Recovering $\lambda_R$ and $V/\sigma$ from seeing-dominated IFS data

Abstract

Observers experience a series of limitations when measuring galaxy kinematics, such as variable seeing conditions and aperture size. These effects can be reduced using empirical corrections, but these equations are usually applicable within a restrictive set of boundary conditions (e.g. S\'ersic indices within a given range) which can lead to biases when trying to compare measurements made across a full kinematic survey. In this work, we present new corrections for two widely used kinematic parameters, $\lambda_R$ and $V/\sigma$, that are applicable across a broad range of galaxy shapes, measurement radii and ellipticities. We take a series of mock observations of N-body galaxy models and use these to quantify the relationship between the observed kinematic parameters, structural properties and different seeing conditions. Derived corrections are then tested using the full catalogue of galaxies, including hydro-dynamic models from the EAGLE simulation. Our correction is most effective for regularly-rotating systems, yet the kinematic parameters of all galaxies -- fast, slow and irregularly rotating systems -- are recovered successfully. We find that $\lambda_R$ is more easily corrected than $V/\sigma$, with relative deviations of 0.02 and 0.06 dex respectively. The relationship between $\lambda_R$ and $V/\sigma$, as described by the parameter $\kappa$, also has a minor dependence on seeing conditions. These corrections will be particularly useful for stellar kinematic measurements in current and future integral field spectroscopic (IFS) surveys of galaxies.