The MUSE view of Lyman-$\alpha$ nebulae in High redshift Radio Galaxies

We present the results of VLT/MUSE integral field spectroscopic observations of the Ly$\alpha\,$ emission nebulae associated with 11 high redshift ($z \geq 2.9$) radio galaxies (HzRGs) with DEC $<25^{\circ}$. When considering the other nine sources with available archival MUSE data, these observations increase the coverage to half of the currently known HzRGs. For two sources we are unable to confirm the original identification, as no Ly$\alpha\,$ emission was detected. We produce narrow band images centered on the Ly$\alpha\,$ line, extract their nuclear spectra, map their ionized gas kinematics, and derive the Ly$\alpha\,$ surface brightness profiles (SBPs). The SBPs are generally well reproduced by an exponential law with a typical scale length of $\sim 20-30$ ckpc. We measure emission line ratios finding most sources in agreement with an AGN origin for their gas ionization, with a single object hinting at strong star formation. Regarding the connection between the radio and ionized gas emission, we find that while the Ly$\alpha\,$ nebulae are preferentially aligned with the direction of the radio emission, there is no clear correlation in terms of size or gas kinematics, and only a weak trend connecting their radio and Ly$\alpha\,$ luminosities. The alignment is most likely the result of anisotropic nuclear emission rather than of a direct impact of the jets into the ionized gas.