In this work, we explore the possibility that the compact object in HESS J1731-347 is a dark-matter-admixed quark star, presenting a new challenge in constraining the equation of state of compact objects. We analyze both single- and two-fluid frameworks while incorporating the latest astrophysical observational constraints. Within this framework, we constrain key dark-matter parameters, namely, the dark-matter self-interaction parameter, particle mass, and Fermi momentum, using the properties of the central compact object in HESS J1731-347. We also analyze the mass profile of HESS J1731-347 within single- and two-fluid frameworks; while both descriptions satisfy the observed mass and radius, the two-fluid approach explicitly separates the quark-matter and dark-matter contributions, illustrating how dark matter modifies the internal mass distribution under the same observational constraints. Our results reveal a clear distinction between the single- and two-fluid descriptions. In the two-fluid model, the maximum mass shows a strong dependence on the dark-matter parameters: it decreases with increasing dark-matter self-interaction strength but increases with increasing dark-matter particle mass. In contrast, the single-fluid model is almost insensitive to the self-interaction parameter, while the maximum mass decreases as the dark-matter particle mass increases. This difference arises because, in the single-fluid picture, the homogeneous mixing of quark matter and dark matter leads to an overall softening of the effective equation of state.

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• Dark matter
• Nuclear astrophysics
• Quark matter
• Quark model