# Extreme close approaches in hierarchical triple systems with comparable masses

## TL;DR

This study uses N-body simulations to analyze close approaches in hierarchical triple systems with comparable masses, revealing conditions that could lead to white dwarf collisions relevant for type Ia supernovae.

## Contribution

It provides an analytical prediction for close approaches in stable hierarchical triples with equal masses and quantifies collision likelihoods based on system parameters.

## Key findings

- Close approaches can be predicted from initial conditions.
- The rate of close approaches scales linearly with tertiary mass.
- Collision probability is about 1% for typical M-dwarf tertiaries.

## Abstract

We study close approaches in hierarchical triple systems with comparable masses using full N-body simulations, motivated by a recent model for type Ia supernovae involving direct collisions of white dwarfs (WDs). For stable hierarchical systems where the inner binary components have equal masses, we show that the ability of the inner binary to achieve very close approaches, where the separation between the components of the inner binary reaches values which are orders of magnitude smaller than the semi-major axis, can be analytically predicted from initial conditions. The rate of close approaches is found to be roughly linear with the mass of the tertiary. The rate increases in systems with unequal inner binaries by a marginal factor of $\lesssim 2$ for mass ratios ${0.5<m_1/m_2<1}$ relevant for the inner white-dwarf binaries. For an average tertiary mass of $\sim 0.3 M_{\odot}$ which is representative of typical M-dwarfs, the chance for clean collisions is $\sim 1$% setting challenging constraints on the collisional model for type Ia's.