The Impact of Magnitude Uncertainties and K-corrections on Standard Siren Measurements of the Hubble Constant
Gravitational-wave standard sirens provide an independent probe of the Hubble constant. Dark siren analyses that rely on galaxy catalogues are sensitive to catalogue-related uncertainties. While incompleteness, weighting schemes, and redshift errors have been studied extensively, the impact of magnitude uncertainties and K-corrections has received little attention so far. We assess how magnitude errors and K-corrections propagate into the Hubble constant inference, and compare their impact to that of realistic spectroscopic redshift errors to determine their relevance. We use a modified version of the gwcosmo Python package to construct line-of-sight redshift priors from a complete, volume-limited mock galaxy catalogue up to $z<0.2$. We simulate and analyse a sample of $\sim200$ binary black hole events with luminosity weighting in the $B$- and $K$-bands and test different uncertainty models for redshifts, magnitudes, and K-corrections. The choice of luminosity-weighting scheme has a substantial impact on the inferred Hubble constant posterior, with the direct $B$- and $K$-band comparison producing differences comparable to the largest uncertainty-induced changes. Spectroscopic redshift errors produce the largest integrated changes in the Hubble constant posterior among the tested uncertainty treatments. Photometric magnitude uncertainties lead to substantially smaller, band-dependent deviations. In the $K$-band, the tested K-correction treatments have only a minor impact in the present low-redshift mock analysis, with the empirical correction slightly reducing the integrated deviation relative to the no-correction case. In realistic, flux-limited catalogues with larger localization areas and photometric or mixed redshift errors, the relative impact of magnitude uncertainties is expected to be even smaller, indicating that they need not be prioritized in near-future dark siren analyses.