1 Introduction

Close double white dwarfs form an interesting population for a number of reasons. First they are binaries that have experienced at least two phases of mass transfer and thus provide good tests for theories of binary evolution. Second it has been argued that type Ia supernovae arise from merging double CO white dwarfs (Webbink 1984; Iben & Tutukov 1984). Thirdly close double white dwarfs may be the most important contributors to the gravitational wave signal at low frequencies, probably even producing an unresolved noise burying many underlying signals (Evans et al. 1987; Hils et al. 1990). A fourth reason to study the population of double white dwarfs is that in combination with binary evolution theories, the recently developed detailed cooling models for (low-mass) white dwarfs can be tested.

The formation of the population of double white dwarfs has been studied analytically by Iben & Tutukov (1986a, 1987) and numerically by Lipunov & Postnov (1988); Tutukov & Yungelson (1993, 1994); Yungelson et al. (1994); Han et al. (1995); Iben et al. (1997, hereafter ITY97), and Han (1998, hereafter HAN98). Comparison between these studies gives insight in the differences that exist between the assumptions made in different synthesis calculations.

Following the discovery of the first close double white dwarf (Saffer et al. 1988), the observed sample of such systems in which the mass of at least one component is measured has increased to 14 (Maxted & Marsh 1999; Maxted et al. 2000). This makes it possible to compare the models to the observations in more detail.

In this paper we present a new population synthesis for double white dwarfs, which is different from previous studies in three aspects. The first are some differences in the modelling of the binary evolution, in particular the description of a common envelope without spiral-in, in which the change in orbit is governed by conservation of angular momentum, rather than of energy (Sect. 2). The second new aspect is the use of detailed models for the cooling of white dwarfs (Sect. 4.3), which are important because it is the rate of cooling which to a large extent determines how long a white dwarf remains detectable in a magnitude-limited observed sample. The third new aspect is that we use different models of the star formation history (Sect. 5). Results are presented in Sect. 6 and discussed in Sect. 7. The conclusions are summarised in Sect. 8. In the Appendix some details of our population synthesis are described.