Context : The Lyman alpha emission line of galaxies is an important tool for finding galaxies at high redshift , and thus probe the structure of the early universe .
However , the resonance nature of the line and its sensitivity to dust and neutral gas is still not fully understood .

Aims : We present measurements of the velocity , covering fraction and optical depth of neutral gas in front of two well known local blue compact galaxies that show Lyman alpha in emission : ESO 338-IG 04 and Haro 11 .
We thus test observationally the hypothesis that Lyman alpha can escape through neutral gas by being Doppler shifted out of resonance .

Methods : We present integral field spectroscopy from the GIRAFFE/Argus spectrograph at VLT/FLAMES in Paranal , Chile .
The excellent wavelength resolution allows us to accurately measure the velocity of the ionized and neutral gas through the H \alpha emission and Na D absorption , which traces the ionized medium and cold interstellar gas , respectively .
We also present independent measurements with the VLT/X-shooter spectrograph which confirm our results .

Results : For ESO 338-IG04 , we measure no significant shift of neutral gas .
The best fit velocity is -15 \pm 16 km/s .
For Haro 11 , we see an outflow from knot B at 44 \pm 13 km/s and infalling gas towards knot C with 32 \pm 12 km/s .
Based on the relative strength of the Na D absorption lines , we estimate low covering fractions of neutral gas ( down to 10 % ) in all three cases .

Conclusions : The Na D absorption likely occurs in dense clumps with higher column densities than where the bulk of the Ly \alpha scattering takes place .
Still , we find no strong correlation between outflowing neutral gas and a high Lyman alpha escape fraction .
The Lyman alpha photons from these two galaxies are therefore likely escaping due to a low column density and/or covering fraction .