Twin stars, characterized by identical stellar masses but distinct internal structures, can arise in dark matter admixed neutron stars (DANSs). This work will focus on one kind of special twin stars—ultimate twin stars (UTSs)—defined as DANSs with identical total masses and normal matter radii. Based on the two-fluid Tolman-Oppenheimer-Volkoff (TOV) equations, we model DANSs with normal matter described by APR3 and dark matter represented by ideal Fermi gas or self-interacting bosonic model. The results demonstrate that UTSs with canonical mass $1.4M_{\odot }$ emerge as the dark matter mass fraction varies, and their tidal deformabilities may differ by up to three orders of magnitude. The huge difference in tidal deformability provides a critical observable for distinguishing UTSs. Moreover, the tidal deformability exhibits correlation with dark matter mass fraction, offering a potential method to constrain dark matter parameters through gravitational wave observations.

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• Dark matter
• Nuclear astrophysics