We exploit ALMA 870 \mu m observations to measure the star-formation rates ( SFRs ) of eight X-ray detected Active Galactic Nuclei ( AGNs ) in a z \approx 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 \approx 220–410 M _ { \odot } yr ^ { -1 } ; the non detection of the other five AGNs places SFR upper limits of \buildrel < \over { \sim } 210 M _ { \odot } yr ^ { -1 } .
The mean SFR of the protocluster AGNs ( \approx 110–210 M _ { \odot } yr ^ { -1 } ) is consistent ( within a factor of \approx 0.7–2.3 ) with that found for co-eval AGNs in the field , implying that the galaxy growth is not significantly accelerated in these systems .
However , when also considering ALMA data from the literature , we find evidence for elevated mean SFRs ( up-to a factor of \approx 5.9 over the field ) for AGNs at the protocluster core , indicating that galaxy growth is significantly accelerated in the central regions of the protocluster .
We also show that all of the four protocluster LABs are associated with an ALMA counterpart within the extent of their Ly \alpha emission .
The SFRs of the ALMA sources within the LABs ( \approx 150–410 M _ { \odot } yr ^ { -1 } ) are consistent with those expected for co-eval massive star-forming galaxies in the field .
Furthermore , the two giant LABs ( with physical extents of \buildrel > \over { \sim } 100 kpc ) do not host more luminous star formation than the smaller LABs , despite being an order of magnitude brighter in Ly \alpha emission .
We use these results to discuss star formation as the power source of LABs .