Stellar kinematics from the symmetron fifth force in the Milky Way disk

It has been shown that the presence of non-minimally coupled scalar fields giving rise to a fifth force can noticeably alter dynamics on galactic scales. Such a fifth force must be screened in the Solar System but if unscreened it can have a similar observational effects as a component of non-baryonic matter. We consider this possibility in the context of the vertical motions of local stars in the Milky Way disk by reframing a methodology used to measure the local density of dark matter. By attempting to measure the properties of the symmetron field required to support vertical velocities we can test it as a theory of modified gravity and understand the behaviour of screened scalar fields in galaxies. In particular this relatively simple setup allows the symmetron field profile to be solved for model parameters where the equation of motion becomes highly nonlinear and difficult to solve in other contexts. We update the existing Solar System constraints for this scenario and find a region of parameter space not already excluded that can explain the vertical motions of local stars out to heights of 1 kpc. At larger heights the force due to the symmetron field profile exhibits a characteristic turn over which would allow the model to be distinguished from a dark matter halo.