3 Anomalous intensity ratio between the UV FeII lines and their satellites

A schematic diagram of the FeII quantum states, radiative transitions, and notations involved in the present problem is shown in Fig. 3. The low-lying metastable state a⁴D_7/2 (m-state) with the energy $E_{\rm m}=0.99$ eV is one of the low-lying metastable states in FeII. The wavelength of the broad HLy$\alpha$ line coincides with that of the absorption lines $\rm a^{4}D_{7/2}\rightarrow5p^{6}F_{9/2}$, $\rm 4p^{4}G_{9/2}$ ( $m\rightarrow2$allowed transition). The radiative transitions from levels 2 down to the long-lived states $\rm c^{4}F_{9/2}$, $\rm c^{4}F_{7/2}$ ( $2\rightarrow1$transitions) include two strong lines (A and C), which terminate on the $\rm c^{4}F_{7/2}$ level, and two weak lines (b and d), which terminate on the $\rm c^{4}F_{9/2}$ level. These spectral lines have anomalous intensities.

For illustration, we present in Fig. 4 spectra from blob B of the UV lines observed with the Hubble Space Telescope (HST) and synthetic spectra based on laboratory intensities (Johansson & Zethson 1999).

Figure 4: UV FeII spectral lines (A, C) and their satellites (b, d) observed in blob B (solid line) of $\eta$ Car and relative intensities expected from laboratory data (dashed lines) (according to atomic data in Johansson & Zethson 1999).

As can be seen, the weak satellite lines (b and d) practically vanish in the spectra of blob B. The simultaneous spectral-selective attenuation of two close spectral lines seems to have an extremely small probability. On the other hand, the anomalous intensity ratio observed between the strong UV spectral lines and their satellites (left-hand part of Fig. 4) can potentially be explained by amplification as a result of stimulated $2\rightarrow1$ transitions (Johansson et al. 1996). It is possible if the stimulated emission rate $W_{21}^{\rm {st.em.}}$ is higher than the stimulated absorption rate $W_{12}^{\rm {st.abs}}$ :

$$W_{21}^{\rm {st.em.}}>W_{12}^{\rm {st.abs.}}%$$ (17)

i.e., in the case of population inversion:

$$\frac{N_2}{g_2}>\frac{N_1}{g_1}\cdot$$ (18)

The lower states 1 have long lifetimes with a decay rate of $A_{21} \simeq0.7\times10^{3}$ s^-1 (Kurucz 1988), but the upper states 2 $\rm (5p ^{6}F_{9/2}$ and $\rm 4p^{4}G_{9/2}$) have short life times and fast decays with $A_{21} \simeq10^{8}$ s^-1, typical for allowed transitions. This means that under steady-state conditions (on a time scale of $\geq$10^-8 s) amplification is only possible in the case of fast depletion of the lower states 1 with the rate $W_{\rm {dep}}^{1}$ :

$$W_{\rm {dep}}^{1}\geq A_{21}\simeq10^{8}\;\rm s^{-1}.$$ (19)

We can consider the following two very fast depopulation alternatives:

(1) An accidental coincidence of some bright lines with an unknown absorption line from state 2, and the occurrence of an accidental coincidence of HLy$\alpha$ with the $m\rightarrow2$ transition in FeII. The probability of an accidental wavelength coincidence for two pairs of lines is extremely low.

(2) Photoionization of FeII in the long-lived state 1 by VUV black body radiation (BBR) with $h\nu>9.94$ eV and trapped Ly$\alpha$ emission with $h\nu=10.2$ eV generated inside the blob (due to photoionization of HI by absorption of photons with $h\nu\geq13.6$ eV) with the rate $W_{\rm {ph}}^{\rm {1i}} > A_{\rm {2m}}$ in accordance with the requirement in Eq. (19).

As shown in our preceding work (Johansson & Letokhov 2001b), $W_{\rm {ph}}^{\rm {1i}}$ can exceed the decay rate of the lower level 1, but it is smaller by several orders of magnitude than the value required by Eq. (19). Nevertheless, this process is potentially important in reducing the accumulation of FeII in the long-lived state 1 and hence the optical density $\tau _{12}$ of the anomalous transition $1\rightarrow2$.

Figure 5: Qualitative explanation of the intensity variation for the pair of a strong (A) and a weak (b) spectral line due to radiative transfer from the centre (r=0) to the surface (r=D/2) of the blob. The line intensities are normalized to the laboratory values. The same explanation is also valid for the another pair of strong (C) and weak (d) lines.