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*Astron. Astrophys. 334, 1-10 (1998)*
## 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*
**Abstract**
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 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 to
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 by less than 2%.
**Key words:** gravitational
lensing
dark matter
*Send offprint requests to:* waerbeke@astro.obs-mip.fr
### Contents
© European Southern Observatory (ESO) 1998
Online publication: May 12, 1998
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