Using the IRAM interferometer , we have observed the nearby starburst galaxy M 82 with a 4 \aas@@fstack { \prime \prime } 2 resolution ( \simeq 70 pc ) in the 1 \rightarrow 0 line of ^ { 13 } CO and in the \lambda 2.6-mm continuum . The spatial distribution of the ^ { 13 } CO line shows the same gross features as the ^ { 12 } CO ( 1 \rightarrow 0 ) map of Shen & Lo ( [ 1995 ] ) , namely two lobes and a compact central source , though with different relative intensities . The lobes are more conspicuous and the central source is fainter in ^ { 13 } CO than in ^ { 12 } CO . The velocity field observed around the nucleus shows a very steep gradient ( 140 km s ^ { -1 } over 75 pc ) , which is very probably caused by the stellar bar visible in the near infrared . The dynamical centre coincides with the IR peak and is shifted 6 ^ { \prime \prime } north-east of the compact ^ { 13 } CO source . The two CO lobes appear to be associated with the ends of the bar and not with a molecular ring , as usually assumed . They are probably shaped by the strong UV radiation from the central region . ^ { 13 } CO must be more photodissociated than the self-shielded ^ { 12 } CO molecules in the central \sim 250 pc region , which may explain the relative weakness of the ^ { 13 } CO central source . A 130 pc-wide bubble of molecular gas has been identified , which happens to host the most luminous compact radio source in M 82 . It lies 120 pc west of the IR peak between the central source and the western lobe and seems characterized by warmer gas , strong UV radio free-free radiation , and an enhanced cosmic ray production rate .