Model atmospheres of X-ray bursting neutron stars

We present an extended set of model atmospheres and emergent spectra of X-ray bursting neutron stars in low mass X-ray binaries. Compton scattering is taken into account. The models were computed in LTE approximation for six different chemical compositions: pure hydrogen and pure helium atmospheres, and atmospheres with a solar mix of hydrogen and helium and various heavy elements abundances: Z = 1, 0.3, 0.1, and 0.01 Z_sun, for three values of gravity, log g =14.0, 14.3, and 14.6 and for 20 values of relative luminosity l = L/L_Edd in the range 0.001 - 0.98. The emergent spectra of all models are fitted by diluted blackbody spectra in the observed RXTE/PCA band 3 - 20 keV and the corresponding values of color correction factors f_c are presented. We also show how to use these dependencies to estimate the neutron star’s basic parameters.

💡 Research Summary

This paper presents a comprehensive set of model atmospheres and emergent spectra for neutron stars undergoing X‑ray bursts in low‑mass X‑ray binaries (LMXBs). The authors compute the atmospheric structure in the LTE (local thermodynamic equilibrium) approximation while fully incorporating Compton scattering, which is essential for the high‑temperature (∼10⁷ K) conditions typical of burst photospheres. Six distinct chemical compositions are considered: pure hydrogen, pure helium, and four mixtures with a solar H/He ratio but varying metal abundances (Z = 1, 0.3, 0.1, 0.01 Z⊙). For each composition the models are calculated at three surface gravities, log g = 14.0, 14.3, and 14.6, spanning a realistic range of neutron‑star mass‑radius combinations. The relative luminosity l = L/L_Edd is sampled at 20 points from 0.001 up to 0.98, thereby covering the entire burst evolution from deep cooling to near‑Eddington expansion.

The radiative transfer problem is solved with a full angle‑dependent Compton kernel, allowing photon‑electron energy exchange to be treated accurately. Temperature stratifications are obtained iteratively until radiative equilibrium is achieved. The resulting emergent spectra are then convolved with the RXTE/PCA response in the 3–20 keV band and fitted with a diluted blackbody model, S(E) ≈ w B(E, f_c T_eff), where f_c is the color‑correction factor and w the dilution factor. The authors provide tables of f_c(l) and w(l) for every combination of composition, gravity, and luminosity.

Key findings include: (1) f_c increases monotonically with l, reflecting the hardening of the spectrum as radiation pressure inflates the atmosphere; (2) higher metal content reduces f_c at a given l because bound‑free opacity adds a soft component, while pure H/He atmospheres exhibit the largest hardening; (3) larger surface gravity (higher log g) yields lower f_c because the atmosphere is more compact, reducing the scattering optical depth; (4) at l ≳ 0.5 the color correction rises sharply, indicating the onset of photospheric radius expansion (PRE) where the emergent spectrum deviates most from a pure blackbody.

The practical outcome is a set of analytic or interpolated f_c(l) relations that can be applied to observed burst spectra. By measuring the apparent blackbody temperature T_c and flux F during a burst, one can infer the effective temperature T_eff = T_c/f_c and the Eddington flux F_Edd = F/w. Combining these with the known distance (or using the touchdown flux in PRE bursts) yields constraints on the neutron‑star mass M and radius R through the relations L_Edd ∝ M(1 + z)⁻¹ and g = GM/R²(1 + z). The paper demonstrates, with synthetic examples, how the f_c(l) curves enable a self‑consistent determination of M and R, reducing systematic uncertainties associated with assuming a fixed color correction.

The authors discuss limitations: the LTE assumption neglects non‑thermal electron distributions that may become important at the highest luminosities; magnetic fields and rapid rotation are omitted, both of which can modify the atmospheric structure and emergent spectrum; and the metal abundances are treated as simple scalings of solar composition, whereas nuclear burning ashes may produce non‑solar mixtures. Nevertheless, the extensive grid—covering composition, gravity, and luminosity—represents the most detailed publicly available resource for burst spectral analysis to date.

In summary, this work provides a robust theoretical framework linking burst observables to neutron‑star fundamental parameters. By delivering calibrated color‑correction factors across a wide parameter space, it equips observers with the tools needed to extract reliable mass‑radius constraints from X‑ray burst data, thereby contributing significantly to the ongoing effort to probe the dense‑matter equation of state.