The Fundamental Plane of Spiral Galaxies: Theoretical Expectations

Abstract

Current theory of disk galaxy formation is used to study fundamental-plane (FP) type of relations for disk galaxies. We examine how the changes in model parameters affect these relations and explore the possibility of using such relations to constrain theoretical models. The distribution of galaxy disks in the space of their fundamental properties are predicted to be concentrated in a plane, with the Tully-Fisher (TF) relation (a relation between luminosity $L$ and maximum rotation velocity $V_m$) being an almost edge-on view. Using rotation velocities at larger radii generally leads to larger TF scatter. In searching for a third parameter, we find that both the disk scale-length $R_d$ (or surface brightness) and the rotation-curve shape are correlated with the TF scatter. The FP relation in the $(\Log L, \Log V_m, \Log R_d)$-space obtained from the theory is $L\propto R_d^{α'} V_m^{β'}$, with ${α'}\sim 0.50$ and ${β'}\sim 2.60$, consistent with the preliminary result we obtain from observational data. Among the model parameters we probe, variation in any of them can generate significant scatter in the TF relation, but the effects of the spin parameter and halo concentration can be reduced significantly by introducing $R_d$ while the scatter caused by varying $m_d$ (the ratio between disk mass and halo mass) is most effectively reduced by introducing the parameters which describes the rotation-curve shape. The TF and FP relations combined should therefore provide useful constraints on models of galaxy formation.