The density-wave theory of galactic spiral-arm structure makes a striking prediction that the pitch angle of spiral arms should vary with the wavelength of the galaxy's image. The reason is that stars are born in the density wave but move out of it as they age. They move ahead of the density wave inside the co-rotation radius, and fall behind outside of it, resulting in a tighter pitch angle at wavelengths that image stars (optical and near infrared) than those that are associated with star formation (far infrared and ultraviolet). In this study we combined large sample size with wide range of wavelengths, from the ultraviolet to the infrared to investigate this issue. For each galaxy we used an optical wavelength image (B-band: 445 nm) and images from the Spitzer Space Telescope at two infrared wavelengths (infrared: 3.6 and 8.0 µm) and we measured the pitch angle with the 2DFFT and Spirality codes (Davis et al. 2012;Shields et al. 2015). We find that the B-band and 3.6 µm images have smaller pitch angles than the infrared 8.0 µm image in all cases, in agreement with the prediction of density-wave theory. We also used images in the ultraviolet from Galaxy Evolution Explorer, whose pitch angles agreed with the measurements made at 8 µm. Because stars imaged at those wavelengths have not had time during their short lives to move out of the star-forming region.

The density-wave theory of spiral structure proposes that star formation occurs in or near a spiral-shaped region of higher density that rotates rigidly within the galactic disk at a fixed pattern speed. In most interpretations of this theory, newborn stars move downstream of this position as they come into view, forming a downstream spiral which is tighter, with a smaller pitch angle than that of the density wave itself. Rival theories, including theories which see spiral arms as essentially transient structures, may demand that pitch angle should not depend on wavelength. We measure the pitch angle of a large sample of galaxies at several wavelengths associated with star formation or very young stars (8.0 μm, H-α line and 151 nm in the far-UV) and show that they all have the same pitch angle, which is larger than the pitch angle measured for the same galaxies at optical and near-infrared wavelengths. Our measurements in the B band and at 3.6 μm have unambiguously tighter spirals than the starforming wavelengths. In addition we have measured in the u band, which seems to fall midway between these two extremes. Thus, our results are consistent with a region of enhanced stellar light situated downstream of a starforming region.

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. Computation time is typically on the order of 2 min per galaxy, assuming 8 GB of working memory. We tested the code using 117 synthetic spiral images with known pitches, varying both the spiral properties and the input parameters. The code yielded correct results for all synthetic spirals with galaxy-like properties. We also compared the code’s results to two-dimensional Fast Fourier Transform (2DFFT) measurements for the sample of nearby galaxies defined by DMS PPak. Spirality’s error bars overlapped 2DFFT’s error bars for 26 of the 30 galaxies. The two methods’ agreement correlates strongly with galaxy radius in pixels and also with i-band magnitude, but not with redshift, a result that is consistent with at least some galaxies’ spiral structure being fully formed by z=1.2, beyond which there are few galaxies in our sample. The Spirality code package also includes GenSpiral, which produces FITS images of synthetic spirals, and SpiralArmCount, which uses a one-dimensional Fast Fourier Transform to count the spiral arms of a galaxy after its pitch is determined. All code is freely available.

Quasi-stationary density wave theory predicts the existence of an age gradient across the spiral arms with a phase crossing at the co-rotation radius. We have examined evidence for such age gradients using star formation history (SFH) maps derived from lightning, a spectral energy distribution (SED) fitting procedure, and by using spatially-resolved stellar clusters. Three galaxies from the LEGUS survey were used to analyse the azimuthal offsets of spatially-resolved stellar clusters. Kernel density estimation plots of azimuthal cluster distance offsets reveal prominent central peaks and secondary peaks on the positive side, relative to the density wave for NGC 5194 and NGC 5236. These secondary downstream peaks in the cluster distributions show overall evidence for an age gradient. NGC 628 shows secondary peaks on both sides of the density wave. The cluster distributions also show an increasing spatial spread with age, consistent with the expectation that they were born in the density wave. SFH maps of 12 nearby galaxies were analysed using spirality, a matlab-based code, which plots synthetic spiral arms over FITS images. The SFH maps reveal a gradual decrement (tightening) in pitch angles with increasing age. By analysing the pitch angle differences between adjacent age bins using the error function, the average of the probabilities shows a $69{{\ \rm per\ cent}}\pm 25{{\ \rm per\ cent}}$ chance that the pitch angle values decrease (tighten) with increasing age. Thus, we see a tightening of the spiral pattern in galaxies, both when segregating stellar populations specifically by age or more generally by colour, as was shown in our previous studies.