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Compressibility and local instabilities of differentially rotating magnetized gas

We study the stability of compressible cylindrical differentially rotating flow in the presence of the magnetic field, and show that compressibility alters qualitatively the stability properties of flows. Apart from the well-known magnetorotational instability that can occur even in incompressible flow, there exist a new instability caused by compressibility. The necessary condition of the newly found instability can easily be satisfied in various flows in laboratory and astrophysical conditions and reads $B_{s} B_ϕ Ω' \neq 0$ where $B_{s}$ and $B_ϕ$ are the radial and azimuthal magnetic fields, $Ω' =d Ω/ds$ with $s$ being the cylindrical radius. Contrary to the magnetorotational instability that occurs only if $Ω$ decreases with $s$, the newly found instability operates at any sign of $Ω'$. The considered instability can arise even in a very strong magnetic field that suppresses the magnetorotational instability.