Radial acceleration relation from symmetron fifth forces

We show that the radial acceleration relation for rotationally supported galaxies may be explained, in the absence of cold dark matter, by a nonminimally coupled scalar field, whose fifth forces are partially screened on galactic scales by the symmetron mechanism. In addition, we show that sufficient energy is stored in the symmetron field to explain the dynamic stability of galactic disks.

Figure 1

The symmetron profile $\phi$, required by Eq. (12) and normalized to the value of the field at $r/r_s=10$ (${\phi }_{10}$) with boundary condition ${\phi }_0/M={10}^{-3}$.

Figure 2

Example rotation curves for $M=M_{\mathrm{Pl}}/10$ and ${\overline{\rho }}_0=1M_{\odot }{\mathrm{pc}}^{-3}$, $v/M=1/150$, and $\mu =3\times {10}^{-39}\mathrm{GeV}$: (a) disk, (b) bulge and (c) gas dominated, and (d) comparable disk and bulge components. Black points: observed rotation velocities and corresponding error bars taken from the SPARC data set [17]. Solid black: total prediction, including the symmetron component. Solid orange: symmetron contribution. Shaded bands indicate 50% variation in ${\overline{\rho }}_0/M^2$. Solid blue: baryon-only prediction. Red dashed: disk component. Green dotted: gas component. Purple dot-dashed: bulge component. Figures (e)–(h) and (i)–(l) show the corresponding symmetron profiles over the observed data range and 10 times that range, respectively.

Figure 3

Acceleration parameters: (a) observed total ($g_{\mathrm{obs}}$) versus baryon-only prediction ($g_{\mathrm{bar}}$), cf. Ref. [8]; (b) predicted total acceleration for the symmetron model ($g_{\mathrm{tot}}$) versus observed total ($g_{\mathrm{obs}}$); and (c) predicted acceleration ($g_{\mathrm{tot}}$) versus baryon-only prediction ($g_{\mathrm{bar}}$). The solid black lines in (a) and (c) correspond to the radial acceleration relation [Eq. (4)].