Bayesian analysis of multimessenger M-R data with interpolated hybrid EoS

<jats:title>Abstract</jats:title><jats:p>We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a set of stiff quark matter EoS at high densities within a finite region of chemical potentials <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mu _H< \mu < \mu _Q$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:mo><</mml:mo> <mml:mi>μ</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mi>μ</mml:mi> <mml:mi>Q</mml:mi> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. Fixing the hadronic EoS as the APR one and choosing the color-superconducting, nonlocal NJL model with two free parameters for the quark phase, we perform Bayesian analyses with this two-parameter family of hybrid EoS. Using three different sets of observational constraints that include the mass of PSR J0740+6620, the tidal deformability for GW170817, and the mass-radius relation for PSR J0030+0451 from NICER as obligatory (set 1), while set 2 uses the possible upper limit on the maximum mass from GW170817 as an additional constraint and set 3 instead of the possibility that the lighter object in the asymmetric binary merger GW190814 is a neutron star. We confirm that in any case, the quark matter phase has to be color superconducting with the dimensionless diquark coupling approximately fulfilling the Fierz relation <jats:inline-formula><jats:alternatives><jats:tex-math>$$\eta _D=0.75$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>D</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.75</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> and the most probable solutions exhibiting a proportionality between <jats:inline-formula><jats:alternatives><jats:tex-math>$$\eta _D$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$\eta _V$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>V</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, the coupling of the repulsive vector interaction that is required for a sufficiently large maximum mass. We used the Bayesian analysis to investigate with the method of fictitious measurements the consequences of anticipating different radii for the massive <jats:inline-formula><jats:alternatives><jats:tex-math>$$2~M_\odot $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace /> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> PSR J0740+6220 for the most likely equation of state. With the actual outcome of the NICER radius measurement on PSR J0740+6220 we could conclude that for the most likely hybrid star EoS would not support a maximum mass as large as <jats:inline-formula><jats:alternatives><jats:tex-math>$$2.5~M_\odot $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.5</mml:mn> <mml:mspace /> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> so that the event GW190814 was a binary black hole merger.</jats:p>