Universal relations for anisotropic interacting quark stars

Interacting quark stars, which are entirely composed of interacting quark matter including perturbative QCD corrections and color superconductivity, can meet constraints from various pulsar observations. In realistic scenarios, pressure anisotropies are expected in the star's interior. Recently, the stellar structural properties of anisotropic interacting quark stars have been investigated. In this study, we further explore the universal relations (URs) related to the moment of inertia $I$, tidal deformability $\Lambda$, compactness $C$, and the $f$-mode nonradial pulsation frequency for such stars. Our results reveal that these approximate URs generally hold, being insensitive to both the EOS variations as well as to the presence of anisotropy. In contrast to previous studies on anisotropic neutron stars, we find that more positive anisotropy tends to enhance the $I-\Lambda$ and $I-C$ URs, but weakens the $C-\Lambda$ UR. For all the URs involving $f$-mode frequency, we find that they are enhanced by the inclusion of anisotropy (whether positive or negative). Utilizing these URs and the tidal deformability constraint from the GW170817 event, we put limits on the structural properties of isotropic and anisotropic quark stars, such as the moment of inertia $I_{1.4}$, the canonical radius $R_{1.4}$ and the canonical $f$-mode frequency $f_{f,1.4}$, all of which are very different compared to those of neutron stars.