To be or not to be oblate: the shape of the dark matter halo in polar ring galaxies

With the aim of determining the spatial distribution of the dark matter halo, we investigate two polar ring galaxies, NGC 4262 and SPRC-7. For both galaxies, the stellar kinematics data for the central galaxy were obtained from optical spectroscopy at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. Information about polar gaseous components was taken from optical three-dimensional spectroscopic observations of ionized gas (for SPRC-7) and from H i radio observations (for NGC 4262). SPRC-7 is a system with a relative angle delta = 73A degrees towards the central galaxy and quite a massive stellar-gaseous polar component. Meanwhile, NGC 4262 is a classic polar case with delta A = 88A degrees, where the polar ring mainly consists of neutral gas with a negligible stellar contribution to the mass. Thus, we are dealing with two different systems, and the results are also diverse. The observed properties of both galaxies were compared with the results of self-consistent simulations of velocity fields of the polar component along with the rotation curve of the central lenticular galaxy. For SPRC-7, we have found a slightly flattened halo towards the polar plane with the axial ratio c/a a parts per thousand integral 1.7 +/- 0.2 for the isothermal halo model and c/a a parts per thousand integral 1.5 +/- 0.2 for the NFW model. NGC 4262 is more unusual, because the shape of the dark matter distribution varies strongly with radius. That is, the dark matter halo is flattened in the vicinity of the galactic disc (c/a a parts per thousand 0.4 +/- 0.1), but it is prolate far beyond the central galaxy (c/a a parts per thousand 1.7 for the isothermal halo model and c/a a parts per thousand 2.3 for the NFW model).