We construct a large data set of global structural parameters for 1300 field and cluster spiral galaxies and explore the joint distribution of luminosity L , optical rotation velocity V , and disk size R at I - and 2MASS K -bands .
We focus our study on scaling relations and residual correlations of benefit to galaxy structure and formation studies , rather than deriving precise distance estimators .
The I - and K -band velocity-luminosity ( VL ) relations have log-slopes of 0.29 and 0.27 , respectively with \sigma _ { ln } ( VL ) \simeq 0.13 , and show a small dependence on color and morphological type in the sense that redder , early-type disk galaxies rotate faster than bluer , later type disk galaxies for most luminosities .
The VL relation at I - and K -bands is independent of surface brightness , size and light concentration .
The modeling of the size-luminosity ( RL ) relation is somewhat sensitive to the adopted fitting method , due in part to strong dependences on surface brightness and color and significant uncertainties in the measurement of disk scale lengths .
The log-slope of the I - and K -band RL relations is a strong function of morphology and varies from 0.25 to 0.5 with a mean of 0.32 for all Hubble types .
At most luminosities , early-type disk galaxies have shorter scale lengths than later-type ones - this latter trend may be reversed at high luminosities .
The average dispersion \sigma _ { ln } ( RL ) decreases from 0.33 at I -band to 0.29 at K , likely due to the 2MASS selection bias against lower surface brightness galaxies .
Measurement uncertainties are \sigma _ { lnV } \simeq 0.09 , \sigma _ { lnL } \simeq 0.14 and somewhat larger and harder to estimate for R .
We show that the color dependence of the VL relation is consistent with expectations from simple stellar population synthesis models ; the RL relation shows a weak but opposite trend expected from those models , suggesting that at a given stellar mass , smaller galaxies are redder .
The VL and RL residuals are largely uncorrelated with each other with a correlation coefficient r = -0.16 and \Delta \log V|L \thinspace / \thinspace \Delta \log R|L = -0.07 \pm 0.01 ; the RV - RL residuals show a weak positive correlation with r = 0.53 .
These correlations suggest that scatter in luminosity is not a significant source of the scatter in the VL and RL relations .
The observed scaling relation slopes , zero-points , and scatters can be understood in the context of a model of disk galaxies embedded in dark matter halos that invokes low mean spin parameters and dark halo expansion , as we describe in our companion paper ( Dutton et al .
2007 ) .
We discuss in two appendices various pitfalls of standard analytical derivations of galaxy scaling relations , including the Tully-Fisher relation with different slopes .
Our galaxy data base is available at www.astro.queensu.ca/ \sim courteau/data/VRL2007.dat .