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Astron. Astrophys. 326, 950-962 (1997)

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3. The star formation history of galaxies

Scenarios of galaxy evolution aim to reproduce the spectral energy distribution of each galaxy type on the most extended wavelength range. The first step is to compute the evolving SED of an instantaneous burst of star formation for a given IMF. The evolution of a real galaxy may then be described by the convolution of an SFR, related for example to the gas content, and of instantaneous bursts of various ages.

3.1. Instantaneous burst

3.1.1. Weight of the evolutionary tracks

As shown by Charlot et al. (1996) from the comparison of the models of Bertelli et al. (1994), Worthey (1994) and Bruzual & Charlot (1996), discrepancies in the evolutionary tracks are the main sources of uncertainty in spectral synthesis. Instantaneous bursts are particularly suitable to test the weight of different evolutionary tracks on spectral synthesis, since spectra

and colors are not smoothed by convolution with the SFR. In what follows, we use the polynomial form of the IMF obtained by Rana & Basu (1992), which accounts for the multiplicity of stars in the solar neighborhood. The slope of massive stars ([FORMULA]) [FORMULA] corresponds to the value adopted in our previous models.

Energy distributions of an instantaneous starburst from 200 Å to [FORMULA] are plotted at various ages in Fig. 1.

[FIGURE] Fig. 1. Spectral evolution of an instantaneous burst of [FORMULA]. Nebular emission and extinction are not considered here.

We show on Fig. 2 the evolution of the bolometric luminosity with time for the tracks of Padova and Geneva. The evolution is very similar for both sets up to 1 Gyr, where the low mass stars of the Padova set ([FORMULA]) undergo the helium flash and provoke a bump in the bolometric luminosity. This bump is due to a flattening of the stellar lifetime slope as a function of the initial mass of the stars in the interval [FORMULA]. A similar feature is obtained at 1.8 Gyr, when the [FORMULA] of the Geneva set also attains the helium flash. The luminosity of the burst computed with Geneva tracks is systematically about [FORMULA] higher after 2 Gyr than that of Padova, maybe because of overshooting. More striking differences may be observed on colors (see Fig. 2). Colors of the instantaneous starburst are derived from convolution of the energy distributions through filter passbands and calibration on the Kurucz (1992) model of Vega. Massive stars of Geneva leave the ZAMS earlier than those of Padova but, whereas the subsequent evolution of [FORMULA] and [FORMULA] colors is similar, presumably because of the adjustment of the stellar evolutionary parameters on optical color-magnitude diagrams of star clusters, [FORMULA] differs by as much as 0.9 magnitude at 12 Myr and 0.75 at 18 Myr. Different treatments of the red supergiant phase are clearly responsible for this, as shown by the isochrones at 12 and 18 Myr (see Fig. 3). While the 12 Myr isochrone of Geneva does not show any blue loop after the crossing of the HR diagram and is therefore redder than that of Padova, the 18 Myr isochrone extends to much higher temperatures and gives bluer colors. The color [FORMULA] then evolves very slowly after 30 Myr, and both sets of tracks are in good agreement up to the helium flash where the bump observed in the bolometric luminosity is also visible. Geneva [FORMULA] then exceeds the value of Padova by [FORMULA] mag up to 13 Gyr, where curves cross one another. The [FORMULA], [FORMULA] and [FORMULA] colors of Geneva then show a flattening trend or a blueing, the reason of which is unclear.

[FIGURE] Fig. 2. Evolution of the bolometric luminosity (left) and colors (right) of an instantaneous burst. Thick lines are for Padova tracks and thin ones for Geneva. Solid: [FORMULA], dashed: [FORMULA], dash-dot-dash-dot: [FORMULA]. The weight of thermal pulses is observed on the V-K curves computed without TP-AGB (dots).
[FIGURE] Fig. 3. Isochrones at 12 Myr (solid) and 18 Myr (dashed) of Padova tracks (thick) and Geneva tracks (thin).

Although the evolution of TP-AGB is poorly known, we show on Fig. 2 that the high-mass ([FORMULA]) TP-AGB stars may not be neglected and strongly redden the [FORMULA] by as much as 0.6 mag at 100 Myr. The weight of TP-AGB becomes negligible after 2 Gyr and is insignificant at all ages for optical colors. Color-magnitude diagrams of optical-NIR colors should help to reduce the discrepancies between the tracks and to reduce the uncertainties on the evolution of red supergiants, but also on the phases following the helium flash.

