In understanding the composition and internal structure of asteroids, their density is perhaps the most diagnostic quantity. We aim here to characterize the surface composition, mutual orbit, size, mass, and density of the small main-belt binary asteroid (939) Isberga. For that, we conduct a suite of multi-technique observations, including optical lightcurves over many epochs, near-infrared spectroscopy, and interferometry in the thermal infrared. We develop a simple geometric model of binary systems to analyze the interferometric data in combination with the results of the lightcurve modeling. From spectroscopy, we classify Ibserga as a Sq-type asteroid, consistent with the albedo of 0.14$^{+0.09}_{-0.06}$ (all uncertainties are reported as 3-$sigma$ range) we determine (average albedo of S-types is 0.197 $pm$ 0.153, Pravec et al., 2012, Icarus 221, 365-387). Lightcurve analysis reveals that the mutual orbit has a period of 26.6304 $pm$ 0.0001 h, is close to circular, and has pole coordinates within 7 deg. of (225, +86) in ECJ2000, implying a low obliquity of 1.5 deg. The combined analysis of lightcurves and interferometric data allows us to determine the dimension of the system and we find volume-equivalent diameters of 12.4$^{+2.5}_{-1.2}$ km and 3.6$^{+0.7}_{-0.3}$ km for Isberga and its satellite, circling each other on a 33 km wide orbit. Their density is assumed equal and found to be $2.91^{+1.72}_{-2.01}$ g.cm$^{-3}$, lower than that of the associated ordinary chondrite meteorites, suggesting the presence of some macroporosity, but typical of S-types of the same size range (Carry, 2012, P&SS 73, 98-118). The present study is the first direct measurement of the size of a small main-belt binary. Although the interferometric observations of Isberga are at the edge of MIDI capabilities, the method described here is applicable to others suites of instruments (e.g, LBT, ALMA).
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