Toward equations of galactic structure

We find that all classes of galaxies, ranging from disks to spheroids and from dwarf spheroidals to brightest cluster galaxies, lie on a two-dimensional surface within the space defined by the logarithms of the half-light radius, r_e, mean I-band surface brightness within r_e, I _e, and internal velocity V² ≡ (1/2)v _c² + σ², where v_c is the rotational velocity and σ is the velocity dispersion. If these quantities are expressed in terms of kpc, L_⊙ pc^-2, and km s ^-1, then this surface is described by the equation log r_e - log V² + log I_e + log Y_e + 0.8 = 0, where we provide a fitting function for Y_e, the mass-to-light ratio within re in units of M_⊙/L_⊙, that depends only on Vand I_e. The scatter about this surface for our heterogeneous sample of 1925 galaxies is small (<0.1 dex), and both the scatter within one of the galaxy subsamples (1319 disks) and the analysis of subsamples with independently derived mass-to-light ratios suggest that the intrinsic scatter could be as low as ∼0.05 dex, or 10%, prior to any correction for observational errors. This small scatter has three possible implications for how gross galactic structure is affected by internal factors, such as stellar orbital structure, nuclear activity, or mass loss history, and by external factors, such as environment or accretion history. These factors either (1) play no role beyond generating some of the observed scatter, (2) move galaxies along the surface, or (3) balance each other to maintain this surface as the locus of galactic structure equilibria. We cast the behavior of Y_e in terms of the fraction of baryons converted to stars, η, and the concentration of those stars within the dark matter halo, ξ ≡ R₂₀₀/r_e, where R₂₀₀ is the standard estimate of the virial radius. We derive expressions for η and ξ, use an independent measurement of η to evaluate leading constant terms, obtain η = 1.9 × 10 ^-5(L/L*)Y*V^-3 and ξ = 1.4Vr _e^-1, and relate these to each other via log η + log ξ = -log Y^e + log Y* + const. Finally, we present the distributions of η and ξ for the full range of galaxies and conclude that the high Y_e of dSph's are due to low η, rather than any differences in ξ, that η is similar for spheroids and disks of a given V, and that η decreases with increasing V for systems with V > 30 km s ^-1. For systems with internal velocities comparable to that of the MilkyWay (149 km s^-1 < V < 163 km s^-1), η = 0.14 ±- 0.05, and ξ is, on average, ∼5 times greater for spheroids than for disks.