A Circumbinary Disk Scenario for the Negative Orbital-period Derivative of the Ultra-compact X-Ray Binary 4U 1820-303

It is generally thought that an ultra-compact X-ray Binary is composed of a neutron star and a helium white dwarf donor star. As one of the most compact binaries, 4U 1820-303 in globular cluster NGC 6624 was predicted to have an orbital period of $\dot{P}/P\sim 1.1\times {10}^{-7}$ yr⁻¹ if the mass transfer is fully driven by gravitational radiation. However, recent analysis of 16 year data from Rossi X-ray Timing Explorer and other historical records has yielded a negative orbital-period derivative in the past 35 years. In this work, we propose an evolutionary circumbinary (CB) disk model to account for this anomalous orbital-period derivative. 4U 1820-30 is known to undergo superburst events caused by runaway thermal nuclear burning on the neutron star. We assume that, for a small fraction of the superbursts, part of the ejected material may form a CB disk around the binary. If the recurrence time of such superbursts is ∼10,000 year and ∼10% of the ejected mass feeds a CB disk, the abrupt angular-momentum loss causes a temporary orbital shrink, and the donor's radius and its Roche lobe radius do not keep in step. Driven by mass transfer and angular-momentum loss, the binary would adjust its orbital parameters to recover a new stable stage. Based on theoretical analysis and numerical simulation, we find that the required feed mass at the CB disk is approximately ∼10⁻⁸ M _⊙.