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Equation-of-state-insensitive measure of neutron star stiffness

Universal relations (i.e., insensitive to the equation of state) between macroscopic properties of neutron stars have proven useful for a variety of applications -- from providing a direct means to extract observables from data to breaking degeneracies that hinder tests of general relativity. Similarly, equation-of-state-insensitive relations directly connecting macroscopic and microscopic properties of neutron stars can potentially provide a clean window into the behavior of nuclear matter. In this work, we uncover a tight correlation between certain macroscopic properties of a neutron star - its compactness $C$, moment of inertia $\bar{I}$ and tidal deformability $\barΛ$ - and the ratio $α_c \equiv p_c/ε_c$ of central pressure to central energy density, which can be interpreted as a mean notion of the stiffness of nuclear matter inside that object. We describe interesting properties of this stiffness measure, quantify the (approximate) universality of the $α_c - C/\bar{I}/\barΛ$ relations, and explore its consequences in the face of recent and future neutron star observations.