Constraining A String Gauge Field by Galaxy Rotation Curves and Perihelion Precession of Planets

Abstract

We discuss a cosmological model in which the string gauge field coupled universally to matter gives rise to an extra centripetal force and will have observable signatures on cosmological and astronomical observations. Several tests are performed using data including galaxy rotation curves of 22 spiral galaxies of varied luminosities and sizes, and perihelion precessions of planets in the solar system. The rotation curves of the same group of galaxies are independently fit using a dark matter model with the generalized Navarro--Frenk--White (NFW) profile and the string model. A Remarkable fit of galaxy rotation curves is achieved using the one-parameter string model as compared to the three-parameter dark matter model with the NFW profile. The average $χ^2$ value of the NFW fit is 9\% better than that of the string model at a price of two more free parameters. Furthermore, from the string model, we can give a dynamical explanation for the phenomenological Tully-Fisher relation. We are able to derive a relation between field strength, galaxy size and luminosity, which can be verified with data from the 22 galaxies. To further test the hypothesis of the universal existence of the string gauge field, we apply our string model to the solar system. Constraint on the magnitude of the string field in the solar system is deduced from the current ranges for any anomalous perihelion precession of planets allowed by the latest observations. The field distribution resembles a dipole field originating from the Sun. The string field strength deduced from the solar system observations is of a similar magnitude as the field strength needed to sustain the rotational speed of the Sun inside the Milky Way. This hypothesis can be tested further by future observations with higher precision.