MUSE Analysis of Gas around Galaxies (MAGG) -- V: Linking ionized gas traced by CIV and SiIV absorbers to Ly${\alpha}$ emitting galaxies at $z\approx 3.0-4.5$

We use 28 quasar fields with high-resolution (HIRES and UVES) spectroscopy from the MUSE Analysis of Gas Around Galaxies survey to study the connection between Ly${\alpha}$ emitters (LAEs) and metal-enriched ionized gas traced by CIV in absorption at redshift $z\approx3-4$. In a sample of 220 CIV absorbers, we identify 143 LAEs connected to CIV gas within a line-of-sight separation ${\rm \pm 500\,km\,s^{-1}}$, equal to a detection rate of $36\pm 5$ per cent once we account for multiple LAEs connected to the same CIV absorber. The luminosity function of LAEs associated with CIV absorbers shows a $\approx 2.4$ higher normalization factor compared to the field. CIV with higher equivalent width and velocity width are associated with brighter LAEs or multiple galaxies, while weaker systems are less often identified near LAEs. The covering fraction in groups is up to $\approx 3$ times larger than for isolated galaxies. Compared to the correlation between optically-thick HI absorbers and LAEs, CIV systems are twice less likely to be found near LAEs especially at lower equivalent width. Similar results are found using SiIV as tracer of ionized gas. We propose three components to model the gas environment of LAEs: i) the circumgalactic medium of galaxies, accounting for the strongest correlations between absorption and emission; ii) overdense gas filaments connecting galaxies, driving the excess of LAEs at a few times the virial radius and the modulation of the luminosity and cross-correlation functions for strong absorbers; iii) an enriched and more diffuse medium, accounting for weaker CIV absorbers farther from galaxies.