Dense gas in nearby galaxies. X. H_2_CO and CH_3_OH: molecular abundances and physical conditions.

Multilevel observations of formaldehyde (H_2_CO) and methanol (CH_3_OH) toward the nearby spiral galaxies NGC 253, Maffei 2, IC 342, M 82 and NGC 6946 are presented. H_2_CO was detected in all galaxies (tentatively in NGC 6946). CH_3_OH was detected in all objects with the notable exception of M 82. H_2_CO line intensity ratios point out differences in gas density both between galaxies and within the central regions of individual objects. Model calculations show that the bulk of the gas emitting H_2_CO in NGC 253 is at a density of ~10^4^cm^-3^, while the H_2_CO lines in M 82 and IC 342 trace two different, spatially separated gas components with densities of <=10^4^cm^-3^ and ~10^6^cm^-3^. The south-western molecular hotspot in M 82 and the center of IC 342 are the regions with the highest density. Methanol is subthermally excited in all galaxies, with the lowest excitation temperatures found in IC 342. The CH_3_OH abundance in NGC 253 and the non-starburst nuclei of IC 342 and Maffei2 are comparable. A map of the 3_k_-2_k_ lines in NGC 253 shows that CH_3_OH traces clumpy structures better than other molecules requiring high gas density to be excited. CH_3_OH toward M 82 is at least an order of magnitude less abundant than in otherwise comparable galaxies. This confirms the existence of global chemical differences, and thus very large scale variations in the state of the molecular gas phase, even between galaxies commonly classified as starburst nuclei.