Limits to the Mass and the Radius of the Compact Star in SAX J1808.4--3658 and Their Implications

We show that a survey of equations of state and observations of X-ray pulsations from SAX J1808.4-3658 give 2.27 solar mass as the upper limit of the compact star mass. The corresponding upper limit of the radius comes out to be 9.73 km. We also do a probabilistic study to estimate the lower limit of the mass of the compact star. Such a limit puts useful constraints on equations of state. We also discuss the implications of the upper mass limit for the the evolutionary history of the source, as well as the detection of it in radio frequencies. We envisage that the possible observation of radio-eclipse may be able to rule out several soft equation of state models, by setting a moderately high value for the lower limit of inclination angle.