Detection of Molecular Clouds in the Interarm of the Flocculent Galaxy NGC 5055

We present high-resolution (~ 4") 12CO (J = 1 - 0) mapping observations with high - velocity resolution (~ 2.6 km s^{-1}) toward the disk of flocculent galaxy NGC 5055, using the Nobeyama Millimeter Array in order to study the physical properties of the molecular clouds in the arm and the interarm. The obtained map shows clumpy structures. Although these are mainly distributed along a spiral arm seen in near-infrared observations, some clouds are located far from the arm, namely in the interarm. These clouds in both the arm and the interarm have a typical size and mass of a few 100 pc and a few 10^6 Mo, respectively. These correspond to the largest Giant Molecular Cloud (GMC) in our Galaxy, and are slightly smaller than Giant Molecular Associations (GMAs) in the grand design spiral M 51. Their CO flux-based masses show good agreement with their virial masses. A size - velocity dispersion relation is also plotted on an extension of the relation for the Galactic GMCs. These facts suggest that the properties of these clouds are similar to that of the Galactic GMCs. We also found no clear systematic offset between the molecular gas and HII regions unlike M 51. This fact and no existense of GMAs suggest the view that, in NGC 5055, cloud formation and following star formation in both the arm and the interarm are due to enhancement of gas by local fluctuation. On the other hand, in grand design spiral galaxies, such as M 51, GMA formations may occur only in the arm due to a strong density wave also enhanced star formation in GMA formation may also occur. These may control the optical morphology of spiral arms in spiral galaxies.Comment: 16 pages, 8 figure

The limit theorem with respect to the matrices on non-backtracking paths of a graph

We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak