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Context.
Submillimeter galaxies (SMGs) have been proposed as the progenitors of massive ellipticals in the local Universe. Mapping the neutral gas distribution and investigating the gas accretion toward the SMGs at high redshift can provide information on the way SMG environments can evolve into clusters at
z
= 0.
Aims.
In this work, we study the members of the protocluster around AzTEC-3, a submillimeter galaxy at
z
= 5.3. We use Ly
α
emission and its synergy with previous CO and [C
II
]158 μm observations.
Methods.
We analyzed the data from the Multi Unit Spectroscopic Explorer (MUSE) instrument in an area of 1.4 × 1.4 arcmin
2
around AzTEC-3 and derived information on the Ly
α
line in emission. We compared the Ly
α
profile of various regions of the environment with the zELDA radiative transfer model, revealing the neutral gas distribution and kinematics.
Results.
We identified ten Ly
α
emitting sources, including two regions with extended emission: one embedding AzTEC-3 and LBG-3, which is a star-forming galaxy located 2″ (12 kpc) north of the SMG and another toward LBG-1, which is a star-forming galaxy located 15″ (90 kpc) to the southeast. The two regions extend for ∼27 × 38 kpc
2
(∼170 × 240 ckpc
2
) and ∼20 × 20 kpc
2
(∼125 × 125 ckpc
2
), respectively. The sources appear distributed in an elongated configuration of about 70″ (430 kpc) in extent. The number of sources confirms the overdensity around AzTEC-3. We study the MUSE spectra of the AzTEC-3+LBG-3 system and LBG-1 in detail. For the AzTEC-3+LBG-3 system, the Ly
α
emission appears redshifted and more spatially extended than the [C
II
] line emission. Similarly, the Ly
α
line spectrum is broader in velocity than [C
II
] for LBG-1. In the former spectrum, the Ly
α
emission is elongated to the north of LBG-3 and to the south of AzTEC-3, where a faint Ly
α
emitting galaxy is also located. The elongated structures could resemble tidal features due to the interaction of the two galaxies with AzTEC-3. Also, we find a bridge of gas, revealed by the Ly
α
emission between AzTEC-3 and LBG-3. The Ly
α
emission toward LBG-1 embeds its three components. The HI kinematics support the idea of a merger of the three components.
Conclusions.
Given the availability of CO and [C
II
] observations from previous campaigns, and the Ly
α
information from our MUSE dataset, we find evidence of starburst-driven phenomena and interactions around AzTEC-3. The stellar mass of the galaxies of the overdensity and the Ly
α
luminosity of the HI nebula associated with AzTEC-3 imply a dark matter halo of ∼10
12
M
⊙
at
z
= 5.3. By comparing this with semi-analytical models, the dark matter halo mass indicates that the region could evolve into a cluster of 2 × 10
13
M
⊙
by
z
= 2 and into a Fornax-type cluster at
z
= 0 with a typical mass of 2 × 10
14
M
⊙
.