Elements and number of levels (super-levels) included in the CMFGEN models.
Table A.1 provides the number of levels and super-levels used in our computations. Basic atomic data for the important transitions that influence C iii 5696 and 4650 are listed in Table A.2. There is some uncertainty in the oscillator strengths, and this must be regarded as a source of uncertainty when modeling the C iii lines. For a comparison we provide an alternative f values that is available in the literature for each transition. Fortunately, for the transitions which significantly influence C iii 5696 and 4650, the wavelengths and/or energy levels for the relevant transition are known. The wavelengths of most of the other transitions tested are (very) uncertain, but potentially could have influenced the modeling because of line overlap. A more worrisome concern is there may be some other important transition which overlaps with one of the key UV transitions, and which has a wrong wavelength (because it has not been measured in the laboratory) or was omitted from the model atoms used in the model atmosphere. The work presented in the current paper, and that of Najarro et al. (2006), highlights the need for accurate Fe wavelengths and oscillator strengths for modeling O star spectra.
Basic line data for the important overlapping transitions.
The Grotrian diagram for the C iii singlets (Fig. 2) shows that the C iii 8500 transition should also strongly depend on the efficiency of the C iii 884 and C iii 386 drains since 2s3p 1Po is the upper level of all three transitions. Consequently, any modification of the 2s3p 1Po population will change the C iii 8500 morphology.
In Fig. B.1 we show how this line reacts to the C iii UV lines at Teff = 30 500 K (upper panel) and Teff = 42 000 K (lower panel). As expected, removing the drain from C iii 884 translates into a weaker absorption at low Teff and to emission at high Teff. C iii 386 populates 2s3p 1Po at high Teff and thus removing it leads to absorption in C iii 8500. C iii 690 has also a strong drain effect on 2s3s 1S since removing it leads to a strong absorption. The C iii 8500 transition is of special interest in the context of future observations of O stars by Gaia, since it is basically the only non H/He line in the spectral window of the Radial Velocity Spectrometer onboard the satellite. Understanding its properties is thus important to classify O stars observed by Gaia.
Effect of C iii UV lines on the appearance of C iii 8500 for Teff = 30 500 K (top panel) and 42 000 K (lower panel).
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Figure C.1 presents the effect of a change of metallicity on C iii 5696 in the model with Teff = 42 000 K. We show a model with a global reduction of Z by a factor 5 (dashed line) and a model with the same reduction, but in which C/H is kept at the solar value (dotted line). The solid line is the solar metallicity model. A global reduction of Z (including a reduction of C/H) by a factor 5 leads to a significant reduction of the emission in C iii 5696. But a model with Z = 1/5th Z⊙ and a solar carbon content has a C iii 5696 line slightly stronger than the solar metallicity model. The higher ionizing flux at low Z implies a depopulation of 2s3p 1Po and thus more emission. In addition, the reduced effect of Fe iv 574.232, Fe v 386.262 and S v 884.531 tend to increase emission (see Fig. 10). All in all, the conditions are more favorable at low Z, explaining that for a similar C/H, the emission is stronger than at solar metallicity.
In this section we provide an investigation of the mechanisms responsible for the trend observed in Fig. 20 which shows the effect of mass loss on C iii 4650 and C iii 5696.
We first focus on C iii 5696. Its behavior in the 42 000 K model can be understood as follows. Figure D.1 shows the departure coefficients of the lower and upper levels of C iii 5696 in a model with Ṁ = 4 × 10-7 M⊙ yr-1 (dashed line) and 2 × 10-6 M⊙ yr-1 (solid line). In the low Ṁ model, 88% of the line is formed at log τRosseland > −1.8, corresponding to velocities smaller than 10 km s-1. In that region, the lower level is always less populated than the upper level, a favorable condition for emission. In the high Ṁ model, a significant fraction of C iii 5696 (41%) is formed at velocities higher than 10 km s-1(log τRosseland < −1.2). In the low velocity part of the formation region, the lower level is less populated than the upper level, but above 10 km s-1, the lower level is much more populated. As a result, the global C iii 5696 emission is weaker than in the low Ṁ model. The behavior of C iii 5696 with mass loss observed in the left panel of Fig. 20 is thus a direct consequence of the strengthening of the wind.
