We construct static and mass-shedding limit sequences of hybrid stars , composed of colour flavour locked ( CFL ) quark matter core , for a set of equations of state ( EOSs ) .
The EOS for the hadronic matter is obtained using appropriately calibrated extended field theoretical based relativistic mean-field model .
The MIT bag model is employed to compute the EOSs of the CFL quark matter for different values of the CFL gap parameter in the range of 50 - 150 \text { MeV } with the deconfinement phase transition density ranging from 4 \rho _ { 0 } -6 \rho _ { 0 } ( \rho _ { 0 } = 0.16 \text { fm } ^ { -3 } ) .
We find , depending on the values of the CFL gap parameter and the deconfinement phase transition density , the sequences of stable configurations of hybrid stars either form third families of the compact stars or bifurcate from the hadronic sequence .
The hybrid stars have masses 1.0 - 2.1 M _ { \odot } with radii 9 - 13.5 km .
The maximum values of mass shedding limit frequency for such hybrid stars are 1 - 2 kHz .
For the smaller values of the CFL gap parameter and the deconfinement phase transition density , mass-radius relationships are in harmony with those deduced by applying improved hydrogen atmosphere model to fit the high quality spectra from compact star X7 in the globular cluster 47 Tucanae .
We observed for some cases that the third family of compact stars exist in the static sequence , but , disappear from the mass-shedding limit sequence .
Our investigation suggests that the third family of compact stars in the mass-shedding limit sequence is more likely to appear , provided they have maximum mass in the static limit higher than their second family counterpart composed of pure hadronic matter .