A model for the radio/X-ray correlation in three neutron star low-mass X-ray binaries 4U 1728-34, Aql X-1ad, and EXO 1745-248

Observationally, for neutron star low-mass X-ray binaries, so far, the correlation between the radio luminosity L_R and the X-ray luminosity L_X, i.e. L_R∝ L_X^{β }, has been reasonably well-established only in three sources 4U 1728-34, Aql X-1, and EXO 1745-248 in their hard state. The slope β of the radio/X-ray correlation of the three sources is different, i.e. β ∼ 1.4 for 4U 1728-34, β ∼ 0.4 for Aql X-1, and β ∼ 1.6 for EXO 1745-248. In this paper, for the first time we explain the different radio/X-ray correlation of 4U 1728-34, Aql X-1, and EXO 1745-248 with the coupled advection-dominated accretion flow (ADAF)-jet model, respectively. We calculate the emergent spectrum of the ADAF-jet model for L_X and L_R at different \dot{m} (\dot{m}=\dot{M}/\dot{M}_Edd), adjusting η (η ≡ \dot{M}_jet/\dot{M}, describing the fraction of the accreted matter in the ADAF transferred vertically forming the jet) to fit the observed radio/X-ray correlations. Then, we derive a fitting formula of η as a function of \dot{m} for 4U 1728-34, Aql X-1, and EXO 1745-248, respectively. If the relation between η and \dot{m} can be extrapolated down to a lower value of \dot{m}, we find that in a wide range of \dot{m}, the value of η in Aql X-1 is greater than that of in 4U 1728-34 and EXO 1745-248, implying that Aql X-1 may have a relatively stronger large-scale magnetic field, which is supported by the discovery of the coherent millisecond X-ray pulsation in Aql X-1.