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

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 Alfvén 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 Alfvén 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 Alfvén radius, we can estimate the magnetic fields of neutron star. The obtained lower/upper limits are consistent with the previous results.