Effects of mass loss rate on 2s3p 1Po (blue) and 2s3d 1D (red) departure coefficients in a model with Teff = 42 000 K. The dashed (solid) lines corresponds to a model with Ṁ = 4 × 10-7 (2 × 10-6) M⊙ yr-1. The dot-dashed (short dash – long dashed) line is the line formation region in the low (high) Ṁ model.
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Effect of mass loss rate on total radiative rates for lines from level 2s3p 1Po (left) and level 2s3d1D (right). The models have Teff = 42 000 K. The upper panels correspond to the model with Ṁ = 2 × 10-6 M⊙ yr-1, the lower panel to models with Ṁ = 4 × 10-7 M⊙ yr-1.
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The behavior of 2s3p 1Po and 2s3d 1D when the wind sets in is explained as follows. Figure D.2 shows the total radiative rates in lines connecting the upper and lower levels of C iii 5696. The rates are shown for two mass loss rates discussed above (4 × 10-7 and 2 × 10-6 M⊙ yr-1). When Ṁ is increased, we see 1) that the rate in the C iii 574 line increases slightly (compared to the rate in C iii 5696) and 2) the rate in C iii 386 shows a slightly more negative excursion at the end of the C iii 5696 line formation region. The net effect is to re-populate 2s3p 1Po and to depopulate 2s3d 1D, leading to a reduced emission. The higher rates in C iii 386 and C iii 574 can be understood as a desaturation effect. Due to the higher mass loss rate, the formation region is shifted toward larger velocities. The associated Doppler shift allows C iii 386 and C iii 574 to absorb more photons from the adjacent continuum, and consequently the radiative rates in those lines are increased. As we have seen in Sect. 4.1, C iii 884 does not play an important role in the formation of C iii 4650 in the high temperature model.
In the 30 500 K model, the increase of the emission when Ṁ strengthens from 3 × 10-8 to 2 × 10-6 M⊙ yr-1 is mainly due to a growing contribution of the wind to the line profile, as at higher temperature. The fraction of the line formed above 10 km s-1 grows from 0.6% for Ṁ = 3 × 10-8 M⊙ yr-1 to 23.5% for Ṁ = 2 × 10-6 M⊙ yr-1. Consequently, the contribution of the wind (emission6) is larger for higher mass loss rates. In addition to this dominant effect, there is also a higher radiative rate in the C iii 884 line in the photosphere (below 10 km s-1). In the same time, the rates in the C iii 386 and C iii 574 lines are not significantly modified compared to the other rates. Desaturation is responsible for the enhanced rate in C iii 884. A lower 2s3p 1Po population results from this, with the consequence of stronger C iii 5696 emission. All in all, a higher mass loss rate leads to a stronger C iii 5696 emission at low Teff.
Wind effects can also explain the behavior of the C iii 4650 triplet in Fig. 20. The higher the mass loss rate, the larger the fraction of the line formed at velocities higher than 10 km s-1. The wind contribution to the line profile increases, implying more emission at high effective temperature and less absorption at low temperature. In addition, at high Teff, the UV lines populating the upper and lower level of C iii 4650 are formed at velocities larger in the high Ṁ model than in the low Ṁ model. They all have positive radiative rates over the line formation region. As a result C iii 538 depopulates 2s3s 3S as soon as Doppler shifts allow the line to absorb more continuum photons. In the same time, C iii 1256, C iii 1428, C iii 1578, C iii 2009 populate 2s3p 3Po. The effect is an increase of the C iii 4650 emission, as observed in Fig. 20.
© ESO, 2012