Can the relativistic field theory version of modified Newtonian dynamics avoid dark matter on galactic scales?

A fully relativistic analysis of gravitational lensing in tensor-vector-scalar (TeVeS) theory is presented. By estimating the lensing masses for a set of six lenses from the CASTLES database, and then comparing them to the stellar mass, the deficit between the two is obtained and analyzed. Considering a parametrized range for the TeVeS function $\mu (y)$, which controls the strength of the modification to gravity, it is found that on galactic scales TeVeS requires additional dark matter with the commonly used $\mu (y)$. A soft dependence of the results on the cosmological framework and the TeVeS free parameters is discussed. For one particular form of $\mu (y)$, TeVeS is found to require very little dark matter. This choice is however ruled out by rotation curve data. The inability to simultaneously fit lensing and rotation curves for a single form of $\mu (y)$ is a challenge to a no dark matter TeVeS proposal.

Figure 1

Deflection angle curves for a NFW profile system ($\mathcal{C}=10$). The parameters of the system are $D_l=1000\mathrm{Mpc}$ (the luminosity distance of the lens), $M={10}^{11}{M}_{\odot }$, $k=0.01$, $K=0.01$, ${\varphi }_c=0.001$ and $r_{\mathrm{vir}}=15\mathrm{Kpc}$. Left panel: $\alpha =0$ case. Right panel: $\alpha =1$ case. The deflection angles decrease in MOND and TeVeS as $\alpha$ increases.

Figure 2

A comparison of the need for dark matter for the lenses in GR, MOND, and TeVeS, for $\alpha =0$ (top panels) and $\alpha =1$ (bottom panels). The right-hand panels give the dark matter requirements as a function of the ratio $R_{\mathrm{lens}}/R_e$. Any dark matter needed in TeVeS is especially significant for those masses which probe further out, where the modification to gravity is larger.

Figure 3

The dark matter content of the lenses for $\alpha =-1$ in the parametrization of $f(x)$ in MOND and $\mu (y)$ in TeVeS.