Thermonuclear (type Ia) supernovae are explosions in accreting white dwarfs, but the exact scenario leading to these explosions is still unclear. An important step to clarify this point is to understand the behaviour of accreting white dwarfs in close binary systems. The characteristics of the white dwarf (mass, chemical composition, luminosity), the accreted material (chemical composition) and those related with the properties of the binary system (mass accretion rate), are crucial for the further evolution towards the explosion. An analysis of the outcome of accretion and the implications for the growth of the white dwarf towards the Chandrasekhar mass and its thermonuclear explosion is presented.
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