Validity of sound-proof approximations for magnetic buoyancy

Most models of astrophysical flows employ a ``sound-proof'' approximation, such as the Boussinesq, anelastic, and pseudo-incompressible models, which remove acoustic waves from governing equations. Here, we address accuracy each these for describing magnetic buoyancy in solar interior. We introduce general sound-proof model compare its behavior to that fully compressible system within range astrophysically relevant parameter regimes. determine conditions under can correctly capture linear magneto-buoyancy instability.