Studying molecular gas in the central regions of the star burst galaxies NGC4945 and Circinus enables us to characterize the physical conditions and compare them to previous local and high-z studies. We estimate temperature, molecular density and column densities of CO and atomic carbon. Using model predictions we give a range of estimated CO/C abundance ratios. Using the new NANTEN2 4m sub-millimeter telescope in Pampa La Bola, Chile, we observed for the first time CO 4-3 and [CI] 3P1-3 P0 at the centers of both galaxies at linear scale of 682 pc and 732 pc respectively. We compute the cooling curves of 12CO and 13CO using radiative transfer models and estimate the physical conditions of CO and [CI]. The centers of NGC4945 and Circinus are very [CI] bright objects, exhibiting [CI] 3P1 - 3 P0 luminosities of 91 and 67Kkms-1kpc2, respectively. The [CI] 3P1-3 P0/CO 4-3 ratio of integrated intensities are large at 1.2 in NGC4945 and 2.8 in Circinus. Combining previous CO J= 1-0, 2-1 and 3-2 and 13CO J= 1-0, 2-1 studies with our new observations, the radiative transfer calculations give a range of densities, n(H2) = 10^3-3*104^cm-3, and a wide range of kinetic temperatures, Tkin = 20 - 100K, depending on the density. Future CO J= 7-6 and [CI] 2-1 observations will be important to resolve the ambiguity in the physical conditions and confirm the model predictions.
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