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Background : The emergence of hyperon degrees of freedom in neutron starmatter has been associated to first order phase transitions in somephenomenological models, but conclusions on the possible physical existence ofan instability in the strangeness sector are strongly model dependent. Purpose: The purpose of the present study is to assess whether strangenessinstabilities are related to specific values of the largely unconstrainedhyperon interactions, and to study the effect of the strange meson couplings onphenomenological properties of neutron stars and supernova matter, once theselatter are fixed to fulfill the constraints imposed by hypernuclear data.Method : We consider a phenomenological RMF model sufficiently simple to allowa complete exploration of the parameter space. Results : We show that noinstability at supersaturation density exists for the RMF model, as long as theparameter space is constrained by basic physical requirements. This is atvariance with a non-relativistic functional, with a functional behavior fittedthrough ab-initio calculations. Once the study is extended to include the fulloctet, we show that the parameter space allows reasonable radii for canonicalneutron stars as well as massive stars above two-solar mass, together with animportant strangeness content of the order of 30\%, slightly decreasing withincreasing entropy, even in the absence of a strangeness driven phasetransition. Conclusions : We conclude that the hyperon content of neutron starsand supernova matter cannot be established with present constraints, and isessentially governed by the unconstrained coupling to the strange isoscalarmeson.

Examination of strangeness instabilities and effects of strange meson couplings in dense strange hadronic matter and compact stars