Context. η Tel is an 18 Myr system composed of a 2.09 M⊙ A-type star with an M7-M8 brown dwarf companion, η Tel B. The two objects have a projected separation of 4″.2 (~208 au). This system has been targeted by high-contrast imaging campaigns for over 20 yr, facilitating its orbital and photometric characterization. The companion, η Tel B, both bright and on a wide orbit, is an ideal candidate for a detailed examination of its position and the characterization of its atmosphere. Aims. To explore the orbital parameters of η Tel B, measure its contrast, and investigate its close surroundings, we analyzed three new SPHERE/IRDIS coronagraphic observations. Our objectives are to investigate the possibility of a circumplanetary disk or a close companion around η Tel B, and characterize its orbit by combining this new data set with archival data acquired in the past two decades. Methods. The IRDIS data are reduced with state-of-the-art algorithms to achieve a contrast with respect to the star of 1.0 × 10−5 at the location of the companion. Using the NEGative Fake Companion technique (NEGFC), we measure the astrometric positions and flux of η Tel B for the three IRDIS epochs. Together with the measurements presented in the literature, the baseline of the astrometric follow-up is 19 yr. Results. We calculate a contrast for the companion of 6.8 magnitudes in the H band. The separation and position angle measured are 4″.218 and 167.3 degrees, respectively. The astrometric positions of the companions are calculated with an uncertainty of 4 milliarc-seconds (mas) in separation and 0.2 degrees in position angle. These are the smallest astrometrical uncertainties of η Tel B obtained so far. The orbital parameters are estimated using the Orvara code, including all available epochs. The orbital analysis is performed taking into account the Gaia-HIPPARCOS acceleration of the system. Suppressing its point spread function (PSF), we have produced contrast curves centered on the brown dwarf in order to constrain our detection capabilities for a disk or companions around it. Conclusions. After considering only orbits that could not disrupt the outer debris disk around η Tel A, our orbital analysis reveals a low eccentric orbit (e ~ 0.34) with an inclination of 81.9 degrees (nearly edge-on) and a semi-major axis of 218 au. Furthermore, we determine the mass of η Tel B to be 48 MJup, consistent with previous calculations from the literature based on evolutionary models. Finally, we do not detect any significant residual pointing to the presence of a satellite or a disk around the brown dwarf. The retrieved detection limits allow us to discard massive objects around η Tel B with masses down to 1.6 MJup at a separation of 33 au.
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