Cygnus X-2 is one of the brightest and longest known X-ray sources. We
present high-resolution optical spectroscopy of Cyg X-2 obtained over
4 yr, which gives an improved mass function of 0.69 +/- 0.03 M. (1 si
gma). In addition, we resolve the rotationally broadened absorption fe
atures of the secondary star for the first time, deriving a rotation s
peed of upsilon sin i = 34.2 +/- 2.5 km s(-1) (1 sigma), which leads t
o a mass ratio of q = M-c/M-X = 0.34 +/- 0.04 (1 sigma, assuming a tid
ally locked and Roche lobe-filling secondary). Hence, with the lack of
X-ray eclipses (i.e., less than or similar to 73 degrees) we can set
firm 95% confidence lower limits to the neutron star mass of M-X > 1.2
7 M. and to the companion star mass of M-c > 0.39 M.. However, by addi
tionally requiring that the companion must exceed 0.75 M. (as required
theoretically to produce a steady low-mass X-ray binary), then M-X >
1.88 M. and i < 61 degrees (95% confidence lower and upper limit, resp
ectively), thereby making Cyg X-2 the highest mass neutron star measur
ed to date. If confirmed, this would set significant constraints on th
e equation of state of nuclear matter.