Accelerating Compact Object Mergers in Triple Systems with the Kozai Resonance: A Mechanism for "Prompt" Type Ia Supernovae, Gamma-Ray Bursts, and Other Exotica

White dwarf-white dwarf (WD-WD) and neutron star-neutron star (NS-NS) mergers may produce Type Ia supernovae and gamma-ray bursts (GRBs), respectively. A general problem is how to produce binaries with semi-major axes small enough to in significantly less than the Hubble time (t_H), and thus accommodate the observation that these events closely follow episodes of star formation. I explore the possibility that such systems are not binaries at all, but actually coeval, or dynamical formed, triple systems. The tertiary induces Kozai oscillations in the inner binary, driving it to high eccentricity, and reducing its gravitational wave (GW) merger timescale. This effect significantly increases the allowed range of binary period P such that the merger time is t_merge < t_H. In principle, Chandrasekhar-mass binaries with P ~ 300 days can merge in < t_H if they contain a prograde solar-mass tertiary at high enough inclination. For retrograde tertiaries, the maximum P such that t_merge < t_H is yet larger. In contrast, P < 0.3 days is required in the absence of a tertiary. I discuss implications of these findings for the production of transients formed via compact object binary mergers. Based on the statistics of solar-type binaries, I argue that many such binaries should be in triple systems affected by the Kozai resonance. If true, expectations for the mHz GW signal from individual sources, the diffuse background, and the foreground for GW experiments like LISA are modified. This work motivates future studies of triples systems of A, B,and O stars, and new types of searches for WD-WD binaries in triple systems.