We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components, the temporal component about the Planck mass m Pl and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocity of rotation v 0 is determined by the hierarchy of scales: √ 2v 2 0 = M/m Pl , and M ∼ 10 12 GeV. A natural estimate of Milgrom's acceleration about the Hubble rate is obtained. PACS numbers: 04.40.−b, 95.35.+d, 04.40.Nr, 98.62.Gq 1 An example of an alternative description due to a modification of gravity is given in [15].