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 3) and find an average luminosity of 10^{44.07+-0.01} erg/s and an average black hole accretion rate (BHAR) of 0.42+-0.01 Msun/yr, consistent with moderate to high accreting AGN. We detect 120 sources in deep radio data, implying a LAE radio AGN fraction of 3.2+-0.3%. Approximately half of the LAEs detected in the radio are also detected in the X-rays, resulting in a total AGN fraction of 8.6+-0.4% for >L* LAEs. The total AGN fraction rises with Lya luminosity and declines with increasing redshift. For AGN, we find that Lya luminosities correlate with the BHARs, suggesting that Lya luminosity becomes an accretion rate indicator. Most LAEs (93.1+-0.6%) at 2BHARs<0.009 Msun/yr). We estimate the median star formation rate (SFR) of star-forming LAEs from Lya and radio luminosities and find a SFR of 5.6^{+6.6}_{-2.8} Msun/yr. The black hole to galaxy growth ratio (BHAR/SFR) for LAEs is <0.0016, consistent with typical star forming galaxies and the local BHAR/SFR relation. We conclude that LAEs at 2luminosity 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.