Hybrid stars are compatible with recent astrophysical observations

Compact stars (CS) are stellar remnants of massive stars. Inside CSs the density is so high that matter is in subatomic form composed of nucleons. With an increase of density of matter toward the center of the objects, other degrees of freedom like hyperons, heavier nonstrange baryons, meson condensates may appear. Not only that, at higher densities the nucleons may get decomposed into quarks and form deconfined strange quark matter (SQM). If it is so then CSs may contain SQM in the core surrounded by nucleonic matter forming hybrid stars (HSs). However, the nature and composition of matter inside CSs can only be inferred from the astrophysical observations of these CSs. Recent astrophysical observations in terms of CS mass-radius (M-R) relation and gravitational wave (GW) observation indicate that the matter should be soft in the intermediate density range and stiff enough at higher density range to attain the maximum possible mass above $2M_{\odot }$ which is not compatible with pure hadronic equations of states (EOSs). Consequently, we study the HS properties with different models of SQM and find that within vector bag model considering density dependent bag parameter, the model goes well with the astrophysical observations so far.

Figure 1

Variation of bag parameter $B$ with density for the EOSs we considered with $B_c^{1/4}=130\mathrm{MeV}$. The solid curve, dashed curve, and dotted curve are for $B_s^{1/4}=180$, 170, 160 MeV, respectively.

Figure 2

Variation of pressure with baryon chemical potential (neutron chemical potential) in both phases. Left panel: for density independent $B$ parameters. Right panel: for density dependent $B$ parameters. For both the panels the solid curve is for the nucleonic matter and for SQM matter the parameters values for different curves are as indicated in the figure. The point of PT for each parametrizations of SQM is denoted by black circles.

Figure 3

Variation of pressure with energy density. Left panel: for density independent $B$ parameters. Right panel: for density dependent $B$ parameters. The parameter values for different curves are as indicated in the figure.

Figure 4

Mass-radius relations along with constraints from astrophysical observations for different parametrizations. Left panel: for density independent $B$ parameters. Right panel: for density dependent $B$ parameters. The parameter values for different curves are as indicated in the figure. Contours represent constraints for PSR $\mathrm{J}0740+6620$ [5, 6] and PSR $\mathrm{J}0030+451$ [55, 56]. Horizontal straight lines depict radius constraints as we discussed in introduction section. Upper shaded regions are for GW190814 and PSR J0952-0607.

Figure 5

Tidal deformabilities associated with the both components of the binary of GW170817. The shaded regions indicate the allowed region in the plane from two estimates of $\tilde{\mathrm{\Lambda }}$ from GW170817 observations.

Figure 6

Variation of $\mathrm{\Lambda }$ with stellar mass. The vertical arrows show the constraints from GW190814 and GW170817 event data.

Figure 7

Variation of radius of $1.4M_{\odot }$ star with content of quark matter inside HS for different parametrizations.

Figure 8

Variation of $\mathrm{\Lambda }$ of $1.4M_{\odot }$ star with content of quark matter inside HS for different parametrizations.

Figure 9

Variation of $\tilde{\mathrm{\Lambda }}$ of $1.4M_{\odot }$ star with content of quark matter inside HS for different parametrizations.