Using Spitzer Space Telescope IRAC (3.6-8um) and MIPS (24um) imaging, as well as Hubble Space Telescope optical observations, we identify the IRAC counterparts of the luminous power sources residing within the two largest and brightest Lyman-alpha emitting nebulae (LABs) in the SA22 protocluster at z=3.09 (LAB1 and LAB2). These sources are also both submillimeter galaxies (SMGs). From their rest-frame optical/near-infrared colors, we conclude that the SMG in LAB1 is likely to be starburst dominated and heavily obscured (Av~3). In contrast, LAB2 has excess rest-frame ~2um emission (over that expected from starlight) and hosts a hard X-ray source at the proposed location of the SMG, consistent with the presence of an active galactic nucleus (AGN). We conclude that LAB1 and LAB2 appear to have very different energy sources despite having similar Lyman-alpha spatial extents and luminosities, although it remains unclear whether on-going star-formation or periodic AGN heating is responsible for the extended Lyman-alpha emission. We find that the mid-infrared properties of the SMGs lying in LAB1 and LAB2 are similar to those of the wider SMG population, and so it is possible that extended Lyman-alpha haloes are a common feature of SMGs in general.
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