  Type Ia supernovae, the thermonuclear explosions of white dwarf stars
composed of carbon and oxygen, were instrumental as distance indicators in
establishing the acceleration of the universe's expansion. However, the physics
of the explosion are debated. Here we report a systematic spectral analysis of
a large sample of well observed type Ia supernovae. Mapping the velocity
distribution of the main products of nuclear burning, we constrain theoretical
scenarios. We find that all supernovae have low-velocity cores of stable
iron-group elements. Outside this core, nickel-56 dominates the supernova
ejecta. The outer extent of the iron-group material depends on the amount of
nickel-56 and coincides with the inner extent of silicon, the principal product
of incomplete burning. The outer extent of the bulk of silicon is similar in
all SNe, having an expansion velocity of ~11000 km/s and corresponding to a
mass of slightly over one solar mass. This indicates that all the supernovae
considered here burned similar masses, and suggests that their progenitors had
the same mass. Synthetic light curve parameters and three-dimensional explosion
simulations support this interpretation. A single explosion scenario, possibly
a delayed detonation, may thus explain most type Ia supernovae.
