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Astron. Astrophys. 358, 30-44 (2000)

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7. Conclusion

We have demonstrated the existence of a significant correlation between galaxy ellipticities from 0.5 to 3.5 arc-minutes scales. The signal has the amplitude and the angular dependence expected from theoretical predictions of weak lensing produced by large-scale structures in the universe. We have tested the possible contribution of systematic errors to the measured signal; in particular we discussed three potential sources of spurious alignment of galaxies: overlapping isophotes of very close galaxies, star anisotropy and CCD line/column alignment. The first of these systematics is easy to deal with, simply by removing close pairs, although we may have decreased the signal slightly by removing them. The star anisotropy seems to be very well controlled, in part due to the fact that the bias adds quadratically with the signal. Moreover, in the absolute sense, the bias does not exceed a fraction of 1 percent, which is adequate to accurately measure a variance of the shear of few percent. The only important bias we found seems to be associated with the CCD columns, and it is constant over the survey, it is therefore easy to correct for. The origin of this CCD bias is still unclear.

As an objective test of the reality of the gravitational shear signal, we measured the ellipticity correlation functions [FORMULA], [FORMULA] and [FORMULA]. While the measurement is noisy, the general behavior is fully consistent with the lensing origin of the signal. The tests for systematic errors and the three ellipticity correlation function measurements described above have led us to conclude with confidence that we have measured a cosmic shear signal.

With larger survey area, we expect to be able to measure other lensing statistics, like the aperture mass statistic ([FORMULA]; see Schneider et al. 1998). The [FORMULA] statistic is still very noisy for our survey size because its signal-to-noise is lower than the top-hat smoothing statistic, due to higher sample variance (We verified this statement using the ray tracing simulation data of Jain et al. 1999). Our survey will increase in size in the near future (quickly up to 7 square degrees), leading to a factor of 2 improvement in the signal-to-noise of the results presented here. According to our estimates, this will be enough to measure [FORMULA] at the arc-minute scale with a signal-to-noise of [FORMULA]. The detection of the skewness of the convergence should also be possible with the increased survey area. This will be important in breaking the degeneracy between the amplitude of the power spectrum and [FORMULA] (Bernardeau et al. 1997, Van Waerbeke et al. 1999, Jain et al. 1999). These measures should also provide nearly independent confirmations of the weak gravitational lensing effect as well as additional constraints on cosmology. Thus by combining different measures of lensing by large-scale structure (top-hat smoothing statistics, [FORMULA] statistics, correlation function analysis, power spectrum measurements), higher order moments, and peak statistics (Jain & Van Waerbeke 2000), from forthcoming survey data, we hope to make significant progress in measuring dark matter clustering and cosmological parameters with weak lensing.

We also hope to do a detailed analysis with a more sophisticated PSF correction algorithm. For instance, the mass reconstruction is linear with the amplitude of the residual bias, and a fraction of percent bias is still enough to prevent a definitive detection of filaments or to map the details of large scale structures. Since we show elsewhere (Erben et al. 2000) that such a bias is unavoidable with the present day correction techniques and image quality, there is still room to improve the analysis prior to obtaining accurate large-scale mass maps. Recent efforts to improve the PSF correction are very encouraging (Kaiser 1999). We plan to explore such approaches once we get an essentially homogeneous data set on a larger field.

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© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000