Form of star formation history

The model assumes that all progenitors of early-type galaxies started forming stars at a time tstart and ended forming stars at a time tstop. The star formation rate from tstart and tstop is unlikely to have been constant, and may have been punctuated by bursts and periods of relative quiescence. Examples of star formation histories of massive (top row) and red (bottom row) galaxies in the simulations of Nagamine et al. (2004) are shown below.

It may seem that this complexity should greatly complicate the analysis. However, the details of the star formation history prior to tstop are not important, because the evolution of a complex stellar population is virtually identical to that of a single-age stellar population with the same luminosity weighted age. The figure below shows three very different star formation histories, with the same luminosity weighted mean age:

The bottom panel shows that the luminosity evolution of these galaxies is identical - after they have transformed into passively evolving early-type galaxies. Motivated by this, we characterize the star formation history of the galaxies by a single parameter f*, which describes the luminosity weighted formation time of the stars in relation to tstart and tstop:

t* = f* tstop + (1 - f*) tstart.
The limiting case f*=0 implies that all stars were formed at t=tstart, and the limiting case f*=1 implies that all stars were formed at the end of the star formation history, i.e., right before transformation to early-type galaxy. Examples of star formation histories with intermediate values of f* are shown below.

This approach for characterizing the form of the star formation history has the advantage that it has only one free parameter, and that this parameter (effectively the luminosity-weighted age) is the one which is actually constrained by the observations.