The high-albedo, low polarization disk around HD 114082 that harbors a Jupiter-sized transiting planet Constraints from VLT/SPHERE completed with TESS, Gaia, and radial velocities

Aims. We present new optical and near-infrared images of the debris disk around the F-type star HD 114082 in the Scorpius-Centaurus OB association. We obtained direct imaging observations and analyzed the TESS photometric time series data of this target with the goal of searching for planetary companions to HD 114082 and characterizing the morphology of the debris disk and the scattering properties of dust particles. Methods. HD 114082 was observed with the VLT/SPHERE instrument in different modes - the IRDIS camera in the K band (2.0-2.3 mu m) together with the IFS in the Y, J, and H bands (0.95-1.66 mu m) using the angular differential imaging technique as well as IRDIS in the H band (1.5-1.8 mu m) and ZIMPOL in the I_PRIME band (0.71-0.87 mu m) using the polarimetric differential imaging technique. To constrain the basic geometrical parameters of the disk and the scattering properties of dust grains, scattered light images were fitted with a 3D model for single scattering in an optically thin dust disk using a Markov chain Monte Carlo approach. We performed aperture photometry to derive the scattering and polarized phase functions, the polarization fraction, and the spectral scattering albedo for the dust particles in the disk. This method was also used to obtain the reflectance spectrum of the disk and, in turn, to retrieve the disk color and study the dust reflectivity in comparison to the debris disk HD 117214. We also performed the modeling of the HD 114082 light curve measured by TESS using models for planet transit and stellar activity to put constraints on the radius of the detected planet and its orbit. Last, we searched for additional planets in the system by combining archival radial velocity data, astrometry, and direct imaging. Results. The debris disk HD 114082 appears as an axisymmetric debris belt with a radius of similar to 0.37 '' (35 au), an inclination of similar to 83 degrees, and a wide inner cavity. Dust particles in HD 114082 have a maximum polarization fraction of similar to 17% and a higher reflectivity when compared to the debris disk HD 117214. This high reflectivity results in a spectral scattering albedo of similar to 0.65 for the HD 114082 disk at near-infrared wavelengths. The disk reflectance spectrum exhibits a red color at the position of the planetesimal belt and shows no obvious features, whereas that of HD 117214 might indicate the presence of CO2 ice. The analysis of TESS photometric data reveals a transiting planetary companion to HD 114082 with a radius of similar to 1 R-Jup on an orbit with a semimajor axis of 0.7 +/- 0.4 au. No additional planet was detected in the system when we combined the SPHERE images with constraints from astrometry and radial velocity. We reach deep sensitivity limits down to similar to 5 M-Jup at 50 au and similar to 10 M-Jup at 30 au from the central star.