High-contrast detection of exoplanets with a kernel-nuller at the VLTI

Context: The conventional approach to direct imaging has been the use of a single aperture coronagraph with wavefront correction via extreme adaptive optics. Such systems are limited to observing beyond an inner working (IWA) of a few {\lambda}/D. Nulling interferometry with two or more apertures will enable detections of companions at separations at and beyond the formal diffraction limit. Aims: This paper evaluates the astrophysical potential of a kernel-nuller as the prime high-contrast imaging mode of the Very Large Telescope Interferometer (VLTI). Methods: By taking into account baseline projection effects which are induced by Earth rotation, we introduce some diversity in the response of the nuller as a function of time. This response is depicted by transmission maps. We also determine whether we can extract the astrometric parameters of a companion from the kernel outputs, which are the primary intended observable quantities of the kernel-nuller. This then leads us to comment on the characteristics of a possible observing program for the discovery of exoplanets. Results: We present transmission maps for both the raw nuller outputs and their subsequent kernel outputs. To further examine the properties of the kernel-nuller, we introduce maps of the absolute value of the kernel output. We also identify 38 targets for the direct detection of exoplanets with a kernel-nuller at the focus of the VLTI. Conclusions: With continued upgrades of the VLTI infrastructure that will reduce fringe tracking residuals, a kernel-nuller would enable the detection of young giant exoplanets at separations < 10 AU, where radial velocity and transit methods are more sensitive.