Hints for a gravitational constant transition in Tully-Fisher data

We use an up to date compilation of Tully-Fisher data to search for transitions in the evolution of the Tully-Fisher relation. Using an up to date data compilation, we find hints at $\approx 3\sigma$ level for a transition at critical distances $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$. We split the full sample in two subsamples according to the measured galaxy distance with respect to a splitting distance $D_c$ and identify the likelihood of the best fit slope and intercept of one sample with respect to the best fit corresponding values of the other sample. For $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$ we find a tension between the two subsamples at a level of $\Delta \chi^2 > 17\; (3.5\sigma)$. Using a Monte-Carlo simulation we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances. If the tension is interpreted as due to a gravitational strength transition, it would imply a shift of the effective gravitational constant to lower values for distances larger than $D_c$ by $\frac{\Delta G}{G}\simeq -0.1$. Such a shift is of the anticipated sign and magnitude but at somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions ($\frac{\Delta G}{G}\simeq -0.1$ at transition redshift $z_t\lesssim 0.01$ ($D_c\lesssim 40 Mpc$)).