The steady-state hydrodynamics of a long-lived disc: planetary system architecture and prospects of observing a circumplanetary disc shadow in V4046$\,$Sgr

Abstract

Recent imaging of the disc around the V4046$\,$Sgr spectroscopic binary revealed concentric regions of dust rings and gaps. The object's proximity and expected equilibrated state due to its old age (>20$\,$Myr) make it a superb testbed for hydrodynamical studies in direct comparison to observations. We employ two-dimensional hydrodynamical simulations of gas and multiple dust species to test whether the observed structure conforms with the presence of giant planets embedded in the disc. We then perform radiative transfer calculations of sky images, which we filter for the telescope response for comparison with near-infrared and millimetre observations. We find that the existing data are in excellent agreement with a flared disc and the presence of two giant planets, at 9$\,$au and 20$\,$au, respectively. The different ring widths are recovered by diffusion-balanced dust trapping within the gas pressure maxima. In our radiative transfer model, the diffusion in vertical direction is reduced in comparison to the radial value by a factor of five to recover the spectral energy distribution. Further, we report a previously unaddressed, azimuthally-confined intensity decrement on the bright inner ring in the near-infrared scattered light observation. Our model shows that this decrement can be explained by a shadow cast by a circumplanetary disc around the same giant planet that creates the inner cavity in the hydrodynamical simulations. We examine the shape of the intensity indentation and discuss the potential characterisation of a giant planet and its associated disc by its projected shadow in scattered light observations.