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We exploit ALMA 870um observations to measure the star-formation rates (SFRs)of eight X-ray detected Active Galactic Nuclei (AGNs) in a z~3.1 protocluster,four of which reside in extended Ly-alpha haloes (often termed Ly-alpha blobs:LABs). Three of the AGNs are detected by ALMA and have implied SFRs of~220-410~M_sun/yr; the non detection of the other five AGNs places SFR upperlimits of <210 M_sun/yr. The mean SFR of the protocluster AGNs (~110-210M_sun/yr) is consistent (within a factor of ~0.7-2.3) with that found forco-eval AGNs in the field, implying that galaxy growth is not significantlyaccelerated in these systems. However, when also considering ALMA data from theliterature, we find evidence for elevated mean SFRs (up-to a factor of ~5.9over the field) for AGNs at the protocluster core, indicating that galaxygrowth is significantly accelerated in the central regions of the protocluster.We also show that all of the four protocluster LABs are associated with an ALMAcounterpart within the extent of their Ly-alpha emission. The SFRs of the ALMAsources within the LABs (~150-410 M_sun/yr) are consistent with those expectedfor co-eval massive star-forming galaxies in the field. Furthermore, the twogiant LABs (with physical extents of >100 kpc) do not host more luminous starformation than the smaller LABs, despite being an order of magnitude brighterin Ly-alpha emission. We use these results to discuss star formation as thepower source of LABs.

ALMA observations of a z~3.1 Protocluster: Star Formation from Active Galactic Nuclei and Lyman-Alpha Blobs in an Overdense Environment