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Astron. Astrophys. 324, 185-195 (1997)

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5. Impact of CIA on stellar model atmospheres and synthetic spectra

We have included the CIA data described above in the computation of a grid of photospheric models. The aim is to identify the range of the fundamental stellar parameters ([FORMULA], log(g), and metallicity) within which CIA affects the stellar atmosphere, and to quantify the effect CIA has on such models. The model atmosphere code we use is an updated version (Jorgensen et al. 1992, Helling et al. 1996) of the MARCS code (Gustafsson et al. 1975). This version of the program assumes hydrostatic equilibrium, spherical geometry (applied when appropriate), and line blanketing by molecules treated by the opacity sampling technique. Line opacities were included for a total of approximately 20 million molecular lines of H2 O (from Jorgensen & Jensen 1993), TiO (from Jorgensen 1994), CO (from Goorvitch & Chackerian 1994), SiO (from Langhoff & Bauschlicher 1994), CN (from Jorgensen & Larsson 1990), and CH (from Jorgensen et al. 1996). Spectra were computed as the emergent flux of the model computation as well as in a separate synthetic spectrum program which allows us to study the contribution of each opacity source separately.

We expect the effect of CIA to be largest for stars of low effective temperature (corresponding to a small number density of free electrons and a large abundance of molecular hydrogen), high gravity (corresponding to high density in the atmosphere and therefore a large number density of H2 -H2 and H2 -He "pairs"), and low metallicity (corresponding to a small amount of other absorbers). Therefore we started the computations with low-metallicity dwarf star models, such that our grid of stars will span the coolest and most metal-deficient main sequence stars of our Galaxy, as for example cool M dwarf stars in low-metallicity globular cluster or in the Galactic halo. In the "corner" of our grid ([FORMULA] = 2800 K, log(g) = 5.0, Z = 10 [FORMULA]) CIA was found to be by far the dominant contributor to the opacity at all wavelengths longer than approximately 1 µm and for all depths - even in the surface layers (corresponding to [FORMULA] = 10-4 in this case).

Next, we varied (compared to the choice in our standard model) the fundamental stellar parameters until we saw no more significant effect of CIA in the emergent flux spectrum. In this way we defined the region of interest for CIA inclusion. In Fig. 4 we show the contribution of different absorbers to the synthetic spectrum of a typical model in our grid, representing a typical M dwarf in a globular cluster. The figure shows the continuum, the molecular spectrum, and the spectrum including both molecular lines and CIA, respectively. The latter spectrum is the only one of the three which is internally consistent with the underlying model in the sense that it includes all the opacity sources which are also included in the corresponding model atmosphere computation. Comparison of the three spectra only illustrates the contribution of the different species to the total emergent spectrum. It is seen that even at such relatively high metallicities as adopted here (Z = 0.01 [FORMULA]), CIA is the main contributor to the infrared stellar spectrum. Its presence induces such a strong continuum depression that the bands longward of 1.5 µm (due mainly to water) virtually disappear from the spectrum. The strongest molecular features left in the spectrum are the TiO bands, the water bands shortward of 1.5 µm, and the G band (around 4300Å) due to CH.

[FIGURE] Fig. 4. The contributions of various opacity sources to the spectrum of a stellar model with [FORMULA] = 2800 K, log(g) = 5.0, and Z = 10 [FORMULA] - a typical main sequence member of a globular cluster. The model computation includes opacities of continuum sources, molecular lines, and CIA. The spectra are computed based on the continuum alone (upper, convolving curve), continuum + molecular (b-b) lines, and continuum + molecular lines + CIA. Only the latter is consistent with the underlying model atmosphere, but the difference between the three spectra illustrates the relative contribution of the three sources of opacity.

The results of our analysis of the stellar models in the whole range of fundamental parameters where we found CIA to be of importance are summarized in Figs. 5 to 7. Fig. 5 illustrates the effect of varying the gravity, whereas Fig. 6 and Fig. 7 show how the relative importance of CIA, continuum absorption, and molecular line absorption change when we vary the metallicity and the effective temperature, respectively.

