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

¹ Observatoire de Paris, LERMA, Collège de France, CNRS, PSL University, Sorbonne University, F-75014 Paris, France
² Strasbourg University, CNRS, Observatoire astronomique de Strasbourg, F-67000 Strasbourg, France
³ FZU – Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, Prague 182 21, Czech Republic

^⋆ Corresponding author; michal.bilek@obspm.fr

Received: 27 March 2024
Accepted: 31 July 2024

Abstract

If modified gravity holds, but the weak lensing analysis is done in the standard way, we find that dark matter halos have peculiar shapes that do not follow the standard Navarro-Frenk-White profiles and which are fully predictable from the distribution of baryons. In this work, we study in detail the distribution of the apparent DM around point masses, approximating galaxies and galaxy clusters, along with their pairs for the QUMOND version of modified Newtonian dynamics, taking the 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. Using a₀ to denote the MOND acceleration constant, we find that its density follows ρ(r)=√Ma₀/G /(4πr²) between the galacticentric radii √GM/a₀ and √GMa₀ / g^e, and then ρ ∝ r⁻⁷G²M³a₀³/g_e⁵ at a greater distance. Between a pair of point masses, there is a region of a negative apparent DM density, whose mass can exceed the baryonic mass of the system. The density of the combined DM 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 computed maps of the surface density and the lensing shear for several configurations of the problem and derived 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 ρ(x) = √Ma₀/G d^-2 f(α,x / d,g_ed/ √GMa₀) , where the vector α describes the geometry of the system. Detecting the difference between QUMOND and cold DM (CDM) halos appears to be possible with existing instruments.