The shapes of spiral arms in the S4G survey and their connection with stellar bars

Context. Spiral galaxies are very common in the local Universe, but their formation, evolution, and interplay with bars remain poorly understood after more than a century of astronomical research on the topic. Aims. We use a sample of 391 nearby galaxies from the S(4)G survey to characterise the winding angle and amplitude of spiral arms as a function of disc properties, such as bar strength, in all kinds of spirals (grand-design, multi-armed, and flocculent). Methods. We derived global pitch angles in 3.6 mu m de-projected images from (i) average measurements of individual logarithmic spiral segments, and (ii) for a subsample of 32 galaxies, from 2D Fourier analyses. The strength of spirals was quantified from the tangential-to-radial force ratio and from the normalised m = 2 Fourier density amplitudes. Results. In galaxies with more than one measured logarithmic segment, the spiral pitch angle varies on average by similar to 10 degrees between segments, but by up to greater than or similar to 15-20 degrees. The distribution of the global pitch angle versus Hubble type (T) is very similar for barred and non-barred galaxies when 1 less than or similar to T less than or similar to 5. Most spiral galaxies (>90%) are barred for T > 5. The pitch angle is not correlated with bar strength, and only weakly with spiral strength. The amplitude of spirals is correlated with bar strength (and less tightly, with bar length) for all types of spirals. The mean pitch angle is hardly correlated with the mass of the supermassive black hole (estimated from central stellar velocity dispersion), with central stellar mass concentration, or with shear, questioning previous results in the literature using smaller samples. Conclusions. We do not find observational evidence that spiral arms are driven by stellar bars or by invariant manifolds. Most likely, discs that are prone to the development of strong bars are also reactive to the formation of prominent spirals, explaining the observed coupling between bar and spiral amplitudes.