Offsets between Hα 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 (M99). We used a high-resolution ¹²CO(J = 1 - 0) image obtained by Nobeyama Millimeter Array (NMA) and an Hα image. We derived angular offsets (θ) in the galactic disk, and found that they show a linear dependence on the angular rotation velocity of the gas (Ω_G). This linear relation can be expressed by the equation θ = (Ω_G - Ω_P)· t_Hα, where Ω_P and t_Hα are constant. Here, Ω_P corresponds to the pattern speed of the spiral arms and t_Hα 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 Ω_P and t_Hα simultaneously by fitting a line to our θ - Ω_G plot, if we assume they are constant. From the plot for NGC4254, we obtained t_Hα = (4.8 ± 1.2) × 10⁶yr and Ω_P = 26⁺¹⁰_-6 km s^-1 kpc^-1, which are consistent with previous studies. We suggest that this θ - Ω_G plot can be a new tool to determine the pattern speed and the typical timescale needed for star formations.