Modelling dissipative dynamics of r-mode instability in hybrid stars

Abstract Compact star cores reach extreme densities and may contain exotic dense-matter phases. Information about the exotic interiors of rapidly rotating pulsars can be inferred from r-mode oscillations, whose stability is governed by viscous dissipation. In this work, we model a compact star containing a possible mixed phase of hadronic and quark matter and employ a hybrid statistical framework based on Bayesian inference to infer the dissipation time scales associated with the hybrid phase. Using low-mass X-ray binaries (LMXB) timing observations together with mass–radius constraints from the Neutron Star Interior Composition Explorer (NICER) mission, we estimate the shear and bulk viscosity contributions to r-mode damping for a hybrid star of two layers. Our inference yields shear and bulk viscous dissipation time scales of $$\\tau _s=(4.99^{+0.49}_{-0.52}) \\times 10^8 T^{\\frac{5}{3}}$$ τ s = ( 4 . 99 - 0.52 + 0.49 ) × 10 8 T 5 3 s and $$\\tau _B= (2.150^{+1.23}_{-0.60}) \\times 10^{19} (T^4 10^{-12}+T^2 10^{-6})^{-1}\\Omega ^{-2}$$ τ B = ( 2 . 150 - 0.60 + 1.23 ) × 10 19 ( T 4 10 - 12 + T 2 10 - 6 ) - 1 Ω - 2 s respectively. The timescales thus obtained can be implemented to obtain the minima of the star’s rotation frequency at $$\\Omega =451.87$$ Ω = 451.87 Hz at temperature $$T=0.259$$ T = 0.259 MeV for a hybrid star of mass 1.5 $$M_{\\odot }$$ M ⊙ and $$\\Omega =517.47$$ Ω = 517.47 Hz at $$T=0.234$$ T = 0.234 MeV for $$M=1.75 M_{\\odot }$$