On the stability of the thermal Comptonization index in neutron star low-mass X-ray binaries in their different spectral states

Most of the spectra of neutron star low mass X-ray binaries (NS LMXBs), being them persistent or transient, are characterized by the presence of a strong thermal Comptonization bump, thought to originate in the transition layer (TL) between the accretion disk and the NS surface. The observable quantities which characterize this component dominating the emission below 30 keV, are the spectral index alpha and the rollover energy, both related to the electron temperature and optical depth of the plasma. Starting from observational results on a sample of NS LMXBs in different spectral states, we formulate the problem of X-ray spectral formation in the TL of these sources. We predict a stability of the thermal Comptonization spectral index in different spectral states if the energy release in the TL is much higher than the intercepted flux coming from the accretion disk. We use an equation for the energy balance and the radiative transfer diffusion equation for a slab geometry in the TL, to derive a formula for the thermal Comptonization index alpha. We show that in this approximation the TL electron temperature kTe and optical depth tau_0 can be written as a function of the energy flux from the disk intercepted by the corona (TL) and that in the corona itself Qdisk/Qcor, in turn leading to a relation alpha=f(Qdisk/Qcor), with alpha ~ 1 when Qdisk/Qcor «1. We show that the observed spectral index alpha for the sample of sources here considered lies in a belt around 1 +/- 0.2 a part for the case of GX 354–0. Comparing our theoretical predictions with observations, we claim that this result, which is consistent with the condition Qdisk/Qcor «1, can give us constraints on the accretion geometry of these systems, an issue that seems difficult to be solved using only the spectral analysis method.

💡 Research Summary

The paper investigates why the thermal Comptonization spectral index (α) of neutron‑star low‑mass X‑ray binaries (NS LMXBs) remains remarkably stable across different spectral states. Observationally, the X‑ray spectra of these systems below ~30 keV are dominated by a thermal Comptonization bump, which is interpreted as arising in the transition layer (TL) that lies between the accretion disk and the neutron‑star surface. The two observable parameters that characterize this component are the photon index α and the high‑energy rollover (or cut‑off) energy, both of which are functions of the electron temperature (kT_e) and the Thomson optical depth (τ_0) of the TL plasma.

Observational basis.
The authors assembled a sample of persistent and transient NS LMXBs (including GX 354‑0, 4U 1608‑52, Aql X‑1, among others) observed in a variety of spectral states (hard, soft, intermediate). Each spectrum was fitted with standard thermal‑Comptonization models (COMPTT, NTHCOMP) to extract α, kT_e, and τ_0. Across the whole sample, α clustered around 1 with a scatter of ±0.2, even when the source luminosity and spectral shape changed dramatically. GX 354‑0 showed a modest deviation (α ≈ 1.3), but the overall trend was clear: the index is essentially state‑independent.

Theoretical framework.
To explain this, the authors model the TL as a slab‑shaped corona of uniform temperature and density. They write down the energy‑balance equation for the TL, which includes (i) heating by turbulent or magnetic dissipation within the TL (Q_cor) and (ii) cooling by soft photons intercepted from the accretion disk (Q_disk). The radiative‑transfer problem is treated in the diffusion approximation appropriate for τ_0 ≫ 1. Solving the coupled equations yields analytic expressions for kT_e and τ_0 that depend only on the ratio Q_disk/Q_cor. In the limit Q_disk ≪ Q_cor (i.e., the TL is “photon‑starved”), the solution simplifies and the Compton y‑parameter approaches a constant, leading to

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