Implications and Applications of Kinematic Galaxy Scaling Relations

Galaxy scaling relations, which describe a connection between ostensibly unrelated physical characteristics of galaxies, testify to an underlying order in galaxy formation that requires understanding. I review the development of a scaling relation that 1) unites the well-known Fundamental Plane (FP) relation of giant elliptical galaxies and Tully-Fisher (TF) relation of disk galaxies, 2) fits low mass spheroidal galaxies, including the ultra-faint satellites of our Galaxy, 3) explains the apparent shift of lenticular (S0) galaxies relative to both FP or TF, 3) describes all stellar dynamical systems, including systems with no dark matter (stellar clusters), 4) associates explicitly the numerical coefficients that account for the apparent "tilt" of the FP away from the direct expectation drawn from the virial theorem with systematic variations in the total mass-to-light ratio of galaxies within the half-light radius, 5) connects with independent results that demonstrate the robustness of mass estimators when applied at the half-light radius, and 6) results in smaller scatter for disk galaxies than the TF relation. The relation develops naturally from the virial theorem, but implies the existence of additional galaxy formation physics that must now be a focus of galaxy formation studies. More pragmatically, the relation provides a lynchpin that can be used to measure distances and galaxy masses. I review two applications: 1) the cross-calibration of distance measurement methods, and 2) the determination of mass-to-light ratios of simple stellar populations as a function of age, and implications of the latter for the stellar initial mass function.