Exploring the “L–σ” Relation of H ii Galaxies and Giant Extragalactic H ii Regions Acting as Standard Candles

Cosmological applications of H ii galaxies and giant extragalactic H ii regions (GEHRs) to construct the Hubble diagram at high redshifts require knowledge of the “ L – σ ” relation of the standard candles used. In this paper, we study the properties of a large sample of 156 sources (25 high- z H ii galaxies, 107 local H ii galaxies, and 24 GEHRs) compiled by Terlevich et al. Using the cosmological distances reconstructed through two new cosmology-independent methods, we investigate the correlation between the H β emission-line luminosity L and the ionized gas velocity dispersion σ . The method is based on non-parametric reconstruction using the measurements of Hubble parameters from cosmic clocks, as well as the simulated data of gravitational waves from the third-generation gravitational wave detector (the Einstein Telescope, ET), which can be considered as standard sirens. Assuming the relation between emission-line luminosity and ionized gas velocity dispersion, , we find that the full sample provides a tight constraint on the correlation parameters. However, similar analysis done on three different subsamples seems to support the scheme of treating H ii galaxies and GEHRs with distinct strategies. Using the corrected “ L – σ ” relation for the H ii observational sample beyond the current reach of Type Ia supernovae, we obtain values of the matter density parameter, Ω m = 0.314 ± 0.054 (calibrated with standard clocks) and Ω m = 0.311 ± 0.049 (calibrated with standard sirens), in the spatially flat ΛCDM cosmology.