Measurements of accretion disc corona size in LMXB: consequences for Comptonization and LMXB models

We present results of measurements of the radial extent of the accretion disc corona in low-mass X-ray binaries (LMXB), i.e. of the radial extent of the thin, hot ADC above the accretion disc. These results prove conclusively the extended nature of the ADC, with radial extent varying from 20 000 km in the faintest sources to 700 000 km in the brightest sources, a substantial fraction of the accretion disc radius (typically 15 per cent). This result rules out the Eastern model for LMXB which is extensively used, in which the Comptonizing region is a small central region. The ADC size depends strongly on the 1-30 keV source luminosity via a simple relationship r(ADC) = L0.88+/-0.16 at 99 per cent confidence, which is close to a simple dependence r(ADC) proportional to L. We also present limited evidence that the ADC size agrees with the Compton radius r(C), or maximum radius for hydrostatic equilibrium. Thus, the results are consistent with models in which an extended ADC is formed by illumination of the disc by the central source. However, the dependence on luminosity may reflect the known decrease of coronal temperature as the source luminosity increases, leading to an increase of r(C). The extended nature of the ADC means that the seed photons for Comptonization must consist of emission from the disc to the same radial extent as the corona, providing copious supplies of soft seed photons. We thus demonstrate the importance of the size of the ADC to the correct description of Comptonization, and we derive the Comptonized spectrum of an LMXB based on the thermal Comptonization of these seed photons and show that this differs fundamentally from that of the Eastern model, which assumes a cut-off in the spectrum below I keV. Finally, we argue that our results are inconsistent with the assumption often made that the X-ray emission of accreting black holes and neutron stars has a common mechanism depending on the properties of the accretion flow only.