Rate of WD-WD head-on collisions in isolated triples is too low to explain standard type Ia supernovae

Context. Type Ia supernovae (Ia-SNe) are thought to arise from the thermonuclear explosions of white dwarfs (WDs). The progenitors of such explosions are still highly debated; in particular the conditions leading to detonations in WDs are not well understood in most of the suggested progenitor models. Nevertheless, direct head-on collisions of two WDs were shown to give rise to detonations and produce Ia-SNe - like explosions, and were suggested as possible progenitors. Aims. The rates of such collisions in dense globular clusters are far below the observed rates of type Ia SNe, but it was suggested that quasi-secular evolution of hierarchical triples could produce a high rate of such collisions. With regular secular evolution, the expected Ia-SNe rate from isolated triples is orders of magnitude below the observed rate. Here we aim to test if the rate of WD collisions in triples can be significantly enhanced if quasi-secular evolution is taken into account. Methods. We used detailed triple stellar evolution populations synthesis models coupled with dynamical secular evolution to calculate the rates of WD-WD collisions in triples and their properties. We explored a range of models with different realistic initial conditions and derived the expected SNe total mass, mass-ratio and delay time distributions for each of the models. Results. We find that the SNe rate from WD-WD collisions is of the order of 0.1% of the observed Ia-SNe rate across all our models, and the delay-time distribution is almost uniform in time, and is inconsistent with observations. Conclusions. We conclude that SNe from WD-WD collisions in isolated triples can at most provide for a small fraction of Ia-SNe, and can not serve as the main progenitors of such explosions.