4.2 Ionic and total abundances from ORLs

Using the effective recombination coefficients (given in Table 4), we determine ionic abundances, X${}^{i+}$/H${}^{+}$, from the measured intensities of optical recombination lines (ORLs) as follows:

$$\frac{N({\rm X}^{i+})}{N({\rm H}^{+})}=\frac{I({\lambda})}{I({{\r... ...\AA}})}{4861} \frac{\alpha_{\rm eff}({\rm H}\beta)}{\alpha_{\rm eff}(\lambda)},$$ (1)

where $I({\lambda})$ is the intrinsic line flux of the emission line $\lambda$ emitted by ion ${\rm X}^{i+}$, $I({{\rm H}\beta})$ is the intrinsic line flux of H$\beta$, $\alpha_{\rm eff}({\rm H}\beta)$ the effective recombination coefficient of H$\beta$, and $\alpha_{\rm eff}(\lambda)$ the effective recombination coefficient for the emission line $\lambda$.

Abundances of helium and carbon from ORLs are given in Table 6. We derived the ionic and total helium abundances from HeI $\lambda$4471, $\lambda$5876 and $\lambda$6678 lines. We assumed the Case B recombination for the HeI lines (Porter et al., 2012; Porter et al., 2013). We adopted an electron temperature of $T_{\rm e}=5\,000$ K from HeI lines, and an electron density of $N_{\rm e}=1000$ cm${}^{-3}$. We averaged the He${}^{+}$/H${}^{+}$ ionic abundances from the HeI $\lambda$4471, $\lambda$5876 and $\lambda$6678 lines with weights of 1:3:1, roughly the intrinsic intensity ratios of these three lines. The total He/H abundance ratio is obtained by simply taking the sum of He${}^{+}$/H${}^{+}$ and He${}^{2+}$/H${}^{+}$. However, He${}^{2+}$/H${}^{+}$ is equal to zero, since HeII $\lambda$4686 is not present. The C$^{2+}$ ionic abundance is obtained from C II $\lambda$6462 and $\lambda$7236 lines.

Table 6: Empirical ionic abundances derived from ORLs.

Ion	$\lambda$(Å)	Mult	Value $^{\mathrm{a}}$
He$^+$	4471.50	V14	0.141
	5876.66	V11	0.121
	6678.16	V46	0.115
	Mean		0.124
He$^{2+}$	4685.68	3.4	0.0
He/H			0.124
C$^{2+}$	6461.95	V17.40	3.068($-3$)
	7236.42	V3	1.254($-3$)
	Mean		2.161($-3$)

$^{\mathrm{a}}$

Assuming $T_{\rm e}=5\,000$K and $N_{\rm e}=1000$ ${\rm cm}^{-3}$.