A Selection Aware View of Black Hole-Galaxy Coevolution at High Redshift

Abstract

The large population of broad-line Active Galactic Nuclei (AGN) observed with the James Webb Space Telescope (JWST) at $z \gtrsim 4$ opens a new window onto the black hole-galaxy connection in the first Gyr of cosmic history. We use the JADES survey-level dataset and develop a forward-modeling Bayesian framework that explicitly accounts for broad H$α$ detectability, ensuring that selection effects are incorporated into the likelihood function. With this approach, we constrain the black hole-stellar mass ($M_{\mathrm{BH}}$-$M_\star$) relation to be $\log M_{\rm BH} = -4.06^{+0.50}_{-0.51} + 1.17^{+0.06}_{-0.06}\,\log M_\star$, with an intrinsic orthogonal scatter of $σ_{\rm int} = 0.63^{+0.14}_{-0.11}$ dex. The slope and normalization are consistent with local determinations, indicating that the average scaling was already established by $z \sim 4$-6. This suggests that the primary evolution of the relation occurs in its dispersion rather than in its mean normalization. In contrast, the substantially larger intrinsic scatter relative to the nearby Universe reveals a wider diversity of black hole-galaxy growth histories, likely driven by bursty accretion, delayed feedback, and differences in merger or seeding histories. Future JWST samples will be crucial to test whether this increased scatter is a persistent feature of the high-redshift Universe.

Figures (8)

• Figure 1: Example of spectral fitting for a mock H$\alpha$ emission line. Top panel: synthetic data (black diamonds) overlaid with the single-Gaussian fit (red line) and the double-Gaussian fit (blue line). Bottom panel: residuals for the single-Gaussian (red) and double-Gaussian (blue) models, normalized to the noise RMS. In this case, the broad component is correctly identified with $\Delta{\rm BIC} = 52$.
• Figure 2: Detectability of broad H$\alpha$ emission across the $M_\star$–$M_{\mathrm{BH}}$ parameter space, for two different noise levels. Each pixel represents the average detection rate across 100 realizations with randomly sampled SFR and $\lambda_{\mathrm{Edd}}$. The color scale ranges from $0\%$ (black) to $100\%$ (yellow). The right panel assumes the lowest noise level ($1\times$ the RMS of JADES source 73488), while the left panel corresponds to the highest noise level ($4\times$ RMS). The gold continuous line indicates the detection threshold at each sensitivity, showing how reduced noise broadens the observable regime. Colored dashed lines represent $M_\star$–$M_{\mathrm{BH}}$ relations derived in previous works.
• Figure 3: Recovery test of local scaling relations under our detectability model. Each panel shows a mock sample of $\sim$50 galaxies drawn from a known $M_{\mathrm{BH}}$–$M_\star$ relation with intrinsic scatter (gray points), together with the subset of objects lying above the detectability threshold (blue points). The left panel adopts the KH13 relation, while the right panel assumes the lower-normalization relation of RV15. In the latter case, the blue and green lines largely overlap and are therefore nearly indistinguishable. The orange dashed curves indicate the detectability boundaries. Solid green and red lines show the input relations, whereas the solid blue lines represent the best-fit relations obtained with our truncated-likelihood model. The blue dotted lines show the best fit obtained without accounting for truncation, and the blue dashed lines indicate the mean result over 50 realizations of our model. In both cases, our method successfully recovers the input relation within the uncertainties.
• Figure 4: Black hole--host galaxy scaling relation for the Judobaliz25 sample. The solid blue line indicates our best-fitting $M_{\mathrm{BH}}$--$M_\star$ relation obtained with the truncated-likelihood method. The shaded blue region represents the intrinsic scatter ($\sigma_{\rm int}$) of the relation, not the uncertainty on the mean relation. For comparison, we show the local relations of KH13 and RV15, as well as the high-redshift relation proposed by Pacucci23. The two orange dashed curves mark the dynamic detectability thresholds adopted in our analysis (Sec. \ref{['sec:methods']}). The red star marks the stacked measurement from Geris25, obtained by combining $\sim$ 600 JWST/NIRSpec spectra, which probes individually undetected, low-luminosity AGN and provides a representative constraint on the low-mass end of the relation. Overall, our inferred relation lies well above the low-normalization trend of RV15, is consistent with the KH13 determination, and remains slightly below the Pacucci23 prediction.
• Figure 5: Posterior distributions of the parameters describing the $M_{\mathrm{BH}}$-$M_\star$ relation. The panels show the marginalized one- and two-dimensional posteriors for the normalization $\alpha$, slope $\beta$, and intrinsic orthogonal scatter $\sigma_{\rm int}$, as obtained from the MCMC analysis. Blue lines mark the posterior medians, while red and green dashed lines indicate the values corresponding to the local relations of KH13 and RV15, respectively. Contours in the 2D panels enclose the 68% and 95% credible regions. The additional histogram in the top-right corner shows the posterior distribution of the black-hole–to–stellar mass ratio, $R_{\bullet/\star} = M_{\rm BH}/M_\star$, with the shaded area marking the 68% credible interval. The comparison highlights that while the inferred slope and normalization are consistent with local scaling relations, the intrinsic scatter is significantly larger, indicating that the dominant evolution at $z \gtrsim 4$ lies in the dispersion of the relation rather than in its mean trend.