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Population synthesis for double white dwarfs I.Close detached systems

We model the population of double white dwarfs in the Galaxy and find a better agreement with observations compared to earlier studies, due to two modifications. The first is the treatment of the first phase of unstable mass transfer and the second the modelling of the cooling of the white dwarfs. A satisfactory agreement with observations of the local sample of white dwarfs is achieved if we assume that the initial binary fraction is ~ 50% and that the lowest mass white dwarfs (M < 0.3 Msun) cool faster than the most recently published cooling models predict. With this model we find a Galactic birth rate of close double white dwarfs of 0.05 yr^{-1}, a birth rate of AM CVn systems of 0.005 yr^{-1}, a merger rate of pairs with a combined mass exceeding the Chandrasekhar limit (which may be progenitors of SNe Ia) of 0.003 yr^{-1} and a formation rate of planetary nebulae of 1 yr^{-1}. We estimate the total number of double white dwarfs in the Galaxy as 2.5 10^8. In an observable sample with a limiting magnitude V_lim = 15 we predict the presence of ~855 white dwarfs of which ~220 are close pairs. Of these 10 are double CO white dwarfs of which one has a combined mass exceeding the Chandrasekhar limit and will merge within a Hubble time.