Neutron Star Mass-Radius Constraints using Evolutionary Optimization

Abstract

The equation of state of cold supra-nuclear-density matter, such as in neutron stars, is an open question in astrophysics. A promising method for constraining the neutron star equation of state is modelling pulse profiles of thermonuclear X-ray burst oscillations from hotspots on accreting neutron stars. The pulse profiles, constructed using spherical and oblate neutron star models, are comparable to what would be observed by a next-generation X-ray timing instrument like ASTROSAT, NICER, or LOFT. In this paper, we showcase the use of an evolutionary optimization algorithm to fit pulse profiles to determine the best-fit masses and radii. By fitting synthetic data, we assess how well the optimization algorithm can recover the input parameters. Multiple Poisson realizations of the synthetic pulse profiles, constructed with 1.6 million counts and no background, were fitted with the Ferret algorithm to analyze both statistical and degeneracy-related uncertainty, and to explore how the goodness-of-fit depends on the input parameters. For the regions of parameter space sampled by our tests, the best-determined parameter is the projected velocity of the spot along the observer's line-of-sight, with an accuracy of $\le 3$% compared to the true value and with $\le 5$\% statistical uncertainty. The next best-determined are the mass and radius; for a neutron star with a spin frequency of 600\,Hz, the best-fit mass and radius are accurate to $\le 5$%, with respective uncertainties of $\le 7$% and $\le 10$%. The accuracy and precision depend on the observer inclination and spot co-latitude, with values of $\sim 1$ % achievable in mass and radius if both the inclination and co-latitude are > 60 degrees.

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• Thermonuclear (type-I) X-ray bursts observed by the Rossi X-ray Timing Explorer
• Measuring the neutron star equation of state using X-ray timing
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• Constraining the Neutron Star Mass-Radius Relation and Dense Matter Equation of State with NICER. II. Emission from Hot Spots on a Rapidly Rotating Neutron Star
• Dense matter with eXTP
• Constraining the Neutron Star Mass--Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes
• Relativistic rotating vector model for X-ray millisecond pulsars
• General purpose ray-tracing and polarized radiative transfer in General Relativity
• Constraining the Properties of the Thermonuclear Burst Oscillation Source XTE J1814-338 Through Pulse Profile Modelling
• Bayesian parameter constraints for neutron star masses and radii using X-ray timing observations of accretion-powered millisecond pulsars
• Neutron star pulse profiles in scalar-tensor theories of gravity
• Pulse Profile Modeling of Thermonuclear Burst Oscillations I: The Effect of Neglecting Variability
• Pulse Profile Modelling of Thermonuclear Burst Oscillations II: Handling variability
• Exploring Waveform Variations among Neutron Star Ray-tracing Codes for Complex Emission Geometries