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

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5. The technical selection function

The last unknown quantity in Eq. (18) is [FORMULA], the selection function associated to the probability of measuring orbital periods in novae as a function of P. For obvious reasons eclipses in novae are easier to detect if the orbital period is short (while the probability for eclipses to occur increases with the mass ratio and thus on the mean with P). The same is true for orbital modulations. In this case another effect enhances the probability to detect short periods (in the optical range): In systems with small orbits the accretion disk is necessarily also small and faint. Asymmetric structures such as a hot spot can thus more easily cause detectable orbital modulations in the light curves than in long period systems with brighter disks.

For periods detected through radial velocity measurements, the situation is not as clear. Using Kepler's third law, a secondary star mass - period relation such as that given by Patterson (1984) and basic geometry, it is possible to derive an equation for the radial velocity amplitude [FORMULA] of the white dwarf which depends only on the orbital period and [FORMULA]. At a fixed orbital inclination [FORMULA] increases for a given primary mass roughly by a factor of 3 for periods between [FORMULA] and [FORMULA], implying easier detection of longer periods. Moreover at very short periods, the time required to obtain spectra with a sufficiently high S/N ratio may not be short against the orbital period, hampering easy detection. On the other hand, a short period can be detected in shorter, more easily realizable sections of continuous observations.

Currently, we cannot see an objective way to quantify the detection probability for a given period due to these technical selection effects. However, in view of the relatively few orbital periods detected through radial velocity measurements, we expect this probability to decrease with P. Lacking a better prescription, a simple parametrization will be used for the technical selection function [FORMULA]. We assume:

[EQUATION]

The parameter [FORMULA] will probably be a small positive number. We expect [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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