Dynamical model of the grand - design spiral galaxy NGC 157

Numerical simulations of the interstellarmediumunder the action of a density wave provide an accurate method for determining the positions of the main resonances in grand– design spiral galaxies. Barred spiral galaxies are among the best candidates for a single and well defined wave mode, because bars are standingwaveswhichmay share the same pattern speed as the spiral structure. In line with our previous work on determination of the pattern speed in barred spiral galaxies (M 51, NGC 4321 and NGC 7479) by the method employed in this article, we have applied it to the grand–design spiral NGC 157 and compared the results with previous determinations of the position of the resonances in this galaxy. NGC 157 is an interesting case to test the theoretical predictions on star formation and nuclear activity and their relation with the existence and position of the main resonances induced by a spiral density wave: it is an isolated grand–design galaxy and possesses a weak bar, an inner and an outer pseudo–ring and a nuclear starburst. A pattern speed of Ωp = 40 km s−1 kpc−1 is derived from our numerical model and this places the corotation resonance at a radius of RCR ∼ 5 kpc (∼ 50′′), in the middle of the disc and close to the point where the two inner arms suffer a bifurcation and broadening. This result differs slightly from the optical determination by Elmegreen et al. (1992) and Elmegreen & Elmegreen (1995), who identified the location of the corotation radius at the endpoint of the ridges of star formation, at a radius RCR = 0.44R25 (∼ 56′′). With this pattern speed two inner Lindblad resonances are predicted at radii RILR1 = 0.25 kpc and RILR2 = 0.75 kpc respectively. The bar endswell inside the corotation limited by the disc scale length (∼ 35′′) and a stellar nuclear oval misaligned with themajor axis of the bar could be confinedwithin the ILR2. The Hα image features and the starburst nucleus of NGC 157 are related to the global dynamics of the galaxy and therefore to the positions of the resonances. The Hα image shows a ringlike region of star formation located between the corotation and the outer Lindblad resonance (OLR). An inner pseudo–ring appears surrounding the main bar which is almost Send offprint requests to: M.J. Sempere ? Present address: Observatorio Astronómico Nacional. Campus Universitario. E-28871 Alcalá de Henares (Madrid), Spain void of HII regions with the exception of three hot–spots that appear near the centre of the galaxy, one at the nucleus, and the two others at a radius of ∼ 0.4 kpc, between the ILR1 and the ILR2. These circumnuclear Hα features could be the signature of a patchy ring. NGC 157 has been classified as a late–type galaxy (SAB(rs)bc); its kinematical behaviour as well as the distribution of HII regions along the bar and its nuclear starburst are in agreement with recent surveys of star formation in bars (Arsenault, 1989) and classification of bar types in early and late type galaxies (Combes & Elmegreen 1993).