## 3. The magnitude-limited sampleThe highest probability of detecting a nova is attained during the visual maximum. Around this phase the visual luminosity of the nova is approximately proportional to the bolometric luminosity . This is a good first order approximation since the nova reaches the visual maximum when the photospheric radius is largest and the effective temperature permits hydrogen to recombine ( K) leading to the same bolometric correction for all novae at this phase. It has been shown that many novae undergo a short-lived super-Eddington phase at bolometric maximum [e.g. V1500 Cyg (Wu & Kester 1977), V1668 Cyg (MacDonald 1983)]. For the sake of simplicity it will be considered here that it is short enough to be unimportant for our statistical purposes, neither lasting long enough nor brightening the system enough to considerably increase the probability of detection of the eruption. Therefore, we assume that the magnitude at maximum is determined by the Eddington luminosity. The fact that the slope of the amplitude-period relation for the novae is identical to that of outbursting dwarf novae and can thus be explained by a dependence of intrinsic brightness in quiescence on the period (see Appendix A) indicates that the luminosity at maximum is almost independent of the orbital period and means that the white dwarf mass distribution of novae is - if at all - only a weak function of the orbital period. The Eddington luminosity is proportional to the white dwarf mass (MacDonald 1983): where is the white dwarf mass and where with yielding: may be related to the bolometric magnitude using the distance modulus and the bolometric correction: where where and are constants. Eq. (7) may be solved numerically for . In the case of negligible interstellar extinction Eq. (7) reduces to: Of course, in the general case this approximation is not valid. However, Ritter (1986) has shown that for a wide range of interstellar extinction (0.7 ) the limiting distance is well approximated by: Assuming the interstellar extinction to be homogeneous in the volume occupied by the observed novae, we rewrite Eq. (8) as: Inserting this expression in Eq. (5) and making use of Eq. (1), we finally get: This equation constitutes the selection function . © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |