Cosmological simulations suggest that most of the matter in the Universe is distributed along filaments connecting galaxies. Illuminated by the cosmic UV background (UVB), these structures are expected to emit fluorescent Ly α emission with a surface brightness (SB) that is well below current limits for individual detections. We perform a stacking analysis of the deepest MUSE/VLT data using three-dimensional regions (subcubes) with orientations determined by the position of neighboring Lyα galaxies between redshift 3 to 4.

Our method increases the probability of detecting filamentary Lyα emission, provided that these structures are Lyman-limit systems (LLSs). By stacking 390 oriented subcubes we reach a 2σ sensitivity level of SB ≈ 0.44 × 1e−20 erg/s/cm^2/arcsec^2 in an aperture of 1 arcsec^2 × 6.25 Å, three times below the expected fluorescent Lyα signal from the Haardt & Madau (HM) UVB at z~3.5. No detectable emission is found on intergalactic scales, implying that at least two-thirds of our subcubes do not contain oriented LLSs. On the other hand, significant emission is detected in the circumgalactic medium (CGM) in the direction of the neighbors. The signal is stronger for galaxies with a larger number of neighbors and appears to be independent of any other galaxy properties, suggesting that gas densities in the CGM are typically larger in the direction of neighboring galaxies on cosmological scales.

By building mock cubes from the EAGLE simulations and applying the same selection criteria and subcube extraction as in MUSE data, we observe a strong correlation between redshift and neighboring galaxy distance and the filament detection, and a small correlation with galaxy magnitudes and halo mass. Using our MUSE stacking results in combination with EAGLE constraints, we estimate an average covering fraction of LLSs between galaxies of about 10%, implying a hydrogen photoionization rate below 2e-12 1/s at z~3.5. These results suggest that an optimal Cosmic Web stacking is obtained for neighboring galaxies closer than 2 cMpc, and a detection should be possible with the upcoming deep data-cubes and galaxy catalogs.