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First VLTI-MIDI Direct Determinations of Asteroid Sizes∗

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First VLTI-MIDI Direct Determinations of Asteroid Sizes∗ First VLTI-MIDI direct determinations of asteroid sizes∗ M. Delbo UNS, CNRS, Observatoire de la Cˆote d’Azur, BP 4229 06304 Nice cedex 04 - France. INAF-Osservatorio Astronomico di Torino Strada Osservatorio 20, 10025 Pino Torinese, Torino - Italy [email protected] S. Ligori INAF-Osservatorio Astronomico di Torino Strada Osservatorio 20, 10025 Pino Torinese, Torino - Italy A. Matter UNS, Observatoire de la Cˆote d’Azur, BP 4229 06304 Nice cedex 04 - France. A. Cellino INAF-Osservatorio Astronomico di Torino Strada Osservatorio 20, 10025 Pino Torinese, Torino - Italy and J. Berthier Institut de Mecanique Celeste (IMCCE) 77 av. Denfert Rochereau - 75014 Paris - France ABSTRACT We have obtained the first successful interferometric measurements of asteroid sizes and shapes by means of VLTI-MIDI. VLTI can spatially resolve asteroids in a range of sizes and heliocentric distances that are not accessible to other techniques such as adaptive optics and radar. We have observed, as a typical bench mark, the asteroid (951) Gaspra, visited in the past by the Galileo space probe, and we derive a size in good agreement with the ground truth coming from the in situ measurements by the Galileo mission. Moreover, we have also observed the asteroid (234) Barbara, known to exhibit unusual polarimetric properties, and we found evidence of a potential binary nature. In particular, our data are best fit by a system of two bodies of 37 and 21 km in diameter, separated by a center-to-center distance of ∼24 km (projected along the direction of the baseline at the epoch of our observations). Subject headings: minor planets, asteroids; techniques: interferometric; infrared: solar system 1. Introduction creted into the inner Solar System planets. Most asteroids are too small to allow a di- The study of the physics of asteroids is cru- rect determination of their fundamental physical cial to constrain models of formation, growth and properties including sizes 1, shapes, and masses physical properties of the planetesimals that ac- 1 * Only for the largest hundred main belt asteroids their sizes Based on data obtained at the Very Large Telescope can be directly measured with present day adaptive optics Interferometer (VLTI) of the European Southern Observa- systems at 10–m class telescopes (Conrad et al. 2007) tory (ESO): program ID 076.C-0798. 1 2. According to current expectations, in the next the infrared flux I(λ) carries information about decade, the Gaia mission of the European Space the size of the source. In particular, I(λ) is pro- Agency will provide accurate mass determinations portional to the area of the asteroid visible to the for about 100 of the largest main belt asteroids observer. However, I(λ) depends also upon the (MBAs) and will be able to directly measure the temperature distribution on the asteroid surface. sizes of all MBAs larger than 30 km (∼ 1, 000 ob- Different models of asteroid thermal infrared emis- jects) (Mouret et al. 2007; Mignard et al. 2007). sion (the so–called asteroid thermal models; see At present, however, the most important source §2, Harris and Lagerros 2002; Delbo and Harris of progress in this field is related to the increasing 2002, and references therein) are used to estimate rate of discovery of binary systems. These discov- the surface temperature distribution allowing one eries have been made possible by adaptive optics to derive D from measurements of I(λ). The as- imaging at several large telescopes, radar – partic- teroid’s geometric visible albedo, pV , can then be ularly suited for the study of near-Earth objects obtained from Eq. (1) which represents the fun- (NEAs) – and optical lightcurve observations. Bi- damental relation linking the effective diameter, nary asteroids are extremely important to derive D (in km), the albedo, and the absolute magni- the mass of the system; sizes and shapes of the tude H (the magnitude in the V –band that would components are then needed to estimate average be measured by observing the object at 1 AU dis- densities, which in turn provide crucial informa- tance from both the Sun and the observer, and at tion about the internal structure of the bodies. zero phase angle): Unfortunately, asteroid sizes are generally not log p =6.247 − 2log D − 0.4H (1) measurable by means of direct imaging. Improve- V ments in the performances of modern adaptive We note that the value of pV is per se a very im- optics systems are currently making significant portant physical parameter, because it is a func- progress, but this is forcedly limited to size mea- tion of the composition, texture and roughness surements of the largest MBAa, and very close ap- of an asteroid’s surface. Polarimetric observa- proaching