Offsets between H-alpha and CO arms of a spiral galaxy NGC 4254: A New Method for Determining the Pattern Speed of Spiral Galaxies

We examined offsets between HII regions and molecular clouds belonging to spiral arms of a late type spiral galaxy NGC 4254 (M99). We used a high resolution CO(1-0) image obtained by Nobeyama Millimeter Array (NMA) and an H-alpha image. We derived angular offsets (theta) in the galactic disk, and found that these offsets show a linear dependence on the angular rotation velocity of gas (Omega_G). This linear relation can be expressed by an equation: theta =(Omega_G - Omega_P) * t_{H-alpha}, where Omega_P and t_{H-alpha} are constant. Here, Omega_P corresponds to the pattern speed of spiral arms and t_{H-alpha} is interpreted as the timescale between the peak compression of the molecular gas in spiral arms and the peak of massive star formation. We may thus determine Omega_P and t_{H-alpha} simultaneously by fitting a line to our theta - Omega_G plot, if we assumed they are constant. From our plot, we obtained t_{H-alpha} =4.8 (+/- 1.2) Myr and Omega_P = 26 (+10/-6) km/s/kpc, which are consistent with previous studies. We suggest that this theta - Omega_G plot can be a new tool to determine the pattern speed and the typical timescale needed for star formations.