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.