Determination of the local Hubble constant using Giant extragalactic HII regions and HII galaxies

Abstract: The relationship between the integrated H$\beta$ line luminosity and the velocity dispersion of the ionized gas of HII galaxies and giant HII regions represents an exciting standard candle that presently can be used up to redshifts $z\sim~4$. Locally it is used to obtain precise measurements of the Hubble constant by combining the slope of the relation obtained from nearby ($z<0.2$) HII galaxies with the zero point determined from giant HII regions belonging to an `anchor sample' of galaxies for which accurate redshift-independent distance moduli are available (e.g Cepheids, TRGBs). Through this chapter, we present a general description of the method and results obtained so far in the determination of the local value of the Hubble constant and cosmological constraints. We account for the main systematic effects associated with the method and the possibility of improvement in the future. The discussion presented here is the product of an independent approach to the standard methods used in the literature to measure distances and, although at present less precise than the latest SNIa results, it is amenable to substantial improvement.