Galaxy rotation curves via conformal factors

Abstract

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in the Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other, the so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

Fig. 1

The difference $v-v_{\mathrm{newt}}$ (vertical axis in Km/s) as a function of distance (horizontal axis in kpc), where v is given by Eq. (32) and $v_{\mathrm{newt}}$ is the Newtonian velocity $\mathrm{GM}(r)/r$. The galaxies from top to bottom are as follows: NGC3031, NGC3627, NGC3521, NGC6946 and NGC7793. The galaxy NGC4736 is not shown, but for it always $v-v_{\mathrm{newt}}<0.7$

Fig. 2

(color online) Rotational velocities (in km/s) as a function of distance (in kpc). The black curve represents the best parametric fit of galaxy rotation curves using Eq. (32) for the sub-sample of six THINGS galaxies. The values of the best-fit parameters can be found in Table 1