geko : A tool for modelling galaxy kinematics and morphology in JWST /NIRCam slitless spectroscopic observations

Wide-field slitless spectroscopy (WFSS) is a powerful tool for studying large samples of galaxies across cosmic time. With the arrival of JWST, and its NIRCAM grism mode, slitless spectroscopy can reach a medium spectral resolution of (R ∼ 1600), allowing it to spatially resolve the ionised-gas kinematics out to z ∼ 9. However, the kinematic information is convolved with morphology along the dispersion axis, a degeneracy that must be modelled to recover intrinsic properties. We present the Grism Emission-line Kinematics tOol (geko), a Python package that forward-models NIRCam grism observations and infers emission-line morphologies and kinematics within a Bayesian framework. geko combines Sérsic surface-brightness models with arctangent rotation curves, includes full point-spread function (PSF) convolution and forward-modelling of the grism dispersion, and leverages gradient-based sampling via jax/numpyro for efficient inference. It recovers parameters such as effective radius, velocity dispersion, rotational velocity, rotational support, and dynamical mass, with typical run times of ∼20 minutes per galaxy on GPUs. We validate performance using extensive mock data spanning position angle, S/N, and morphology, quantifying where degeneracies limit recovery. Finally, we demonstrate applications to real FRESCO Hα emitters at z ≈ 4 − 6, recovering both rotation- and dispersion-dominated systems. geko opens the way to statistical studies of galaxy dynamics in the early Universe and is publicly available at https://github.com/angelicalola-danhaive/geko.