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:
\begin{displaymath}f_{\rm CSP}(t) = \int_0^t \psi(t-\tau) f_{\rm SSP}(\tau)\,d\tau\end{displaymath}

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 --
\begin{figure}\centerline {\psfig{,width=0.99\textwidth}}\end{figure}
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 $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil$\displaystyle ...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.

micol bolzonella