We introduce the flattening equation , which relates the shape of the dark halo to the angular velocity dispersions and the density of a tracer population of stars .
It assumes spherical alignment of the velocity dispersion tensor , as seen in the data on stellar halo stars in the Milky Way .
The angular anisotropy and gradients in the angular velocity dispersions drive the solutions towards prolateness , whilst the gradient in the stellar density is a competing effect favouring oblateness .
We provide an efficient numerical algorithm to integrate the flattening equation .
Using tests on mock data , we show that the there is a strong degeneracy between circular speed and flattening , which can be circumvented with informative priors .
Therefore , we advocate the use of the flattening equation to test for oblateness or prolateness , though the precise value of q can only be measured with the addition of the radial Jeans equation .
We apply the flattening equation to a sample extracted from the Sloan Digital Sky Survey of \sim 15000 halo stars with full phase space information and errors .
We find that between Galactocentric radii of 5 and 10 kpc , the shape of the dark halo is prolate , whilst even mildly oblate models are disfavoured .
Strongly oblate models are ruled out .
Specifically , for a logarithmic halo model , if the asymptotic circular speed v _ { 0 } lies between 210 and 250 kms ^ { -1 } , then we find the axis ratio of the equipotentials q satisfies 1.5 \lesssim q \lesssim 2 .