The bar rotation rate as a diagnostic of dark matter content in the centre of disc galaxies

Abstract: We investigate the link between the bar rotation rate and dark matter content in barred galaxies by concentrating on the cases of the lenticular galaxies NGC4264 and NGC4277. These two gas-poor galaxies have similar morphologies, sizes, and luminosities. But, NGC4264 hosts a fast bar, which extends to nearly the corotation, while the bar embedded in NGC4277 is slow and falls short of corotation. We derive the fraction of dark matter $f_{\rm DM, bar}$ within the bar region from Jeans axisymmetric dynamical models by matching the stellar kinematics obtained with the MUSE integral-field spectrograph and using SDSS images to recover the stellar mass distribution. We build mass-follows-light models as well as mass models with a spherical halo of dark matter, which is not tied to the stars. We find that the inner regions of NGC4277 host a larger fraction of dark matter ($f_{\rm DM, bar} = 0.53 \pm 0.02$) with respect to NGC4264 ($f_{\rm DM, bar} = 0.33 \pm 0.04$) in agreement with the predictions of theoretical works and the findings of numerical simulations, which have found that fast bars live in baryon-dominated discs, whereas slow bars experienced a strong drag from the dynamical friction due to a dense DM halo. This is the first time that the bar rotation rate is coupled to $f_{\rm DM, bar}$ derived from dynamical modelling.