The optical light curves of Cygnus X-2 (V1341 Cyg) and the mass of its neutron star

We present U, B and V light curves (taken from the literature) of the low-mass X-ray binary Cygnus X-2. We show that the most significant photometric periods seen in the B and V light curves are consistent with half of the orbital period found from spectroscopy (P = 9.8444 d). The 'lower envelopes' of the light curves folded on the orbital period are ellipsoidal (i.e. they have two maxima and two minima per orbital cycle). We fit an ellipsoidal model to the lower envelopes of the B and V light curves to derive inclination constraints. This model includes light from an accretion disc, and accounts for eclipses and X-ray heating. Using the extreme assumption that there is no disc light, we derive a lower limit on the inclination of i greater than or equal to 49 degrees. If we assume the accretion disc is steady-state where its radial-temperature profile goes as T(r) proportional to r(-3/4); we find an inclination of i = 62.degrees 5 +/- 4 degrees. However, the predicted ratio of the disc flux to the total flux in B (the 'disc fraction') is larger than what is observed (approximate to 0.55 compared with less than or equal to 0.3). If we use a flatter radial-temperature profile of the disc expected for strongly irradiated discs [T(r) proportional to r(-3/7)], then we find an inclination of i = 54.degrees 6 and a disc fraction in B of approximate to 0.30. However, in this case the value of chi(2) is much larger (48.4 with 36 degrees of freedom compared with 40.9 for the steady-state case). Adopting i = 62.degrees 5 +/- 4 degrees and using a previous determination of the mass ratio (q = M(c)/M(x) = 0.34 +/- 0.04) and the optical mass function [f(M) = 0 69 +/- 0.03 M.], we find that the mass of the neutron star is M(x) = 1.78 +/- 0.23 M. and the mass of the secondary star is M(c) = 0.60 +/- 0.13 M.. We derive a distance of d = 7.2 +/- 1.1 kpc, which is significantly smaller than a recent distance measurement of d = 11.6 +/- 0.3 kpc derived from an observation of a type I radius-expansion X-ray burst, but consistent with earlier distance estimates.