A unified scaling law in spiral galaxies

We investigate the origin of a unified scaling relation in spiral galaxies. Observed spiral galaxies are spread on a plane in the three-dimensional lo garithmic space of luminosity L, radius R, and rotation velocity V. The pla ne is expressed as L proportional to (VR)(alpha) in the I passband, where a lpha is a constant. On the plane, observed galaxies are distributed in an e longated region which looks like the shape of a surfboard. The well-known s caling relations LV (Tully-Fisher [TF] relation), V-R (also the TF relation ), and R-L (Freeman's law) can be understood as oblique projections of the surfboard-like plane into two-dimensional spaces. This unified interpretati on of the known scaling relations should be a clue to understand the physic al origin of all the relations consistently. Furthermore, this interpretati on can also explain why previous studies could not find any correlation bet ween TF residuals and radius. In order to clarify die origin of this plane, we simulate formation and evolution of spiral galaxies with the N-body/smo othed particle hydrodynamics method, including cooling, star formation, and stellar feedback. Initial conditions are set to 14 isolated spheres with t wo free parameters, such as mass and angular momentum. The cold dark matter (h = 0.5, Omega(0) = 1) cosmology is considered as a test case. The simula tions provide the following two conclusions: (1) The slope of the plane is well reproduced but the zero point is not. This zero-point discrepancy coul d be solved in a low-density (Omega(0) < 1) and high-expansion (h > 0.5) co smology. (2) The surfboard-shaped plane can be explained by the control of galactic mass and angular momentum.