Star Formation Rate

To build a Composite Stellar Population (CSP) we need the birthrate of stars. The Star Formation Rate depends on the amount of gas converted in stars in the galaxy: $\psi(t) = -\frac{df_{\rm gas}}{dt}$. The Schmidt's (1959) law assumes that the rate of star formation varies with a power $n$ of the density of interstellar gas, $\psi(t)=\psi_0 f_{\rm gas}^n [M_\odot/$yr], with $1 \le n \le 2$ (see also Tinsley 1980). Assuming $n=1$ and a closed-box model (constant total mass) with instantaneous recycling of the gas ejected by the stellar remnants, the Schmidt's law leads to the analytic approximation $\psi(t) \propto\exp(-t/\tau)$, also called $\mu$-model, being $\tau=1/\psi_0$ the timescale. The integrated spectrum of a stellar population with an arbitrary star formation rate $\psi(t)$ can be obtained from the spectrum of a SSP by means of the convolution integral: $$f_{\rm CSP}(t) = \int_0^t \psi(t-\tau) f_{\rm SSP}(\tau)\,d\tau$$

assuming that the IMF does not change with time. To reproduce the colours of galaxies of different spectral types, we use the parameters of SFR listed in Table 2: the early galaxies can be matched by a delta burst or by an exponentially decaying SFR with $\tau=1$Gyr, S0 and Spiral galaxies are well reproduced by a Schmidt law with timescales ranging from 2 and 30Gyr, and the Irregulars can be represented by a constant SFR.
 
 

Table:Characteristics of the SFR adopted to match the SEDs of different spectral types of observed galaxies.

 

file	SpT	SFR	Timescale
./ZPHOT/templates/Burst.ised	Burst	Single Burst	--
./ZPHOT/templates/E.ised	E	Exponential	$\tau=1$ Gyr
./ZPHOT/templates/S0.ised	S0	Exponential	$\tau=2$ Gyr
./ZPHOT/templates/Sa.ised	Sa	Exponential	$\tau=3$ Gyr
./ZPHOT/templates/Sb.ised	Sb	Exponential	$\tau=5$ Gyr
./ZPHOT/templates/Sc.ised	Sc	Exponential	$\tau=15$ Gyr
./ZPHOT/templates/Sd.ised	Sd	Exponential	$\tau=30$ Gyr
./ZPHOT/templates/Im.ised	Im	Constant	--

Figure:Evolution of the SEDs of different spectral types computed using the spectral evolutionary models of Bruzual & Charlot (1993), with Miller & Scalo IMF, solar metallicity and characteristics of the SFR as shown in Table 1.

In Figure 3 we show the evolution of the SEDs for 6 of the considered spectral types. The CSP are built with the GISSEL98 library, with Miller & Scalo IMF, solar metallicity and different SFRs, as in Table 2. The represented ages range from$10^{6}$yr to $2 \times 10^{10}$yr: we can remark that at the younger ages all the SEDs resemble each other, whereas they start to differentiate at ages yr, when the 4000Å break becomes detectable. Moreover it is evident that the size of the 4000Å break is much more conspicuous for earlier types.
 

2000-12-10