Title:Redshift Evolution of the HII Galaxy $L$-$σ$ Relation: Gaussian Process Analysis and Cosmological Implications

Abstract:The utility of HII starburst galaxies (HIIGs) as cosmic standard candles relies on the empirical $L$-$\sigma$ relation between the H$\beta$ luminosity ($L$) and ionized gas velocity dispersion ($\sigma$). However, the classic scaling $L$-$\sigma$ relation well-calibrated with the low-redshift HIIGs fails to properly describe their high-redshift counterparts. To address this, we try to explore new parameterization of the $L$-$\sigma$ relation, which is expected to be valid across all redshifts. Using Gaussian process reconstruction of the Hubble diagram from the Pantheon+ supernovae Ia sample, we compare three modified versions of the $L$-$\sigma$ relation against the classic scaling form through Bayesian evidence analysis. Our results identify the logarithmic redshift-dependent correction as the most statistically favored parameterization. This conclusion remains valid when repeating the analysis in the $\Lambda$CDM model with cosmological parameters fixed to their Planck 2018 fiducial values, which demonstrates the robustness of our results across different cosmological distance estimation approaches. After accounting for Malmquist bias effects, we still detect redshift evolution in the $L-\sigma$ relation, albeit with reduced statistical significance. Furthermore, we perform cosmological analysis within the $\Lambda$CDM model from a joint sample of HIIGs and giant extragalactic HII regions (GEHRs), and yield constraints on $H_0$ and $\Omega_m$ that are approximately one order of magnitude less precise than Planck 2018 results.