Mimicking dark matter in galaxy clusters through a nonminimal gravitational coupling with matter

In this work, one shows that a specific nonminimal coupling between the scalar curvature and matter can mimic the dark matter component of galaxy clusters. For this purpose, one assesses the Abell cluster A586, a massive nearby relaxed cluster of galaxies in virial equilibrium, where direct mass estimates and strong-lensing determinations are possible. One then extends the dark matter mimicking to a large sample of galaxy clusters whose density profiles are obtained from the Chandra high quality data, also in virial equilibrium. The total density, which generally follows a cusped profile and reveals a very small baryonic component, can be effectively described within this framework.

Figure 1

Mass-density profiles for the visible matter component (gray line), the dark matter density profile (dark line), and the mimicked density profiles (dashed lines) for different values of $n$, where the dashing length increases with $n$. The best fit is obtained for $n=0.43$ (dark dashed line). The horizontal dotted line corresponds to $\rho =200{\rho }_c$.

Figure 2

Mass radial profile, resulting from the integration of the mass-density profile. The dotted line is for the dynamical mass of $M=4.25\times {10}^{14}{M}_{\odot }$ (polytropic case) [31].

Figure 3

Different dark matter mimicked density profiles for different values of the characteristic length scale, $r_n=1.00$, 6.31, 10.00, 15.84, and $25.12\mathrm{Mpc}$, where the dashing increases with the value of $r_n$, compared with the observed dark matter component (black line). These values are obtained for the best-fit value $n=0.43$.

Figure 4

Additional radial velocity resulting from the nongeodesic motion due to the dark matter component (dashed lines) and to the mimicked dark matter (dot-dashed lines) for different values of $n$, and also for the total density profile (black line).

Figure 5

Resulting power-law couplings, $f_2(R)=(R/R_n{)}^n$, after the integration of the differential equation, for different values of $n$.

Figure 6

The obtained dark matter mimicked profile using a power-law function fixed at $n=0.2$ (dashed lines), along with the density profiles for dark matter (black lines) and visible (gray lines) components for each cluster.

Figure 7

Same as Fig. 6 except for different clusters. The last graph corresponds to the Abell A586 cluster.