5.2. Comparison of model atmospheres
As mentioned in the last section, I find some outliers, especially in temperature and metallicity. When looking at the mass-temperature plot of Fig. 5.5, I derive too low temperatures for the group of outliers on the right below the theoretical relation from Baraffe et al. (1998). All these stars have spectral types earlier than ~M1.5 V, which means the expected temperatures lie around 3 900 K instead of 3 500 K. This leads to the hypothesis that there could be 2 sets of parameters, namely lowTeff and [Fe/H] and highTeff and [Fe/H], where models look very similar. To support my theory I assume a reference model spectrum with parameters 4 000 K, 5.0 logg and +0.5 [Fe/H]. With loggfixed I then compare models with different temperatures (3 000–4 000 K, step size 100 K) and metallicities (-1.0, -0.5, 0.0,+0.5 and +1.0 dex) to the reference model and calculate the deviations for the lines I use for fitting (see Section 2.3). The result of that test is presented in Fig. 5.6. Whereas lines/regions like theγ-TiO band, Ti-, Fe- and Mg-lines show a similar pattern, the behaviour of the K- and Na-Mg-lines proves the hypothesis.
Deviations minimise forTeff ~3 600 K almost independent of metallicity. Since I apply higher weights to these lines due to their sensitivity to metallicity, the algorithm might find a local minimum here and prefers the solution for lower temperature and sub-solar metallicity for hot M dwarfs (i.e. with spectral types earlier than ~M1.5 V). It cannot be excluded that this also happens the other way around, meaning a hot and metal-rich model is preferred for a cooler star.
Fig. 5.7 presents a CARMENES spectrum of the M0.0 star V2689 Ori. For this star, the algorithm found two parameter sets with lowχ2, a hot one (Teff=4081 K, logg=4.62, [Fe/H]=+0.18, plotted in blue and red) and a cool one (Teff=3675 K, logg=5.04, [Fe/H]=– 0.7, plotted in purple and green), the former being preferred by a slightly smallerχ2. The deviation between the two models is also plotted for each wavelength range. The plot illustrates that the two models have deviations of more than 25% in the TiO bands, simi-lar to the Mg-line with up to 20%. As stated before, the two models deviate only slightly from each other in the Na-line pair. While the cores are identical, the wings differ by less than 5%. The same deviations applies to the Ti-lines between 841 and 844 nm. This analysis shows that the K- and Na-lines seem to be not as suitable for metallicity de-termination as stated in Section 2.3. Additionally, the models are having problems to reproduce the depth of the Na-lines, since these lines are formed in or near the chromo-sphere for active stars like V2689 Ori, which can also be seen in Fig. 5.7. However, the wings can still be used.
This finding can explain almost all outliers, e.g. the hot group of Gaidos & Mann (2014) in the upper panel of Fig. 5.2, the large spread in metallicity in the lower panel of the same figure, the different results for DS Leo and the outliers in the CFH and CARMENEScomparison.
A similar discrepancy was not found by other authors before. For optical spectra Gaidos
& Mann (2014) fitted temperatures from BT-Settl models, but metallicities are deter-mined from the NIR. Mann et al. (2015) used a similar approach, deriving temperatures from BT-Settl model fits and metallicities from empirical relations of equivalent width in the NIR. The work of Rajpurohit et al. (2014) is more similar to mine, they also used high-resolution spectra and determined stellar parameters from interpolating model
5. Discussion
spectra andχ2-minimisation. But they fitted BT-Settl models to a small sample of 18 M dwarfs. This work is the first to deriveTeff, loggand [Fe/H] from fitting PHOENIX-ACES models to a large sample of high-resolution spectra, which also allows to reveal inconsistencies in the models.
A study similar to mine was done by Lindgren et al. (2016). They determined metallici-ties of 8 single M dwarfs and 4 FGK+M systems from high-resolution infrared spectra.
They used MARCS models (Gustafsson et al., 2008) together with the Spectroscopy Made Easy (SME) package (Valenti & Piskunov, 1996) and find the best fit using inter-polation between the model grid points andχ2-minimisation. Other than for PHOENIX, the solar abundances come from Grevesse et al. (2007). Effective temperatures are es-timated from FeH lines, the metallicities result from fits to all atomic species (except for C-lines due to possible non-LTE effect in the FGK companions). As presented in the contour plots of their Fig. 2, the FeH line strength shows a strong dependency on temperature, but only a weak dependency on metallicity, which leads to a large degener-acy between these two parameters. On the other hand, the metallicities derived from the hot and cool companion of the FGK+M systems agree with each other and confirm the validity of their method. However, the study shows that other synthetic models as well suffer from degeneracies.
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5.2. Comparison of model atmospheres
Figure 5.6.: Deviations of model spectra with different parameters to the reference model as a function of effective temperature. Metallicity is colour-coded on the right
5. Discussion
Figure 5.7.: CARMENES spectrum of V2689 Ori (black) with two PHOENIX-ACES models; The blue/red lines present the hot model (Teff=4081 K, logg=4.62, [Fe/H]=+0.18) and the purple/green lines show the cool model (Teff=3675 K, logg=5.04, [Fe/H]=–0.7). As in the previous plots, the green and red parts present the regions used forχ2calculation. Below each wavelength range the deviation between the hot and the cool model is shown. The red regions illustrate again the lines used for χ2calculation. Only a selection of wavelength ranges is presented.
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