4. Atomic fine structure lines
Our SWS full-grating spectra of the supergiants Sco and Ori show strong atomic fine-structure lines of two species, [Fe II] at 25.99 and 35.35 µm and [Si II] at 34.81 µm (Fig. 1). We list the line fluxes in Table 1.
The two [Fe II] lines originate in the same ladder connecting the three lowest fine-structure levels of the D state. The line at 25.99 µm is from the J=7/2 to the J=9/2 (ground) state while the 35.35 µm line is between the J=5/2 and 7/2 state. The ratio of the line fluxes is then a good temperature indicator. The line intensity, for the optically thin case, can be calculated from
where is the column density of the upper (j) level, is the transition frequency between levels (j) and (i), and is the Einstein A coefficient for spontaneous emission. For the [Fe II] lines, assuming that both arise in the same region, we can calculate the excitation temperature, T, of the emitting gas from the ratio of the populations in the levels J=5/2 and J=7/2 using the expression
where is the statistical weight of level i.
The supergiant Ori has been extensively studied from the KAO in the atomic fine-structure lines. It is known that the line intensity of the [O I] 63 µm line varies with time (HGT), corresponding to the variation in the V band with an amplitude of about 0.25 magnitude (Krisciunas 1992, 1994). Our observed line flux in the [Si II] line agrees reasonably well with that observed by HGT.
We measure the line fluxes of the two [Fe II] lines and these are listed in Table 1. Directly from the ratio of the [Fe II] 26 to 35 µm line fluxes, we can calculate the excitation temperature of the gas and estimate the total numer of atoms involved in the cooling process in the circumstellar envelope, independent of model assumption which we will later investigate. The line flux ratio is 3.43 which translates to a ratio of the column densities of the J=5/2 to J=7/2 levels of 0.54. Using Eq. 2, we obtain a temperature of 1230 K. The assumption made here is that the emission is optically thin; hence, we see all the emitting atoms. The numbers of atoms in the upper levels (Nj) is listed in Table 3. They can be converted to the total mass of gas, assuming an excitation temperature of 1230 K and assuming the solar abundance for Si (3.8), and Fe (3.4), and using the measured O abundance for Ori from Lambert et al. (1984) of 5.9. The average mass of the gas cooling through these atomic fine structure lines derived from our observations are in reasonable agreement, of the order of 10-4 M. At this temperature, the emission originates inside the dust forming region since the condensation temperature for silicate is 1000 K, and probably arises in the chromospheric region of the star.
Table 3. The total number of atoms in the upper level (Nj) calculated from the line fluxes and their corresponding gas mass (see text for details).
Our observations can also be compared to the detailed model developed for Ori by RG. The line fluxes predicted by this model are given by
where is the gas mass loss rate, D is the distance to the star, is the abundance of element x and is the fractional abundance of level j at radius r. Fig. 3 shows the temperature structure of the RG model, and we also indicate the ratio of the [Fe II] populations calculated from the model. The [Fe II] ratio equals the observed ratio at a radius of 8.5 cm. Fig. 4 shows the fractional population of the upper levels of [Fe II], [Si II] and [O I].
We calculate the total number of emitting atoms of all the species observed, interior to the emitting region which produce the observed line fluxes. The normalised populations of the upper level of each transition for each species are used to calculate the flux in Eq. 3. HGT assumed a mass loss rate of 4 M yr-1 and a constant velocity of 16 km s-1 within a radius of 3 cm in order to match their observed fluxes of [O I] and [Si II] lines. The derived fluxes depend directly on the mass loss rate assumed. The estimated gas mass loss rate for Ori ranges between 2-4 M yr-1, as measured by the [C I] line (Huggins et al. 1994, van der Veen et al. 1999) and by [K I] scattering observation (Mauron et al. 1984). Here, we will use a value of 4 M yr-1 for the subsequent line flux calculation and assume RG temperature profile for the star. We can directly compare predicted fluxes from RG with the observations (Table 4 in RG). Their model predicts line fluxes for [Si II] and [O I] which are very close to the observed values. Here, we include [Fe II] in their model and the results are listed in Table 4 (see Table 1 for observed line fluxes) which show excellent agreement between the model results and the observations.
Table 4. Calculated model line flux based on RG's model
Fig. 5 shows the integrated population of the upper levels of different atomic species investigated here (Eq. 3) which shows where the flux of each line arises. We note here that although the bulk of the flux for the [O I] 63 µm line originate from within 1.5 cm, there is about 25% of emission coming from beyond this radius. This is due to the slow decline of the relative population of oxygen as a function of radius, assuming the RG temperature profile (Fig. 4). As previously discussed, the predicted line fluxes agree very well with the observed ones. However, the calculated 63/146 µm [O I] flux ratio is much higher than observed by HGT, 40 vs. 10 although it is worthy to note here that the 146 µm line is a 2.5-sigma detection only. Recently, Barlow (1999) reported a line flux for [O I] 146 µm of about 4 W cm-2. This large 63/146 µm flux ratio may be due to the 63 µm being optically thick (Tielens & Hollenbach 1985) while the 146 µm is optically thin hence the assumption of Eq. 1 then breaks down.
