# Broadband aperiodic variability in X-ray pulsars: accretion rate fluctuations propagating under the influence of viscous diffusion

## TL;DR

This paper models aperiodic X-ray variability in accreting neutron stars by analyzing viscous diffusion in truncated accretion discs, linking observed spectral features to disc dynamics and magnetic field influences.

## Contribution

It introduces the most general analytical solutions for viscous diffusion in truncated accretion discs, enhancing understanding of variability origins in X-ray pulsars.

## Key findings

- Break in power density spectra linked to dynamo process timescale.
- Initial variability timescale is a few times longer than local Keplerian time.
- Model fits well with observational data from A 0535+26.

## Abstract

We investigate aperiodic X-ray flux variability in accreting highly magnetized neutron stars - X-ray pulsars (XRPs). The X-ray variability is largely determined by mass accretion rate fluctuations at the NS surface, which replicate accretion rate fluctuations at the inner radius of the accretion disc. The variability at the inner radius is due to fluctuations arising all over the disc and propagating inwards under the influence of viscous diffusion. The inner radius varies with mean mass accretion rate and can be estimated from the known magnetic field strength and accretion luminosity of XRPs. Observations of transient XRPs covering several orders of magnitude in luminosity give a unique opportunity to study effects arising due to the changes of the inner disc radius. We investigate the process of viscous diffusion in XRP accretion discs and construct new analytical solutions of the diffusion equation applicable for thin accretion discs truncated both from inside and outside. Our solutions are the most general ones derived in the approximation of Newtonian mechanics. We argue that the break observed at high frequencies in the power density spectra of XRPs corresponds to the minimal time scale of the dynamo process, which is responsible for the initial fluctuations. Comparing data from the bright X-ray transient A 0535+26 with our model, we conclude that the time scale of initial variability in the accretion disc is a few times longer than the local Keplerian time scale.