The Stellar Mass-Black Hole Mass Relation at z 2 down to {{M }}_{\mathrm{BH}}∼ {10}(7} {M) _{⊙ } Determined by HETDEX

We investigate the stellar mass-black hole mass ( ${{ \mathcal M }}_{* }\mbox{--}{{ \mathcal M }}_{\mathrm{BH}}$ ) relation with type 1 active galactic nuclei (AGNs) down to ${{ \mathcal M }}_{\mathrm{BH}}={10}^{7\,}{M}_{\odot }$ , corresponding to a ≃ -21 absolute magnitude in rest-frame ultraviolet, at z = 2-2.5. Exploiting the deep and large-area spectroscopic survey of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX), we identify 66 type 1 AGNs with ${{ \mathcal M }}_{\mathrm{BH}}$ ranging from 10⁷-10¹⁰ M _⊙ that are measured with single-epoch virial method using C IV emission lines detected in the HETDEX spectra. ${{ \mathcal M }}_{* }$ of the host galaxies are estimated from optical to near-infrared photometric data taken with Spitzer, the Wide-field Infrared Survey Explorer, and ground-based 4-8 m class telescopes by CIGALE spectral energy distribution (SED) fitting. We further assess the validity of SED fitting in two cases by host-nuclear decomposition performed through surface brightness profile fitting on spatially resolved host galaxies with the James Webb Space Telescope/NIRCam CEERS data. We obtain the ${{ \mathcal M }}_{* }\mbox{--}{{ \mathcal M }}_{\mathrm{BH}}$ relation covering the unexplored low-mass ranges of ${{ \mathcal M }}_{\mathrm{BH}}\,\sim \,{10}^{7}\mbox{--}{10}^{8}\,{M}_{\odot }$ , and conduct forward modeling to fully account for the selection biases and observational uncertainties. The intrinsic ${{ \mathcal M }}_{* }\mbox{--}{{ \mathcal M }}_{\mathrm{BH}}$ relation at z ~ 2 has a moderate positive offset of 0.52 ± 0.14 dex from the local relation, suggestive of more efficient black hole growth at higher redshift even in the low-mass regime of ${{ \mathcal M }}_{\mathrm{BH}}\,\sim \,{10}^{7}\mbox{--}{10}^{8}\,{M}_{\odot }$ . Our ${{ \mathcal M }}_{* }\mbox{--}{{ \mathcal M }}_{\mathrm{BH}}$ relation is inconsistent with the ${{ \mathcal M }}_{\mathrm{BH}}$ suppression at the low- ${{ \mathcal M }}_{* }$ regime predicted by recent hydrodynamic simulations at a 98% confidence level, suggesting that feedback in the low-mass systems may be weaker than those produced in hydrodynamic simulations.