Published online by Cambridge University Press: 19 May 2006
Polar ring galaxies, where matter is in equilibrium in perpendicularorbits around spiral galaxies, are ideal objects to probe the 3D shapesof dark matter halos. The conditions to constrain the halos are that theperpendicular system does not strongly perturb the host galaxy, or thatit is possible to derive back its initial shape, knowing the formationscenario of the polar ring. The formation mechanisms are reviewed:mergers, tidal accretion, or gas accretion from cosmic filaments.The Tully-Fisher diagram for polar rings reveals that the velocityin the polar plane is higher than in the host plane, which can only be explained if the dark matter is oblate and flattened along the polar plane. Only a few individual systems havebeen studied in details, and 3D shapes of their haloes determinedby several methods. The high frequency of warps could be explainedby spontaneous bending instability, if the disks are sufficientlyself-gravitating, which can put constraints on the dark matter flattening.