  The representation of the seesaw orthogonal matrix in the complex plane
establishes a graphical correspondence between neutrino mass models and
geometrical configurations, particularly useful to study relevant aspects of
leptogenesis. We first derive the CP asymmetry bound for hierarchical heavy
neutrinos and then an expression for the effective leptogenesis phase,
determining the conditions for maximal phase and placing a lower bound on the
phase suppression for generic models. Reconsidering the lower bounds on the
lightest right-handed (RH) neutrino mass M_1 and on the reheating temperature
T_reh, we find that models where one of the two heavier neutrino masses is
dominated by the lightest right-handed (RH) neutrinos, typically arising from
connections with quark masses, undergo both phase suppression and strong
wash-out such that M_1 (T_reh)\gtrsim 10^{11} (10^{10}) GeV. The window 10^9
GeV \lesssim M_1,T_reh \lesssim 10^{10}GeV is accessible only for a class of
models where m_1 is dominated by the lightest RH neutrino, with no
straightforward connections with quark masses. Within this class we describe a
new scenario of thermal leptogenesis where the baryon asymmetry of the Universe
is generated by the decays of the second lightest RH neutrino, such that the
lower bound on M_1 disappears and is replaced by a lower bound on M_2.
Interestingly, the final asymmetry is independent on the initial conditions. We
also discuss the validity of the approximation of hierarchical heavy neutrinos
in a simple analytical way.
