# A physical interpretation of the variability power spectral components in accreting neutron stars

## TL;DR

This paper presents a physical model explaining the variability power spectral components in accreting neutron stars using a turbulent hot inner flow and Lense-Thirring precession, successfully matching observed QPO frequencies.

## Contribution

It introduces a comprehensive physical framework linking spectral features to accretion flow geometry and turbulence, validated against neutron star atoll systems.

## Key findings

- Model reproduces observed QPO frequencies within 25% accuracy.
- Truncation radius decreases from 20 to 8 Rg during spectral transitions.
- Constant surface density assumption aligns with observed low frequency QPOs.

## Abstract

We propose a physical framework for interpreting the characteristic frequencies seen in the broad band power spectra from black hole and neutron star binaries. We use the truncated disc/hot inner flow geometry, and assume that the hot flow is generically turbulent. Each radius in the hot flow produces fluctuations, and we further assume that these are damped on the viscous frequency. Integrating over radii gives broad band continuum noise power between low and high frequency breaks which are set by the viscous timescale at the outer and inner edge of the hot flow, respectively. Lense-Thirring (vertical) precession of the entire hot flow superimposes the low frequency QPO on this continuum power. We test this model on the power spectra seen in the neutron star systems (atolls) as these have the key advantage that the (upper) kHz QPO most likely independently tracks the truncation radius. These show that this model can give a consistent solution, with the truncation radius decreasing from 20-8 Rg while the inner radius of the flow remains approximately constant at ~4.5 Rg i.e. 9.2 km. We use this very constrained geometry to predict the low frequency QPO from Lense-Thirring precession of the entire hot flow from r_o to r_i. The simplest assumption of a constant surface density in the hot flow matches the observed QPO frequency to within 25 per cent. This match can be made even better by considering that the surface density should become increasingly centrally concentrated as the flow collapses into an optically thick boundary layer during the spectral transition. The success of the model opens up the way to use the broad band power spectra as a diagnostic of accretion flows in strong gravity.