  For a sample of 4378 nearby spiral and S0 galaxies, Yu and Ho (2020) used
Fourier analysis of Sloan Digital Sky Survey images to show that the strengths
of the spiral arms and the pitch angles of the arms are inversely correlated
with central concentration. In the current study, we search for trends in the
Yu and Ho (2020) spiral arm parameters with environment and specific star
formation rate (sSFR). When comparing galaxies with similar concentrations, we
do not find a significant difference in the arm strengths or pitch angles of
spiral galaxies in clusters compared to field galaxies. When differences in
concentration are taken into account, we also find no significant difference in
the parameter f3 for cluster spirals compared to field spirals, where f3 is the
normalized m = 3 Fourier amplitude. When concentration is held fixed, both arm
strength and pitch angle are correlated with sSFR, but f3 is not. These
relations support the suggestion by Davis et al. (2015) of a `fundamental
plane' of spiral structure involving pitch angle, bulge stellar mass, and gas
surface density. We discuss these results in terms of theories of spiral arm
production and quenching in galaxies. To aid comparison with earlier studies
based on Galaxy Zoo, we explore how the Yu and Ho (2020) parameters relate to
similar parameters measured by Galaxy Zoo (i.e., f3 vs. number of arms, pitch
angle vs. winding parameter, and concentration vs. bulge class).
