  We test whether the spiral patterns apparent in many large disk galaxies
should be thought of as dynamical features that are stationary in a co-rotating
frame for > t_{dyn}, as implied by the density wave approach for explaining
spiral arms. If such spiral arms have enhanced star formation (SF),
observational tracers for different stages of the SF sequence should show a
spatial ordering, from up-stream to downstream in the corotating frame: dense
HI, CO, tracing molecular hydrogen gas, 24 micron emission tracing enshrouded
SF and UV emission tracing unobscured young stars. We argue that such a spatial
ordering should be reflected in the angular cross-correlation (CC, in polar
coordinates) using all azimuthal positions among pairs of these tracers; the
peak of the CC should be offset from zero, in different directions inside and
outside the corotation radius. Recent spiral SF simulations by Dobbs & Pringle,
show explicitly that for the case of a stationary spiral arm potential such
angular offsets between gas and young stars of differing ages should be
observable as cross-correlation offsets. We calculate the angular
cross-correlations for different observational SF sequence tracers in 12 nearby
spiral galaxies, drawing on a data set with high quality maps of the neutral
gas HI, THINGS), molecular gas (CO, HERACLES) along with 24 micron emission
(Spitzer, SINGS); we include FUV images (GALEX) and 3.6 $\mu$m emission
(Spitzer, IRAC) for some galaxies, tracing aging stars and longer timescales.
In none of the resulting tracer cross-correlations for this sample do we find
systematic angular offsets, which would be expected for a stationary dynamical
spiral pattern of well-defined pattern speed. This result indicates that spiral
density waves in their simplest form are not an important aspect of explaining
spirals in large disk galaxies.
