Atmospheric Escape Rates of Planets in Stellar Tidal Fields from 3-D Hydrodynamic Simulations1

Thermally driven atmospheric escape, including photo-evaporation and core-powered mass-loss, plays a key role in shaping the evolution of close-in exoplanets, yet most current models rely on simplified one-dimensional descriptions of atmospheric escape. In this work, we perform 3D hydrodynamic simulations of atmospheric outflows from a Jupiter-sized planet embedded in the gravitational potential of a solar-type host star, and compare these results with 1D models to identify the regimes where they perform well and where they break down. We explore a range of configurations by varying the degree of Roche-lobe filling and the thermal state of the outflow. We find that systems with weak tidal influence and high-temperature winds produce nearly spherical and isotropic outflows, whereas more Roche-lobe-filling and cooler winds develop strong anisotropy and form two-tailed structures. We show that the commonly used 1D Parker wind model performs well only in the weak-tides regime, while including tidal corrections yields reasonable estimates of mass-loss rates and captures the mean radial density profile across all regimes, but fails to reproduce the intrinsically three-dimensional, angle-dependent nature of the flow as the outflow transitions from spherical to tidally structured tails. Motivated by these results, we develop a physically informed Mixture Model, calibrated using our 3D simulations, that accurately predicts mass-loss rates across the parameter space explored and outperforms 1D model with tidal corrections.