Primordial 4He abundance: a determination based on the largest sample of HII regions with a methodology tested on model HII regions

TL;DR

This study validates an empirical method for deriving the primordial $^4$He abundance $Y_{ m p}$ by applying it to a comprehensive grid of CLOUDY v13.01 H II region models with updated He I emissivities and non-recombination corrections for hydrogen lines. The authors derive $Y_{ m p}=0.254\pm0.003$ from 111 high-quality, high-excitation regions and find a cosmological implication of $N_{ m eff}=3.51\pm0.35$ and $\Omega_{ m b}h^2=0.0234\pm0.0019$ when combined with the D/H abundance, suggesting a potential deviation from the standard model. Methodological advances include analytic fits to He I emissivities, robust ionisation correction factors, and a careful treatment of non-recombination hydrogen excitation, validated against CLOUDY inputs. The work strengthens constraints on BBN and neutrino-sector physics and demonstrates the value of large, carefully selected spectroscopic samples for precision cosmology, while acknowledging systematic uncertainties that remain a limiting factor.

Abstract

We verified the validity of the empirical method to derive the 4He abundance used in our previous papers by applying it to CLOUDY (v13.01) models. Using newly published HeI emissivities, for which we present convenient fits as well as the output CLOUDY case B hydrogen and HeI line intensities, we found that the empirical method is able to reproduce the input CLOUDY 4He abundance with an accuracy of better than 1%. The CLOUDY output data also allowed us to derive the non-recombination contribution to the intensities of the strongest Balmer hydrogen Halpha, Hbeta, Hgamma, and Hdelta emission lines and the ionisation correction factors for He. With these improvements we used our updated empirical method to derive the 4He abundances and to test corrections for several systematic effects in a sample of 1610 spectra of low-metallicity extragalactic HII regions, the largest sample used so far. From this sample we extracted a subsample of 111 HII regions with Hbeta equivalent width EW(Hbeta) > 150A, with excitation parameter x = O^{2+}/O > 0.8, and with helium mass fraction Y derived with an accuracy better than 3%. With this subsample we derived the primordial 4He mass fraction Yp = 0.254+/-0.003 from linear regression Y-O/H. The derived value of Yp is higher at the 68% confidence level (CL) than that predicted by the standard big bang nucleosynthesis (SBBN) model, possibly implying the existence of different types of neutrino species in addition to the three known types of active neutrinos. Using the most recently derived primordial abundances D/H = (2.60+/-0.12)x10^{-5} and Yp = 0.254+/-0.003 and the chi^2 technique, we found that the best agreement between abundances of these light elements is achieved in a cosmological model with baryon mass density Omegab h^2 = 0.0234+/-0.0019 (68% CL) and an effective number of the neutrino species Neff = 3.51+/-0.35 (68% CL).

Figures (14)

• Figure 1: Comparison of calculated and fitted emissivities of the strongest He i emission lines for three values of the electron number densities $N_{\rm e}$ = 10, 10$^2$, and 10$^3$ cm$^{-3}$. Collisional excitation is taken into account.
• Figure 2: Ratio of the CLOUDY-calculated intensities with all processes included to CLOUDY case B intensities for several brightest He i emission lines as a function of the oxygen abundance for the models with low electron number density $N_{\rm e}$ = 10 cm$^{-3}$. For clarity only models with log $Q$(H) = 53 are shown.
• Figure 3: Ionisation correction factors $ICF$(He) vs. excitation parameter $x$ = O$^{2+}$/O from the CLOUDY models with various oxygen abundances 12+logO/H and starburst ages. Red dashed, blue solid, and green dotted lines correspond to the starburst ages of 1.0-2.0, 3.5, 4.0 Myr, respectively. Symbols are CLOUDY-modelled data.
• Figure 4: Non-recombination contribution of Balmer hydrogen line intensities as a function of the oxygen abundance. The red dashed, blue solid, and green dotted lines show fits for starburst ages of 2.0, 3.5, and 4.0 Myr, respectively. The dependences for starburst age of 1.0 Myr are identical to those for 2.0 Myr. Symbols are CLOUDY-modelled data.
• Figure 5: Distribution with the oxygen abundance of the empirically derived weighted mean $Y$ (a) and $N_{\rm e}$ (b) values calculated with the P13 He i emissivities. Nine He i$\lambda$3889, $\lambda$4026, $\lambda$4388, $\lambda$4471, $\lambda$4922, $\lambda$5876, $\lambda$6678, $\lambda$7065, and $\lambda$10830 emission lines are used for $\chi^2$ minimisation and determination of $Y$. In the lower parts of the panels showing $Y$ as a function of O/H we indicate the mean of all $Y$ values derived from the models, together with the dispersion. Top The electron temperature $T_{\rm e}$(He$^+$) is randomly varied in the range (0.95 -- 1.05)$\times$$\widetilde{T}_{\rm e}$(He$^+$) where $\widetilde{T}_{\rm e}$(He$^+$) is defined by Eq. \ref{['tHeOIII']}, and the best derived values of $T_{\rm e}$(He$^+$) for every model are shown in (c). The solid line in (a) shows the input CLOUDY $Y$ value of 0.254, the dotted lines are 1% deviations, and $<$$Y$$>$ is the average value of $Y$s shown by filled circles. Middle The same as in the top panel, but $T_{\rm e}$(He$^+$) = $\widetilde{T}_{\rm e}$(He$^+$). Bottom The same as in the top panel, but $T_{\rm e}$(He$^+$) = $T_{\rm e}$(O iii).