Hard-tail emission in the soft state of low-mass X-ray binaries and their relation to the neutron star magnetic field

Abstract

Average hard-tail X-ray emission in the soft state of nine bright Atoll low-mass X-ray binaries containing a neutron star (NS-LMXBs) are investigated by using the light curves of MAXI/GSC and Swift/BAT. Two sources (4U 1820$-$30 and 4U 1735$-$44) exhibit large hardness ratio (15--50 keV$/$2--10 keV: {\it HR} $>$ 0.1), while the other sources distribute at {\it HR} $\ltsim$ 0.1. In either case, {\it HR} does not depend on the 2--10 keV luminosity. Therefore the difference of {\it HR} is due to the 15--50 keV luminosity, which is Comptonized emission. The Compton cloud is assumed to be around the neutron star. The size of the Compton cloud would affect the value of {\it HR}. Although the magnetic field of NS-LMXB is weak, we could expect a larger Alfv\'{e}n radius than the innermost stable circular orbit or the neutron star radius in some sources. In such cases, the accretion inflow is stopped at the Alfv\'{e}n radius and would create relatively large Compton cloud. It would result in the observed larger Comptonized emission. By attributing the difference of the size of Compton cloud to the Alfv\'{e}n radius, we can estimate the magnetic fields of neutron star. The obtained lower/upper limits are consistent with the previous results.