Dynamics of Quadruple Systems Composed of Two Binaries: Stars, White Dwarfs, and Implications for Ia Supernovae

TL;DR

This paper studies the long-term dynamics of quadruple star systems with two binaries, revealing enhanced high-eccentricity events and implications for white dwarf mergers and Type Ia supernovae.

Contribution

It provides a detailed analysis of quadruple system dynamics at quadrupole and octupole order, highlighting their increased potential for high-eccentricity events and mergers compared to triples.

Findings

Over 30% of star-star quadruples reach high eccentricity within a Hubble time.

WD-WD merger rate is increased by a factor of 3.5-10 in quadruples.

Merger delay-time distribution follows approximately 1/t, impacting supernova progenitor models.

Abstract

[Abridged]We investigate the long-term secular dynamics and Lidov-Kozai(LK) eccentricity oscillations of quadruple systems composed of two binaries at quadrupole and octupole order in the perturbing Hamiltonian. We show that the fraction of systems reaching high eccentricities is enhanced relative to triple systems, over a broader range of parameter space. We show that this fraction grows with time, unlike triple systems evolved at quadrupole order. This is fundamentally because with their additional degrees of freedom, quadruple systems do not have a maximal set of commuting constants of the motion, even in secular theory at quadrupole order. We discuss these results in the context of star-star and white dwarf-white dwarf(WD) binaries, with emphasis on WD-WD mergers and collisions relevant to the Type Ia supernova problem. For star-star systems, we find that more than 30% of systems reach high eccentricity within a Hubble time, potentially forming triple systems via stellar mergers or close binaries. For WD-WD systems, taking into account general relativistic and tidal precession and dissipation, we show that the merger rate is enhanced in quadruple systems relative to triple systems by a factor of 3.5-10, and that the long-term evolution of quadruple systems leads to a delay-time distribution ~1/t for mergers and collisions. In GW-driven mergers of compact objects, we classify the mergers by their evolutionary patterns in phase space and identify a regime in ~8% of orbital shrinking mergers, where eccentricity oscillations occur on the general relativistic precession timescale, rather than the much longer LK timescale. Finally, we generalize previous treatments of oscillations in the inner binary eccentricity to eccentric mutual orbits. We assess the merger rate in quadruple and triple systems and the implications for their viability as progenitors of stellar mergers and SNe Ia.