3.1.2. Weight of the nebular emission

As shown in Fig. 4,

[FIGURE] Fig. 4. Comparison of the spectra of an instantaneous burst at initial time with nebular emission (thick) and without (thin). 70% of Lyman continuum photons ionize the gas and lack shortward of 912 Å in the spectrum with nebular emission.

the inclusion of nebular emission leads to prominent features, emission lines and discontinuities of the nebular continuum, which may not be neglected in the spectrum of an early instantaneous burst. To quantify the relative effect of the nebular component, in particular in the NIR, Table 1 gives the initial fraction of burst light through various filters, due to stars, lines and nebular continuum, respectively.


[TABLE]

Table 1. Weight (in %) of stellar radiation, nebular continuum and emission lines at various wavelengths at initial time for an instantaneous burst.


3.1.3. The inner part of elliptical galaxies

The E1 template, characterizing the metal-rich inner part of ellipticals, compiled by Arimoto (1996) from the data of Bica (1988), Burstein et al. (1988) and Persson et al. (1979), is well fitted on Fig. 5 by a 17-Gyr-old burst model from the U to the K. Though slightly deficient, the predicted flux in the J -band at solar metallicity is notably better than in previous models of ellipticals, as noted by Arimoto (1996). The reason is likely the careful calibration of stellar spectra and colors between the J and K bands. The E1 template shows a steep UV upturn in the far UV, due presumably to old metal-rich stars of which discussion is beyond the scope of this paper. Its metallicity is therefore very likely higher than solar as in the central part of typical giant ellipticals (Munn 1992). Because of the age-metallicity degeneracy in the optical-NIR (Worthey 1994), the best-fitting age of 17 Gyr obtained with the solar metallicity model is thus only an upper limit. Integrated spectra on the whole galaxy of spheroidal galaxies are however bluer in the optical-NIR and have a mean lower metallicity than the core (Munn 1992), allowing us to fit them at the younger age of 13 Gyr (see  3.2.1).

[FIGURE] Fig. 5. Comparison of a 17-Gyr-old instantaneous burst (thin) with the E1 spectrum built by Arimoto (1996) (thick line and crosses) from various sources.

The general agreement of the E1 template with our burst spectrum makes us confident for using our model to build various scenarios of evolution and a new atlas of synthetic spectra (see Rocca-Volmerange & Fioc (1996), in Leitherer et al. (1996b)). Timescales and resolution allow to simulate starbursts as well as evolved galaxies.

3.2. Galaxies of the Hubble sequence

Normal galaxies are the sum of stellar populations of different ages, well simulated with our basic instantaneous starburst. Because of the insufficient knowledge of star formation physics, we prefer to follow the classical hypothesis of an SFR law [FORMULA] depending on the gas fraction g by [FORMULA] and to explore the values of the astration rate [FORMULA] leading to best fits of Hubble sequence galaxies.

3.2.1. Optical-NIR colors

Spectral templates observed through large apertures for each Hubble type are needed for high-redshift predictions. The litterature has essentially published spectra obtained through small apertures (Kinney et al. 1996) or limited to the optical wavelength range (Kennicutt 1992). Thus, we are limited to use statistical samples of colors. A coherent set of optical-NIR colors of nearby galaxies related to morphological type have been obtained by Aaronson (1978) (including Huchra (1977) data) for an aperture [FORMULA].

We plot on Fig. 6 the time evolution of [FORMULA] and [FORMULA] colors for scenarios fitting the observed colors. An inclination of 1 rad, which is the mean inclination integrated over solid angles, is assumed for spiral galaxies. Ages of about [FORMULA] Gyr are obtained for giant spirals (Sa-Sc). Neglecting the effect of extinction would lead to excessive ages, as shown by Fig. 6. The [FORMULA] diagram shows a strong degeneracy for late spirals. The confusion of curves corresponding to slowly-evolving SFR in this region allows a large interval of ages for these galaxies. Maximal age solutions are obtained for 10 Gyr-old Sd and 4-5 Gyr-old Im. If we assume an increasing SFR, very similar colors may however be obtained at 10 Gyr for Im.

