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 } \geq 2 \times 10 ^ { 10 } h ^ { -1 } { M } _ { \odot } ) elliptical galaxies .