# Millihertz Quasi-Periodic Oscillations from Marginally Stable Nuclear Burning on an Accreting Neutron Star

**Authors:** Alexander Heger, Andrew Cumming, Stanford E. Woosley  
**arXiv:** [astro-ph/0511292](https://arxiv.org/abs/astro-ph/0511292)  
**Date:** 2005-11-10  
**Summary page:** https://www.summarizepaper.com/en/paper/astro-ph--0511292v1/

## Key points

- Marginally stable nuclear burning on the surface of accreting neutron stars is investigated as a possible explanation for millihertz quasi-periodic oscillations (QPOs) in low mass X-ray binaries.
- The focus is on the boundary between unstable and stable burning, where the nuclear heating rate and cooling rate nearly cancel each other out.
- This cancellation leads to an oscillatory mode of burning with an oscillation period close to the geometric mean of the thermal and accretion timescales.
- A simple one-zone model and detailed multizone hydrodynamical calculations using the KEPLER code are presented to illustrate this phenomenon.
- The models successfully explain why millihertz QPOs are observed only within a narrow range of X-ray luminosities and exhibit a characteristic 2-minute period.
- The oscillation period is sensitive to factors such as the accreted hydrogen fraction and surface gravity, suggesting that these parameters can be probed through observations of millihertz QPOs.
- Theoretical models predict a higher accretion rate for which these oscillations appear compared to what is implied by X-ray luminosity when observing millihertz QPOs, creating a major puzzle.
- At higher luminosities, it is suggested that only part of the neutron star surface may be covered by accreted material.
- The study provides valuable insights into marginally stable nuclear burning on neutron stars and its connection to millihertz QPOs while raising questions about our current understanding of these phenomena.

## Summary

This study investigates marginally stable nuclear burning on the surface of accreting neutron stars as a possible explanation for the observed millihertz quasi-periodic oscillations (QPOs) in three low mass X-ray binaries. The authors focus on the boundary between unstable and stable burning, where the temperature dependence of the nuclear heating rate and cooling rate nearly cancel each other out. This cancellation leads to an oscillatory mode of burning, with an oscillation period close to the geometric mean of the thermal and accretion timescales for the burning layer. To illustrate this phenomenon, the authors present a simple one-zone model and then proceed to conduct detailed multizone hydrodynamical calculations using the KEPLER code. These calculations provide insights into nuclear burning close to the stability boundary. The models successfully explain why millihertz QPOs are observed only within a narrow range of X-ray luminosities and why they exhibit a characteristic 2-minute period. The study also highlights that the oscillation period is sensitive to factors such as the accreted hydrogen fraction and surface gravity, suggesting that these parameters can be probed through observations of millihertz QPOs. However, a major puzzle arises from the fact that theoretical models predict an order of magnitude higher accretion rate for which these oscillations appear compared to what is implied by X-ray luminosity when observing millihertz QPOs. The implications of these findings extend to our general understanding of nuclear burning on accreting neutron stars. One possibility discussed by the authors is that at higher luminosities (Lx > ~1E37 erg/s), only part of the neutron star surface may be covered by accreted material. Overall, this study provides valuable insights into marginally stable nuclear burning on neutron stars and its connection to millihertz QPOs, while also raising intriguing questions about our current understanding of these phenomena.