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We investigate the dynamical instability of the one-armed spiral m=1 mode indifferentially rotating stars by means of 3+1 hydrodynamical simulations inNewtonian gravitation. We find that both a soft equation of state and a highdegree of differential rotation in the equilibrium star are necessary to excitea dynamical m=1 mode as the dominant instability at small values of the ratioof rotational kinetic to potential energy, T/|W|. We find that this spiral modepropagates outward from its point of origin near the maximum density at thecenter to the surface over several central orbital periods. An unstable m=1mode triggers a secondary m=2 bar mode of smaller amplitude, and the bar modecan excite gravitational waves. As the spiral mode propagates to the surface itweakens, simultaneously damping the emitted gravitational wave signal. Thisbehavior is in contrast to waves triggered by a dynamical m=2 bar instability,which persist for many rotation periods and decay only after aradiation-reaction damping timescale.Comment: 15 pages, 19 figures included, uses emulateapj5.sty (included).  Accepted for publication in The Astrophysical Journa

One‐armed Spiral Instability in Differentially Rotating Stars