abridged: 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 $\bar{R}$ and dispersion $\sigma_{\ln R}$. For late-type galaxies, there is a characteristic luminosity at $M_{r,0}\sim -20.5$ (assuming $h=0.7$) corresponding to a stellar mass $M_0\sim 10^{10.6}\Msun$. Galaxies more massive than $M_0$ have $\bar{R}\propto M^{0.4}$ and $\sigma_{\ln R}\sim 0.3$, while less massive galaxies have $\bar{R}\propto M^{0.15}$ and $\sigma_{\ln R}\sim 0.5$. For early-type galaxies, the $\bar{R}$ - $M$ relation is significantly steeper, $\bar{R}\propto M^{0.55}$, but the $\sigma_{\ln R}$ - $M$ relation is similar to that of late-type galaxies. Faint red galaxies have sizes quite independent of their luminosities.Comment: 42 pages, 18 figures, 2 tables; replaced with the version accepted by MNRA

The rapidly expanding field of galaxy formation lies at the interface between astronomy, particle physics, and cosmology. Covering diverse topics from these disciplines, all of which are needed to understand how galaxies form and evolve, this book is ideal for researchers entering the field. Individual chapters explore the evolution of the Universe as a whole and its particle and radiation content; linear and nonlinear growth of cosmic structure; processes affecting the gaseous and dark matter components of galaxies and their stellar populations; the formation of spiral and elliptical galaxies; central supermassive black holes and the activity associated with them; galaxy interactions; and the intergalactic medium. Emphasizing both observational and theoretical aspects, this book provides a coherent introduction for astronomers, cosmologists, and astroparticle physicists to the broad range of science underlying the formation and evolution of galaxies.

We develop a simple analytic model for the gravitational clustering of dark matter haloes to understand how their spatial distribution is biased relative to that of the mass. The statistical distribution of dark haloes within the initial density eld (assumed Gaussian) is determined by an extension of the Press-Schechter formalism. Modi cations of this distribution caused by gravitationally induced motions are treated using a spherical collapse approximation. We test this model against results from a variety of N-body simulations, and nd that it gives an accurate description of a bias function, b(M; R; ) = h (M; R; )= , where h (M; R; ) is the mean overdensity of haloes of mass M within spheres which have radius R and mass overdensity ; the results depend only very weakly on how haloes are identi ed in the simulations. This bias function is su cient to calculate the cross-correlation between dark haloes and mass, and again we nd excellent agreement between simulation results and analytic predictions. Because haloes are spatially exclusive, the variance in the count of objects within spheres of xed radius and overdensity is signi cantly smaller than the Poisson value. This seriously complicates any analytic calculation of the autocorrelation function of dark halos. Our simulation results show, however, that this autocorrelation function is proportional to that of the mass over a wide range in R, even including scales where both functions are signi cantly greater than unity. Furthermore, the constant of proportionality is very close to that predicted on large scales by the analytic model. Since analytic formulae for the nonlinear autocorrelation function of the mass are already known, this result permits an entirely analytic estimate of the autocorrelation function of dark haloes. We use our model to study how the distribution of galaxies may be biased with respect to that of the mass. In conjunction with other data these techniques should make it possible to measure the amplitude of cosmic mass uctuations and the density of the Universe.