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 the offsets between H II regions and molecular clouds belonging to spiral arms of a late-type spiral galaxy, NGC 4254 (M 99). We used a high-resolution (CO)-C-12 (J = 1-0) image obtained by 'Nobeyama Millimeter Array (NMA) and an Hot image. We derived angular offsets (0) in the galactic disk. and found that they show a linear dependence on the angular rotation velocity of the gas (Omega(G)). This linear relation can be expressed by the equation theta = (Omega(G) - Omega(P)) (.) t(Halpha), where Omega(P) and t(Halpha), are constant. Here, Omega(P) corresponds to the pattern speed of the spiral arms and t(Halpha) is interpreted as being the timescale between the peak compression of the molecular gas in the spiral arms and the peak of massive star formation. We could thus determine Omega(P) and iota(Halpha) simultaneously by fitting a line to our theta-Omega(G) plot, if we assume they are constant. From the plot for NGC 4254. we obtained iota(Halpha),, = (4.8 +/- 1.2) x 10(6)yr and Omega(P) = 26(-6)(+10) km s(-1)kpc(-1), 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.