Spatial distribution of C4H and c-C3H2 in cold molecular cores

C${}_4$H and $c$-C${}_3$H${}_2$, as unsaturated hydrocarbon molecules, are important for forming large organic molecules in the interstellar medium. We present mapping observations of C${}_4$H ($N$=9$-8$) lines, $c$-C${}_3$H${}_2$ ($J_{Ka,Kb}$=2${}_{1,2}$-1${}_{0,1}$) %at 85338.894 MHz and H${}^{13}$CO${}^{+}$ ($J$=1$-0$) %at 86754.2884 MHz toward 19 nearby cold molecular cores in the Milky Way with the IRAM 30m telescope. C${}_4$H 9–8 was detected in 13 sources, while $c$-C${}_3$H${}_2$ was detected in 18 sources. The widely existing C${}_4$H and $c$-C${}_3$H${}_2$ molecules in cold cores provide material to form large organic molecules. Different spatial distributions between C${}_4$H 9–8 and $c$-C${}_3$H${}_2$ 2–1 were found. The relative abundances of these three molecules were obtained under the assumption of local thermodynamic equilibrium conditions with a fixed excitation temperature. The abundance ratio of C${}_4$H to $c$-C${}_3$H${}_2$ ranged from 0.34 $\pm$ 0.09 in G032.93+02 to 4.65 $\pm$ 0.50 in G008.67+22. A weak correlation between C${}_4$H/H${}^{13}$CO${}^{+}$ and $c$-C${}_3$H${}_2$/H${}^{13}$CO${}^{+}$ abundance ratios was found, with a correlation coefficient of 0.46, which indicates that there is no tight astrochemical connection between C${}_4$H and $c$-C${}_3$H${}_2$ molecules.