We investigate an unique accreting millisecond pulsar with X-ray eclipses , SWIFT J1749.4 - 2807 ( hereafter J1749 ) , and try to limit the binary system by various methods including that of the Roche lobe , the mass-radius relations of both a main sequence ( MS ) and a white dwarf ( WD ) companion stars , as well as the measured mass function of the pulsar .
The calculations are based on the assumption that the radius of the companion star has reached its Roche radius ( or at 90 % ) , but the pulsar ’ s mass has not been assumed to be a certain value .
Our results are as follows .
The companion star should be a MS. For the case that the radius equals to its Roche one , we have a companion star with mass M \simeq 0.51 M _ { \odot } and radius R _ { c } \simeq 0.52 R _ { \odot } , and the inclination angle is i \simeq 76.5 ^ { \circ } ; for the case that the radius reaches 90 % of its Roche one , we have M \simeq 0.43 M _ { \odot } , R _ { c } \simeq 0.44 R _ { \odot } and i \simeq 75.7 ^ { \circ } .
We also obtain the mass of J1749 , M _ { p } \simeq 1 M _ { \odot } , and conclude that the pulsar could be a quark star if the ratio of the critical frequency of rotation-mode instability to the Keplerian one is higher than \sim 0.3 .
The relatively low pulsar mass ( about \sim M _ { \odot } ) may also challenge the conventional recycling scenario for the origin and evolution of millisecond pulsars .
The results presented in this paper are expected to be tested by future observations .