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Context: In the centre of pre-stellar cores, the deuterium fractionation isenhanced due to the cold temperatures and high densities. Therefore, thechemistry of deuterated molecules can be used to probe the evolution and thekinematics in the earliest stages of star formation. Aims: We analyse emissionmaps of cyclopropenylidene, c-C$_3$H$_2$, to study the distribution of thedeuteration throughout the prototypical pre-stellar core L1544. Methods: We usesingle-dish observations of c-C$_3$H$_2$, c-H$^{13}$CC$_2$H, c-C$_3$HD, andc-C$_3$D$_2$ towards the pre-stellar core L1544, performed at the IRAM 30mtelescope. We derive the column density and deuterium fraction maps, andcompare these observations with non-LTE radiative transfer simulations.Results: The highest deuterium fractions are found close to the dust peak atthe centre of L1544, where the increased abundance of H$_2$D$^+$ ions drivesthe deuteration process. The peak values areN(c-C$_3$HD)/N(c-C$_3$H$_2)=0.17\pm0.01$,N(c-C$_3$D$_2$)/N(c-C$_3$H$_2)=0.025\pm0.003$ andN(c-C$_3$D$_2$)/N(c-C$_3$HD$)=0.16\pm0.03$, which is consistent with previoussingle point observations. The distributions of c-C$_3$HD and c-C$_3$D$_2$indicate that the deuterated forms of c-C$_3$H$_2$ in fact trace the dust peakand not the c-C$_3$H$_2$ peak. Conclusions: The N(c-C$_3$D$_2$)/N(c-C$_3$HD)map confirms that the process of deuteration is more efficient towards thecentre of the core and demonstrates that carbon-chain molecules are stillpresent at high densities. This is likely caused by an increased abundance ofHe$^+$ ions destroying CO, which increases the amount of carbon atoms in thegas phase.

Deuteration of c-C$_3$H$_2$ towards the pre-stellar core L1544