All Tables

Table 1: Observed double white dwarfs discussed in this paper. The table shows for each system the orbital period $P_{\rm orb}$ , the orbital separation $a_{\rm orb}$ , the masses M₁ and M₂, the mass ratio q₂ = M₂/M₁, the estimated cooling age of the youngest white dwarf $\tau _2$ and the difference between the cooling ages of the components $\Delta \tau$ . M₁ is the mass of the oldest white dwarf and thus presumably the original primary. The errors on the periods are smaller than the last digit. The values for $a_{\rm orb}$ are calculated by the authors and meant to give an indication. References: (1) Saffer et al. (1988); (2) Bergeron et al. (1989); (3) Bragaglia et al. (1990); (4) Marsh (1995); (5) Moran et al. (1997); (6) Moran et al. (1999); (7) Maxted et al. (2000); (8) Bergeron & Liebert (2002); (9) Maxted et al. (2002a); (10) Maxted et al. (2002b); (11) Napiwotzki et al. (2002); (12) Karl et al. (2003a); (13) Karl et al. (2003b). Note: (a) WD 1704+481a is the close pair of a hierarchical triple. It seems unclear which of the two stars in this pair is the youngest (see the text).
Table 2: Narrowest ranges for $\gamma$ and $\alpha _{\rm ce}$ that contain at least one solution to the envelope-ejection scenario per observed system and their central values. The six different prescriptions are explained in the main text.
Table 3: Comparison of the different prescriptions used to reconstruct the observed double white dwarfs. The symbols +, $\sim$ and - mean that the model solutions are in good, moderate or bad agreement with the observations. The first of the two symbols in each column is based on the mass ratio only and the second includes the age difference. The method for obtaining the first symbol in each entry is described in Sect. 6.3, that for the second symbol in Sect. 6.4. The symbols in the headers of the columns labelled 1-6 are explained in the main text. The columns for $\gamma _{\rm a}\gamma _{\rm d}$ and $\gamma _{\rm d}\gamma _{\rm d}$ were left out because they do not contain any solutions. The last two columns show the optimum result and the prescriptions that give this result (1-6). For the different prescriptions we demanded that $1.46\!<\!\gamma_{\rm s}\!<\!1.79$ , $0.90\!<\!\gamma_{\rm a}\!<\!1.10$ , $0.90\!<\!\gamma_{\rm d}\!<\!1.10$ and $0.80\!<\!\alpha_{\rm ce}\!<\!1.20$ .
Table 4: Results for the various evolution scenarios for double white dwarfs with two unstable mass-transfer episodes. The range of observed $\Delta \tau$ is the observed cooling-age difference $\pm~50\%$ . Columns labelled 1 through 6 give the number of model solutions for each scenario followed by the range in age difference of these solutions in Megayears. The columns with $\gamma _{\rm a}\gamma _{\rm d}$ and $\gamma _{\rm d}\gamma _{\rm d}$ were left out, because they do not contain any solutions. In addition to a value for $\gamma$ or $\alpha$ in the desired ranges (see Table 3), we demand that $q_{\rm 1i} > 1.03$ .
Table 5: Selected model solutions for the double envelope-ejection scenario. This table is an excerpt of the total list of 122 entries. The first nine columns show the number of the entry, the double white dwarf that the model is a solution for, the prescription used, the two envelope-ejection parameters, the age difference of the two components as observed and in the model ( $\Delta \tau$ ) in Myr, the relative difference between the observed and model age difference, defined as $\Delta(\Delta\tau) \equiv \left\vert\frac{\Delta\tau_{\rm mod} - \Delta\tau_{\rm obs}}{\Delta\tau_{\rm obs}}\right\vert$ in %, the time of the formation of the double white dwarf since the ZAMS ( $\tau _2$ ) in Gyr. The last nine columns list binary parameters: the initial (ZAMS) masses, mass ratio and orbital period, the intermediate mass ratio and period and the final masses and period.
Table 6: Selected model solutions for the double envelope-ejection scenario. This table is the total list of which an excerpt can be found as Table 5 in the article. The first nine columns show the number of the entry, the double white dwarf that the model is a solution for, the prescription used, the two envelope-ejection parameters, the age difference of the two components as observed and in the model ( $\Delta \tau$ ) in Myr, the relative difference between the observed and model age difference, defined as $\Delta(\Delta\tau) \equiv \left\vert\frac{\Delta\tau_{\rm mod} - \Delta\tau_{\rm obs}}{\Delta\tau_{\rm obs}}\right\vert$ in %, the time of the formation of the double white dwarf since the ZAMS ( $\tau _2$ ) in Gyr. The last nine columns list binary parameters: the initial (ZAMS) masses, mass ratio and orbital period, the intermediate mass ratio and period and the final masses and period.