Waves in Thin Oceans on Oblate Neutron Stars

TL;DR

This paper studies how oblateness and gravitational variation in rapidly rotating neutron stars influence different fluid wave modes, revealing specific changes in wave vectors and confinement properties.

Contribution

It provides the first detailed analysis of hydrodynamic modes on oblate neutron stars considering gravitational acceleration variations and oblateness effects.

Findings

g- and Yanai modes' wave vectors increase with oblateness

Kelvin modes become less confined with increased oblateness

r-modes' wave vectors decrease as oblateness increases

Abstract

Waves in thin fluid layers are important in various stellar and planetary problems. Due to rapid rotation such systems will become oblate, with a latitudinal variation in the gravitational acceleration across the surface of the object. In the case of accreting neutron stars, rapid rotation could lead to a polar radius smaller than the equatorial radius by a factor $\sim 0.8$. We investigate how the oblateness and a changing gravitational acceleration affect different hydrodynamic modes that exist in such fluid layers through analytic approximations and numerical calculations. The wave vectors of $g$-modes and Yanai modes increase for more oblate systems compared to spherical counterparts, although the impact of variations in the changing gravitational acceleration is effectively negligible. We find that for increased oblateness, Kelvin modes show less equatorial confinement and little change in their wave vector. For $r$-modes, we find that for more oblate systems the wave vector decreases. The exact manner of these changes for the $r$-modes depends on the model for the gravitational acceleration across the surface.