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

Context. Most of the spectra of neutron star low-mass X-ray binaries (NS LMXBs), whether they are persistent or transient, are characterized by the presence of a strong thermal Comptonization bump, which is thought to originate in the transition layer (TL) between the accretion disk and the NS surface. The observable quantities that characterize this component, which is 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. Aims. 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. Methods. 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 kT(e) 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, Q(disk)/Q(cor). Because the spectral index a depends on kT(e) and tau(0), this in turn leads to a relation alpha = f (Q(disk)/Q(cor)), with alpha similar to 1 when Q(disk)/Q(cor) << 1. Results. We show that the observed spectral index a for the sample of sources here considered lies in a belt around 1 +/- 0.2 apart for the case of GX 354-0. Comparing our theoretical predictions with observations, we claim that this result, which is consistent with the condition Q(disk)/Q(cor) << 1, can give us constraints on the accretion geometry of these systems, an issue that seems difficult to be solved with only the spectral analysis method.