7 Small scale signal

Our correlation function measurements extend to much smaller scales than shown in the figures above. The limit is set only by the fact that we reject one member of all pairs closer than 3 arcsec. Figures 17 and 18 show the tangential, radial and total shear correlation functions. The pair separation bins are much smaller than in Figs. 5 and 6, which explains why the error bars are larger. Even at the smallest scales, the shear correlation function $\langle\gamma\gamma\rangle_\theta$ is consistent with the model predictions.

Figure 17: Tangential (top panel) and radial (bottom panel) shear correlation functions $\langle\gamma_{\rm t}\gamma_{\rm t}\rangle_\theta$ and $\langle\gamma_{\rm r}\gamma_{\rm r}\rangle_\theta$ down to 3''. The solid, long-dashed (hidden by the solid line) and short-dashed lines are predictions from the same models as in Fig. 3.

The surprising result for the small scale correlations is the behavior of the tangential and radial shear correlation functions: at scales smaller than 5'' we find an increased amplitude for $\langle\gamma_{\rm t}\gamma_{\rm t}\rangle_\theta$, and a ${\it negative}$ $\langle\gamma_{\rm r}\gamma_{\rm r}\rangle_\theta$. Though surprinsing, a negative $\langle\gamma_{\rm r}\gamma_{\rm r}\rangle_\theta$ is not unphysical: for instance in Kaiser (1992) (Table 1), a shallow mass power spectrum (n>-1) implies such an effect. In terms of halo mass profile, it corresponds to a projected profile steeper than -1.5. However, regardless of the nature of this signal, it is important to note that this is a very small scale effect which has no impact on the statistics discussed in preceding sections. The contribution of the increased signal from $\langle\gamma_{\rm t}\gamma_{\rm t}\rangle_\theta$to the variance at 1' is less than $1\%$; moreover since $\langle\gamma\gamma\rangle_\theta$ is not affected at all, the variance is also unaffected. As an explicit test, we checked that by removing one member of the pairs closer than 7'' the measured signal in Figs. 3-6 is unchanged. In a similar cosmic shear analysis using the Red-sequence Cluster Survey (Gladders & Yee 2000) another group finds a similar small scale behavior, though at lower statistical significance (H. Hoekstra, private communication).

The cross-correlation $\langle\gamma_{\rm t}\gamma_{\rm r}\rangle_\theta$ vanishes down to 3'', therefore no obvious systematic is responsible for this effect. The effect is unlikely to be caused by overlapping isophotes, or close neighbors effects because $\langle\gamma_{\rm t}\rangle_\theta^2 << \langle\gamma_{\rm t}\gamma_{\rm t}\rangle_\theta$: if it were a close neighbor alignment we would expect that $\langle\gamma_{\rm t}\rangle_\theta$ (the average tangential ellipticity for all the pair members in each pair separation bin $\theta$) carries all of the signal, which is not the case. In fact we find $\langle\gamma_{\rm t}\rangle_\theta^2 \sim 0.2 \langle\gamma_{\rm t}\gamma_{\rm t}\rangle_\theta$, which means that a close neighbor effect can hardly exceed $20\%$ of the small scale signal.

A forthcoming paper using the same data set will be devoted to the measurement of E and B modes (as defined in Crittenden et al. 2000a), and we will study this small scale signal in more detail. At this stage of the analysis we cannot exclude a possible residual systematic. However, a preliminary analysis shows that the B mode down to 3'' is much smaller than the E mode, which is hard to understand if the signal comes entirely from residual systematics.

Figure 18: Same as Fig. 17 but for the shear correlation function $\langle\gamma\gamma\rangle_\theta$. The open circles correspond to the cross-correlation $\langle\gamma_{\rm t}\gamma_{\rm r}\rangle$.