Below we present in detail the resulting 26 Al production for two sets of population models. The sets differ only in the assumed initial mass ratio distribution in main-sequence binaries. Set A assumes , with , and predicts a value for the present CV formation rate (Politano 1996a). This corresponds to a total number of CVs in the Galaxy of . Set B was obtained using CV formation calculations by deKool (1992) where the component masses in main-sequence binaries were picked independently from the same IMF. The resulting present CV birthrate is , which corresponds to CVs in the Galaxy. For each set, population models were computed for 4 different values of the mixing parameter : = 1, 1.2, , and 2.
Models of set B produce roughly ten times as many CVs as models of set A. This is understood easily from the fact that the progenitor main-sequence binaries are required to have a mass ratio, , less than in order to avoid an unstable configuration at turn-on of mass transfer as a CV (Politano 1996a). Since set A strongly favors equal component masses (), fewer binaries in the corresponding population are successful in becoming CVs. The two sets represent rather extreme cases as far as the degree of correlation of the component masses is concerned (strong correlation [set A] versus no correlation at all [set B]); generally the total number of CVs in a population increases with decreasing (de Kool 1992; Politano 1994).
The models in sets A and B are identical to models pm3 and pm5 in Kolb (1993a), respectively. We note that, from an evolutionary point of view, models with are somewhat extreme, since the WD loses twice as much mass through nova outbursts as it gains via accretion and therefore is eroded substantially (e.g., the WD in a CV born at an orbital period of 6 hr would have lost when the system detaches at the upper edge of the period gap).
For three values of (, , and 2), we plot the amount of 26 Al produced by ONeMg novae as a function of the critical WD mass, , for population models of sets A and B using the production function computed in Sect. 2.1 in Figs. 2 and 3, respectively. (As we noted previously, a negligible amount of 26 Al is produced for .)
Finally, Fig. 4 shows how varies in models of set B with the free parameters and when the parameterized 26 Al production function introduced in Sect. 2.2 is used. For this purpose we compute for the value of which results in (here ). Plotted in Fig. 4 is the change of relative to as a function of . is the value of for the "standard model" with and . Recall that (6) and (7) with and closely mimic the results obtained with (3) and (4), so that the normalization to M0 allows for an easy comparison with the production function in Sect. 2.1. The solid curves refer to models with and to (from bottom to top), the dashed curves to models with and (from bottom to top), respectively. Necessarily, the lines for intersect at , .
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998