We present interferometric observations of the CN 1-0 (113.491 GHz), N2H+ 1-0 (93.173 GHz), H(41)a (92.034 GHz), CH3CN (91.987 GHz), CS 3-2 (146.969 GHz), c-C3H2 3-2 (145.089 GHz), H2CO 2-1 (145.603 GHz) and HC3N 16-15 (145.601 GHz) lines towards M82
, carried out with the IRAM Plateau de Bure Interferometer (PdBI). PDR chemical modelling is used to interpret these observations. Our results show that the abundances of N2H+, CS and H13 CO+ remain quite constant across the galaxy confirming that these species are excellent tracers of the dense molecular gas. On the contrary, the abundance of CN increases by a factor of 3 in the inner x2 bar orbits. The [CN]/[N2 H+ ] ratio is well correlated with the H(41)a emission at all spatial scales down to 100 pc. Chemical modelling shows that the variations in the [CN]/[N2H+] ratio can be explained as the consequence of differences in the local intestellar UV field and in the average cloud sizes within the nucleus of the galaxy. Our high-spatial resolution imaging of the starburst galaxy M 82 shows that the star formation activity has a strong impact on the chemistry of the molecular gas. In particular, the entire nucleus behaves as a giant photon-dominated region (PDR) whose chemistry is determined by the local UV flux. The detection of N2H+ shows the existence of a population of clouds with Av >20 mag all across the galaxy plane. These clouds constitute the molecular gas reservoir for the formation of new stars and, although distributed all along the nucleus, the highest concentration occurs in the outer x1 bar orbits (R = 280 pc).
