Optimizing the $L$-$σ$ Relation of HII Galaxies for improving cosmological application

Abstract: The basic premise of using HII starburst galaxies (HIIGs) as cosmic ``standard candles'' is the significant correlation between the H$\beta$ luminosity ($L$) and the velocity dispersion ($\sigma$) of the ionized gas from HIIGs measurements, which can be called as the empirical $L$ - $\sigma$ relation. However, the classic scaling $L$ - $\sigma$ relation well-calibrated with the low-redshift HIIGs is unfitted for the high-redshift ones. To solve this problem, we try to explore new relational expression for the $L$ - $\sigma$ relation, which is expected to be suitable for both the low and high redshift HIIGs. After reconstructing the Hubble diagram with the Gaussian process method from the Pantheon+ supernovae Ia sample, we compare three different revised forms of the $L$ - $\sigma$ relation with the classic scaling one. By using the Bayesian evidence to do the comparison, we find that the logarithmic redshift-dependent correction is the most competitive option for the $L$ - $\sigma$ relation. Then, we conduct the cosmological analysis with a joint sample of HIIGs and local giant extragalactic HII regions (GEHRs) in the case of choosing the logarithmic redshift-dependent form for the $L$ - $\sigma$ relation, and find that the power of HIIGs $+$ GEHRs on constraining the Hubble constant is almost compatible with that of the observational Hubble parameter data. It suggests that the appropriate optimization to the classic $L$ - $\sigma$ relation should be taken into account when the HIIGs are used as a kind of promising cosmological probes.