The model calculation implicitly assumes that all Fe is singly ionized. The energy requires to ionize Fe I to Fe II is 8.1 eV while to ionize it further requires a very high energy of 16.2 eV. The expected [Fe III] lines at 13.53 and 22.93 µm are not seen in the spectrum. The relatively strong UV radiation from the chromosphere should ensure that the atoms remain singly ionize. The same argument applies for Si since its ionization energies are very similar to those for Fe. From the model calculation, we estimate the total mass of the emitting gas within the radius of 3 cm to be 1.2 M, slightly higher than obtained from simple LTE estimate from Table 2. Note that for the [O I] 3P1, the mass outside this may provide some contribution to the observed flux (Fig. 5). The excitation energy for this level is 228 K hence it does not require high gas temperature to excite it up to the 3P1 level.
The mass loss rates derived from the atomic fine structure lines of [O I], [Si II], and [Fe II] are in seemingly good agreement with those obtained from [C I] emission and [K I] scattering (van der Veen et al. 1999; Mauron et al. 1984). However, our data really measure a total mass of emitting gas and this gas is located within the dust condensation radius. Hence, actually, a much lower flow velocity ( 2 km s-1; Habing et al. 1994) should be used to calculate the mass loss rate from these data than adopted by RG (16 km s-1). As a result the mass loss rate calculated near the stellar surface is only M yr-1; a factor 4-8 less than from the [C I] and [K I] data for the outer envelope. Evidence for variable mass loss (i.e., discrete dust mass loss events of modest size) have been reported by Bester et al. (1996) in their 11 µm interferometric study of the dust emission. It seems therefore that, compared to the mass loss measured in [C I] and [K I], we have caught Ori in a quiescent episode. With either mass loss rate, the density inside the dust condensation radius is well above the critical densities for all species (Table 1). It is interesting to note the very high gas-to-dust mass ratio of 550 which is much higher than 160, suggested by Knapp (1985) for AGB stars. The presence of the chromosphere around Ori may inhibit grain formation thereby resulting in such a low dust mass loss rate compared to the gas mass loss rate.
This star is known to have a B2 companion which is only 3" from the supergiant, Sco A (Hjellming & Newell 1983). The source of ionizing photons may originate from both the chromosphere, as for the case of Ori, as well as from the hot companion. The large aperture size of SWS (14) also ensures that both stars are present in the beam.
Following a similar approach we took for Ori, the ratio of the column density of the [Fe II] J=5/2 to J=7/2 is 0.60. Using Eq. 2, this leads to a temperature of the emitting region for [Fe II] of 1785 K, slightly hotter than for Ori. The total number of emitting atoms and the corresponding hydrogen masses derived from the observed line fluxes are listed in Table 3. The average mass of the gas from all lines considered is 1.3 M. We note that the [Si II]/[Fe II] 35 µm ratio is a factor of two larger in this star than in Ori.
We calculate the expected line fluxes using Eq. 3 and integrate the flux within the dust condensation radius of 3 cm. We obtained line fluxes close to those observed (Table 4), using a gas mass loss rate of 6.4 M yr-1 and a constant velocity of 17 km s-1 (Bernat 1982). Here, we assume the same abundances of all the elements considered to be the same as for Ori and also using the same gas temperature distribution.
From the derived excitation of the [Fe II] flux ratio, the emission comes from within the dust condensation radius. This is also supported by RG's temperature (Fig. 3). This may have a similar implication as for Ori case that the wind in this region has not yet reached the terminal velocity of 17 km s-1.
Finally, we determined the gas mass within the emitting region from fitting the observed line fluxes using Eq. 3 to be 1.7 M. This value is comparable to the average derived from Table 2. Bernat (1982) quoted a gas mass loss rate of 6.4 M yr-1 but with a large spread of (0.38-10) M yr-1. Our derived dust mass loss rate for Sco is 6 M yr-1 hence the deduced gas-to-dust mass ratio is very large ( 600), making it one of the highest gas-to-dust mass ratio. As we noted earlier, the system is complicated by a presence of the B2 companion. Hjellming & Newell (1983) detected radio emission around the companion. UV observations also suggest that the companion is a source of ionizing Fe III line, not seen in Ori (van der Hucht et al. 1979). It is possible that both the chromosphere of the supergiant and the intense radiation from the companion disrupts the dust formation process, or destroys dust grains in the supergiant wind.
© European Southern Observatory (ESO) 1999
Online publication: April 19, 1999