ALMA view of the $^{12}$C/$^{13}$C isotopic ratio in starburst galaxies

We derive molecular-gas-phase $^{12}$C/$^{13}$C isotope ratios for the central few 100 pc of the three nearby starburst galaxies NGC 253, NGC 1068, and NGC 4945 making use of the $\lambda$ $\sim$ 3 mm $^{12}$CN and $^{13}$CN $N$ = 1--0 lines in the ALMA Band 3. The $^{12}$C/$^{13}$C isotopic ratios derived from the ratios of these lines range from 30 to 67 with an average of 41.6 $\pm$ 0.2 in NGC 253, from 24 to 62 with an average of 38.3 $\pm$ 0.4 in NGC 1068, and from 6 to 44 with an average of 16.9 $\pm$ 0.3 in NGC 4945. The highest $^{12}$C/$^{13}$C isotopic ratios are determined in some of the outskirts of the nuclear regions of the three starburst galaxies. The lowest ratios are associated with the northeastern and southwestern molecular peaks of NGC 253, the northeastern and southwestern edge of the mapped region in NGC 1068, and the very center of NGC 4945. In case of NGC 1068, the measured ratios suggest inflow from the outer part of NGC 1068 into the circum-nuclear disk through both the halo and the bar. Low $^{12}$C/$^{13}$C isotopic ratios in the central regions of these starburst galaxies indicate the presence of highly processed material.