On the Dynamics and Tidal Dissipation Rate of the White Dwarf in 4u 1820-30

Abstract

It has been suggested that the 170 day period in the light curve of the low mass X-ray binary 4U 1820-30 arises from the presence of a third body with a large inclination to the binary orbit. We show that this long period motion arises if the system is librating around the stable fixed point in a Kozai resonance. We demonstrate that mass transfer drives the system toward this fixed point, and calculate, both analytically and via numerical integrations, that the period of libration is of order 170 days when the mutual inclination is near the Kozai critical value. The non-zero eccentricity of the binary, combined with tidal dissipation, implies that the rate of change of the binary period would be slower than, or even of opposite sign to, that implied by standard mass transfer models. If the 170 day period results from libration, then, contrary to appearances, the orbital period of the inner binary is increasing with time; in that case, (e/0.009) 2 Q/k 2 2.5 × 10 9 , where k 2 ≈ 0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the inner binary. It appears unlikely that the observed negative period derivative results from the smaller than expected (but positive) value ofṖ combined with the previously suggested acceleration of the system in the gravitational field of the host globular cluster NGC 6624. The discrepancy between the observed and expected period derivative requires further investigation.

Formation of Dark Matter Tori Around Supermassive Black Holes via the Eccentric Kozai-Lidov Mechanism

“…The EKL mechanism can drive the DM particles that are initially in a near-polar configuration to very large eccentricities that may result in their accretion onto the BH. Depletion near the polar axis yields a torus-like configuration (as was noted for different configurations, e.g., Antonini et al 2010 andProdan et al 2014).…”

“…It has been shown that the Kozai-Lidov mechanism (and specifically the EKL) has important implications in different astrophysical settings, such as triple stars (e.g., Harrington 1969;Mazeh & Shaham 1979;Kiseleva et al 1998;Fabrycky & Tremaine 2007;Perets & Fabrycky 2009;Thompson 2010;Naoz et al 2013a;Prodan & Murray 2012;Shappee & Thompson 2013;Prodan et al 2013;Naoz & Fabrycky 2014) and extrasolar planetary systems with an additional distant companion (e.g., Holman et al 1997;Fabrycky & Tremaine 2007;Wu et al 2007;Takeda et al 2008;Naoz et al 2011aNaoz et al , 2012Li et al 2014b;Teyssandier et al 2013;Petrovich 2014). In addition, the Kozai-Lidov mechanism has been suggested to play an important role in both the growth of black holes (BHs) at the centers of dense stellar clusters and the formation of shortperiod binary BHs (Blaes et al 2002;Miller & Hamilton 2002;Wen 2003).…”

Black hole and neutron star mergers in galactic nuclei: the role of triples

“…To date, only one triple star system is known to exist in the dense environments characteristic of GCs (e.g. Prodan & Murray 2012). The system in question, called 4U 1820-30, lives near the centre of the GC NGC 6624.…”

Relativistic Binaries in Globular Clusters

“…4U 1820-30 is a WD-NS binary in the globular cluster NGC 6624 with a period of ∼ 685 seconds [447] and a factor-of-two luminosity variation with a period of ∼ 171 days [394, 73]. It has been shown that this system is probably a hierarchical triple [175] where the third body is in a Kosai resonance with the inner binary [491, 395]. The most recent work of Prodan and Murray [395] gives a detailed investigation of the nature of the Kosai resonance in 4U 1820-30 and a plausible dynamical history.…”

“…It has been shown that this system is probably a hierarchical triple [175] where the third body is in a Kosai resonance with the inner binary [491, 395]. The most recent work of Prodan and Murray [395] gives a detailed investigation of the nature of the Kosai resonance in 4U 1820-30 and a plausible dynamical history. However these authors state that a better understanding of both the long-term evolution of compact X-ray binaries and the potential of NGC 6624 are necessary to fully understand this system.…”