The Lyman alpha reference sample. XV. Relating ionised gas kinematics with Lyman-alpha observables

Gas kinematics affect the radiative transfer and escape of hydrogen Lyman-alpha (Lyalpha ) emission from galaxies. We investigate this interplay empirically by relating the ionised gas kinematics of 42 galaxies in the extended Lyalpha Reference Sample (eLARS) with their Lyalpha escape fractions, $f_ esc Ly alpha $, Lyalpha equivalent widths, $ EW Ly alpha $, and Lyalpha luminosities, $L_ Ly alpha $. To this aim we use PMAS integral-field spectroscopic observations of the Balmer-alpha line. Our sample contains 18 rotating discs, 13 perturbed rotators, and 13 galaxies with more complex kinematics. The distributions of $f_ esc Ly alpha EW Ly alpha $, and $L_ Ly alpha $ do not differ significantly between these kinematical classes, but the largest Lyalpha observables are found amongst the kinematically complex systems. We find no trends between either $f_ esc Ly alpha $ or $ EW Ly alpha $ and kinematic or photometric inclinations. We calculate shearing velocities, $v_ shear $, and intrinsic velocity dispersions, $ obs obs $) and more than half of the sources show dispersion-dominated kinematics. We uncover clear trends between Lyalpha observables and global kinematical statistics: $ EW Ly alpha $ and $L_ Ly alpha $ correlate with $ obs $, while $f_ esc Ly alpha $ anti-correlates with $v_ shear $ and $v_ shear obs $. Moreover, we find, that galaxies with $ EW Ly alpha are characterised by higher $ and lower $v_ shear obs $ than galaxies below this threshold. We discuss the statistical importance of $v_ shear obs $, and $v_ shear obs $ for regulating the Lyalpha observables in comparison to other galaxy parameters. It emerges that $ obs $ is the dominating parameter for regulating $ EW Ly alpha $ and that is as important as nebular extinction, gas covering fraction, and ionising photon production efficiency in regulating $f_ esc Ly alpha $. A simple scenario where the starburst age is simultaneously regulating turbulence, $ EW Ly alpha $, and $f_ esc esc $ is not supported by our observations. However, we show that the small-scale distribution of dust appears to be influenced by turbulence in some galaxies. In support of our observational result, we discuss how turbulence is theoretically expected to play a significant role in modulating $f_ esc Ly alpha