A Circumbinary Disk Scenario For The Negative Orbital-Period Derivative Of The Ultracompact X-ray Binary 4u1820-303

It is generally thought that an ultracompact X-ray binary is composed with 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 an orbital-period derivative at a rate of $\dot{P}/P\sim1.1\times10^{-7}$ ${\rm yr^{-1}}$ if the mass transfer is fully driven by gravitational radiation. However, the recent analysis of the 16 ${\rm yr}$ data from \textit{Rossi X-ray Timing Explorer} and other historical records yielded a negative orbital-period derivative in the past $35$ yr. In this work, we propose an evolutionary circumbinary (CB) disk model to account for this anomalous orbital-period derivative. 4U 1820-30 was known to undergo superbust 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 $\sim10,000$ yr and $\sim10$% 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 the theoretical analysis and numerical simulation, we find that the required feed mass at the CB disk is approximately $\sim 10^{-8}$ ${\rm M_{\odot}}$.