Peculiar dark matter halos inferred from gravitational lensing as a manifestation of modified gravity

If modified gravity holds, but the weak lensing analysis is done in the standard way, one finds that dark matter halos have peculiar shapes, not following the standard Navarro-Frenk-White profiles, and are fully predictable from the distribution of baryons.

Here we study in detail the distribution of the apparent dark matter around point masses, which approximate galaxies and galaxy clusters, and their pairs for the QUMOND MOND gravity, taking an external gravitational acceleration $g_e$ into account.

At large radii, the apparent halo of a point mass $M$ is shifted against the direction of the external field.

When averaged over all lines-of-sight, the halo has a hollow center, and denoting the by $a_0$ the MOND acceleration constant, its density behaves like $\rho(r)=\sqrt{Ma_0/G}/(4\pi r^2)$ between the galacticentric radii $\sqrt{GM/a_0}$ and $\sqrt{GMa_0}/g_e$, and like $\rho\propto r^{-7}G^2M^3a_0^3/g_e^5$ further away.

Between a pair of point masses, there is a region of a negative apparent dark matter density, whose mass can exceed the baryonic mass of the system.

The density of the combined dark matter halo is not a sum of the densities of the halos of the individual points.

The density has a singularity near the zero-acceleration point, but remains finite in projection.

We compute maps of the surface density and the lensing shear for several configurations of the problem, and derive formulas to scale them to further configurations.

In general, for a large subset of MOND theories in their weak field regime, for any configuration of the baryonic mass $M$ with the characteristic size of $d$, the total lensing density scales as $\rho({\vec{x}})=\sqrt{Ma_0/G}d^{-2}f\left(\vec{\alpha},\vec{x}/d,g_ed/\sqrt{GMa_0}\right)$, where the vector $\vec{\alpha}$ describes the geometry of the system.

Distinguishing between QUMOND and cold dark matter seems possible with the existing instruments.

;Comment: 34 pages, ca. 14 pages main text, 26 figures.

Accepted for publication in Astronomy and Astrophysics.

The figures from Appendix C will not appear in the main journal.

They are available at: https://doi.org/10.5281/zenodo.13304952