This paper presents a detailed analysis of two giant Lyman-alpha (Lya) arcs detected near known galaxies at z=3.038 and z=3.754 lensed by the massive cluster MACS 1206 (z=0.44). The Lya nebulae revealed in deep MUSE observations exhibit a double-peak profile with a dominant red peak that indicates expansion/outflowing motions. One of the arcs stretches over 1 around the Einstein radius of the cluster, resolving the velocity field of the line-emitting gas on kpc scales around a group of three star-forming galaxies of 0.3-1.6L* at z=3.038. The second arc spans 15 in size, roughly centered around a pair of low-mass Lya emitters of ~0.03L* at z=3.754. All three galaxies in the z=3.038 group exhibit prominent damped Lya absorption (DLA) and several metal absorption lines, in addition to nebular emission lines such as HeII1640 and CIII]1906,1908. Extended Lya emission appears to emerge from star-forming regions to larger distances with suppressed surface brightness at the center of each galaxy, suggesting the presence of dusty outflowing cones of size 1-5 kpc across. There are significant spatial variations in the Lya line profile, consistent with the presence of a steep negative velocity gradient in a continuous flow of high column density gas from star-forming regions into a low-density halo environment. While the observed UV nebular line ratios show no evidence of AGN activity in the galaxies, the observed Lya signals can be explained by a combination of resonant scattering and recombination radiation due to photoionization by ionizing photons escaping from the nearby star-forming regions. These observations provide the most detailed insights yet into the kinematics of galactic superwinds associated with star-forming galaxies thought to be responsible for the chemical enrichment in the intergalactic medium.
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