We derived a two-dimensional map of the molecular fraction , f _ { mol } , ( ratio of the molecular gas density to that of total gas ) in the spiral galaxy M51 , and examined the behavior of molecular fronts ( MF ) , where MF represents the place where f _ { mol } changes drastically from nearly zero to unity and vice versa .
We show that the MF phenomenon occurs not only radial , but also in the azimuth direction through the spiral arms , and f _ { mol } changes rapidly in the arm-to-inter-arm transition regions .
The existence of the azimuthal MF indicates that the atomic gas ( HI ) is quickly transformed to molecular gas ( H _ { 2 } ) during the passage through spiral arms .
We performed a numerical simulation of MF based on an HI-to-H _ { 2 } phase transition theory , and reproduced the observations .
We estimated a azimuthal scale length of the transition to be less than 200 pc , corresponding to a time scale of \sim 2 Myr for H _ { 2 } gas formation .
The azimuthal width of a molecular arm is estimated to be at most 2.5 kpc , where the gas can remain in molecular phase for about 25 Myr .

Kew words : galaxies : spiral — galaxies : ISM — galaxies : cluster of — Molecular gas — HI gas