GRAVITATIONAL-INSTABILITY AND 2-D GALAXY SURVEYS

Perturbation theory allows to relate the variance of cosmological dens ity fluctuations on a given spatial smoothing scale to their gravitati onally induced skewness. This prediction can be used for observational tests of the gravitational instability theory and as a constraint on models with strongly non-Gaussian initial conditions. Because of a hug e number of objects contained in angular surveys and absence of uncert ainties connected with the redshift-distance relation, a very importan t goal is to obtain results applicable to 2-D surveys of galaxies. Usi ng the small angle approximation, we calculate variance and skewness o f the projected density field. Spatial smoothing is performed by a 2-D counterpart of a top-hat filter, which is a cone filter. We obtain a semi-analytic formula for skewness for arbitrary power spectra of dens ity fluctuations thus extending the results of Bernardeau (1995) appli cable for pure power-law power spectra only. The observed power spectr um in the APM survey cannot be fitted by a pure power-law. Consequentl y, our formula with an observationally motivated model for the power s pectrum allows to obtain much better agreement between the predicted v alue of skewness and that measured in the APM survey.