Introduction to Methodology
This study utilizes specific cosmological parameters based on reference 51, adopting a Λ cold dark matter (ΛCDM) model with a total matter density (Ωm) of 0.310 and a Hubble constant (H0) of 67.7 km s−1 Mpc−1. Uncertainties are generally given as 1σ or 68% confidence intervals, with upper limits at the 2σ level unless specified otherwise.
Spectroscopic Sample Selection
The research employs public data collected by the James Webb Space Telescope's (JWST) Near-Infrared Spectrograph (NIRSpec) from various observational programs, including CEERS and JADES. These observations were uniformly reduced and made publicly available through the DAWN JWST Archive (DJA). Galaxies were selected from this archive if they showed a broad Hα component in medium-resolution grating spectra, had a spectroscopic redshift, and a full width at half-maximum (FWHM) linewidth exceeding approximately 1,000 km s−1. High signal-to-noise ratio (SNR) objects were prioritized, with lower SNR objects also included for stacked spectra to prevent bias. The sample exhibits a range of colors, which may be influenced by redshift effects, strong optical emission lines, and current photometric selection criteria limitations. However, electron scattering by ionized gas is not found to be dependent on the object's color.
Emission Line Modeling
Best-fit results were generated using the Monte Carlo Markov Chain (MCMC) NUTS sampler from PyMC v. 5.17.0, with some exceptions. The broad Hα profile was modeled assuming either Doppler velocity broadening (Gaussian function) or Compton scattering broadening (symmetric exponential function). Models also included narrow Gaussians for host galaxy Hα and [N ii] doublet, with occasional additional absorption components or P Cygni profiles. Specific wavelength regions were excluded from the fitting process. It was determined that most Hα lines in the sample are predominantly exponential. To reconstruct intrinsic Doppler widths, lines were modeled as a Gaussian convolved with an exponential, accounting for instrumental resolution. The study found that an exponential fit was significantly better than a Lorentzian, indicating negligible contributions from turbulence broadening. Double-Gaussian models were statistically disfavored for the majority of objects, suggesting a single exponential shape is more physically representative.
Optical Depth Measurement
The approximate optical depth (τ) of scatter was estimated from the exponential linewidth measurement (W) using Monte Carlo simulations of electron scattering at 10,000 K within a spherical shell geometry. A linear relationship was established: W = 428τ + 370 km s−1. It was noted that at higher temperatures (e.g., 20,000 K), inferred optical depths would be lower by about 30%.
Spectral Stacking Process
Individual noisy spectra were combined to create a median spectral stack with improved SNR. This involved fitting each Hα line with an exponential broad Hα component, subtracting the continuum, normalizing individual line widths and amplitudes to the median values of the stack, and then resampling spectra to a consistent rest-frame wavelength grid. The final stacked spectrum was produced by taking the median of the stack, with uncertainties estimated via Gaussian draws.
Black Hole Mass Estimation Reliability
The black hole mass estimates in this work are considered extrapolations, as the active galactic nuclei (AGN) properties studied here differ from typical type I AGN. While generally consistent with the M BH –σ ⋆ relation within 1–2σ, some objects fell below this relation. Potential factors affecting these estimates include a possible higher broad-line region (BLR) covering factor (close to unity) compared to typical assumptions, which could lead to overestimations by a factor of about three. Alternative BLR sizes could also introduce biases. The study concludes that current estimates are likely not significantly affected but emphasizes the need for future research to validate these relations with a larger sample and multi-epoch observations.
Spectral Energy Distribution Modeling
Stellar masses of host galaxies were estimated by modeling their spectral energy distributions (SED) using JWST and HST photometry. The rest-UV-to-optical SEDs were modeled with the BAGPIPES code, employing a double power-law star-formation history. Priors were set for various parameters including timescale, rising and falling exponents of star formation, total formed mass, stellar metallicity, dust attenuation, nebular ionization, and intrinsic line velocity dispersion. Redshifts were fixed to spectroscopic values.