Astron. Astrophys. 353, 557-568 (2000)

3. Calculations

Local Thermodynamic Equilibrium was assumed for the spectrum synthesis calculations. The code we employed for spectrum synthesis has been improved over the past thirty years, and has been described in Spite (1967), Barbuy (1982) and Cayrel et al. (1991). Solar abundances for the various elemental species were adopted from Grevesse et al. (1996). Oscillator strengths (gf values) for atomic lines were adopted from Wiese et al. (1969), Fuhr et al. (1988) and Martin et al. (1988) whenever available, otherwise they were obtained by fits to the solar spectrum.

The heavy neutron-capture elements lines and corresponding gf values given by Sneden et al. (1996) were added to our list of solar-identified lines. Hyperfine structure (HFS) corrections were taken into account for the elements Eu and Ba (Steffen 1985; François 1996). In the case of barium, the HFS correction is a delicate problem since this element has odd isotopes (mainly produced by r-process and having broad HFS) and even isotopes (produced by s-process and showing no HFS). The adopted HFS correction therefore depends on the s/r fraction assumed to have contributed to the enrichment of the star. On the other hand, Sneden et al. (1996) have shown that this issue is only important for the 4554 Å and 4934 Å lines, and unimportant for the three other lines 5854, 6142, and 6497 Å. Therefore, for the two bluest lines, we used the HFS structure given by François (1996) (an adaptation of the original Rutten 1978) assuming a solar s/r mixture, and no HFS for the three reddest lines. Following Sneden et al. (1996), should the solar s/r mixture hypothesis be false and the enrichment be purely r-process, one would expect to have overestimated the Ba abundance from these two lines by at most 0.2 dex. The fact that we do not find any systematic difference between the blue and red Ba lines is a good indicator that the adopted hypothesis is acceptable.

3.1. Molecular lines

Absorption lines of the following molecules were taken into account in the calculations: MgH (-), C₂ (-), CN blue (-), CH (-), CH (-), CN red (-), TiO (-), and TiO (-). ¹³CH lines were also included, where wavelengths by Kurucz (1993) were corrected following Norris et al. (1997b) and Bonifacio et al. (1998).

In all cases where possible, the Franck-Condon factors with dependence on the rotational quantum number J, as given in Dwiwedi et al. (1978) and Bell et al. (1979), were computed and adopted. For vibrational bands where such values were not available, we adopted a constant value kindly provided to us through computations by Singh (1998, private communication).

For the blue CH and CN systems, the line lists by Kurucz (1993) were adopted, where we transformed his tables to our format, recomputing for each line the Hönl-London factors using the formulae by Kovacs (1979), revised according to Sharp (1983). For the C₂ lines we have carried out a detailed comparison between the Kurucz (1993) line list and the laboratory list by Phillips & Davis (1968). The resulting molecular bands are very similar, thus we have kept the laboratory line list in most of our calculations.

We have adopted the electronic oscillator strengths (CN red) = 6.76E-3 (Larsson et al. 1983; Davis et al. 1986; Bauschlicher et al. 1988) and (CN blue) = 0.0338 (Duric et al. 1978), (C₂) = 0.033 (Kirby et al. 1979), (CH) = 5.257E-3 for the CH (-) (Brzozowski et al. 1976) and 2.5E-3 for the CH (-) (Lambert 1978) and dissociation potentials (CN) = 7.65 eV, (C₂) = 6.21 eV, (CH) = 3.46 eV (Huber & Herzberg 1979).

3.2. Model atmospheres

A special grid of plane-parallel model atmosphere was computed, hereafter referred to as MARCS99, using a revised version of the models described in Plez et al. (1992), taking into account the large enhancement of carbon and nitrogen in the atmosphere. These models are preliminary calculations, part of a new grid of Uppsala models based on an extensive update of the MARCS code (originally described by Gustafsson et al. 1975) and its input data. The grid (4250 5250 K, 0.0 log g 3.0, [Fe/H]=-3.0,-2.0 and [C/Fe]=+2.0, [N/Fe]=+2.0) was especially adapted to represent these stars. The predicted colours for this grid of models were also calculated (Table 3), following Bessell et al. (1998), and used in the determination of the temperatures of our stars (Table 4).

Table 3. Predicted colours and bolometric corrections computed from the MARCS99 CN-enhanced models.

Table 4. Stellar parameters: effective temperatures, surface gravities, metallicities, and microturbulence velocities . In the upper part of the table, the temperatures deduced by a comparison of the observed and predicted colours are given, assuming two different chemical compositions: (1) [C/H] = [N/H] = -1.0, [Fe/H] = -3.0, (2) [C/H] = [N/H] = 0.0, [Fe/H] = -2.0

3.3. Atmospheric parameter determination: , log g , [Fe/H],

The colours of such metal-poor and C,N-enhanced stars are strongly affected by the presence of CH, CN and C₂ bands, producing large gaps in the stellar flux distribution. It is therefore mandatory to take these effects into account when deducing the temperature.

