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 surface brightness within r _ { e } , I _ { e } , and internal velocity , V ^ { 2 } \equiv ( { 1 \over 2 } v _ { c } ^ { 2 } + \sigma ^ { 2 } ) , where v _ { c } is the rotational velocity and \sigma is the velocity dispersion .
If these quantities are expressed in terms of kpc , L _ { \odot } pc ^ { -2 } , and km s ^ { -1 } , then this surface is described by the equation \log r _ { e } - \log V ^ { 2 } + \log I _ { e } + \log \Upsilon _ { e } +0.8 = 0 , where we provide a fitting function for \Upsilon _ { e } , the mass-to-light ratio within r _ { e } in units of M _ { \odot } / L _ { \odot } , that depends only on V and 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 \sim 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 \Upsilon _ { e } in terms of the fraction of baryons converted to stars , \eta , and the concentration of those stars within the dark matter halo , \xi \equiv R _ { 200 } / r _ { e } , where R _ { 200 } is the standard estimate of the virial radius .
We derive expressions for \eta and \xi , use an independent measurement of \eta to evaluate leading constant terms , obtain \eta = 1.9 \times 10 ^ { -5 } ( L / L ^ { * } ) \Upsilon _ { * } V ^ { -3 } and \xi = 1.4 Vr _ { e } ^ { -1 } , and relate these to each other via \log \eta + \log \xi = - \log \Upsilon _ { e } + \log \Upsilon _ { * } + const .
Finally , we present the distributions of \eta and \xi for the full range of galaxies and conclude that the high \Upsilon _ { e } ’ s of dSphs are due to low \eta rather than any differences in \xi , that \eta is similar for spheroids and disks of a given V , and that \eta decreases with increasing V for systems with V > 30 km sec ^ { -1 } .
For systems with internal velocities comparable to that of the Milky Way ( 149 < V < 163 km s ^ { -1 } ) , \eta = 0.14 \pm 0.05 , and \xi is , on average , \sim 5 times greater for spheroids than for disks .