# Study on Correlations between the Twin Kilohertz Quasi-periodic Oscillations in Low-mass X-ray Binaries

## TL;DR

This study analyzes updated data of twin kHz QPOs in neutron star low-mass X-ray binaries, fitting correlations with power-law and linear models, and compares these with theoretical models to understand their relationship.

## Contribution

It provides a comprehensive analysis of correlations in kHz QPOs using updated data and evaluates the fit of different models to these observations.

## Key findings

- Both power-law and linear models fit the data well.
- The data supports multiple correlation models for kHz QPOs.
- Comparison with theoretical models offers insights into QPO mechanisms.

## Abstract

The recently updated data of the twin kilohertz quasi-periodic oscillations (kHz QPOs) in the neutron star low-mass X-ray binaries are analyzed. The power-law fitting $\nu_{1}=a(\nu_{2}/1000)^{b}$ and linear fitting $\nu_{2}=A\nu_{1}+B$ are applied, individually, to the data points of four Z sources (GX 17+2, GX 340+0, GX 5-1 and Sco X-1) and four Atoll sources (4U 0614+09, 4U 1608-52, 4U 1636-53 and 4U 1728-34). The $\chi^{2}$-tests show that the power-law correlation and linear correlation both can fit data well. Moreover, the comparisons between the data and the theoretical models for kHz QPOs are discussed.