Angular momentum transfer and the size - mass relation in early - type
  galaxies
  Early - type galaxies (ETGs) define a narrow strip in the size - mass plane
because of the observed correlation between the effective radius $R_{eff}$ and
the total stellar mass $M_{\star}$. When expressed in logarithmic units, a
linear relation, $\log{R_{eff}} \propto \gamma \log{M_{\star}}$, is indeed
observationally found, but the slope $\gamma$ deviates from the canonical
$\gamma = 1/2$ value which can be naively predicted for a spherically symmetric
isotropic system. We propose here that a transfer of angular momentum to the
stellar component induces an anisotropy in the velocity space thus leading to a
modified distribution function (DF). Assuming an Osipkov - Merritt like
anisotropic DF, we derive an analytic relation between the slope $\gamma$ of
the size - mass relation and the slope $\alpha$ of the angular momentum term in
the DF. With this simple model, we are then able to recover the observed
$\gamma$ value provided $\alpha$ is suitably set. It turns out that an
anisotropy profile which is tangential inside $\sim 0.6 r_a$ and radial
outside, with $r_a$ the anisotropy radius, is able to reproduce the observed
size - mass relation observed for massive ($M_{\star} \ge 2 \times 10^{10} \
h^{-1} {\rm M}_{\odot}$) elliptical galaxies.
