Mass Ratio, Not Peak Position: Three Lensing Tests of Quasi-Linear MOND in the Bullet Cluster

In the Bullet Cluster (1E 0657-558) the lensing mass is concentrated on the galaxies, whereas most of the baryons are in the X-ray-emitting gas. We test the quasi-linear formulation (QUMOND) of modified Newtonian dynamics (MOND) against three lensing measurements of the smaller cluster: the position of its mass peak, the projected mass within 250 kpc of its brightest cluster galaxy (BCG), and the ratio R of the projected masses in two circles of radius 80 kpc, one centered on its X-ray peak and one on its BCG. In QUMOND the additional gravity can be described by a phantom density, the density that would produce it in Newtonian gravity. Besides standard QUMOND, we consider extended MOND, individually modeled galaxies, and a phenomenological model in which the phantom density is generated by the baryons, keeps their velocity, and decays on a response time τ. Standard QUMOND places the mass peak on the gas, 224 kpc from the galaxies. A response time τ ≳ 0.4 Gyr adds a second maximum on the galaxies, which becomes the higher of the two only for τ ≳ 2.5 Gyr. QUMOND predicts one third of the mass within 250 kpc measured with the Hubble Space Telescope (HST) and agrees with the lower value from one of the two James Webb Space Telescope (JWST) analyses. No MOND model without additional mass reproduces the mass ratio: all give R ≥ 0.87, whereas the HST measurement gives 0.49 ± 0.05 and our measurement on the public JWST strong-lensing model of Rihtaršič et al. gives 0.62 (0.61 to 0.64 over 100 samples of the model). The phantom mass alone has R ≥ 0.74 in every model we tabulate, so rescaling it cannot remove the discrepancy, and the conclusion holds for any correlation between the errors of the two circle masses. Collisionless mass that moves with the galaxies allows QUMOND to pass all three tests at their two-standard-deviation limits: 1.1 to 1.3 × 10^14 solar masses, distributed like the stars, for the HST masses, or at least 0.9 × 10^13 solar masses for a scale radius of 30 kpc, rising to 2.1 × 10^13 solar masses for 100 kpc, for the lower JWST mass within 250 kpc. On the JWST strong-lensing model, however, the two circles contain 1.7 to 1.9 times the mass of these low-mass solutions and close to that of the HST solution, which favors the larger amount of additional mass. Code and reference outputs: https://doi.org/10.5281/zenodo.23305152