The size distribution of galaxies in the Sloan Digital Sky Survey

We use a complete sample of about 140000 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 data base 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 R̄ and dispersion σ_{ln R}. For late-type galaxies, there is a characteristic luminosity at M_r,0 ∼ -20.5 (assuming h = 0.7) corresponding to a stellar mass M₀ ∼ 10^10.6 M⊙. Galaxies more massive than M₀ have R̄ M^0.4 and σ_{ln R} ∼ 0.3, while less massive galaxies have R̄ M^0.15 and σ_{ln R} ∼ 0.5. For early-type galaxies, the R̄-M relation is significantly steeper, R̄ M^0.55, but the σ_{ln R}- M relation is similar to that of bright late-type galaxies. Faint red galaxies have sizes quite independent of their luminosities. We use simple theoretical models to interpret these results. The observed R̄-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 σ_{ln R}-M relation requires in addition that the bulge/disc mass ratio be larger in haloes of lower angular momentum and that the bulge material transfers part of its angular momentum to the disc. This can be achieved if bulge formation occurs so as to maintain a marginally stable disc. For early-type galaxies, the observed σ_{ln R}-M relation is inconsistent with formation through single major mergers of present-day discs. 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.