Linear analysis of I-C-Love universal relations for neutron stars

Neutron stars (NSs) are excellent laboratories for testing gravity theories as they are strongly self-gravitating bodies and have rich observational phenomena. However, strong-gravity effects in NS could be degenerate with their equation of state (EOS) which is largely unknown. Fortunately, there exist the so-called universal relations among the NS macroscopic quantities that are found to be insensitive to the underlying EOS. Studying the origin of these relations can lead to a better understanding of NSs and the gravitational interaction. We develop a new perspective of view to analyze the I-C and I-Love universal relations for NSs. At the linear order, we separate the deviation of the universal relations into two parts, where one is the EOS perturbation while the other only depends on the background star structures. The smallness of the second part fully determines the universality of the relation irrespective of the form of the first part. We discuss the validity of our linear approximation when considering the difference among realistic EOSs. Our study can be regarded as a new frame for quantitative representation of the universality and may provide new insights to the universal relations of NSs.