Fourier photometric analysis of isolated galaxies in the context of the AMIGA project

We present here the results of a Fourier photometric decomposition of a representative sample of similar to 100 isolated CIG galaxies (Catalog of Isolated Galaxies) in the morphological range Sb-Sc. This study is an integral part of the AMIGA (Analysis of the Interstellar Medium of Isolated Galaxies) project. It complements the photometric analysis presented in our previous paper for the same sample of disc galaxies by allowing a description of the spiral structure morphology. We also estimate dynamical measures like torque strength for bar and spiral, and also the total non-axisymmetric torque by assuming a constant mass-to-light ratio, and explore the interplay between the spiral and bar components of galaxies. Both the length (l(bar)) and the contrast (e.g. A(2b)) of the Fourier bars decrease along the morphological sequence Sb-Sbc-Sc, with bars in earlier types being longer and showing higher contrast. The bars of Sb galaxies are similar to three times longer than the bars in Sc types, consistent with our previous study. We find that the longer bars are not necessarily stronger (as quantified by the torque Q(b) measure), but longer bars show a higher contrast A(2b), in very good agreement with theoretical predictions. Our data suggest that bar and spiral components are rather independent in the sense that the torque strengths of the two components are not correlated. The total strength Q(g) is a very reliable tracer of the bar strength measure Q(b), the two quantities showing a very tight linear correlation. Comparison with a similar sample of disc galaxies (same morphological range) extracted from the OSUBGS (Ohio State University Bright Galaxy Survey) indicates that the isolated CIG/AMIGA galaxies host significantly longer Fourier bars and possibly show a different distribution of spiral torque Q(s). The Fourier analysis also revealed a potential case of counterwinding spiral structure (KIG 652/NGC 5768), which deserves further kinematic study. We find that m = 2 (i.e. dominating two-armed pattern) is the most common spiral arm multiplicity among the sample of Sb-Sc CIG/AMIGA galaxies (similar to 40 per cent), m = 2 and 3 and m = 1 and 2 are found in similar to 28 and similar to 13 per cent of isolated galaxies, respectively.