The VIMOS Public Extragalactic Redshift Survey: Measuring the growth rate of structure around cosmic voids

Abstract

We identified voids in the completed VIMOS Public Extragalactic Redshift Survey (VIPERS), using an algorithm based on searching for empty spheres. We measured the cross-correlation between the centres of voids and the complete galaxy catalogue. The cross-correlation function exhibits a clear anisotropy in both VIPERS fields (W1 and W4), which is characteristic of linear redshift space distortions. By measuring the projected cross-correlation and then deprojecting it we are able to estimate the undistorted cross-correlation function. We propose that given a sufficiently well measured cross-correlation function one should be able to measure the linear growth rate of structure by applying a simple linear Gaussian streaming model for the redshift space distortions (RSD). Our study of voids in 306 mock galaxy catalogues mimicking the VIPERS fields would suggest that VIPERS is capable of measuring $\beta$ with an error of around $25\%$. Applying our method to the VIPERS data, we find a value for the redshift space distortion parameter, $\beta = 0.423^{+0.104}_{-0.108}$, which given the bias of the galaxy population we use gives a linear growth rate of $f\sigma_8 = 0.296^{+0.075}_{-0.078}$ at $z = 0.727$. These results are consistent with values observed in parallel VIPERS analysis using standard techniques.