SMBH Seeds: Model Discrimination with High Energy Emission Based on Scaling Relation Evolution

We explore the expected X-ray (0.5-2keV) signatures from super massive black holes (SMBHs) at high redshifts ($z\sim5-12$) assuming various models for their seeding mechanism and evolution. The seeding models are approximated through deviations from the M$_{BH}-\sigma$ relation observed in the local universe. We use results from N-body simulations of the large-scale structure to estimate the density of observable SMBHs. We focus on two families of seeding models: (\textit{i}) light seed BHs from remnants of Pop-III stars; and (\textit{ii}) heavy seeds from the direct collapse of gas clouds. We investigate several models for the accretion history, such as sub-Eddington accretion, slim disk models allowing mild super-Eddington accretion and torque-limited growth models. We consider observations with two instruments: (\textit{i}) the Chandra X-ray observatory, and (\textit{ii}) the proposed Lynx. We find that all the simulated models are in agreement with the current results from Chandra Deep Field South (CDFS) - \textit{i.e.,} consistent with zero to a few observed SMBHs in the field of view. In deep Lynx exposures, the number of observed objects is expected to become statistically significant. We demonstrate the capability to limit the phase space of plausible scenarios of the birth and evolution of SMBHs by performing deep observations at a flux limit of $1\times10^{-19}\mathrm{erg\,cm^{-2}\,s^{-1}}$. Finally, we estimate the expected contribution from each model to the unresolved cosmic X-ray background (CXRB), and show that our models are in agreement with current limits on the CXRB and the expected contribution from unresolved quasars. We find that an analysis of CXRB contributions down to the Lynx confusion limit yields valuable information that can help identify the correct scenario for the birth and evolution of SMBHs.