H II and H I emission as seen with MUSE and VLA around SBS 0335−052E. Top panel: continuum-subtracted Hα narrowband image. Fluxes are encoded via an asinh-scaled cyclic colour map from 0 to 10⁻¹⁸ erg s⁻¹ cm⁻² in the low surface-brightness, and from 10⁻¹⁸ erg s⁻¹ cm⁻² to 10⁻¹⁶ erg s⁻¹ cm⁻² in the central high surface-brightness region. The cyan solid contours demarcate Hα isophotes at SB_Hα = {1.5, 2.5, 5, 12.5}×10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² while the white dotted contour demarcates the limiting surface-brightness of SB_Hα = 7.5 × 10⁻¹⁹ erg s⁻¹ cm⁻² arcsec⁻². The image has been smoothed with a Gaussian of 0.4″ FWHM. Subdued grey contours indicate HI column densities N_HI = {5, 10, 20, 30, 40}×10²⁰ cm⁻² from our VLA-B configuration observations; these contours are displayed more prominently in Fig. 4. The dashed white contour demarcates the 2.5σ = 2.5 × 10²⁰ cm⁻² detection limit. The VLA-B configuration beam, 6.1″ × 4.6″ oriented 23.6° west of north, is indicated via a grey shaded ellipse in the top left. The displayed field of view is 1′35″ × 1′46″ corresponding to 26.2 kpc × 29.2 kpc in projection. The dashed violet square in the centre indicates the viewport used in Fig. 4. North is up and east is to the left. Bottom panels: signal-to-noise of the three principal emission lines (Hα, Hβ, and [O III] λ5007 in the left, centre, and right panel, respectively) in which extended ionised gas is detected (see text for details). The maps are displayed with a linear cyclic colour map from 0 to 90 and from 90 to 900. White dotted contours mark out regions with SN > 8. The chartreuse dashed rectangles in the Hα panel outline the rectangular regions used for the line ratio analysis in Sect. 3.2.