  We analyze the physical properties of 8 X-ray selected active galactic nuclei
(AGN) and one candidate protoquasar system (ADF22A1) in the $z = 3.09$ SSA22
protocluster by fitting their X-ray-to-IR spectral energy distributions (SEDs)
using our SED fitting code, Lightning. We recover star formation histories
(SFH) for 7 of these systems which are well-fit by composite stellar population
plus AGN models. We find indications that 4/9 of the SSA22 AGN systems we study
have host galaxies below the main sequence, with $\rm SFR/SFR_{MS} \leq -0.4$.
The remaining SSA22 systems, including ADF22A1, are consistent with obscured
supermassive black hole (SMBH) growth in star forming galaxies. We estimate the
SMBH accretion rates and masses, and compare the properties and SFH of the 9
protocluster AGN systems with X-ray detected AGN candidates in the Chandra Deep
Fields (CDF), finding that the distributions of SMBH growth rates, star
formation rates, SMBH masses, and stellar masses for the protocluster AGN are
consistent with field AGN. We constrain the ratio between the sample-averaged
SSA22 SMBH mass and CDF SMBH mass to $<1.41$. While the AGN are located near
the density peaks of the protocluster, we find no statistically significant
trends between the AGN or host galaxy properties and their location in the
protocluster. We interpret the similarity of the protocluster and field AGN
populations together with existing results as suggesting that the protocluster
and field AGN co-evolve with their hosts in the same ways, while AGN-triggering
events are more likely in the protocluster.
