Primordial helium abundance determination using sulphur as metallicity tracer

The primordial helium abundance $Y_P$ is calculated using sulphur as metallicity tracer in the classical methodology (with $Y_P$ as an extrapolation of $Y$ to zero metals). The calculated value, $Y_{P,\,S}=0.244\pm0.006$, is in good agreement with the estimate from the Planck experiment, as well as, determinations in the literature using oxygen as the metallicity tracer. The chemical analysis includes the sustraction of the nebular continuum and of the stellar continuum computed from simple stellar population synthesis grids. The $S^{+2}$ content is measured from the near infrared $\left[SIII\right]\lambda\lambda9069\AA,9532\AA$ lines, while an $ICF\left(S^{3+}\right)$ is proposed based on the $Ar^{3+}/Ar^{2+}$ fraction. Finally, we apply a multivariable linear regression using simultaneously oxygen, nitrogen and sulphur abundances for the same sample to determine the primordial helium abundance resulting in $Y_{P-O,\,N,\,S}=0.245\pm0.007$