Probing the Nonlinear Density Wave Theory of Spiral Galaxies by Baryonic Tully–Fisher Relation

The baryonic mass–velocity relation provides an important test of different galaxy dynamics models such as Lambda–cold dark matter (ΛCDM) and alternatives like Modified Newtonian Dynamics (MOND). Novel nonlinear density wave theory with a soliton solution gives an opportunity to test whether the derived rotational velocity expression is able to support the well known Tully–Fisher empirical relation between mass and rotation velocity in disk galaxies. Initial assumptions do not involve any larger dark matter halo that supports the stability of the very thin galactic disk nor any modified gravitational acceleration acting on galactic scales. It rather follows an important gravitational interaction between constituents of disk mass in the outer part of the disk via gravitational potential. Data are obtained by a fitting procedure applied on the sample of 81 rotational curves of late type spirals using expressions for the rotational velocity derived as an exact, a self-consistent solution of the nonlinear Schrodinger (NLS) equation for galactic surface mass density. The location of these selected objects in the baryonic mass–rotation velocity plane follows the relation logMb=3.7±0.2logVflat+2.7±0.4 in marginal agreement with the findings in the literature.