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Astron. Astrophys. 334, 1-10 (1998)

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Scale dependence of the bias investigated by weak lensing

L. van Waerbeke

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, Postfach 1523, D-85740 Garching, Germany

Received 29 October 1997 / Accepted 17 February 1998


The statistical analysis of the lensing effects coupled with the statistical analysis of the number counts is a tool to probe directly the relation between the mass and the light. In particular, some properties of the bias parameter can be investigated. The correlation between the shear of a given population of galaxies, and the number counts of a different population of galaxies along the same line of sight is calculated for the linear and the non-linear power spectra of density fluctuations for different cosmologies. The estimator R defined as the ratio of this correlation and the variance of the number counts is inversely proportional to the bias parameter. The signal-to-noise ratio of R shows a significant decrease in the non-linear regime where the number of galaxies per smoothing area is small. At these scales, the noise is dominated by the intrinsic ellipticities of the galaxies and by the shot noise, the cosmic variance playing a minor role. Hence, only galaxy samples larger than one square degree may allow a precise determination of R. Unfortunately, R is highly dependent on the cosmological model, which makes a direct measure of the bias quite difficult. However, it is showed that Rb is independent on the power spectrum and the smoothing scale, thus R is a direct measure of the inverse of the bias times a function of the cosmological parameters. From R, a new estimator [FORMULA] is defined which is only sensible to the scale dependence of the bias. It is showed that with a sample of 25 square degrees, one can measure a scale variation of the bias larger than 20% in the [FORMULA] to [FORMULA] scale range, almost independently of the cosmological parameters, the redshift distribution of the galaxies, and the power spectrum, which affect the estimate of the variation of b from [FORMULA] by less than 2%.

Key words: gravitational lensing – dark matter

Send offprint requests to: waerbeke@astro.obs-mip.fr

© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998