Study of the Relation between the Spiral Arm Pitch Angle and the Kinetic Energy of Random Motions of the Host Spiral Galaxies, A

In this work, we report a relation between the kinetic energy of random motions of the corresponding host galaxies and spiral arm pitch angles (Mdynσ 2 - P), (M*σ 2 - P) where Mdyn is the bulge dynamical mass, M* is bulge stellar mass, and σ is the velocity dispersion of the host galaxy bulge. We measured the spiral arm pitch angle (P) for a sample of Spitzer/IRAC 3.6-µm images of 54 spiral galaxies, estimated by using a 2D Fast Fourier Transform decomposition technique (2DFFT). We selected a sample of nearly face-on spiral galaxies and used IRAF ellipse to determine the ellipticity and major-axis position angle in order to deproject the images to face-on, and using a 2D Fast Fourier Transform decomposition technique, we determined the spiral arm pitch angles. We estimated the kinetic energy of random motions of the corresponding host galaxies (Mdynσ 2 , M*σ 2 ) by using Mdyn, M*, and σ, where the stellar velocity dispersion (σ) of the bulge was taken from the literature. We determined the bulge dynamical mass (Mdyn) using the virial theorem, and the bulge stellar mass (M*) was estimated by using the bulge 3.6-μm luminosity with the appropriate stellar mass-to-light ratio (M/L).