Star formation and asymmetry in the spiral arms of M51: Variable star formation caused by more than one spiral density wave

In the inner 3 kpc of M51, we find that logarithmic spirals provide good fits to the peak intensities in molecular gas observed by the Berkeley-Illinois-Maryland Association array in the CO (J=1-0) emission line along the spiral arms. However, we measure significant asymmetries between the location and density of the arms observed on one side of the galaxy compared with those on the opposite side. Between a radius of 1 and 2.2 kpc, the gas distribution traced in CO is lopsided with densities twice as large in one arm than the opposite one. In the same region, the spiral arms are offset by 20degrees from the position of the arm on the opposite side of the galaxy after a rotation of 180degrees. We use the ratio of CO emission to the emission in the Paalpha hydrogen recombination line to estimate the efficiency of star formation along each arm. Except for a narrow region at about 2 kpc in which star formation is surprisingly inefficient, the gas depletion time is approximately 200 million years despite large variations in the molecular gas density in the arms. We account for the deviations from two-armed bisymmetric structure with a simple model that includes an additional three-armed spiral density wave. This model accounts for the angular offset between the arm on one side compared with its opposite, the lopsided distribution in molecular gas, and interarm star formation to the northeast of the galaxy nucleus. Since the star formation efficiency is unaffected by the variations in gas density, and the variations in gas density can be accounted for by the presence of an additional three-armed density wave, we suggest that the star formation rate is variable and is highest where and when the maxima of the two spiral density waves coincide or constructively add. The inner region of M51 provides good evidence for the presence of more than one spiral density wave and a resulting variable rate of star formation.