An Improved Photoionization Model for Analysis of H II Region Spectra for the Determination of Primordial \({}^{\boldsymbol{4}}\)He Abundance

The observed abundances of primordial elements such as D, \({}^{4}\)He, and \({}^{7}\)Li are key quantities for studying the physical processes that took place in the early Universe. Obtaining the primordial \({}^{4}\)He abundance (Y\({}_{p}\)) with sub-percent accuracy is one of the major goals of modern observational cosmology. The most widely used method for determining Y\({}_{p}\) is based on the analysis of spectra from blue compact dwarf galaxies. This approach involves measuring the fluxes of helium, hydrogen, and metal emission lines, followed by detailed modeling aimed at estimating the physical conditions and chemical composition of their interstellar medium, as well as accounting for systematic effects. One of the most significant systematic effects affecting the estimate of Y\({}_{p}\) is underlying stellar absorption. This effect arises from the overlap of emission lines from the interstellar medium with the same absorption lines formed in stellar photospheres, which contribute to the stellar continuum of H II regions. As a result, the observed emission line fluxes may be significantly altered. In this paper, we present an improved algorithm for full-spectrum modeling of H II regions. The method incorporates both the stellar and nebular continuum, as well as the emission line profiles. The stellar continuum component is constructed by modeling the integrated spectrum of multiple stellar populations using the pPXF package. This approach eliminates the need to separate the measurement of integrated fluxes from the subsequent modeling process. It provides a more self-consistent framework and allows for a more accurate treatment of the underlying absorption effect, thereby increasing the precision of the derived model parameters. Examples of \({}^{4}\)He abundance measurements in individual objects demonstrate up to a threefold improvement in precision compared to previous methods. The proposed method can be used to obtain more accurate estimates of the primordial \({}^{4}\)He abundance, as well as to address other problems related to the analysis of H II region spectra.