How to recover both velocity components in discs of barred galaxies with integral-field spectroscopy

We present a new method that derives both velocity components in the equatorial plane of a barred stellar disc from the observed line-of-sight velocity, assuming geometry of a thin disc. The method can be applied to large departures from circular motion, and does not require multipole decomposition. It is based on assumptions that the bar is close to steady-state (i.e. does not evolve fast), and that both morphology and kinematics are symmetrical with respect to the major axis of the bar. We derive the equations used in the method, and analyze the effect of observational errors on the inferred velocity fields. We show that this method produces meaningful results via a simple toy model. We also apply the method on integral-field data of NGC 936, for which we recover both velocity components in the disc. Knowing both velocity components in the disc, i.e. the non-observable transverse velocity in addition to the line-of-sight velocity, puts additional constraints on dynamical models and allows for new ways of determining parameters that are crucial in characterizing galaxies.