The Stellar Mass - Black Hole Mass Relation at $z\sim2$ Down to $\mathcal{M}_\mathrm{BH}\sim10^7 M_\odot$ Determined by HETDEX

We investigate the stellar mass - black hole mass ($\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$) relation with type 1 AGN down to $\mathcal{M}_\mathrm{BH}=10^7 M_\odot$, corresponding to a $\simeq -21$ absolute magnitude in rest-frame ultraviolet (UV), 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 AGN with $\mathcal{M}_\mathrm{BH}$ ranging from $10^7$ to $10^{10} M_\odot$ that are measured with single-epoch virial method using C{\sc 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, WISE, and ground-based 4-8m class telescopes by CIGALE 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 JWST/NIRCam CEERS data. We obtain the $\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ relation covering the unexplored low-mass ranges of $\mathcal{M}_\mathrm{BH}~\sim~10^7-10^8~M_\odot$, and conduct forward modelling to fully account for the selection biases and observational uncertainties. The intrinsic $\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ relation at $z\sim 2$ has a moderate positive offset of $0.52\pm0.14$~dex from the local relation, suggestive of more efficient black hole growth at higher redshift even in the low-mass regime of $\mathcal{M}_\mathrm{BH}~\sim~10^7-10^8~M_\odot$. Our $\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ 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.