Environmental Evidence for Overly Massive Black Holes in Low-mass Galaxies and a Black Hole-Halo Mass Relation at z ∼ 5

JWST observations have unveiled faint active galactic nuclei (AGNs) at high redshift that provide insights into the formation of supermassive black holes (SMBHs). However, disentangling their stellar from AGN light is challenging. Here, we use an empirical approach to infer the average stellar mass of five faint broad-line (BL) Hα emitters at z = 4-5 with BH masses ≈6 × 10⁶ M_⊙, with a method independent of their spectral energy distribution (SED). We use the deep JWST/NIRcam grism survey “All the Little Things” to measure the overdensities around BL-Hα emitters and around a spectroscopic reference sample of ∼300 galaxies. In our reference sample, we find that megaparsec-scale overdensity correlates with stellar mass. Their large-scale environments suggest that BL-Hα emitters are hosted by galaxies with stellar masses ≈5 × 10⁷ M_⊙, ≈40 times lower than those inferred from galaxy-only SED fits. Adding measurements around more luminous z ≈ 6 AGNs, we find tentative correlations between line width, BH mass, and the overdensity, suggestive of a steep BH to halo mass relation. The main implications are (1) when BH masses are taken at face value, we confirm extremely high BH to stellar mass ratios of ≈10%, (2) the galaxies of low stellar mass that host growing SMBHs are in tension with typical hydrodynamical simulations, except those without feedback, (3) a 1% duty cycle implied by the host mass hints at super-Eddington accretion, (4) the masses are at odds with an interpretation of the line broadening in terms of high stellar density, (5) our results imply a luminosity-dependent diversity of galaxy masses, environments, and SEDs among AGN samples.