The Lyman alpha reference sample. VII. Spatially resolved H$\alpha$
  kinematics
  We present integral field spectroscopic observations with the Potsdam Multi
Aperture Spectrophotometer of all 14 galaxies in the $z\sim 0.1$ Lyman Alpha
Reference Sample (LARS). We produce 2D line of sight velocity maps and velocity
dispersion maps from the Balmer $\alpha$ (H$\alpha$) emission in our data
cubes. These maps trace the spectral and spatial properties of the LARS
galaxies' intrinsic Ly$\alpha$ radiation field. We show our kinematic maps
spatially registered onto the Hubble Space Telescope H$\alpha$ and Lyman
$\alpha$ (Ly$\alpha$) images. Only for individual galaxies a causal connection
between spatially resolved H$\alpha$ kinematics and Ly$\alpha$ photometry can
be conjectured. However, no general trend can be established for the whole
sample. Furthermore, we compute non-parametric global kinematical statistics --
intrinsic velocity dispersion $\sigma_0$, shearing velocity $v_\mathrm{shear}$,
and the $v_\mathrm{shear}/\sigma_0$ ratio -- from our kinematic maps. In
general LARS galaxies are characterised by high intrinsic velocity dispersions
(54\,km\,s$^{-1}$ median) and low shearing velocities (65\,km\,s$^{-1}$
median). $v_\mathrm{shear}/\sigma_0$ values range from 0.5 to 3.2 with an
average of 1.5. Noteworthy, five galaxies of the sample are dispersion
dominated systems with $v_\mathrm{shear}/\sigma_0 <1$ and are thus
kinematically similar to turbulent star forming galaxies seen at high redshift.
When linking our kinematical statistics to the global LARS Ly$\alpha$
properties, we find that dispersion dominated systems show higher Ly$\alpha$
equivalent widths and higher Ly$\alpha$ escape fractions than systems with
$v_\mathrm{shear}/\sigma_0 > 1$. Our result indicates that turbulence in
actively star-forming systems is causally connected to interstellar medium
conditions that favour an escape of Ly$\alpha$ radiation.
