  We have made hydro/N-body simulations with and without star formation to shed
some light on the conditions under which a central kinematically cold stellar
component (characterized by a velocity dispersion drop or \sigma-drop) could be
created in a hot medium (e.g. a bulge) and survive enough time to be observed.
We found that the timescale for a \sigma-drop formation could be short (less
than 500 Myr) whereas its lifetime could be long (more than 1 Gyr) provided
that the central region is continuously or regularly fed by fresh gas which
leads to a continuous star formation activity. Star formation in the central
region, even at a low rate as 1M_{sol} yr^{-1}, is mandatory to sustain a
permanent \sigma-drop by replacing heated particles by new low-\sigma ones. We
moreover show that as soon as star formation is switched off, the \sigma-drop
begins to disappear.
