  We demonstrate that the ground state of a trapped spin-1 and spin-2 spinor
ferromagnetic Bose-Einstein condensate (BEC) can be well approximated by a
single decoupled Gross-Pitaevskii (GP) equation. Useful analytic models for the
ground-state densities of ferromagnetic BECs are obtained from the Thomas-Fermi
approximation (TFA) to this decoupled equation. Similarly, for the ground
states of spin-1 anti-ferromagnetic and spin-2 anti-ferromagnetic and cyclic
BECs, some of the spin component densities are zero which reduces the coupled
GP equation to a simple reduced form. Analytic models for ground state
densities are also obtained for anti-ferromagnetic and cyclic BECs from the TFA
to the respective reduced GP equations. The analytic densities are illustrated
and compared with the full numerical solution of the GP equation with realistic
experimental parameters.
