A gravitational explanation in which the inferred dark matter effect is a function of the ellipticity of the baryonic matter distribution gives rise to the same relationship.
Also, it confirms that inferred cold dark matter halos tend not to be spherically symmetric as many dark matter particle halo models, such as the NFW halo model inferred analytically, would predict, without a good reason for this being the case in a cosmology model where halos give rise to baryonic matter clustering that gives rise to galaxies, and without a good reason for the predominance of spiral shaped galaxies, both of which are natural expectations of a gravitational based explanation in which the weak gravitational fields of galaxies are strengthened when they are no spherically symmetrical.
Cold dark matter haloes are expected to be triaxial, and so appear elliptical in projection. We use weak gravitational lensing from the Canada-France Imaging Survey (CFIS) component of the Ultraviolet-Near Infrared Optical Northern Survey (UNIONS) to measure the ellipticity of the dark matter haloes around Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Data Release 7 (DR7) and from the CMASS and LOWZ samples of the Baryon Oscillation Spectroscopic Survey (BOSS), assuming their major axes are aligned with the stellar light. We find that DR7 LRGs with masses M∼2.5×10^13M⊙/h have halo ellipticities e=0.35±0.09. Expressed as a fraction of the galaxy ellipticity, we find fh=1.4±0.4. For BOSS LRGs, the detection is of marginal significance: e=0.17±0.10 and fh=0.1±0.4. These results are in agreement with other measurements of halo ellipticity from weak lensing and, taken together with previous results, suggest an increase of halo ellipticity of 0.10±0.05 per decade in halo mass. This trend agrees with the predictions from hydrodynamical simulations, which find that at higher halo masses, not only do dark matter haloes become more elliptical, but that the misalignment between major axis of the stellar light in the central galaxy and that of the dark matter decreases.