Characterization of debris disks observed with SPHERE

Aims. This study aims to characterize debris disk targets observed with SPHERE across multiple programs, with the goal of identifying systematic trends in disk morphology, dust mass, and grain properties as a function of stellar parameters. By combining scattered-light imaging with photometric and parametric modeling, we seek to improve our understanding of the composition and evolution of circumstellar material in young debris systems and to place debris disks in the broader context of planetary system architectures. Methods. We analyzed a sample of 161 young main-sequence stars using archival SPHERE observations at optical and near-infrared (IR) wavelengths. Disk geometries were derived from ellipse fitting and model grids, while dust mass and properties were constrained by modified blackbody (MBB) and size distribution (SD) modeling of spectral energy distributions (SEDs). We also carried out dynamical modeling to assess whether the observed disk structures can be explained by the presence of unseen planets. Results. We resolve 51 debris disks, including four new detections where disks are resolved for the first time: HD 36968, BD-20 951, and the inner belts of HR 8799 and HD 36546. In addition, we find a second transiting giant planet in the HD 114082 system, with a radius of 1.29 ± 0.05 R _Jup and an orbital distance of ~1 au, providing an important new benchmark for planet–disk interaction studies. Beyond these new detections, we identify nine multi-belt systems, with outer-to-inner belt radius ratios of 1.5–2, and find close agreement between scattered-light and millimeter continuum belt radii with a mean ratio R _belt(near-IR)/R _belt(mm) of 1.05 ± 0.04. Belt radii scale weakly with stellar luminosity (R _belt ∝ L _⋆^0.11±0.05), but show steeper dependencies when separated by CO and CO₂ freeze-out regimes, and also increase with age as R _belt ∝ t _age^0.37±0.11. Uniform image modeling yields vertical disk aspect ratios of 0.02–0.06, consistent with collisionally stirred belts, while gas-rich systems show unusually small values. Inner density slopes steepen with stellar luminosity, indicating more efficient dust removal around luminous stars. Disk fractional luminosities follow collisional decay trends, declining as t _age^{−1.18±0.14} for A-type and t _age^{−0.81±0.12} for F-type stars. SD modeling yields minimum grain sizes consistently above the blowout limit, typically >0.8 μm, with a mean SD index of q = 3.6, assuming astrosilicate composition. The inferred dust masses span 10⁻⁵−1 M _⊕ from MBB modeling (and 0.01–1 M _⊕ from SD modeling for detected disks). These masses scale as R _beltⁿ with n > 2 in belt radius and super-linearly with stellar mass, consistent with trends seen in protoplanetary disks (PPDs). Our detailed analysis of disk scattered-light non-detections indicates that they are mainly caused by low dust masses, unfavorable viewing geometries, or suboptimal observing conditions. SD modeling combined with Mie theory further shows that bulk albedos are consistently above 0.5 with little variation, making albedo differences an unlikely explanation. To explore this further, we introduced a new parametric approach based on scattered-light and polarized-light images, which provides independent estimates of dust albedo and maximum polarization fraction. We find a correlation between measured disk polarized flux and IR excess, with a slope shallower than that of optical total-intensity fluxes measured with HST/STIS. The offset of ~1 dex between total-intensity and polarized fluxes arises because polarized flux represents only a fraction of the total scattered light which depends on both grain properties and disk inclination. Finally, a comparison of planetary architectures shows that most benchmark systems resemble the Solar System, with multiple planets located inside wide Kuiper-belt analogues. Dynamical modeling further indicates that many observed gaps and inner edges can be explained by unseen planets below current detection thresholds, typically with Neptune- to sub-Jovian masses, underscoring the likely ubiquity of such planets in shaping debris disk morphologies.