Zero-points

In this Section we compare the index measurements taken in the smoothed Jones spectra with the standard Lick/IDS measurements from Worthey et al. (1994) and Worthey & Ottaviani (1997) for stars common to the two spectral libraries in order to derive zero-point transformations between the two index systems. Such comparisons are shown in Figures 1a-b, where the residual differences between measurements in the two sets of spectra are plotted as a function of index strength. These Figures are worthy of some contemplation and a few thoughts. First, we call attention to the large scatter found for all the indices (the standard deviations are listed in Table 1). This is a striking result, given the fact that the EWs were measured in very high S/N spectra of bright stars. In fact, such a large scatter should not come as a surprise, as any spectroscopist is acquainted with the fact that even EW measurements taken in repeat spectra of the same star, taken with the same instrumental setup, are also characterized by a sizable scatter, which is probably due to a combination of wavelength-calibration, background-subtraction, and flat-fielding errors, low resolution, poor determination of the latter, cosmic-ray residuals, bad pixels, variations in spectrograph focus along an observing night, and a myriad of other possible factors that can spoil the measurement of an equivalent width. Second, zero-point differences are found for some indices, most notably the wider-baseline molecular-band indices such as Mg$_2$, CN$_2$ and G4300. Zero-point differences are also found for some narrower indices, such as $H\delta _A$, $H\gamma _A$, and Mg $b$. Such differences, especially in the case of the wide-baseline indices, are mostly (but not only, see below) due to the fact that, contrary to case of the Jones spectra, those of the Lick/IDS standards are not flux-calibrated, so that wide-band indices measured in the latter are liable to be affected by the response curve of the Lick Image Dissector Scanner. Third, there is a hint of a systematic trend of the residuals as a function of index strength for some of the indices, like CN$_2$, Ca4227, G4300, and Mg$_2$. Such trends are not uncommon (see, for instance, Paper III), and Figures 1a-b highlight the importance, in any observational work dealing with Lick indices, to secure large amounts of standard star spectra, covering a wide range of index values, in order to guarantee a safe conversion into the Lick system.

It is very difficult, from the comparisons shown in Figures 1a-b alone, to have an idea of the true quality of our EW measurements, given that they are compared with lower quality measurements taken with the Lick/IDS instrument. In Figures 2a-b, our measurements are compared to those taken in high quality, flux-calibrated, spectra presented in Paper III for stars in common with this program. These were taken with the FAST spectrograph (Fabricant et al. 1998), attached to the 1.5 m telescope at the Fred Whipple Observatory. One can see that the residuals are much smaller than those between our index measurements and the original Lick/IDS standard values (Figures 1a-b). Comparison between Figures 1a-b and 2a-b should serve as an eloquent statement of the vast improvement in the quality of the equivalent widths upon which our models are based. The line indices of standard stars are of course in the very root of our models and, without such high quality measurements, the task of making accurate model predictions would be hopeless.

It is interesting to note, however, that even when flux-calibrated spectra are employed, there are zero-point differences between this work's and FAST measurements, as clearly visible in the case of Fe5015 (Figure 2b) and, to a lesser extent, $H\delta _A$, $H\gamma _A$, and Fe4383. This serves as a demonstration that flux calibration alone cannot eliminate the need for zero-point determinations, based on extensive measurements taken on high quality standard star spectra. In other words, any equivalent width measurement necessarily depends on the instrumental set up and reduction techniques employed in obtaining the spectra, so that conversion into the equivalent system defined by a given set of standard values will always be necessary. While it is true that most zero-point differences in Figures 2a-b are very small, the increasing quality of both models and data will certainly push the need towards higher and higher accuracy measurements, thus requiring precise zero-point determinations.

In view of the above considerations we decided to maintain measurements taken on flux-calibrated spectra, like those of the Jones library, because they are more easily reproducible by observers using different instrumental setups. Therefore, we decided not to convert our EWs into the Lick/IDS system, but rather redefine it on the basis of the measurements performed on the Jones spectral library. To that effect, the EWs of all line indices are given in Table A in the Appendix. Observers wishing to compare their data to the models presented in this paper should seek to reproduce the EWs of the Jones standards provided in Table A. with measurements performed in spectra obtained with their own instrumental setups.

Finally, in order to conform with the vast amount of previous work based on the Lick/IDS system, we estimate zero-point conversions between our EWs and the Lick/IDS standards. These conversions are listed in Table 1. Those wishing to compare the models presented here with measurements taken in the Lick/IDS system should first take those conversions into account.