Effects of color superconductivity on the nucleation of quark matter in neutron stars

¹ Dipartimento di Fisica “Enrico Fermi” Università di Pisa and INFN Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy e-mail: [bombaci;lugones]@df.unipi.it
² Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, Avda. Diagonal 647, 08028 Barcelona, Spain e-mail: vidana@ecm.ub.es

Received: 23 March 2006
Accepted: 27 September 2006

Abstract

Aims.We study the nucleation of quark matter drops at the center of cold deleptonized neutron stars. These drops can be made up of unpaired quark matter or of color-superconducting quark matter, depending on the details of the equations of state for quark and hadronic matter. The nature of the nucleated phase is relevant in determining the critical mass M_cr of hadronic stars above which a transition to a quark star (strange or hybrid) is possible.

Methods.We investigate the dependence of M_cr upon the parameters of the quark model (the Bag constant B, the pairing gap Δ, and the surface tension σ of the quark-hadron interface) and for different parametrizations of the hadronic equation of state. We also calculate the energy released when a pure hadronic star with the critical mass is converted into a quark star.

Results.In general, the dependence of M_cr on B, Δ, and σ is mild if the parameters of the quark model correspond to hybrid stars, and strong if they correspond to strange stars. Also, the critical mass always decreases with Δ and increases with B and σ. The total released energy is in the range .

Conclusions.For a large part of the parameter space corresponding to hybrid stars, the critical mass is very close to (but smaller than) the maximum mass of hadronic stars, so compatible with a “mixed” population of compact stars (pure hadronic up to the critical mass and hybrid above the critical mass). For very large B the critical mass is never lower than the maximum mass of hadronic stars, implying that quark stars cannot form through the mechanism studied here. The energy released in the conversion is sufficient for powering a gamma ray burst.