Astrophysical constraints on color-superconducting phases in compact stars within the RG-consistent NJL model

We determine parameters of the renormalization group-consistent three-flavor color-superconducting Nambu–Jona-Lasinio (NJL) model that are suited to investigate possible compact-star configurations. Our goal is to provide quark-matter equations of state (EOSs) that can be used for hadron-quark hybrid-star constructions. To that end, we mainly focus on the parameters of the quark-matter model. By varying the vector and diquark coupling constants, we analyze their impact on the EOS, the speed of sound, the maximum diquark gap, and the mass-radius relation. In almost all configurations, a stable color-flavor-locked (CFL) phase appears in the core of the maximum-mass configurations, typically spanning several kilometers in radius. In other cases, the star’s two-flavor color-superconducting (2SC) branch of the EOS becomes unstable before reaching the CFL transition density. At neutron-star densities, the speed of sound squared reaches up to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msubsup><a:mrow><a:mi>c</a:mi></a:mrow><a:mrow><a:mi>s</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msubsup><a:mo>∼</a:mo><a:mn>0.6</a:mn></a:mrow></a:math> and the CFL gap up to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">Δ</c:mi><c:mo>∼</c:mo><c:mn>250</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>MeV</c:mi></c:math>. We argue that adding a hadronic EOS at lower densities by performing a Maxwell construction does not increase the maximum mass substantially. Thus we use the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>2.0</f:mn><f:msub><f:mi>M</f:mi><f:mo stretchy="false">⊙</f:mo></f:msub></f:math> constraint to constrain the NJL model parameters that are suited for the construction of hybrid-star EOS. We construct three examples of the hybrid-star model, demonstrating that there is room for different color-superconducting compositions. The hybrid EOSs obtained in this way can have no 2SC matter or different ratios of 2SC and CFL quark matter in the core. We show that early hadron-quark transitions are possible that can modify the tidal deformability at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>1.4</i:mn><i:msub><i:mi>M</i:mi><i:mo stretchy="false">⊙</i:mo></i:msub></i:math>. We find that these EOSs are consistent with the imposed constraints from astrophysics and perturbative QCD. They allow for different hybrid-star scenarios with a hadronic EOS that is soft at low to intermediate densities (<l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mo>∼</l:mo><l:mn>1</l:mn><l:mi>–</l:mi><l:mn>3</l:mn><l:msub><l:mi>n</l:mi><l:mi>sat</l:mi></l:msub></l:math>).