussin and colleagues have found that a thermal inertia in the range 0-10 Jm− s− K− best matches the temperature distribution observed by the mission Deep-Impact on the nucleus of the comet Temple 1. Would this will be true also for the nucleus of 8P/Tuttle ? UT3-UT4 visibilities are also very sensitive to the thermal inertia and the presence of possible active regions on the dark side of the nucleus. The raw accuracy of visibility measurements is typically 10%. ∼ Our MIDI observations of asteroids indicates a relative accuracy of flux measurements (around 5 Jy) <15%. We expect a nucleus size determination within 5-10% relative error.

-4- Radar delay-doppler imaging of the ﬁrst bilobate comet

2008 Jan 3.9

2008 Jan 4.9 Conclusions

• Measured the sizes and shapes of some asteroids. • (Determined surface properties of asteroids) • Observations of close binaries underway... important future prospects. • Active comet nuclei can be observed.