ON THE DYNAMICS OF ULTRA COMPACT X-RAY BINARIES: 4U 1850-087, 4U 0513-40, AND M15 X-2

In this work, we extend our dynamical study of ultra compact X-ray binaries (UCXB) 4U 1820-30 from Prodan and Murray to three more UCXBs in globular clusters: 4U 1850-087, 4U 0513-40, and M15 X-2. These three UCXBs have orbital periods ≲ 20 minutes. Two of them, 4U 1850-087 and 4U 0513-40, have suspected luminosity variations of the order of ∼1 yr. There is insufficient observational data to make any statements regarding the long periodicity in the light curve of M15 X-2 at this point. The properties of these three systems are quite similar to 4U 1820-30, which prompt us to model their dynamics in the same manner. As in the case of 4U 1820-30, we interpret the suspected long periods as the period of small oscillations around a stable fixed point in the Kozai resonance. We provide a lower limit on the tidal dissipation factor Q, which is in agreement with results obtained for the case of 4U 1820-30