[FIGURE] Fig. 5. Showing the effect of varying g for models with [FORMULA] = 2800 K, metallicity Z = 10 [FORMULA], and C/O = 0.43 (the solar value). The first column of plots in this figure shows the emergent flux from models with (highest peak) and without (lowest peak) CIA included in the opacity. The two next columns show log10 of the opacity (in units of cm2 per gram of stellar material) due to various species (for those models from column one where CIA is included) at [FORMULA] = 0.01 (second column of plots) and at [FORMULA] = 1.0 (third column), respectively. Dotted lines correspond to the opacity of CIA, dashed lines represent the sum of the opacities due to all continuum sources other than CIA, and the full drawn lines represent the molecular line opacity. The different rows of plots in the figure correspond to models of different gravity, decreasing from log(g) = 5.0 in the uppermost row of plots to log(g) = 4.0, 2.0 and 1.0, respectively, in the rows below.
[FIGURE] Fig. 6. Showing the effect of varying Z. Same as Fig. 5, but for models of [FORMULA] = 2800 K, log(g) = 5.0, and Z increasing from Z = 10 [FORMULA] in the uppermost row of plots to Z = 10 [FORMULA], Z = 0.01 [FORMULA], and Z = 0.1 [FORMULA] in the lower rows.
[FIGURE] Fig. 7. Showing the effect of varying the effective temperature. Same as Fig. 5, but for models of log(g) = 5.0, Z = 10 [FORMULA] and [FORMULA] increasing from [FORMULA] = 2800 K in the uppermost row of plots to [FORMULA] = 3400 K, 3800 K, and 4200 K, respectively, in the lower rows.

In each of the Figs. 5 to 7, the first column shows the emergent flux spectra computed based on models respectively with and without CIA included in the opacity. Here all the spectra and the underlying model atmospheres are internally consistent, in the sense that the spectrum based on the atmospheric structure computed without CIA also itself is without CIA, and vice versa. Hence these are the complete, self-consistent spectra one would predict based on models respectively with and without CIA included in the computations.

Each row of plots in Figs. 5 to 7 represents a given set of fundamental parameters. Whereas the first column illustrates the results of models respectively with and without CIA, the two next columns concentrate only on the models with CIA included in the model calculations. The plots in column two correspond to the depth in the atmosphere where [FORMULA] = 0.01, whereas plots in column three correspond to depths where [FORMULA] = 1.0. Both columns show the total opacity (in units of cm2 per gram of stellar material) due to CIA (dotted lines), due to the sum of all other continuum sources (dashed lines), and due to the sum of all bound-bound molecular line transitions (full drawn lines).

It is seen from the spectra that the major effect of the CIA is to absorb energy in the infrared and to re-emit it at visible wavelengths. For the model shown in Fig. 4, this re-distribution of the flux is so pronounced that the infrared (J-H, H-K) colours change from (0.6, 0.3) to (0.3, -0.1) when CIA is included in the model atmosphere and the corresponding synthetic spectrum. The B-V colour, on the other hand, is only very little affected. The effect of CIA on the emergent infrared spectrum is still substantial even for the cool low-metallicity sub-giant model (i.e., log(g) = 2.0) in Fig. 5. The impact of CIA is also seen in the Z = 0.1 [FORMULA] cool dwarf model in Fig. 6, and in the spectrum of the [FORMULA] = 4200 K low-metallicity dwarf model of Fig. 7. These models define the boundary-region of the grid of models where CIA seems to be important for the spectrum. The effect described for Fig. 4, that the infrared molecular bands "disappear" when CIA is included in the computations (i.e., that the flux distribution becomes very "smooth" at the shown resolution), is seen in several of the flux diagrams of Figs. 5 to 7. The intensity of the G-band due to CH, on the other hand, is either unchanged or even increased (due to the increased re-emitted flux in the blue spectral region) when CIA is included in the opacities.

For the cooler, low-metallicity, dwarf models, the impact of CIA on the spectral distribution is seen to be dramatic, and it is much larger than the impact of other molecular species. It is caused by the relative heating and cooling effect which CIA has on the atmospheric structure. General features of atmospheric heating and cooling and the corresponding flux re-distribution are described in standard text-books on stellar atmospheres (e.g., Mihalas 1978) and they have been the subject of detailed discussion in several papers (e.g., Gustafsson & Olander 1979, Scholz & Wehrse 1994, Gustafsson & Jorgensen 1994). The particularly large impact of CIA is due to its substantial pressure dependence which results in a backwarming in the very deep atmospheric layers where the continuum is formed (as opposed to the effect of, for example, H2 O, where the main effect is in the more shallow atmospheric layers above the continuum forming region). The heating-cooling balance is shown for two models (of log(g)=5.0, C/O = 0.43, and log(Z/ [FORMULA])=10-3, and with [FORMULA] = 2800 K and [FORMULA] = 3800 K, respectively) in Fig. 8. The [FORMULA] = 2800 K model with CIA shows a cooling as large as almost 500 K (compared to the corresponding model without CIA) in the layers around log([FORMULA]) = -2. A corresponding heating of 200 to 300 K results in the deeper layers where log([FORMULA]) [FORMULA] 0 and where most of the continuum is formed. This substantial heating increases the continuum flux at the shorter wavelengths and gives rise to the marked shortward shift of the wavelengths of the emergent flux spectrum. The corresponding model with [FORMULA] = 3800 K shows much less surface cooling and backwarming from CIA than do the [FORMULA] = 2800 K model, and, as is already seen in Fig. 7, the corresponding change in the emergent flux (and the frequency of the flux-maximum) is affected much less.

