We report here the results of operation of a torsion balance with a period of $\sim 1.27 \times 10^4$ s. The analysis of data collected over a period of $\sim$115 days shows that the difference in the accelerations towards the Galactic Center of test bodies made of aluminum and quartz was $(0.61 \pm 1.27) \times 10^{ -15} \, \mathrm{ m \, s}^{ -2}$. This sets a bound on the violation of the equivalence principle by forces exerted by Galactic dark matter which is expressed by the E\"otv\"os parameter $\eta_{ DM} = (1.32 \pm 2.68) \times 10^{ -5}$, a significant improvement upon earlier bounds.
Categories: gr-qc