We report an empirical relation between the radial accelerations by baryons ( a _ { B } ) and dark matter ( a _ { DM } ) derived from kinematic analyses of \sim 7000 nearly round , pure bulge , non-rotating elliptical galaxies , selected from Sloan Digital Sky Survey DR7 .
For an acceleration range a _ { 0 } < a _ { B } < 30 a _ { 0 } above a _ { 0 } = 1.2 \times 10 ^ { -10 } m s ^ { -2 } , we find a _ { DM } / a _ { B } = 10 ^ { p } ( a _ { B } / a _ { 0 } ) ^ { q } with p = -0.08 \pm 0.02 ( stat ) \pm 0.1 ( sys ) and q = -0.93 \pm 0.03 ( stat ) \pm 0.1 ( sys ) .
This relation constrains the higher acceleration part of the radial acceleration relation observed for rotating galaxies near or below a _ { 0 } .
Our results point to a particular direction in theories of dark matter or modified gravity .