We report the results of extended high–resolution numerical integrations of the Vlasov–Poisson equation for the collapse of spherically symmetric WDM halos .
For thermal relics with mass m = 1 keV/ c ^ { 2 } , we find collapsed halos with cores of size from 0.1 to 0.6 kpc .
The typical core is hollow , with the mass density decreasing towards the core center by almost three orders of magnitude from its maximum near the core radius r _ { c } .
The core is in equilibrium with the diffused part of the halo but far from virialization .
These properties are rooted in the conservation of the squared angular momentum and in the original excess , proper of WDM initial conditions , of kinetic energy in the core region .
In a sample of more than one hundred simulated collapses , the values of r _ { c } and of the core density \rho _ { c } are in the range typical of dwarf spheroids , while the maximal circular velocities V _ { max } are proper of small disk galaxies .
The product \mu _ { c } = \rho _ { c } r _ { c } takes values between 116 M _ { \odot } / pc ^ { 2 } and 283 M _ { \odot } / pc ^ { 2 } , while the surface density \mu _ { 0 } , as determined from a Burkert fit , is roughly three times larger .
From these data and data obtained at smaller values of m , we extrapolate for one particular halo \mu _ { c } = 263 ( 308 ) M _ { \odot } / pc ^ { 2 } and \mu _ { 0 } = 754 ( 855 ) M _ { \odot } / pc ^ { 2 } at m = 2 ( 3.3 ) keV/ c ^ { 2 } , to be compared with the observed value 140 ^ { +83 } _ { -52 } M _ { \odot } /pc ^ { 2 } .
In view of the many improvements and enhancements available , we conclude that WDM is a viable solution for explaining the presence and the size of cores in low mass galaxies .