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Astron. Astrophys. 318, 841-869 (1997)

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9. The effect of convection on Balmer lines

According to Fuhrmann et al. (1994), the wings of the Balmer profiles may be used to fix effective temperatures in cool type stars.

In the previous sections we showed the effect of the "overshooting" option on ([FORMULA]), ([FORMULA]), ([FORMULA]), and [FORMULA] colour indices. In this section we investigate its effect on the Balmer lines. Furthermore, we will try to state whether Balmer lines from K95 models or rather those from models without "overshooting" (NOVER models) give [FORMULA] more close to the value derived from the ([FORMULA]) indices, which is almost independent of the "overshooting" option (Sect. 7.1).

We compared the equivalent widths of [FORMULA], [FORMULA], and [FORMULA] obtained from the K95 models with those derived from the NOVER models. Fig. 23 displays this comparison for [FORMULA], [FORMULA] ranging from 4000 K to 8500 K, and [M/H]=0.0 and [M/H]=-3.0. For the same equivalent widths, [FORMULA] from models with [M/H]=-3.0 are larger than [FORMULA] from models with [M/H]=0.0, or viceversa, for the same [FORMULA], Balmer profiles become weaker with decreasing metallicity. For both metallicities, [FORMULA] from K95 models are larger than [FORMULA] from NOVER models. For [FORMULA], the difference [FORMULA] [FORMULA] = [FORMULA] (K95)- [FORMULA] (NOVER) is plotted as function of [FORMULA] in Fig. 24. [FORMULA] (K95) was obtained by interpolating in the [FORMULA] (NOVER) equivalent widths for the [FORMULA] (K95) equivalent widths. Fig. 24 shows that NOVER and K95 models yield [FORMULA] from [FORMULA] which may differ up to 340 K. For [FORMULA] [FORMULA] 6250 K, [FORMULA] [FORMULA] is nearly independent of metallicity, but for [FORMULA] included between 5000 K and 6250 K, [FORMULA] [FORMULA] increases with decreasing metallicity. At 5500 K, [FORMULA] [FORMULA] for [M/H]=-3.0 is 130 K larger than [FORMULA] [FORMULA] for [M/H]=0.0.

[FIGURE] Fig. 23. Equivalent widths of [FORMULA], [FORMULA], and [FORMULA] profiles as a function of [FORMULA] for [FORMULA]. Full lines are for [M/H]=0.0, dashed lines are for [M/H]=-3.0. For each metallicity, equivalent widths from K95 models are compared with those from NOVER models
[FIGURE] Fig. 24. [FORMULA] [FORMULA] as a function of [FORMULA], where [FORMULA] [FORMULA] is the difference between [FORMULA] derived from [FORMULA] and the K95 models and [FORMULA] derived from [FORMULA] and the NOVER models. Full line is for [M/H]=0, dashed line is for [M/H]=-3.0

Fig. 25 compares [FORMULA] profiles from K95 and NOVER models having parameters 6500,4.0, [M/H]=0. Upper plot and lower plot show profiles in absolute flux units and profiles normalized to the continuum level, respectively. When profiles are analysed, it becomes manifest that the [FORMULA] [FORMULA] differences related with the convection are mostly due to the different shape of the profiles rather than to a different level of the continuum. In Sect. 4 we showed that, viceversa, changes of the mixing-length parameter affect more the level of the continuum than the shape of the wings.

[FIGURE] Fig. 25. Comparison between [FORMULA] profiles computed from K95 models (dashed line) and NOVER models (full line) having parameters 6500 K, [FORMULA] =4.0, and [M/H]=0.0. Upper and lower plots show profiles in absolute flux units and profiles normalized to the continuum level, respectively. Absolute flux is [FORMULA] in 107  erg cm-2 sec-1 nm-1

To state whether the "overshooting" or the "no overshooting" models give more consistent [FORMULA] when different methods are used, we compared [FORMULA] from ([FORMULA]) index with [FORMULA] derived from [FORMULA] for a sample of seven subdwarf stars. Table 6 lists the stars. Observations in the [FORMULA] region were performed at the 182 cm Copernicus reflector of Asiago Astrophysical Observatory. A REOSC Echelle spectrograph having a resolving power of about 15000 was used. The spectra have a S/N ratio of about 250 (see also Clementini et al., 1995). Observed ([FORMULA]) indices were taken from Alonso et al. (1994) (TCS system) and Laird et al. (1988) (CIT system) (Table 6, column 4). Indices from both sources were transformed into the Johnson system using the relations given by Alonso et al. (1994) (Table 6, column 5). For all the stars, except for HD 194598, we adopted metallicity and gravity which approximate those listed in Axer et al. (1994) (Table 6, Columns 2 and 3). For HD 194598, the weak observed Fe I lines lying in the [FORMULA] region resulted too strong when computed for the metallicity [M/H]=-1.0, which approximates the value [M/H]=-0.99 given by Axer et al. (1994). We therefore assumed [M/H]=-2.0 for this star. According to Sect. 7.2, ([FORMULA]) index weakly depends on gravity, metallicity, and options for convection. According to Fuhrmann et al. (1993), also [FORMULA] is almost independent of gravity and metallicity. Fig. 23 shows that at 6000 K, a metallicity difference of -3.00 dex implies a difference in [FORMULA] of about 200 K. We may deduce that small metallicity uncertainties should yield very small [FORMULA] [FORMULA] differences.


[TABLE]

Table 6. [FORMULA] for Procyon from different methods and from K95 and NOVER models


We derived [FORMULA] from [FORMULA] by comparing observed and computed profiles. The uncertainty related with the fitting procedure is on the order of 50 K. H [FORMULA] effective temperatures from K95 models and the NOVER models are listed in columns 7 and 10 of Table 6. [FORMULA] from the K95 models are 250 K larger than those from the NOVER models. We determined [FORMULA] from ([FORMULA]) indices by interpolating in the COLK95 and COLNOVER grids for the ([FORMULA]) observed indices. On the basis of E([FORMULA])=0.0 for all the seven stars (Laird et al., 1988) we assumed zero reddening for the ([FORMULA]) index. The resulting effective temperatures are listed in columns 6 and 9 of Table 6. The effective temperature differences [FORMULA] [FORMULA] between [FORMULA] from ([FORMULA]) and [FORMULA] from [FORMULA] are listed in Table 6, columns 8 and 11, for the K95 and the NOVER models respectively. When NOVER models are considered, [FORMULA] from [FORMULA] agree within 100 K with [FORMULA] derived from ([FORMULA]) for six out of the seven examined stars. Only for HD 114762, the K95 models yield a good agreement between [FORMULA] derived from the ([FORMULA]) index and [FORMULA] derived from [FORMULA]. For HD19445 there is a somewhat large discrepancy between the ([FORMULA]) index from Laird et al. (1988) and that from Alonso et al. (1994), which yields an uncertainty of about 100 K for the derived effective temperatures.

For comparison, column 12 of Table 6 shows [FORMULA] derived by Fuhrmann et al. (1994) on the basis of models different from those used by us. [FORMULA] from Fuhrmann et al. (1994) agree with those from [FORMULA] and NOVER models within limits included between 10 K and 200 K. For HD 114762 the difference is 14 K. The differences are included between 240 K and 450 K when the K95 models are considered.

We may conclude that the NOVER models seem to yield more consistent [FORMULA] than the K95 models when [FORMULA] are derived from the ([FORMULA]) indices and from the [FORMULA] profiles. The average differences are about 200 K and 80 K for the K95 and the NOVER models respectively.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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