MEASURING Q(0), FROM THE DISTORTION OF VOIDS IN REDSHIFT SPACE

Because the transformation from distance to redshift is nonlinear, map s in redshift space become increasingly distorted as the redshift z be comes greater. As noted by Alcock & Paczynski, observed redshift disto rtions can be used to estimate the deceleration parameter q(0). If q(0 ) is greater than -1, voids in redshift space will be elongated along the line of sight. In addition, distant voids will have a greater volu me in redshift space than nearby voids. Accurate measurement of the vo lume and the axis ratio of voids, as a function of their central redsh ift, will provide an estimate of q(0). To test this method of estimati ng q(0), I create a two-dimensional toy universe, free of peculiar vel ocities, in which the galaxies are located near the walls of Voronoi c ells. The galaxies are then mapped into redshift space by adopting dif ferent values of q(0). In redshift space, I estimate the area and the axis ratio of the voids by fitting ellipses within the voids, and by u sing an algorithm which maximizes the area of the empty ellipses and e nsures that ellipses do not overlap. The accuracy of the estimated val ues of q(0) is limited by the intrinsic scatter in the size and shape of the voids. In the toy universe, distinguishing between a q(0) = -1 universe and a q(0) = 1/2 universe requires a survey which goes to a d epth z greater than or similar to 0.1 in redshift space. Peculiar velo cities will create an additional source of uncertainty for the values of q(0) measured in N-body simulations and in the real universe.