The Limitations of Optical Spectroscopic Diagnostics in Identifying Active Galactic Nuclei in the Low-mass Regime

Intermediate-mass black holes (IMBHs) with masses between $100\,\mathrm{and}\,{10}^{5}{M}_{\odot }$ are crucial to our understanding of black hole seed formation and are the prime targets for the Laser Interferometer Space Antenna, yet black holes in this mass range have eluded detection by traditional optical spectroscopic surveys aimed at finding active galactic nuclei (AGNs). In this Letter, we have modeled for the first time the dependence of the optical narrow emission line strengths on the black hole mass of accreting AGN over the range of $100\mbox{--}{10}^{8}{M}_{\odot }$. We show that as the black hole mass decreases, the hardening of the spectral energy distribution from the accretion disk changes the ionization structure of the nebula. The enhanced high-energy emission from IMBHs results in a more extended partially ionized zone compared with models for higher mass black holes. This effect produces a net decrease in the predicted [O iii]/Hβ and [N ii]/Hα emission line ratios. Based on this model, we demonstrate that the standard optical narrow emission line diagnostics used to identify massive black holes fail when the black hole mass falls below $\approx {10}^{4}{M}_{\odot }$ for highly accreting IMBHs and for radiatively inefficient IMBHs with active star formation. Our models call into question the ability of common optical spectroscopic diagnostics to confirm AGN candidates in dwarf galaxies, and indicate that the low-mass black hole occupation fraction inferred from such diagnostics will be severely biased.