Population synthesis of triple systems in the context of mergers of carbon–oxygen white dwarfs

Abstract

Hierarchical triple systems are common among field stars yet their long-term evolution is poorly understood theoretically. In such systems Kozai cycles can be induced in the inner binary system during which the inner orbit eccentricity and the inclination between both binary orbits vary periodically. These cycles, combined with tidal friction and gravitational wave emission, can significantly affect the inner binary evolution. To investigate these effects quantitatively we perform a population synthesis study of triple systems and focus on evolutionary paths that lead to mergers of carbon–oxygen (CO) white dwarfs (WDs), which constitute an important candidate progenitor channel for Type Ia supernovae (SNe Ia). We approach this problem by Monte Carlo sampling from observation-based distributions of systems within the primary mass range 1.0–6.5 M⊙ and inner orbit semimajor axes a1 and eccentricities e1 satisfying a1(1 − e21) > 12 au, i.e. non-interacting in the absence of a tertiary component. We evolve these systems by means of a newly developed algorithm that couples secular triple dynamics with an existing binary population synthesis code. We find that the tertiary significantly alters the inner binary evolution in about 24 per cent of all sampled systems. In particular, we find several channels leading to CO WD mergers. Amongst these is a novel channel in which a collision occurs in wide inner binary systems as a result of extremely high eccentricities induced by Kozai cycles. With assumptions on which CO WD mergers lead to a SN Ia explosion we estimate the SNe Ia delay time distribution resulting from triples and compare to a binary population synthesis study and to observations. Although we find that our triple rate is low, we have determined a lower limit of the triple-induced SNe Ia rate and further study is needed that includes triples with initially tighter inner orbits.