Statistical Studies Of Galaxy Size Distribution

We use a complete sample of about 140,000 galaxies from the Sloan Digital Sky Survey (SDSS) to study the size distribution of galaxies and its dependence on their luminosity, stellar mass, and morphological type. The large SDSS database provides statistics of unprecedented accuracy. For each type of galaxy, the size distribution at given luminosity (or stellar mass) is well described by a log-normal function, characterized by its median R and dispersion InR. For late-type galaxies, there is a characteristic luminosity at Mr0--20.5 (assuming h = 0.7) corresponding to a stellar mass M0- 1010.6 M Galaxies more massive than M0 have R oc M0.4 and InR -0.3, while less massive galaxies have R M0.15 and InR-0.5. For early-type galaxies, the R - M relation is significantly steeper, R M0.55, but the InR - M relation is similar to that of bright late-type galaxies. For the size-luminosity relation, the sizes of galaxies weakly depend on the band we choose. The galaxy population, as a whole, has the size distribution like the early-type galaxies at bright end, while similar to late-type galaxies at faint end. Faint red galaxies have sizes quite independent of their luminosities. The early type galaxies with luminosity Mr-20.5 show the brightest surface brightness.We use simple theoretical models to interpret the results of size-mass relation of each type galaxy. The observed R - M relation for late-type galaxies can be explained if the fraction of baryons that form stars is as predicted by the standard feedback model. Fitting the observed InR - M relation requires in addition that the bulge/disk mass ratio be larger in haloes of lower angular momentum and that the bulge material transfer part of its angular momentum to the disk. This can be achieved if bulge formation occurs so as to maintain a marginally stable disk. For early-type galaxies the observed R - M relation is inconsistent with formation through single major mergers of present-day disks. It is consistent with formation through repeated mergers, if the progenitors have properties similar to those of faint ellipticals or Lyman break galaxies and merge from relatively strongly bound orbits.We further use the theoretical model to investigate the third parameter of the Tully-Fisher(TF) relation. We find the distribution of galaxy disks in the space of their fundamental properties are predicted to be concentrated in a plane, with the (TF) relation 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 Rd and the rotation-curve shape are correlated with the TF scatter. The FP relation in the (LogL, Log Vm, Log Rd)-space obtained from the theory is L∝Rdα Vmβ , with α-0.50 and β- 2.60, consistent with the preliminary result we obtain from observational data.Using isophotal radius instead of Rd leads to higher , lower and smaller scatter. 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 Rd while the scatter caused by varying md (the ratio between disk mass and halo mass) is most effectively reduced by introducing the parameters which describe the rotation-curve shape. The TF relation and fundamental plane combined should therefore provide useful constraints on models of galaxy formation.