  Type Ia supernovae (SNe Ia), thermonuclear explosions of carbon-oxygen white
dwarfs (CO-WDs), are currently the best cosmological "standard candles", but
the triggering mechanism of the explosion is unknown. It was recently shown
that the rate of head-on collisions of typical field CO-WDs in triple systems
may be comparable to the SNe Ia rate. Here we provide evidence supporting a
scenario in which the majority of SNe Ia are the result of such head-on
collisions of CO-WDs. In this case, the nuclear detonation is due to a well
understood shock ignition, devoid of commonly introduced free parameters such
as the deflagration velocity or transition to detonation criteria. By using
two-dimensional hydrodynamical simulations with a fully resolved ignition
process, we show that zero-impact-parameter collisions of typical CO-WDs with
masses $0.5-1\,M_{\odot}$ result in explosions that synthesize $^{56}$Ni masses
in the range of $\sim0.1-1\,M_{\odot}$, spanning the wide distribution of
yields observed for the majority of SNe Ia. All collision models yield the same
late-time ($>60$ days since explosion) bolometric light curve when normalized
by $^{56}$Ni masses (to better than $30\%$), in agreement with observations.
The calculated widths of the $^{56}$Ni-mass-weighted-line-of-sight velocity
distributions are correlated with the calculated $^{56}$Ni yield, agreeing with
the observed correlation. The strong correlation, shown here for the first
time, between $^{56}$Ni yield and total mass of the colliding CO-WDs
(insensitive to their mass ratio), is suggestive as the source for the
continuous distribution of observed SN Ia features, possibly including the
Philips relation.
