Colour-Flavour Locked Quark Stars in Light of the Compact Object in HESS J1731-347 and the GW190814 Event

The central compact object within HESS J1731- 347 possesses unique mass and radius properties that renders it a compelling candidate for a self-bound star. In this research, we examine the capability of quark stars composed of colour superconducting quark matter to explain the latter object by using its marginalised posterior distribution and imposing it as a constraint on the relevant parameter space. Namely, we investigate quark matter for $N_f=2,3$ in the colour superconducting phase, incorporating perturbative QCD corrections, and we derive their properties accordingly. The utilised thermodynamic potential of this work possesses an MIT bag model formalism with the parameters being established as flavour-independent. In this instance, we conclude the favour of 3-flavour over 2-flavour colour superconducting quark matter, isolating our interest on the former. The parameter space is further confined due to the additional requirement for a high maximum mass ($M_{\text{TOV}} \geq 2.6 M_{\odot}$), accounting for GW$190814$'s secondary companion. We pay a significant attention on the speed of sound and the trace anomaly (proposed as a measure of conformality [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.252702}{10.1103/PhysRevLett.129.252702}]). We conclude that it is possible for colour-flavour locked quark stars to reach high masses without violating the conformal bound or the $\langle \Theta \rangle _{\mu_B} \geq 0$ if the quartic coefficient value $\alpha_4$ does not exceed an upper limit which is solely dependent on the established $M_{\text{TOV}}$. For $M_{\text{TOV}}=2.6 M_{\odot}$, we find that the limit reads $\alpha_4 \leq 0.594$. Lastly, a further study takes place on the agreement of colour-flavour locked quark stars with additional astrophysical objects including the GW$170817$ and GW$190425$ events, followed by a relevant discussion.