  Barred galaxies constitute about two thirds of observed disc galaxies. Bars
affect not only the mass distribution of gas and stars, but also that of the
dark matter. An elongation of the inner dark matter halo is known as the halo
bar. We aim to characterise the structure of the halo bars, with the goal of
correlating them with the properties of the stellar bars. We use a suite of
simulated galaxies with various bar strengths, including gas and star
formation. We quantify strengths, shapes, and densities of these simulated
stellar bars. We carry out numerical experiments with frozen and analytic
potentials in order to understand the role played by a live responsive stellar
bar. We find that the halo bar generally follows the trends of the disc bar.
The strengths of the halo and stellar bars are tightly correlated. Stronger
bars induce a slight increase of dark matter density within the inner halo.
Numerical experiments show that a non-responsive frozen stellar bar would be
capable of inducing a dark matter bar, but it would be weaker than the live
case by a factor of roughly two.