NEAs (Conrad et al. 2007). Radar has tions can also be used to estimate the value of pV been proven to be a powerful tool to infer shapes (Muinonen et al. 2002; Cellino et al. 2005) from and sizes for a sample of km– and sub–km–sized empirical relations between the albedo and the de- objects. This technique, however, is mostly lim- gree of polarization of the reflected light from the ited to the population of NEAs, which can expe- asteroid surface. The asteroid effective diameter rience close encounters with our planet. This is D can then be determined from pV using Eq. (1). due to the fact that the intensity of the radar echo We note that the value of the absolute magni- decreases with the fourth power of the distance. tude H is derived from photometric observations To summarize, the vast majority of asteroid of the asteroid under different illumination condi- sizes, due to their small apparent angular exten- tions (Muinonen et al. 2002). However, in prac- sion and orbital location in the Main Belt, remain tice, the H–value is usually not determined at the beyond the range of measurability using current same time of radiometric or polarimetric obser- techniques. As a consequence, nearly all of the vations. Its value is in most circumstances sim- available information we have today about aster- ply taken from public catalogs, such as the Mi- oid sizes comes from the results of indirect meth- nor Planet Center’s orbital database, which are ods of size determination. known to be affected by significant systematic er- The most widely adopted technique to deter- rors of 0.3 magnitudes or more, mainly for aster- mine asteroid sizes is thermal infrared radiome- oids smaller than ∼40–50 km (Cellino et al. 2008; try (see Harris and Lagerros 2002, and references Parker et al. 2008). therein). This method is based on the fact that As a conclusion, it can be said that there are currently significant uncertainties on the size 2 At the time of writing, only fifteen multiple main belt as- (and albedo) values for MBAs of moderate sizes teroids had their components resolved, allowing determina- tion of their orbits and thus of the masses of the systems (D<50km): all but about a thousand of the over (Marchis et al. 2008) one million asteroids in the main belt are smaller than 50 km. 2 There is thus a strong need to extend direct size measurements to smaller asteroids. However, this 234 Barbara is a very challenging task. The only technique that has been so far nominally available, namely the 951 Gaspra measurement of stellar occultations, is hardly ap- plicable in practice due to the very narrow strips 1459 Magnya of observability of occultation events and to the actual limits in current accuracies of stellar astro- Diameter (km) metric catalogues and of asteroid orbital elements (see Tanga and Delbo 2007). As we show in this paper, a new very powerful facility for the direct measurement of asteroid sizes is now available, namely the Very Large Telescope Orbital semimajor axis (AU) Interferometer (VLTI) of the European Southern Observatory (ESO). In particular, VLTI can be Fig. 1.— Asteroids for which MIDI can provide direct successfully applied to objects that (i) are not too size determination, according to the present instru- big (apparent angular diameters . 100–200 mas), ment requirements: i.e i) a correlated thermal infrared × but, on the other hand, (ii) are sufficiently bright flux (flux visibility) at 11.8 µm greater or equal to (brighter than visible magnitude ∼13 –14). Al- 1 Jy and ii) a visibility greater or equal to 0.1. Dia- monds: MBAs. Squares: NEAs. Orbital element are though these constraints certainly limit the num- from the Minor Planet Center (MPC). Diameters have ber of objects for which VLTI can provide direct been calculated from the MPC H values assuming an size and shape determinations, a large number of average albedo of 0.2. Ephemerides have been calcu- asteroids still exist that fall within the above mag- lated every 5 days for NEAs and every 15 days for nitude and size ranges (see Fig. 1 and Delbo et al. MBAs for a time span of 15 years starting from June 2006; Loreggia et al. 2008). The results presented 1, 2005, to check for those bodies meeting conditions in this paper, based on our pilot program, are a i and ii. nice confirmation of the above statement. Generally speaking, VLTI has the capability coherent) spectral energy distribution, I(λ), of the of measuring sizes (and shapes) of asteroids from source in the 8-13 µm spectral interval. This ther- measurements of the visibility (contrast) of inter- mal infrared data can then be used to derive as- ferometric fringes. Visibility is a function of the teroid sizes, through the application of asteroid apparent angular extension of the body along the thermal models (see e.g. Harris and Lagerros 2002; projected interferometer baseline.
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