Updated Orbital Ephemeris and Detection of Superhump Modulation in X-Ray Band for the Ultra-compact Low Mass X-Ray Binary 4U 1820-30

The 4U 1820-30 is an ultra-compact low-mass X-ray binary (LMXB) near the center of the globular cluster NGC 6624. Its negative orbital period derivative, observed from the phase evolution of its sinusoidal-like orbital variation, contradicts the positive value that was obtained from the theoretical prediction. In this paper, we present the analysis of the 4U 1820-30 orbital modulation from light curves obtained from the Neutron star Interior Composition ExploreR (NICER) observations from 2017 to mid-2022. Combined with historical records, the orbital derivative is measured from the orbital phase evolution between 1976 and 2002 is (P) over dot/P = (- 5.21 +/- 0.13) x 10(-8) yr(-1). No significant second order orbital period derivative is detected with a 2 sigma upper limit of vertical bar(sic)vertical bar < 5.48 x 10(-22) s s(-2). We discuss the possible intrinsic orbital period derivative of 4U 1820-30 and suggest that this binary system may have a significant mass outflow similar to some other LMXBs. In addition, a periodic modulation with a period of 691.6 +/- 0.7 s, which is consistent with the superhump period discovered in the far-ultraviolet band of the Hubble Space Telescope, was also detected in the X-ray light curves that were collected by NICER. We conclude that this modulation is probably caused by a period of 0.8 +/- 0.1 day apsidal precession of the accretion disk, similar to the SU UMa type dwarf novae and some LMXBs. However we cannot exclude the possibility that it is induced by a hierarchical third star that orbits around the binary system.