Highly-accurate Neutron Star Solutions in the Hartle-Thorne Approximation

The physics and astrophysics inferences that we will draw from future X-ray observations with NICER and LOFT and gravitational-wave observations with current and next-generation ground-based detectors will require accurate models of neutron stars. In this talk, I will describe the construction of highly-accurate solutions for slowly-rotating neutron stars, extending the Hartle-Thorne approximation to seventh-order in the slow-rotation expansion. This approximation allows us to calculate second, fourth and sixth order spin corrections to the observed mass and the moment of inertia, the second and fourth-order spin correction to the quadrupole and octopole moments, the second-order in spin correction to the hexadecapole and dotricontapole moment, and the leading-order-in-spin expressions for the hexacontatetrapole and the hectoicosaoctapole, while simultaneously providing accurate error estimates. These accurate solutions enable the calculation of similarly accurate X-ray pulse profile models, I-Love-Q relations, and three-hair relations for slowly-rotating neutron stars that be able useful to break parameter degeneracies in future observations.