[FIGURE] Fig. 8. Effect on the T- [FORMULA] structure of including CIA in models of log(g) = 5.0, Z/ [FORMULA] = 10-3, C/O = 0.43, and with [FORMULA] = 2800 K and [FORMULA] = 3800 K, respectively.

Expressed in terms of the gas pressure, the effect of CIA on the [FORMULA] = 2800 K model is, for a given temperature, to lower the gas pressure by about one order of magnitude (in the deeper atmospheric layers), or for a given gas pressure to increase the temperature with approximately 1000 K.

A deeper understanding of the reason for the spectral changes can be obtained by comparing the various contributions to the total opacities at different depths of the atmosphere, as is shown in the columns two and three of Figs. 5 to 7. In each of the three figures, the contribution of CIA relative to the continuum sources (mainly H [FORMULA]) decreases "downward" along the figure (i.e., for decreasing gravity, increasing metallicity, and increasing effective temperature, respectively), until CIA is no longer the dominant opacity source. For such models, inclusion of CIA will no longer change the shape of the emergent flux from the shape of the continuum spectrum, although the total opacity of the CIA can still be appreciable at various depths.

The contribution of the molecular line opacities relative to the CIA and the continuum opacity can also be seen from Figs. 5 to 7, although the curve representing the line opacities must be interpreted a bit more cautiously, because the plotted molecular line opacities are necessarily the average of the opacities over a given wavelength range, inside which the value of the true line opacity may fluctuate very much up and down. Qualitatively, it is seen that the molecular features show up in the spectrum when (and where) the average molecular opacity is large compared to the continuum and CIA opacities. It is also, qualitatively, seen from these plots that when the CIA opacity is much larger than the (average) molecular line opacity (such that the sum of the two opacities is almost identical to the CIA opacity alone), then the spectrum appears smooth and featureless. It can be difficult observationally to recognize the contribution of the CIA to such a spectrum, unless the colours and/or the flux distribution over a substantial wavelength range is compared with the predicted synthetic flux distribution. As opposed to models computed without CIA, it is nevertheless easily seen from Figs. 5 to 7 that the predicted low-resolution spectra of stars over a considerable region in low-metallicity HR diagrams will be almost featureless throughout the infrared.

By comparing columns two and three in each row of the figures (corresponding to a given model) it is seen that the collision induced opacity increases with increasing depth, which is due to the increased number density (of H2 and He). The UV/blue continuum opacity (due to bound-free edges of neutral atoms) is almost independent of optical depth (and choice of fundamental stellar parameters) as long as both the metallicity and effective temperature are relatively low. The visible and infrared continuum opacities, on the other hand, increase markedly with increasing depth in the model, because of the increasing number of free electrons available to form H [FORMULA]. The molecular line opacity (e.g., per unit mass of stellar material) is proportional to the number of molecules (of a given type) in the gas. This number will in general be a function of temperature as well as of gas pressure. The higher pressures at larger depths will favour larger molecules, but at the same time the increasing temperature will act in the opposite direction. In the infrared, where the opacity of water dominates the line opacity, the net effect is seen to be an almost unchanged opacity, with the individual bands, however, being considerably broader at large depths due to the increased contribution of hot bands and high excitation lines at high temperatures. The relative distribution between polyatomic molecules (mainly H2 O) and diatomics (mainly TiO and CH) is very sensitive to temperature, the diatomics being strongly favoured at the larger optical depths where the temperature is highest. In particular, it is seen that the contribution of CH (around the G-band at 4300 Å) increases dramatically relative to the water-bands with increasing depths. For low metallicities, the opacity of CH increases in importance relative to TiO (because it contains only one "metal") as is seen from Fig. 6. Also, CH is more important relative to TiO at high effective temperatures than at low (Fig. 7), whereas the dependence on gravity is less pronounced (Fig. 5).

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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