Incompatibility of rotation curves with gravitational lensing for TeVeS theory

We constrain the one-parameter ($\alpha$) class of TeVeS models by testing the theory against both rotation curve and strong gravitational lensing data on galactic scales, remaining fully relativistic in our formalism. The upshot of our analysis is that—at least in its simplest original form, which is the only one studied in the literature so far—TeVeS is ruled out, in the sense that the models cannot consistently fit simultaneously the two sets of data without including a significant dark matter component. It is also shown that the details of the underlying cosmological model are not relevant for our analysis, which pertains to galactic scales. The choice of the stellar initial mass function—which affects the estimates of baryonic mass—is found not to change our conclusions.

Figure 1

Likelihood maps of the best fit for the rotation curves of disk galaxies, treating the core radius (horizontal axis) and the TeVeS $\alpha$ parameter (vertical axis) as free parameters. The black or red (grey or blue) contours correspond to the 75%, 90%, and 95% confidence levels of the Chabrier (Salpeter) initial mass function, respectively.

Figure 2

Marginalized likelihood distributions with respect to the TeVeS $\alpha$ parameter for all six disk galaxies. The solid (dashed) lines correspond to the Chabrier (Salpeter) initial mass functions.

Figure 3

Total marginalized likelihood distributions with respect to the TeVeS $\alpha$ parameter combining the data for all six disk galaxies. The result for the Chabrier (Salpeter) IMF is shown as a solid (dashed) line.

Figure 4

Constraining the lensing mass of galaxy HE1104-1805 ($z=0.73$). The lines come in pairs, and represent the constraint on true source position ($\beta$, vertical axis) and lensing mass (horizontal axis) from each of the two observed positions of the images of the background source. The intersection of each pair of lines gives the lensing mass. The standard GR solution is shown as a grey solid line, the best fit is shown as a black solid line, and the $\alpha =0$ case discussed in the text is given as a dashed black line. Each panel corresponds to a different choice of initial mass function, as labeled. The stellar mass is given as a large black dot along with error bars, from Ref. 15.