Hydromagnetic Instability in Differentially Rotating Flows

We study the stability of a compressible differentially rotating flows in the presence of the magnetic field, and we show that the compressibility profoundly alters the previous results for a magnetized incompressible flow. The necessary condition of newly found instability can be easily satisfied in various flows in laboratory and astrophysical conditions and reads $B_{s} B_{\phi} \Omega' \neq 0$ where $B_{s}$ and $B_{\phi}$ are the radial and azimuthal components of the magnetic field, $\Omega' = d \Omega/ds$ with $s$ being the cylindrical radius. Contrary to the well-known magnetorotational instability that occurs only if $\Omega$ decreases with $s$, the instability considered in this paper may occur at any sign of $\Omega'$. The instability can operate even in a very strong magnetic field which entirely suppresses the standard magnetorotational instability. The growth time of instability can be as short as few rotation periods