Constraints on neutron star mass and radius in GS 1826-24 from sub-Eddington X-ray bursts

We investigate the constraints on neutron star mass and radius in GS 1826-24 from models of lightcurves and spectral evolution of type I X-ray bursts. This source shows remarkable agreement with theoretical calculations of burst energies, recurrence times, and lightcurves. We first exploit this agreement to set the overall luminosity scale of the observed bursts. When combined with a measured blackbody normalization, this leads to a distance and anisotropy independent measurement of the ratio between the redshift 1+z and color correction factor f_c. We find 1+z=1.19-1.28 for f_c=1.4-1.5. We then compare the evolution of the blackbody normalization with flux in the cooling tail of bursts with predictions from spectral models of Suleimanov et al. (2011b). The observations are well described by the models at luminosities greater than about one third of the peak luminosity, with deviations emerging at luminosities below that. We show that this comparison leads to distance independent upper limits on R_\infty and neutron star mass of R_\infty\lesssim 9.0-13.2 km and M<1.2-1.7 M_\odot, respectively, for solar abundance of hydrogen at the photosphere and a range of metallicity and surface gravity. The radius limits are low in comparison to previous measurements. This may be indicative of a subsolar hydrogen fraction in the GS 1826-24 photosphere, or of larger color corrections than that predicted by spetral models. Our analysis also gives an upper limit on the distance to GS 1826-24 of d<4.0-5.5 kpc \xi_b^{-1/2}, where \xi_b is the degree of anisotropy of the burst emission.

💡 Research Summary

This paper presents a novel, distance‑ and anisotropy‑independent method for constraining the mass (M) and radius (R) of the neutron star in the low‑mass X‑ray binary GS 1826‑24, using sub‑Eddington type I X‑ray bursts. The authors exploit two complementary approaches. First, they compare the observed burst lightcurve with the theoretical model of Heger et al. (2007), which reproduces the recurrence time, energetics, and overall shape of the bursts in GS 1826‑24. By scaling the model peak luminosity to match the observed peak flux, they derive a ratio between the observed flux and model flux, F_obs/F_model ≈ 2.2 × 10⁻³³. This ratio, together with the assumed redshift (1+z = 1.26) used in the model, yields a distance‑independent relation (1+z)/f_c ≈ 1.19–1.28 for plausible color‑correction factors f_c = 1.4–1.5. Hence the redshift is constrained without any knowledge of the source distance or burst anisotropy.

The second approach focuses on the cooling tail of the bursts. The authors fit the evolution of the blackbody normalization (K) versus flux (F) with the atmosphere models of Suleimanov et al. (2011b). The data agree with the models for luminosities above roughly one‑third of the peak, but deviate at lower luminosities. By exploiting the model‑predicted relationship between K, F, the Eddington flux, and the apparent radius at infinity (R_∞), they obtain distance‑independent upper limits: R_∞ ≲ 9.0–13.2 km and M ≲ 1.2–1.7 M_⊙, assuming a solar‑abundance hydrogen photosphere and exploring a range of metallicities and surface gravities. These radius limits are notably smaller than those derived from photospheric‑radius‑expansion (PRE) bursts in other sources, suggesting either a sub‑solar hydrogen fraction in the photosphere or larger color‑correction factors than predicted by current atmosphere models.

The paper also discusses anisotropy of burst (ξ_b) and persistent (ξ_p) emission. Using geometric arguments for a thin accretion disk that intercepts a fraction of the burst radiation, they estimate ξ_b in the range 0.85–1.1 for plausible inclination angles (i < 70°). Since ξ appears only in the combination ξ^{1/2} d, the uncertainty in anisotropy translates directly into an uncertainty in distance. By keeping the analysis independent of d and ξ, they derive an upper limit on the distance: d ≲ 4.0–5.5 kpc · ξ_b^{‑1/2}.

Overall, the study demonstrates that even sub‑Eddington bursts, when combined with well‑matched theoretical lightcurves and modern atmosphere models, can provide stringent constraints on neutron‑star parameters without relying on uncertain distances or emission beaming. The authors suggest that further improvements in nuclear reaction networks, convection prescriptions, and atmosphere modeling could tighten these limits and help discriminate among competing equations of state for dense matter.