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

Abstract

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≥ 49°. If we assume the accretion disc is steady-state where its radial-temperature profile goes as T(r)∝ r-3/4, we find an inclination of i=62°.5 ± 4°. However, the predicted ratio of the disc flux to the total flux in B (the `disc fraction') is larger than what is observed (≈0.55 compared with ≤0.3). If we use a flatter radial-temperature profile of the disc expected for strongly irradiated discs [T(r) ∝ r-3/7], then we find an inclination of i = 54° 6 and a disc fraction in B of ≈ 0.30. However, in this case the value of χ2 is much larger (48.4 with 36 degrees of freedom compared with 40.9 for the steady-state case). Adopting i=62°.5 ±4° and using a previous determination of the mass ratio (q=Mc/Mx=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 Mx=1.78 ± 0.23 M⊙ and the mass of the secondary star is Mc=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.