2 Previous works: Understanding the D₄₀₀₀

The $\lambda$4000 Å break is a sudden onset of absorption features bluewards 4000 Å which is clearly noticeable for stellar types cooler than G0 (see Fig. 3). In Fig. 1 we show a typical spectrum of a cool star in this spectral region, together with the identification of the most prominent spectral features. Considering the large wavelength range employed in the measurement of the D₄₀₀₀, it is expected the strength of this discontinuity to be a function of the distribution of the continuum light in this region (governed by the effective temperature) modulated by the absorption line strengths (which must depend primarily on both temperature and metallicity, and secondly on gravity). This behaviour converts the break in a potential tool to investigate composite stellar populations in early-type systems.

The relevance of the line-blanketing discontinuity near $\lambda$4000 Å was the object of a systematic study by [64, Wildey et al. (1962)]. These authors measured the energy subtracted in the spectra of some stars due to Fraunhofer lines, showing that the effect was important below $\lambda$4000 Å. [60, Van den Bergh (1963)], and [61, van den Bergh & Sackmann (1965)] defined a break, $\Delta$, as the ratio of the smoothed observed continuum at both sides of $\lambda$4000 Å. These authors measured this break in a sample of 200 stars concluding that $\Delta$ depended both on stellar metallicity and B-V color. Analogous discontinuity definitions, like C(38-41) [38, (McClure & van den Bergh 1968)], and $\Gamma(38-41)$ [9, (Carbon et al. 1982)], have been also employed in the spectroscopic analysis of stars, star clusters and galaxies.

Using spectrophotometric stellar libraries, [5, Bruzual (1983)] and [28, Hamilton (1985)] studied the variation of the $\lambda$4000 Å break with spectral types and luminosity classes (compare Fig. 3 in Bruzual with Fig. 6 in Hamilton). Both authors concluded that, as a function of temperature, the D₄₀₀₀ increases slowly for spectral types in the range from O5 to G0, and faster from G0 to M0, whereas the break decreases for the later types, M0 to M5. In addition, whilst for spectral types hotter than G0 the break does not depend on gravity, a clear dichotomy between main sequence stars on one hand, and giant and supergiant stars on the other, is apparent for lower temperatures. Given the scarcity of the employed stellar libraries, no dependence on metallicity could be obtained in these works.

From the analysis of moderate-resolution spectra of 950 galaxies in 12 rich clusters, [21, Dressler & Shectman (1987)] argued that, in composite stellar populations, the break is insensitive to changes in metal abundance, at least in the metallicity range spanned by their galaxy sample. This result was employed by [41, Munn (1992)] to conclude that the ${\rm CN}-D_{4000}$ diagram is effective at separating metallicity and age effects on the integrated spectra of early-type galaxies. However, [33, Kimble et al. (1989)] obtained that the break correlated strongly with metallicity indicators, such as the Mgb index.

  

Figure 2: Gravity-temperature diagram for the sample of stars used to derive the empirical fitting function. Different symbols are used to indicate stars of different metallicities, as shown in the key

More recently, [45, Poggianti & Barbaro (1997)], working with Kurucz's models, have obtained a theoretical calibration of the break as a function of stellar parameters. They present (Fig. 1 in their paper) the behaviour of the D₄₀₀₀ in the ranges $5500 < T_{\rm eff} < 35000$ K, $0 < \log g < 5$, and $-2 < \log Z < 0$. This work clearly shows the strong dependence of the break on effective temperature, as previously reported from the studies based on stellar libraries, and quantifies, for a small sample of temperatures, the variation of the break as a function of metallicity and gravity. The D₄₀₀₀ is shown to be insensitive to metallicity for hot stars ($T_{\rm eff} = 9000$ K), whereas the contrary is true for $T_{\rm eff} = 5500$ K. In addition, using the stellar spectra of [56, Straizys & Sviderskiene (1972]; note that these spectra are those also employed by [5, Bruzual 1983)], these authors obtain that, for stars with $3500 < T_{\rm eff} < 5500$ K, the D₄₀₀₀ always exhibits values above 2, with a maximum of 3 at $T_{\rm eff}=4000$ K. Using this theoretical calibration, [2, Barbaro & Poggianti (1997)] have also elaborated an evolutionary synthesis model which predicts, in the integrated spectrum of a galaxy, the variation of the D₄₀₀₀ as a function of the star formation rate (SFR). More interestingly, they conclude that the break can be employed to yield the ratio of the SFR averaged over the last 5 billion years to the present SFR.

From all these previous works, it is quite clear that the D₄₀₀₀ is a suitable tool to face the study of stellar systems, in particular to reveal their stellar composition. However, a detailed empirical calibration, such as that presented in this paper, is needed to i) overcome the unavoidable uncertainties associated to the theoretical calibrations, ii) extend our understanding of the break behaviour for stars with $T_{\rm eff} < 5500$ K (note that these late-type stars constitute a fundamental ingredient in the modeling of old stellar populations), and iii) use in conjunction with other indices previously calibrated with the same stellar library.