White dwarf–white dwarf collisions in AGN discs via close encounters.

White dwarfs (WDs) in active galactic nucleus (AGN) discs might migrate to the inner radii of the discs and form restricted three-body systems with two WDs moving around the central supermassive black hole (SMBH) in close orbits. These systems could be dynamically unstable, which can lead to very close encounters or direct collisions. In this work, we use N -body simulations to study the evolution of such systems with different initial orbital separation p , relative orbital inclination Δ i , and SMBH mass M. It is found that close encounters of WDs occur mainly at |$1.1R_{\rm H} \lesssim p \lesssim 2\sqrt{3}R_{\rm H}$|⁠ , where R H is the mutual Hill radius. For p < 1.1 R H, the majority of WDs move in horseshoe or tadpole orbits, and only few of them with small initial orbital phase difference undergo close encounters. For p = 3.0 R H, WD–WD collisions occur in most of the samples within a time 105 P 1, and considerable collisions occur within a time t < 62 P 1 for small orbital radii, where P 1 is the orbital period. The peak of the closest separation distribution increases and the WD–WD collision fraction decreases with an increase in relative inclination. The closest separation distribution is similar in cases with different SMBH mass, but the WD–WD collision fraction decreases as the mass of SMBHs increases. According to our estimation, the event rate of cosmic WD–WD collisions in AGN discs is about 300 Gpc−3 yr−1, roughly 1 per cent of that of observed Type Ia supernovae. The corresponding electromagnetic emission signals can be observed through large surveys of AGNs. [ABSTRACT FROM AUTHOR]