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 } \propto L _ { X } ^ { \beta } , 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 \beta of the radio/X-ray correlation of the three sources is different , i.e. , \beta \sim 1.4 for 4U 1728-34 , \beta \sim 0.4 for Aql X-1 , and \beta \sim 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 ( 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 \eta ( \eta \equiv \dot { M } _ { jet } / \dot { M } , describing the fraction of the accreted matter in the ADAF transfered vertically forming the jet ) to fit the observed radio/X-ray correlations .
Then we derive a fitting formula of \eta as a function of \dot { m } for 4U 1728-34 , Aql X-1 and EXO 1745-248 respectively .
If the relation between \eta 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 \eta 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 .