Stability of hybrid stars via catastrophe theory

We discuss the possible topologies of the mass-radius relation for hybrid stars in light of catastrophe theory. We show that different branches of compact stars emerge or disappear depending on the bifurcation structure of the underlying catastrophe potential function, the mathematical analog of an effective potential. For that we assume a single first-order phase transition between nuclear and quark matter. After a warm up with incompressible fluids, we present a qualitative discussion explaining the (dis)appearance of (un)stable branches for hybrid stars as the control parameters change.