Figure 7

Figure 7: The Faber–Jackson relation for spheroidal galaxies, including both elliptical galaxies (red squares, [85, 232]) and Local Group dwarf satellites [285] (orange squares are satellites of the Milky Way; pink squares are satellites of M31). In analogy with the Tully–Fisher relation for spiral galaxies, spheroidal galaxies follow a relation between stellar mass and line of sight velocity dispersion (σ). The dotted line represents a constant value of the acceleration parameter 4 σ ∕ (GM ∗). Note, however, that this relation is different from the BTFR because it applies to the bulk velocity dispersion while the BTFR applies to the asymptotic circular velocity. In the context of Milgrom’s law (Section 5) the Faber–Jackson relation is predicted only when relying on assumptions such as isothermality, isotropy, and the slope of the baryonic density distribution (see 3rd law of motion in Section 5.2). In addition, not all pressure-supported systems are in the weak-acceleration regime. So, in the context of Milgrom’s law, deviations from the weak-field regime, from isothermality and from isotropy, as well as variations in the baryonic density distribution slope, would thus explain the scatter in this relation.