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<p><strong>Introduction</strong></p>
<p>Asteroid (22) Kalliope is the second largest M-type asteroid in the main-belt after (16) Psyche. Kalliope has a bright satellite (D ~ 28km), Linus, discovered in 2001 [Me01, Ma01]. Albeit being a privileged target for adaptive optics (AO) ground-based observations, its density remains elusive with values ranging between 2.4 and 3.7 g cm-<sup>3</sup> [Ma03, Dr21]. Here, we present a complete characterization of the topography, bulk density, and internal structure of Kalliope, as well as the dynamic of the system based on high angular resolution imaging observations performed with VLT/SPHERE as part of an ESO large programme (ID: 199.C-0074).</p>
<p><strong>Observation</strong></p>
<p>We obtained 35 images of Kalliope at 7 epochs near opposition between March and May 2018 and in June 2019 with the VLT/SPHERE/ZIMPOL AO instrument. The first apparition in 2018 covered the south pole of Kalliope while during the second it was close to an equator-on geometry. The north pole was not completely imaged, although 88% of the surface was covered at least once. We compiled 145 lightcurves from databases and we acquired new ones during the 2018 apparition to be used in the 3D shape modelling.</p>
<p>For the determination of Linus&#8217;s orbit, we complemented the SPHERE images with a compilation of archival data from other large ground-based AO instruments (KeckII/NIRC2, ESO/VLT/NACO and Gemini-North/NIRI). We obtained a total of 82 measurements spanning 42 epochs from 2001 to 2019.</p>
<p><strong>Methods</strong></p>
<p>We generated shape models of Kalliope with three different shape modelling techniques. We first used the inversion algorithm ADAM [Vi15] and the genetic algorithm SAGE [B18, Du20] that both take lightcurves and AO images as inputs.</p>
<p>We then applied our Multi-resolution PhotoClinometry by Deformation (MPCD; [C13, F20]) method on the SPHERE images to reconstruct Kalliope&#8217;s 3D shape, starting from both the ADAM and the SAGE models as initial meshes.</p>
<p>To study the dynamic of the system, the relative position of Kalliope and Linus were first measured on the images. Then, we used the meta-heuristic algorithm Genoid [Va12] to accurately determine the orbital elements.</p>
<p><strong>Results and conclusions</strong></p>
<p>The volume of Kalliope from the different modelling techniques and the mass constrained by the precise measurements of its satellite orbit yield a density of ~4.1 g cm-<sup>3</sup>. This high density is comparable within errors to that of the metallic asteroid (16) Psyche. The best orbital solutions for the satellite are found when the quadrupole J2 tends toward 0. However, Kalliope&#8217;s shape implies a non-zero J2 when assuming a homogeneous interior density. This suggests an inhomogeneous, differentiated internal structure.</p>
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<p><strong>Bibliography</strong></p>
<p>[B18] Bartczak, P. and Dudzinski, G. 2018, MNRAS, 473</p>
<p>[C13] Capanna, C., Gesqui&#232;re, G., Jorda, L., Lamy, P., & Vibert, D. 2013, The Visual Computer, 29, 825</p>
<p>[Dr21] Drummond, J. D., Merline, W. J., Carry, B., et al. 2021, Icarus, 358</p>
<p>[Du20] Dudzinski, G., Podlewska-Gaca, E., Bartczak, P., et al. 2020, MNRAS, 499</p>
<p>[F20] Ferrais, M., Vernazza, P., Jorda, L., et al. 2020, A&A, 638, L15</p>
<p>[Ma01] Margot, J. L. and Brown, M. E. 2001, IAU Circ., 7703, 3</p>
<p>[Ma03] Margot, J. L. and Brown, M. E. 2003, Science, 300, 1939</p>
<p>[Me01] Merline, W. J., Menard, F., Close, L., et al. 2001, IAU Circ., 7703, 2</p>
<p>[Va12] Vachier, F., Berthier, J. and Marchis, F. 2012, A&1, 543, A68</p>
<p>[Vi15] Viikinkoski, M., Kaasalainen, M., & Durech, J. 2015, A&A, 576, A8</p>
Volume uncertainty of (7) Iris shape models from disc-resolved images
