Continuous spectrum of evanescent acoustic-gravity waves in an isothermal atmosphere

Waves in the Sun's atmosphere play a very important role in the redistribution of energy and momentum. This motivates to search for new types of wave motions that could be realized in the solar atmosphere. The main focus is traditionally given to freely propagating waves, which transfer energy outwards. However, after the discovery of the f-mode, it became clear that an important role in the dynamics of the atmosphere can be played by horizontally propagating and vertically evanescent wave modes. We here proposed a new approach to describing these waves in an isothermal stratified atmosphere. It is based on the use of a constraint on the solution of the equations of hydrodynamics, which: (1) selects only evanescent modes; (2) excludes the solutions with singularities in the polarization relations. As a result, a family of solutions for evanescent waves is obtained and analysed, parametrized by some real value and continuously filling the region of the diagnostic diagram between the regions of freely propagating acoustic and gravity waves. It is shown that the known evanescent modes, in particular the f-mode, for certain values of the parameter also belong to the family that we found. The results of this work can be used to interpret the observed features of waves in the atmosphere of the Sun and planets.