We have computed , based on 17 infrared radial velocities , the first set of orbital elements for the M giant in the symbiotic binary V2116 Ophiuchi .
The giant ’ s companion is a neutron star , the bright X-ray source GX 1+4 .
We rule out the previously proposed period of 304 days , and instead , find an orbital period of 1161 days , by far the longest of any known X-ray binary .
The orbit has a modest eccentricity of 0.10 with an orbital circularization time of \lesssim 5 \times 10 ^ { 6 } years .
The large mass function of the orbit significantly restricts the mass of the M giant .
Adopting a neutron-star mass of 1.35 M _ { \sun } , the maximum mass of the M giant is 1.22 M _ { \sun } , making it the less massive star .
Spectrum synthesis analysis of several infrared spectral regions results in slightly subsolar abundances for most metals .
Carbon and nitrogen are in the expected ratio resulting from the red-giant first dredge-up phase .
The lack of ^ { 17 } O suggests that the M-giant has a mass less than 1.3 M _ { \sun } , consistent with our maximum mass .
The surface gravity and maximum mass of the M giant result in a radius of 103 R _ { \sun } , much smaller than its estimated Roche lobe radius .
Thus , the mass loss of the red giant is via a stellar wind .
These properties argue that the M giant is near the tip of the first-ascent giant-branch .
Although the M giant companion to the neutron star has a mass similar to the late-type star in low-mass X-ray binaries , its near-solar abundances and apparent runaway velocity are not fully consistent with the properties of this class of stars .
Thus , in many ways this symbiotic and X-ray binary system is unique , and various scenarios for its possible evolution are discussed .