# MHD simulations of oscillating cusp-filling tori around neutron stars -- missing upper kHz QPO

## TL;DR

This study uses axisymmetric MHD simulations to analyze oscillating cusp-filling tori around neutron stars, revealing dominant radial epicyclic modes and their impact on accretion and luminosity, with implications for understanding kHz QPOs.

## Contribution

It presents the first detailed MHD simulation of oscillating cusp-filling tori around neutron stars, highlighting the suppression of vertical oscillations and their effect on accretion modulation.

## Key findings

- Radial epicyclic mode dominates oscillations.
- Vertical oscillations are suppressed by the cusp.
- Mass accretion rate modulates boundary layer luminosity.

## Abstract

We performed axisymmetric, grid-based, ideal magnetohydrodynamic (MHD) simulations of oscillating cusp-filling tori orbiting a non-rotating neutron star. A pseudo-Newtonian potential was used to construct the constant angular momentum tori in equilibrium. The inner edge of the torus is terminated by a "cusp" in the effective potential. The initial motion of the model tori was perturbed with uniform sub-sonic vertical and diagonal velocity fields. As the configuration evolved in time, we measured the mass accretion rate on the neutron star surface and obtained the power spectrum. The prominent mode of oscillation in the cusp torus is the radial epicyclic mode. It would appear that vertical oscillations are suppressed by the presence of the cusp. From our analysis it follows that the mass accretion rate carries a modulation imprint of the oscillating torus, and hence so does the boundary layer luminosity.