We present the results of high-resolution ^ { 13 } CO ( J = 1–0 ) mapping observations with the NRO 45m telescope of the area toward the southern bright arm region of M 51 , including the galactic center , in order to study the physical conditions of the molecular clouds in the arm and the interarm .
The obtained map shows the central depression of the ^ { 13 } CO ( J = 1–0 ) emission , the circumnuclear ring ( radius \sim \timeform 10 ” – \timeform 20 ” ) , and the spiral arm structure .
The arm-to-interarm ratio of the ^ { 13 } CO ( J = 1–0 ) integrated intensity is 2 – 4 .
We also have found a feature different from that found in the ^ { 12 } CO results .
For example , the ^ { 13 } CO distribution shows a depression in part of the spiral arm .
The ^ { 12 } CO/ ^ { 13 } CO ratio spatially varies , and shows high values ( \sim 20 ) for the interarm and the central region , but low values ( \sim 10 ) for the arm .
Their values indicate that there is a denser gas in the spiral arm than in the interarm .

The distribution of the ^ { 13 } CO shows a better correspondence with that of the H \alpha emission than with the ^ { 12 } CO in the disk region , except for the central region .
We found that the ^ { 13 } CO emission is located on the downstream side of the ^ { 12 } CO arm , namely there is an offset between the ^ { 12 } CO and the ^ { 13 } CO as well as the H \alpha emission .
This suggests that there is a time delay between the accumulation of gas caused by the density wave and dense gas formation , accordingly star formation .
This time delay is estimated to be \sim 10 ^ { 7 } yr based on the assumption of galactic rotation derived by the rotation curve and the pattern speed of the M 51 spiral pattern .
It is similar to the growth timescale of a gravitational instability in the spiral arm of M 51 , suggesting that the gravitational instability plays an important role for dense gas formation .