Rotating Star Model Refines X-ray Analysis, Improves Astronomy.

The accurate determination of neutron star mass and radius remains a significant challenge in astrophysics, critically dependent on precise modelling of observed X-ray emissions. Subtle errors in calculating the redshift, the stretching of light wavelengths due to gravity, can propagate into uncertainties in these fundamental stellar parameters. Zsombor Jakab and Sharon M. Morsink, from the University of Alberta, alongside their colleagues, address a specific source of error within the commonly used Oblate Schwarzschild (OS) approximation, a method for modelling the gravitational redshift from rapidly rotating neutron stars. Their research, detailed in the article ‘Gravitational Redshift for Rapidly Rotating Neutron Stars’, presents a straightforward correction to the standard redshift calculation, minimising flux errors and improving the precision of future observations, particularly for those pulsars approaching spin frequencies of 600 Hz. The OS approximation combines the effects of a star’s oblate shape – flattened due to rotation – with the Schwarzschild metric, which describes the gravitational field around a non-rotating, spherically symmetric mass.

Researchers have identified a systematic error within the Oblate Schwarzschild (OS) approximation, a frequently employed technique for modelling X-ray emissions originating from rapidly rotating neutron stars. The OS approximation simplifies calculations by treating the neutron star’s shape as an oblate spheroid, a sphere flattened at the poles, and utilising the Schwarzschild metric, a solution to Einstein’s field equations describing the gravitational field outside a spherically symmetric, non-rotating mass. The study reveals that standard applications of redshift corrections within this approximation consistently underestimate observed flux, the amount of energy received.

This underestimation arises from inaccuracies in how the oblate shape interacts with the assumptions inherent in the Schwarzschild metric. Redshift, in this context, refers to the stretching of light waves as they escape the intense gravitational field of the neutron star, affecting the observed energy. The magnitude of this error, while small – less than 1% for the pulsar PSR J0740+6620 – is nonetheless significant for precise astrophysical modelling. Current uncertainties in measuring distances to these pulsars, rapidly rotating neutron stars that emit beams of electromagnetic radiation, necessitate highly accurate flux calculations.

The error becomes more pronounced as the neutron star’s rotational frequency increases, approaching 600 Hz. Faster rotation exacerbates the deviation from the spherical symmetry assumed by the Schwarzschild metric, amplifying the inaccuracies. Researchers have developed a straightforward correction method, resulting in a constant, absolute reduction in calculated flux. This correction effectively accounts for the oblate shape’s influence on the observed redshift, improving the fidelity of the model. The refinement enhances the accuracy of X-ray emission calculations, contributing to a more precise understanding of these extreme celestial objects.