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 days ) .
The “ lower envelope ” 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 \geq 49 ^ { \circ } .
If we assume the accretion disc is steady-state where its radial temperature profile goes as T ( r ) \propto r ^ { -3 / 4 } , we find an inclination of i = 62.5 ^ { \circ } \pm 4 ^ { \circ } .
However , the predicted ratio of the disc flux to the total flux in B ( the “ disc fraction ” ) is larger than what is observed ( \approx 0.55 compared to \leq 0.3 ) .
If we use a flatter radial temperature profile of the disc expected for strongly irradiated discs ( T ( r ) \propto r ^ { -3 / 7 } ) , then we find an inclination of i = 54.6 ^ { \circ } and a disc fraction in B of \approx 0.30 .
However , in this case the value of \chi ^ { 2 } is much larger ( 48.4 with 36 degrees of freedom compared to 40.9 for the steady-state case ) .
Adopting i = 62.5 \pm 4 ^ { \circ } and using a previous determination of the mass ratio ( q = M _ { c } / M _ { x } = 0.34 \pm 0.04 ) and the optical mass function ( f ( M ) = 0.69 \pm 0.03 M _ { \sun } ) , we find that the mass of the neutron star is M _ { x } = 1.78 \pm 0.23 M _ { \odot } and the mass of the secondary star is M _ { c } = 0.60 \pm 0.13 M _ { \odot } .
We derive a distance of d = 7.2 \pm 1.1 kpc , which is significantly smaller than a recent distance measurement of d = 11.6 \pm 0.3 kpc derived from an observation of a type I radius-expansion X-ray burst , but consistent with earlier distance estimates .