Is the central compact object in HESS J1731-347 a hybrid star with a quark core? An analysis with the constant speed of sound parametrization

In this work, we investigate the possibility of the compact object in HESS J1731-347 with $M=0.77_{-0.17}^{+0.20}M_{\odot}$ and $R=10.4_{-0.78}^{+0.86} km$ to be a hybrid star with quark matter in the inner core. The observation of this low mass compact star dictates the use of softer equation of state which on the contrary cannot explain the massive compact stars. This poses a new challenge for the astrophysicists in their search for the equation of state of compact objects. The hybrid equations of state are constructed using the IUFSU parametrization based on the relativistic mean field (RMF) theory for the hadronic part and the generic constant speed of sound parametrization (CSS) for the phase transition to quark matter.The CSS framework is characterized by three key parameters, namely the transition density $(\rho_{tr})$, the energy jumps $(\Delta\varepsilon)$ and the speed of sound $(C_s)$. Here, our primary aim is to investigate the influence of individual CSS parameters on the formation of a object of small mass and radius compatible with HESS J1731-347 parameters. We have also examined the effect of hadronic parameters such as effective mass, symmetry energy, and the slope of the symmetry energy at saturation densities on the formation of this compact object.Finally our analysis suggests that, within a 1$\sigma$ credible level, HESS J1731-347 aligns with the scenario of a stable hybrid star with early deconfinement and higher energy gap