Blue compact dwarf galaxies ( BCDs ) form stars at , for their sizes , extraordinarily high rates .
In this paper , we study what triggers this starburst and what is the fate of the galaxy once its gas fuel is exhausted .
We select four BCDs with smooth outer regions , indicating them as possible progenitors of dwarf elliptical galaxies .
We have obtained photometric and spectroscopic data with the FORS and ISAAC instruments on the VLT .
We analyse their infra-red spectra using a full spectrum fitting technique which yields the kinematics of their stars and ionized gas together with their stellar population characteristics .
We find that the stellar velocity to velocity dispersion ratio ( ( v / \sigma ) _ { \star } ) of our BCDs is of the order of 1.5 , similar to that of dwarf elliptical galaxies .
Thus , those objects do not require significant ( if any ) loss of angular momentum to fade into early type dwarfs .
This finding is in discordance with previous studies , which however compared the stellar kinematics of dwarf elliptical galaxies with the gaseous kinematics of star forming dwarfs .
The stellar velocity fields of our objects are very disturbed and the star-formation regions are often kinematically decoupled from the rest of the galaxy .
These regions can be more or less metal rich with respect to the galactic body , and sometimes they are long lived .
These characteristics prevent us from pinpointing a unique trigger of the star formation , even within the same galaxy .
Gas impacts , mergers , and in-spiraling gas clumps are all possible star-formation ignitors for our targets .