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

TL;DR

This paper investigates the stability of the thermal Comptonization spectral index in neutron star low-mass X-ray binaries across different spectral states, linking it to accretion geometry and energy flux ratios.

Contribution

It introduces a theoretical model predicting a stable spectral index based on energy balance in the transition layer, supported by observational data.

Findings

Spectral index alpha remains around 1 +/- 0.2 in most sources.

The index stability correlates with a low ratio of disk to corona flux (Qdisk/Qcor).

The model constrains accretion geometry based on spectral index observations.

Abstract

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.