[FIGURE] Fig. 6. Left: color evolution (solid) of the synthetic spectra for various star formation histories in the [FORMULA] diagram. The dashed line corresponds to 13 Gyr-old galaxies. Extinction and nebular emission are considered. Right: the same without extinction. Circles are the data as in Aaronson (1978).

However, for early-type galaxies, a gas-dependent SFR in a closed-box model with constant IMF would lead to an excessive residual current star formation and too blue colors, whatever the star formation law may be. Indeed, if the bulk of the stars formed very early, the mass ejection of old stars [FORMULA] will depend mainly on age and not on the detailed star formation history. In the hypothesis of some residual star formation, high-mass stars which have just formed and died in releasing large amounts of gas will also contribute to the gas content. This component is proportional to the current SFR and may be written [FORMULA]. The classical equation of evolution of the gas fraction in a closed model leads with previous approximations, for a decreasing gas fraction, to

[EQUATION]

and we finally get

[EQUATION]

The resulting minimal SFR gives excessively blue [FORMULA] (1.35 at 16 Gyr) and, even more importantly, UV colors. A possible star formation must thus be quenched to recover the colors of normal spheroidal galaxies. However, the gas ejected by old low-mass stars alone since the age of 1 Gyr amounts to nearly 10% of the mass, depending slightly on the IMF, anyway much more than observed (Faber & Gallagher 1976). The fate of this gas is unclear and a dynamical model would be required to determine it, which is beyond the scope of this model. For this reason, we simply assume the following star formation law: [FORMULA], where [FORMULA] and [FORMULA] is a threshold that we conveniently take equal to 0.01; [FORMULA] is nearly equal to 1 at high gas fraction and decreases rapidly to 0 when gas rarefies, suppressing star formation. The remainder ([FORMULA]) is assumed to be expelled by late galactic winds induced by SNIa in a low-density environment or locked in the formation of very low-mass stars. By relaxing the hypotheses of a closed box or constant IMF, we obtain reasonable colors for E/S0.

Our sequence of galaxy colors also compares favorably with the Bershady (1995) data (see Fig. 7). Although the dispersion is due partly to photometric uncertainties, extinction effects (inclination) and irregular star formation histories are certainly also important. The slightly bluer [FORMULA] of the Bershady (1995) data relative to our synthetic galaxies may be due to the fact that Bershady (1995) magnitudes are computed over the whole galaxy, whereas those of Aaronson (1978) are given for an aperture of [FORMULA]. We prefer however to keep the Aaronson (1978) values, because Bershady (1995) does not give a correspondence with morphological type that we need for galaxy counts.

[FIGURE] Fig. 7. Comparison to Bershady (1995) data (dots). U, J and F are the photographic bands of Koo (1980) and Kron (1986). Left: [FORMULA] diagram. Right: [FORMULA] diagram. Squares are our synthetic templates at [FORMULA].

The [FORMULA] color may finally be compared with the mean values of RC3 published by Buta et al. (1994) to check that the identifications of the morphological types of Aaronson (1978) are correct. Since these are face-on corrected values, we correct spiral RC3 colors to an inclination of 1 rad corresponding to a value of [FORMULA] and gather RC3 types to agree with our types when necessary. Differences never exceed 0.05 mag.

The characteristics and the main colors of the computed spectra as well as the RC3 values are given in Table 2.


[TABLE]

Table 2. Evolutionary parameters and colors of the synthetic templates.


3.2.2. Optical spectra

We may compare our spectra in the optical range with those of Kennicutt (1992). Our spectral continua are in very close agreement with that sample (Fig. 8), after correction for redshift and deletion of emission lines by Galaz & de Lapparent (1996). In particular, typical features such as the Balmer jump and the MgI and TiO lines are surprisingly well reproduced.

[FIGURE] Fig. 8. Comparison of our synthetic spectra at [FORMULA] (solid) to Kennicutt (1992) spectra (dotted). Top left: synthetic elliptical vs. NGC 3379 (RC3 type=-5). Top right: synthetic Sa vs. NGC 3368 (RC3 type=2). Bottom left: synthetic Sbc vs. NGC 3147 (RC3 type=4). Bottom right: synthetic Sd vs. NGC 6643 (RC3 type=5).
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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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