The Carnegie-Irvine Galaxy Survey. VI. Quantifying Spiral Structure
  The Carnegie-Irvine Galaxy Survey provides high-quality broad-band optical
images of a large sample of nearby galaxies for detailed study of their
structure. To probe the physical nature and possible cosmological evolution of
spiral arms, a common feature of many disk galaxies, it is important to
quantify their main characteristics. We describe robust methods to measure the
number of arms, their mean strength, length, and pitch angle. The arm strength
depends only weakly on the adopted radii over which it is measured, and it is
stronger in bluer bands than redder bands. The vast majority of clearly
two-armed ("grand-design") spiral galaxies have systematically higher relative
amplitude of the $m=2$ Fourier mode in the main spiral region. We use both
one-dimensional and two-dimensional Fourier decomposition to measure the pitch
angle, finding reasonable agreement between these two techniques with a scatter
of $\sim$2$\deg$. To understand the applicability and limitations of our
methodology to imaging surveys of local and distant galaxies, we create mock
images with properties resembling observations of local ($z$ $\lesssim$ 0.1)
galaxies by the Sloan Digital Sky Survey and distant galaxies (0.1 $\lesssim$
$z$ $\lesssim$ 1.1) observed with the $Hubble$ $Space$ $Telescope$. These
simulations lay the foundation for forthcoming quantitative statistical studies
of spiral structure to understand its formation mechanism, dependence on galaxy
properties, and cosmological evolution.
