Dynamical Modeling of CXOGBS J175553.2-281633: A 10 Hour Long Orbital Period Cataclysmic Variable

We present modeling of the long term optical light curve and radial velocity curve of the binary stellar system CXOGBS J175553.2-281633, first detected in X-rays in the \textit{Chandra} Galactic Bulge Survey. We analyzed 7 years of optical I-band photometry from OGLE and found long term variations from year to year. These long term variations can be explained with either an accretion disk of changing shape or luminosity, or a spotted secondary star. The phased light curve has a sinusoidal shape, which we interpret as being due to ellipsoidal modulations. We improve the orbital period to be $P = 10.34488(6)$ h with a time of inferior conjunction of the secondary $T_0 = {\rm HJD\ } 2455260.8204(8)$. Moreover, we collected 37 spectra over 6 non-consecutive nights. The spectra show evidence for a K7 secondary donor star, from which we obtain a semi-amplitude for the radial velocity curve of $K_2 = 161 \pm 6 $ km s$^{-1}$. Using the light curve synthesis code {\tt XRbinary}, we derive the most likely orbital inclination for the binary of $i = 63.0\pm0.7$ deg, a primary mass of $M_1 = 0.83 \pm 0.06$ M$_\odot$, consistent with a white dwarf accretor, and a secondary donor mass of $M_2 = 0.65 \pm 0.07$ M$_\odot$, consistent with the spectral classification. Therefore, we classify the source as a cataclysmic variable star with a long orbital period.