To determine the effective temperatures, we used the observed colours (Table 2), and compared them with the computed colours of the C,N-enhanced models (Table 3, assuming ). In Table 4, these deduced temperatures are given assuming two different chemical composition for the models: ([C/H] = [N/H] =-1.0, [Fe/H] = -3.0) and ([C/H] = [N/H] =0.0, [Fe/H] = -2.0). The dependence of temperature on the assumed C and N content is striking, emphasizing the need to use proper colour-temperature calibrations for C,N-enhanced stars. We note that the use of "normal" (i.e., non C,N-enhanced) colour calibrations would have led to a discrepancy in inferred temperatures for our stars as obtained from and of more than 700 K!

We have found that a temperature = 4800 K is the optimal choice for both stars. The measured H profiles from our spectra are compatible with 4800 K, which, when combined with photometric temperatures of Table 3, makes this a best choice. This temperature is also compatible with the excitation equilibrium of the Fe I lines and with the relative intensities of the (0,0) (1,1) and (1,0) (2,1) and (3,2) bandheads of C₂.

The same Fe I and Fe II line list (given in Paper I) was then used to determine the surface gravity log g  (via ionization equilibrium) and  (via the requirement that estimated abundances are independent of the strength of the lines). The iron lines in the newly obtained blue spectra were not used for this purpose because of very severe blends with molecular lines.

The resulting atmospheric parameters are given in Table 4.

3.4. Constraints from proper motions

Comparisons with the recent STARNET (STN; Fuchs 1999, private communication) and the Yale/San Juan Southern Proper Motion (SPM) 2.0 catalogs (Platais et al. 1998) has indicated that both of our program stars have measured proper motions. The data are presented in Table 5.

Table 5. Proper motions (given in mas)

In both catalogs, the proper motions in declination are substantially larger than the corresponding errors. The SPM catalog proper motion in the right ascension component is also clearly much larger than the reported error. This has an important consequence on the maximum distances of our two stars, as it would be unreasonable to assume that our objects have total velocities greater than the escape velocity of the Galaxy. We now check if our choice of atmospheric parameters ( = 4800 K, log g = 1.8) is acceptable in this respect. From the following relationship:

and assuming , one obtains

and from:

is easily derived, assuming = 4.75 in conformity with the recommendations of the IAU (Andersen 1999).

The resulting value is:

Adopting the calculated MARCS99 bolometric correction appropriate to the effective temperature of 4800 K (Table 3) yields:

and a distance modulus, , of ( 4 kpc) for CS 22948-27 and ( 3.2 kpc) for CS 29497-34. Here we have assumed that the two stars are of identical luminosity and we neglect any interstellar absorption, as is appropriate for these high Galactic latitude objects.

Combining the estimated distances with the measured proper motions to obtain transverse velocities, and using our measured radial velocities, we obtain the velocities given in Table 6. We have adopted the convention that U is pointing towards the Galactic center, V towards the Galactic rotation direction, and W towards the north Galactic pole. We adopt the basic solar motion of Delhaye (1965; ), and the relation between V_rot and V_LSR is . The total space velocities obtained are, respectively, 373 km s^-1 and 277 km s^-1, well below the escape velocity corresponding to their location in the Galaxy, assuming a gravitational potential with constant rotational velocity.

Table 6. Deduced spatial velocities (km s^-1)

Note that if we had adopted a significantly lower temperature, this would have induced a lower estimate of the surface gravity for our stars. A surface gravity of log g = 1.2, for example, would make these two stars unbound to the Galaxy. Many of the carbon-enhanced stars found in the HK survey have significant proper motions, making it improbable that they are "normal" AGB stars of high luminosity, a hypothesis which might have otherwise been invoked to account for the very large carbon abundances via the classical third dredge-up scenario (though such a hypothesis would also have difficulty given that these stars are expected to be quite old based on their observed metallicities).

Both of our stars exhibit clear retrograde orbits in the Galaxy. The components of their velocities are rather similar (small changes in their distance estimates could make them even more similar). This commonality of orbital motion for two stars which are so widely separated on the sky (and of similarly low metal abundance) could be due to chance, but it is intriguing to consider the possibility that they share a common origin, having been born in the same star forming region. Clearly, larger samples of such interesting stars are necessary to further explore this question.

© European Southern Observatory (ESO) 2000

Online publication: December 17, 1999
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