We now discuss the properties of the new library spectra which result from the correction algorithm developed above, and which are most important in the context of population and evolutionary synthesis.
-color relations
Figure 14 (click here) illustrates the -color relations
obtained after correction of the giant sequence spectra from the
K- and 
-libraries. Comparison with the corresponding
Fig. 6 (click here) for the uncorrected spectra shows that the original
differences which existed both between overlapping spectra of the two
libraries and between the synthetic and empirical relations
have indeed almost entirely been eliminated. While remaining
differences between libraries are negligible, those between theoretical
and empirical relations are below 0.1 mag.
Figure 15 (click here) illustrates similar results for the main sequence. Again, comparison with the corresponding Fig. 7 (click here) before correction shows that the present calibration algorithm provides theoretical color-temperature relations which are in almost perfect agreement with the empirical data.
Thus at this point, we can say that for solar abundances, the new
library provides purely synthetic giant and dwarf star spectra that in
general fit empirical color-temperature calibrations to within better
than 0.1 mag over significant ranges of wavelengths and temperatures,
and even to within a few hundredths of a magnitude for the hotter
temperatures, 
.
Bolometric corrections, BCV, are indispensable for the direct
conversion of the theoretical HR diagram, 
, into
the observational color-absolute magnitude diagram, MV(B-V):
where the bolometric magnitude,
provides the direct link to the effective temperature (scale). Of
course, bolometric corrections applying to any other (arbitrary)
passbands are then consistently calculated from
BCi=BCV+(MV-Mi), where the color MV-Mi is
synthesized from the corrected library spectra.
Figure 11: Correction functions for a range of effective temperatures
Figure 16 (click here) provides a representative plot of bolometric
corrections, BCV, for solar-abundance dwarf model spectra. The
arbitrary constant in Eq. (11) has been defined in order to fix to
zero the smallest bolometric correction (Buser & Kurucz
1978) found for the non-corrected models, which gives
. Comparison with the
empirical calibration given by Schmidt-Kaler (1982)
demonstrates that the present correction algorithm is reliable in this
respect, too: predictions everywhere agree with the empirical data to
within 
- which is excellent. Similar tests for the
giant models also indicate that the correction procedure provides
theoretical bolometric corrections in better agreement with the
observations. These results will be discussed in a subsequent paper
based on a more systematic application to multicolor data for cluster and
field stars (Lejeune et al. 1997).
Since comprehensive empirical calibration data have only been available for the full temperature sequences of solar-abundance giant and dwarf stars, direct calibration of the present library spectra using these data has, by necessity, also been limited to solar-abundance models. However, because one of the principal purposes of the present work has been to make available theoretical flux spectra covering a wide range in metallicities, it is important that the present calibration for solar-abundance models be propagated consistently into the remaining library spectra for parameter values ranging outside those represented by the calibration sequences. We thus have designed our correction algorithm in such a way as to preserve, at each temperature, the monochromatic flux ratios between the original spectra for different metallicities [M/H] and/or surface gravities log g. Justification of this procedure comes from the fact that, if used differentially, most modern grids of model-atmosphere spectra come close to reproducing observed stellar properties with relatively high systematic accuracy over wide ranges in physical parameters (e.g., Buser & Kurucz 1992; Lejeune & Buser 1996).
In order to check the extent to which preservation of monochromatic
fluxes propagates into the broad-band colors, we have calculated the
differential colors due to metallicity differences between models of
the same effective temperature and surface gravity:
We can then calculate the residual color differences between the
corrected and the original grids:
Results are presented in Figs. 17 (click here) and 18 (click here) for the
coolest K-library models 
and for the -library models for M giants 
, respectively. Residuals are plotted as a
function of the model number, which increases with both surface gravity
and effective temperature, as given in the calibration sequences. The
different lines represent different metallicities, 
, as explained in the captions.
Figure 12: Normalized corrected (solid lines) and original (dashed lines)
library spectra for ranges in effective temperature and
metallicity and covering wavelengths from the photometric
U-through K-passbands. Top panels: K-library dwarf
models; middle panels: K-library giant models; bottom
panels: -library giant models
Figure 13: Same as Fig. 12 (click here), but for the visible-near
infrared wavelength ranges only
Figure 14: Empirical color-effective temperature calibrations for
solar-metallicity red giant stars (solid lines, according to
Table 2 (click here)) compared to the corresponding
theoretical relations calculated from corrected synthetic
library spectra (symbols, according to key in insert). Compare with
Fig. 6 (click here)
Figure 15: Empirical color-effective temperature calibrations for
solar-metallicity dwarf stars (solid lines, see text for
sources) compared to the corresponding theoretical relations
calculated from corrected synthetic K-library spectra
(symbols). Compare with Fig. 7 (click here)
The most important conclusion is that, in general, the correction
algorithm does not alter the original differential grid properties
significantly for most colors and most temperatures - in fact, the
residuals are smaller than only a few hundredths of a magnitude.
Typically, the largest residuals are found for the coolest
temperatures 
and the shortest-wavelength
colors, UBVRI, where the correction functions of Fig. 11 (click here) show
the largest variations not only between the different passbands, but also
within the individual passbands. This changes their
effective wavelengths and, hence, the baselines defining the color
scales (cf. Buser 1978). Since this effect tends to grow
with the width of the passband, it is mainly the coincidence of large
changes in both amplitudes and slopes of the correction functions
with the wide-winged R-band which causes residuals for the R-I colors
to be relatively large in Fig. 18 (click here).
Calculations of color effects induced by surface gravity changes lead to similar results. This corroborates our conclusion that the present correction algorithm indeed provides a new model spectra library which essentially incorporates, to within useful accuracy for the purpose, the currently best knowledge of fundamental stellar properties: a full-range color-calibration in terms of empirical effective temperatures at solar abundances (where comprehensive calibration data exist) and a systematic grid of differential colors predicted by the original theoretical model-atmosphere calculations for the full ranges of metallicities and surface gravities (where empirical data are still too scarce to allow comprehensive grid calibration).
Of course, we are aware that the present correction algorithm becomes increasingly inadequate with the complexity of the stellar spectra growing with decreasing temperature and/or increasing surface gravity and metallicity. For example, because under these conditions the highly nonlinear effects of blanketing due to line saturation and crowding and broad-band molecular absorption tend to dominate the behavior of stellar colors, particularly at shorter (i.e., visible) wavelengths, even the corresponding differential colors cannot either be recovered in a physically consistent manner by a simple linear model such as the present. However, the limits of this approach will be further explored in Paper II, where the calibration of theoretical spectra for M-dwarfs will be attempted by introducing the conservation of original differential colors of grid spectra as a constraint imposed to the correction algorithm.