Emission Line Diagnostics for IMBHs in Dwarf Galaxies: Accounting for BH Seeding and ULX Excitation

Dwarf AGN serve as the ideal systems for identifying intermediate mass black holes (IMBHs) down to the most elusive regimes ($\sim 10^3 - 10^4 M_{\odot}$). However, the ubiquitously metal-poor nature of dwarf galaxies gives rise to ultraluminous X-ray sources (ULXs) that can mimic the spectral signatures of IMBH excitation. We present a novel photoionization model suite that simultaneously incorporates IMBHs and ULXs in a metal-poor, highly star-forming environment. We account for changes in $M_{BH}$ according to formation seeding channels and metallicity, and changes in ULX populations with post-starburst age and metallicity. We find that broadband X-rays and UV emission lines are insensitive to $M_{BH}$ and largely unable to distinguish between ULXs and IMBHs. Many optical diagnostic diagrams cannot correctly identify dwarf AGN. The notable exceptions include He~II~$\lambda$4686 and [O~I]~$\lambda$6300, for which we redefine typical demarcations to account for ULX contributions. Emission lines in the mid-IR show the most promise in separating stellar, ULX, IMBH, and shock excitation while presenting sensitivity to $M_{BH}$ and $f_{\text{AGN}}$. Overall, our results expose the potential biases in identifying and characterizing dwarf AGN purely on strong line ratios and diagnostic diagrams rather than holistically evaluating the entire spectrum. As a proof of concept, we argue that recently discovered over-massive BHs in high-$z$ JWST AGN might not represent the overall BH population, with many galaxies in these samples potentially being falsely classified as purely star-forming.