Improved universality in the neutron star three-hair relations

No-hair-like relations between the multipole moments of the exterior gravitational field of neutron stars have recently been found to be approximately independent of the star's internal structure. This approximate equation-of-state universality arises after one adimensionalizes the multipole moments appropriately, which then begs the question of whether there are better ways to adimensionalize the moments to obtain stronger universality. We here investigate this question in detail by considering slowly rotating neutron stars to quartic order in spin, an approximation that is valid for spin frequencies roughly below 500 Hz, both in the nonrelativistic limit and in full general relativity. We find that there exist normalizations that lead to stronger equation-of-state universality in the relations among the moment of inertia and the quadrupole, octopole and hexadecapole moments of neutron stars. We determine the optimal normalization that minimizes the equation-of-state dependence in these relations. The results found here may have applications in the modeling of x-ray pulses and atomic line profiles from millisecond pulsars with NICER and LOFT.