Mass-Discrepancy Acceleration Relation: A Natural Outcome of Galaxy Formation in Cold Dark Matter Halos

We analyze the total and baryonic acceleration profiles of a set of well-resolved galaxies identified in the eagle suite of hydrodynamic simulations. Our runs start from the same initial conditions but adopt different prescriptions for unresolved stellar and active galactic nuclei feedback, resulting in diverse populations of galaxies by the present day. Some of them reproduce observed galaxy scaling relations, while others do not. However, regardless of the feedback implementation, all of our galaxies follow closely a simple relationship between the total and baryonic acceleration profiles, consistent with recent observations of rotationally supported galaxies. The relation has small scatter: Different feedback implementations—which produce different galaxy populations—mainly shift galaxies along the relation rather than perpendicular to it. Furthermore, galaxies exhibit a characteristic acceleration $g_{†}$, above which baryons dominate the mass budget, as observed. These observations, consistent with simple modified Newtonian dynamics, can be accommodated within the standard cold dark matter paradigm.

Figure 1

Stellar mass versus halo virial mass (left) and stellar half-mass radius (right). Solid black lines show the median trends for the “REF” model; blue and red lines show, respectively, the variations if feedback is entirely limited to active galactic nuclei (AGN) (OnlyAGN) or to stars (NoAGN). Semitransparent dots of the same color show individual halos. Individual halos are also shown for runs with strong (StrongFB, orange squares) and weak (WeakFB, green circles) stellar feedback and for apostle galaxies (diamonds). The dashed line in the left panel plots the $M_{\star }-M_{\mathrm{halo}}$ relation derived from abundance matching (see [31] for details). Lines of constant effective surface brightness are plotted in the right-hand panel. The outsized blue and red symbols identify the two halos shown in Fig. 2.

Figure 2

Circular velocity (upper panels) and acceleration profiles (lower panels) for galaxies highlighted in Fig. 1. The left and middle panels correspond to individual halos cross-matched between the NoAGN (blue) and OnlyAGN (red) models; the rightmost panels compare the median profiles for halos in NoAGN (blue) and StrongFB (yellow) that fall in the narrow mass range $12.3\le {\log }_{10}{M}_{200}/[M_{\odot }]\le 12.5$ (vertical shaded band in Fig. 1). The baryonic circular velocity profiles (upper panels) are shown using dashed lines; symbols indicate that of DM. [For comparison, solid black lines show the $V_c^{\mathrm{DM}}(r)$ profiles for the same halo identified in the corresponding DM-only simulation.] Lower panels show the acceleration diagrams. The linear scaling is shown as a solid black line and Eq. (1) (using $g_{†}=2.6\times {10}^{-10}\mathrm{m}{\mathrm{s}}^{-2}$) as a dashed line; shaded regions indicate the scatter brought about by increasing or decreasing the enclosed baryon mass by factors of 3 (light) and 2 (dark). For comparison, we also show Eq. (1) with $g_{†}=1.2\times {10}^{-10}\mathrm{m}{\mathrm{s}}^{-2}$ (brown line), consistent with the observational result of Ref. [15].

Figure 3

Total acceleration profiles for all halos as a function of their baryonic acceleration. The left panel shows results for all halos in all simulations at $z=0$. Lines, points, and colors have the same meaning as in Fig. 1. The right-hand panel shows (for REF) the redshift evolution for progenitor galaxies. The dashed lines in the left- and right-hand panels show Eq. (1) with $g_{†}=2.6\times {10}^{-10}\mathrm{m}{\mathrm{s}}^{-2}$. Inset panels show the relative scatter around this curve after combining all simulations (left) and for individual redshifts (right); the solid lines represent the observational scatter in Ref. [15]. The middle panel plots the $g_{\mathrm{obs}}-g_{\mathrm{bar}}$ relation after rescaling galaxy stellar masses so that they fall on the abundance matching relation shown in Fig. 1 (left). The thick gray line and shaded band indicate the mean trend and scatter, respectively, obtained by Ref. [15] from observations of rotationally supported galaxies.