5.4 The Turn-Off for different stellar samples
5.4.3 Dependency and errors in the edge-determination
Another important test is to investigate biases due to quality and quantity of the data. For doing this, we selected subsamples with different uncertainties in the atmosphere param- eters (Teff and [Fe/H]) and also with different χ2 values for the fitting in the parameter
estimation. We randomly selected a sample of 20,000 stars of each of the subsamples de- scribed below. Like this we were unbiased by the size of the stellar sample, which affects the uncertainties, as will be discussed in Sect. 5.2.3. The tests here were done using the MAχ parameters because we can control better the errors and χ2 of the fitting for our
Figure 5.12: [Fe/H] - Teff diagrams for different accuracies in the metallicity (left side)
and temperature (right side) determination. Three levels of accuracy are selected to detect the TO:“bad” (red), “intermediate” (green) and “good” (blue). The domains of these levels of accuracy are indicated in each plot. Lower panels: Bootstrap error of the TO determination for each of the subsamples.
Errors in the atmosphere parameters
We have selected three subsamples with the classification of “bad” (σ[Fe/H] > 0.3), “in- termediate” (0.3 < σ[Fe/H] > 0.15 dex) and “good” (σ[Fe/H] < 0.15) measurements of metallicity; as well as “bad” (σTeff > 100K), “intermediate” (100 > σTeff > 70K) and
5.4 The Turn-Off for different stellar samples 75 “good” (σTeff >70K) measurements of temperature. The [Fe/H] - Teff diagrams of these
subsamples are illustrated in Fig. 5.12, where the left panels correspond the classifications for metallicity and the right panels for temperature. Each [Fe/H] - Teff diagram contains
also the MSTO for each of the subsamples, for the “bad” , “intermediate” and “good” measurements in red, green and blue, respectively. The bottom panels are the behavior of the error in the MSTO determination for the different subsamples, with each color line corresponding to the respective classification.
The distribution of stars in the [Fe/H] - Teff diagram with “bad” [Fe/H] determination
is scattered over the whole parameter space and does not show a clear envelope for the MSTO, as can be seen in Fig. 5.12A. For [Fe/H]>−2.0, the accuracies in the metallicity estimates become better and therefore we find less stars in panel A, which do not allow to detect a turn-off, as seen with the red line. In any case, for stars with [Fe/H]<−2.0, it is possible to detect an edge which agrees with the “intermediate” and “good” samples. The errors in the MSTO detection are also small for low metallicities, while for [Fe/H]>−2.0 they start to increase significantly, as seen in panel D. A different behavior is found at “intermediate” metallicity accuracies , where a clear envelope is seen at the complete metallicity region in Fig. 5.12B. The MSTO detection for this sample is represented with the green line and shows a smooth behavior in the errors at panel D. For “good” metallicity determinations the distribution of stars is biased towards higher metallicities. Although the MSTO detection (blue line) agrees with those of the samples discussed above, the er- rors at lower metallicities increase significantly, as seen with the blue line at panel D. The reason is that at low metallicities there are less “good” metallicity estimates, in the same way as at high metallicities there were less “bad” estimates.
Concerning temperature, “bad” determinations are scattered over the entire [Fe/H] - Teff diagram of Fig. 5.12E and become more frequent for metal rich stars. The edge-
detection is in any case well determined for a large part of the metallicity domain, with a slight increase of the errors towards low metallicities (see the red line at panel H). As in the metallicity case, for the “intermediate” temperature determinations allow an accurate and smooth MSTO detection, which is represented by the green line. Note that in the [Fe/H] - Teff diagram of panel F there are considerably less stars at low metallicities which
does not affect the final MSTO detection significantly. Finally, the distribution of stars with “good” temperature estimations are biased towards metal-poor stars, as we can see at panel G of Fig. 5.12. The MSTO shows a clear envelope for lower metallicities and the errors are small, but increases abruptly at [Fe/H]= -1.8, where the number of stars decreases significantly.
Value of χ2 in the parameter recovery
As explained in Chap. 2, the atmosphere parameters correspond to those of the synthetic spectrum that fit the best the observed spectrum, meaning that MAχ yields the value of the χ2 when recovering the parameters. We used this value to classify subsamples with
Figure 5.13: [Fe/H] - Teff diagrams for differentχ2 in the fitting for the parameter estima-
tion. Three levels of accuracy are selected to detect the TO: “bad” (red), “intermediate” (green) and “good” (blue). The domains for theχ2 value are indicated in each plot. Panel
D: Bootstrap error of the TO-determination for each of the subsamples.
“intermediate” (2.5< χ2 <5.5) and “good” (2.5> χ2) fittings. The [Fe/H] - T
eff diagrams
for these groups are displayed in Fig. 5.13 at panels A, B and C, respectively. The errors of the TO-detection for each of the samples are displayed at panel D, with red, green and blue line corresponding to “bad”, “intermediate” and “good”, respectively.
The “bad” fittings are biased to more metal-rich stars, where the large concentration of stars does not show a clear turn-off. The errors in the TO-detection for “bad” fits increases towards high metallicities, as can be seen with the red line in panel D of Fig. 5.13. It is not surprising to see this effect, because metal-rich stars have more lines in their spectra, meaning that there are more data-points that are sensitive to the parameters. With more lines, a “good” fit is more difficult and theχ2 value becomes larger. In the same way, metal- poor stars have less lines, which also have smaller equivalent widths. The calculation of the
χ2 is mainly concentrated in the continuum, from which it is easier to produce a “good”
fit.
On the other side, “intermediate” χ2 values show a smooth behavior over the [Fe/H]
- Teff diagram in panel B. The TO is well detected and its errors are small in the cho-
5.5 Summary and Conclusions 77