Bayesian study of quark models in view of recent astrophysical constraints

In this work, we perform a comparative analysis between the density-dependent quark model and the vector MIT bag model using Bayesian analysis. We use the equations of state generated by these two models to describe quark stars. We impose four recent observational astrophysical constraints on both models to determine their model-dependent parameters in an optimized manner assuming that the compact objects observed are composed entirely of self-bound quarks. The restrictions are aimed at producing stars with maximum masses $2-2.35M_{\odot }$ and a mass-radii diagram compatible with the observed pulsars PSR $\mathrm{J}0740+6620$, PSR J0952-0607, and PSR $\mathrm{J}0030+0451$ and the compact object XMMU J173203.3-344518. With this analysis, the parameter dependence of the nuclear equation of state of both models is restricted.

Figure 1

Corner plot showing the posterior distributions of the parameters of DDQM model on the left and the parameters of the vector MIT bag model on the right for case I. The dark to light contours represent the $1\sigma$, $2\sigma$ and $3\sigma$, respectively. The dashed vertical lines in the histograms represent the 0.16, 0.5, and 0.84 quantiles.

Figure 2

Corner plot showing the posterior distributions of the parameters of DDQM model on the left and the parameters of the vector MIT bag model on the right for case II. The dark to light contours represent the $1\sigma$, $2\sigma$ and $3\sigma$, respectively. The dashed vertical lines in the histograms represent the 0.16, 0.5, and 0.84 quantiles.

Figure 3

Corner plot showing the posterior distributions of the parameters of DDQM model on the left and the parameters of the vector MIT bag model on the right for case III. The dark to light contours represent the $1\sigma$, $2\sigma$ and $3\sigma$, respectively. The dashed vertical lines in the histograms represent the 0.16, 0.5, and 0.84 quantiles.

Figure 4

Corner plot showing the posterior distributions of the parameters of DDQM model on the left and the parameters of the vector MIT bag model on the right for case IV. The dark to light contours represent the $1\sigma$, $2\sigma$ and $3\sigma$, respectively. The dashed vertical lines in the histograms represent the 0.16, 0.5, and 0.84 quantiles.

Figure 5

The stability window for the DDQM model.

Figure 6

In the figures above we compare the EOSs from the DDQM (left panel) with the EOSs for the vector MIT bag model (right panel).

Figure 7

Comparing the mass-radius diagram of the DDQM (left) and the vector MIT bag model (right).

Figure 8

Here we compare the square velocity of sound $c_s^2$ resulting from the two models as a function of baryon density $n$.

Figure 9

We compare the adiabatic indices $\mathrm{\Gamma }$ of DDQM (left panel) and the vector MIT bag model (right panel) as a function of baryon density $n$.

Figure 10

Tidal deformability $\mathrm{\Lambda }$ as a function of the mass $M[M_{\odot }]$ for the DDQM model (left panel) and vector MIT bag model (right panel).