Restoring the full velocity field in the gaseous disk of the spiral galaxyNGC 157

This paper is the first in a series of articles devoted to the construction and analysis of three-component vector velocity fields in the gaseous disk s of spiral galaxies, and to the discovery of giant anticyclones near corot ation which were predicted earlier. We analyse the line-of-sight velocity f ield of ionized gas in the spiral galaxy NGC 157 which has been obtained in the H alpha emission line at the 6 m telescope of SAO RAS. The field conta ins more than 11 000 velocity estimates. The existence of systematic deviat ions of the observed gas velocities from pure circular motion is shown. A d etailed investigation of these deviations is undertaken by applying a recen tly formulated method based on Fourier analysis of the azimuthal distributi ons of the line-of-sight velocities at different distances from the galacti c center. To restore the three-component vector velocity field from the obs erved line-of-sight velocity field, two assumptions were made: 1) the pertu rbed surface density and residual velocity components can be approximated t o the formulae C-i cos(2(theta) + F-i), where C-i and F-i are respectively the amplitude and the phase; 2) the perturbed surface density and residual velocity components satisfy the Euler equations. The correctness of both as sumptions is proven on the basis of the observational data. As a result of the analysis, all the main parameters of the wave spiral pattern are determ ined: the corotation radius, the amplitudes and phases of the gas velocity perturbations at different radii, as well as the velocity of circular rotat ion of the disk corrected for the influence of the velocity perturbations c onnected with the spiral arms. Finally, a restoration of the vector velocit y field in the gaseous disk of NGC 157 is performed. At a high confidence l evel, the presence of the two giant anticyclones in the reference frame rot ating with the spiral pattern is shown; their sizes and the localization of their centers are consistent with the results of the analytic theory and o f numerical simulations. Besides the anticyclones, the existence of cyclone s in any residual velocity field is predicted. In the reference frame of th e spiral pattern, detection of such cyclones is possible in the galaxies wi th a radial gradient of azimuthal residual velocity steeper than that of th e rotation velocity.