ARDENT: A Python package for fast dynamical detection limits with radial velocities

The architecture of planetary systems is a key piece of information to our
understanding of their formation and evolution. This information also allows us
to place the Solar System in the exoplanet context. An important example is the
impact of outer giant planets on the formation of inner super-Earths and
sub-Neptunes. Radial velocity (RV) surveys aim at drawing statistical insights
into the (anti-)correlations between giants and inner small planets, which
remain unclear. These surveys are limited by the completeness of the systems,
namely, the sensitivity of the data to planet detections. Here, we show that we
can improve the completeness by accounting for orbital stability. We introduce
the Algorithm for the Refinement of DEtection limits via N-body stability
Threshold (ARDENT), an open-source Python package for detection limits that
include the stability constraint. The code computes the classic data-driven
detection limits, along with the dynamical limits via both analytical and
numerical stability criteria. We present the code strategy and illustrate its
performance on TOI-1736 using published SOPHIE RVs. This system contains an
eccentric cold giant on a 570-day orbit and an inner sub-Neptune on a 7-day
orbit. We demonstrate that no additional planet can exist in this system beyond
150 days due to the gravitational influence of the giant. This outcome allows
us to significantly refine the system completeness and also carries
implications for RV follow-ups. ARDENT is user-friendly and can be employed
across a wide variety of systems to refine our understanding of their
architecture.