We discuss a procedure to build new sequences of magnetised, equilibrium tori around Kerr black holes which combines two approaches previously considered in the literature. For simplicity we have assumed that the test-fluid approximation holds, and hence we neglected the self-gravity of the fluid. The models were built assuming a particular form of the angular momentum distribution from which the location and morphology of equipotential surfaces can be computed. This ansatz includes, in particular, the constant angular momentum case originally employed in the construction of thick tori – or Polish doughnuts – and it has already been used to build equilibrium sequences of purely hydrodynamical models. We discuss the properties of the new models and their dependence on the initial parameters. These new sequences can be used as initial data for magnetohydrodynamical evolutions in general relativity.
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