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Astron. Astrophys. 322, 807-816 (1997)

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3. The magnitude-limited sample

The highest probability of detecting a nova is attained during the visual maximum. Around this phase the visual luminosity [FORMULA] of the nova is approximately proportional to the bolometric luminosity [FORMULA]. 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 ([FORMULA]  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 [FORMULA] is proportional to the white dwarf mass (MacDonald 1983):

[EQUATION]

where [FORMULA] is the white dwarf mass and X is the hydrogen mass fraction. Neglecting the effect of the chemical composition, this equation predicts a bias in the sample of known classical novae (see Fig. 1) towards systems with large white dwarf masses since they can be detected in a larger volume. The number of detectable novae with an orbital period P in a magnitude-limited sample is given by the volume integral:

[EQUATION]

where r, [FORMULA] and [FORMULA] are the distance, the azimutal and the elevation angle, respectively, and n is the space density of novae. [FORMULA] = [FORMULA] is the distance corresponding to the limit in magnitude, [FORMULA], imposed by the observations. The systems under consideration in this study are bright enough to permit the period determination at quiescence. If the mean value for the absolute magnitude of novae at minimum ([FORMULA] =4.6, Bruch 1982b; [FORMULA] =4.3, Warner 1986) is considered, one finds that the maximum distance in our sample is small enough that Eq. (2) may be formulated in cylindrical coordinates, assuming a constant surface density of progenitors in the galactic disk. This is so because novae in the galactic bulge, where the nova density may be expected to depend on the galactocentric distance, do not contaminate our sample. If [FORMULA] is the surface density of novae, Eq. (2) may be written in the approximation of a thin disk ([FORMULA]):

[EQUATION]

with

[EQUATION]

yielding:

[EQUATION]

[FORMULA] may be related to the bolometric magnitude using the distance modulus and the bolometric correction:

[EQUATION]

where a is the mean interstellar absorption per unit of length. After some algebric manipulations, using Eq. (1) and Pogson's equation, one finds:

[EQUATION]

where [FORMULA] and [FORMULA] are constants. Eq. (7) may be solved numerically for [FORMULA]. In the case of negligible interstellar extinction Eq. (7) reduces to:

[EQUATION]

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 [FORMULA]) the limiting distance is well approximated by:

[EQUATION]

Assuming the interstellar extinction to be homogeneous in the volume occupied by the observed novae, we rewrite Eq. (8) as:

[EQUATION]

Inserting this expression in Eq. (5) and making use of Eq. (1), we finally get:

[EQUATION]

This equation constitutes the selection function [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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