Scientific measurements

Integrated flux

For a line model \(f_\lambda^\mathrm{line}\),

\[F = \int f_\lambda^\mathrm{line}(\lambda)\,d\lambda.\]

The result reports input-unit flux integrated from the prepared rest-frame \(F_\lambda\), and cgs flux when the input metadata provides a cgs scale. No additional redshift factor is applied during measurement conversion.

Profile centroid and dispersion

For the summed broad profile,

\[\bar{\lambda} = \frac{\int \lambda f(\lambda)\,d\lambda}{\int f(\lambda)\,d\lambda},\]

\[\sigma_\lambda = \sqrt{\frac{\int(\lambda-\bar{\lambda})^2f(\lambda)\,d\lambda} {\int f(\lambda)\,d\lambda}}.\]

Centroid offsets and dispersion are also reported in velocity units.

Numerical FWHM

FWHM is measured on the summed broad profile, not by adding individual Gaussian widths. The fitter locates the blue and red half-maximum crossings of an interpolated profile and converts their separation to km/s.

Equivalent width

Rest-frame equivalent width is

\[\mathrm{EW} = \int \frac{f_\lambda^\mathrm{line}(\lambda)} {f_\lambda^\mathrm{continuum}(\lambda)}\,d\lambda.\]

Host fractions

Where constrained by observed coverage,

\[f_\mathrm{host}(\lambda)= \frac{f_\lambda^\mathrm{host}} {f_\lambda^\mathrm{host}+f_\lambda^\mathrm{AGN}}.\]

Uncertainty

Covariance errors describe the fitted statistical model. They do not include all continuum, host-decomposition, calibration, or model-choice systematics. Monte Carlo summaries are stored separately. Warning statistical_uncertainty_excludes_continuum_host records this limitation where relevant.

Units

Wavelengths are in Å and velocities in km/s. DESI/SDSS flux-density presets use \(10^{-17}\,\mathrm{erg\,s^{-1}\,cm^{-2}\,\mathring{A}^{-1}}\). When the physical scale is unknown, cgs-derived quantities are omitted.