Dark Matter Behaves Like Matter: Halos Set by Starlight Transfer from Disks to Dwarfs, and One Modified Gravity Law Does Not

The missing mass of galaxies behaves like matter whose amount the stars set. Three tests across 286 systems, each scored on systems left out of the fit, show it. First, a finite dark halo whose mass follows a galaxy's stellar mass and size through three shared coefficients, with a published concentration relation, predicts the rotation of unseen disk galaxies as well as the radial acceleration relation of modified Newtonian dynamics (0.1533 against 0.1531 dex), and, frozen on disks, predicts 44 dwarf spheroidal galaxies 28 percent better (0.479 against 0.669 dex), better even than that relation refitted on the dwarfs themselves (0.548 dex). Second, any modification that adds an effective density proportional to the ordinary matter through a fixed positive kernel, as nonlocal gravity and constant-parameter MOG do, can raise gravity at a source's half-mass radius by at most a factor 1 + 2α. With the published α the ceilings are 22.9 and 18.8, and 31 and 33 of the 44 dwarfs need more. Third, one acceleration scale does not carry across: disks want a0 = 1.16 x 10^-10 m/s^2 and clusters 7.2 x 10^-10, and the extra mass that repairs MOND in clusters by following hot gas, which transfers between two cluster surveys with 7.6 percent error, must vanish in gas-rich disks, where carrying it over gives 99.7 percent speed errors. A halo rule of three coefficients set by starlight transfers where a universal force law needs a new scale for each population. Every coefficient is fixed before the systems it predicts are seen; full lensing and cosmological likelihoods are left to later work.