The X-ray and radio activity of typical and luminous Lya emitters from z~2 to z~6: evidence for a diverse, evolving population

Despite recent progress in understanding Lyman-alpha (Lya) emitters (LAEs), relatively little is known regarding their typical black hole activity across cosmic time. Here, we study the X-ray and radio properties of ~4000 LAEs at 2.2<z<6 from the SC4K survey in the COSMOS field. We detect 254 (6.8±0.4%) of the LAEs individually in the X-rays (S/N>3) and find an average luminosity of 10^{44.31±0.01} erg/s and an average black hole accretion rate (BHAR) of 0.72±0.01 Msun/yr, consistent with moderate to high accreting AGN. We detect 120 sources in deep radio data (radio AGN fraction of 3.2%±0.3%). The global AGN fraction (8.6%±0.4%) rises with Lya luminosity and declines with increasing redshift. For X-ray detected LAEs, Lya luminosities correlate with the BHARs, suggesting that Lya luminosity becomes an accretion rate indicator. Most LAEs (93.1±0.6%) at 2<z<6 have no detectable X-ray emission (BHARs<0.017 Msun/yr). The median star formation rate (SFR) of star-forming LAEs from Lya and radio luminosities is 7.6^{+6.6}_{-2.8} Msun/yr. The black hole to galaxy growth ratio (BHAR/SFR) for LAEs is <0.0022, consistent with typical star forming galaxies and the local BHAR/SFR relation. We conclude that LAEs at 2<z<6 include two different populations: an AGN population, where Lya luminosity traces BHAR, making them bright in Lya, and another with low SFRs which remain undetected in even the deepest X-ray stacks but is detected in the radio stacks.