Astronomy and Astrophysics – Astrophysics
Scientific paper
2003-11-13
Mon.Not.Roy.Astron.Soc. 350 (2004) 927-938
Astronomy and Astrophysics
Astrophysics
14 pages, 4 figures, minor additions, accepted for publication in MNRAS
Scientific paper
10.1111/j.1365-2966.2004.07695.x
An understanding of the oscillations of differentially rotating systems is key to many areas of astrophysics. It is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess significant differential rotation immediately after birth or binary merger. In a previous paper we analysed the normal modes of a simple system exhibiting differential rotation. In this complementary paper we address the initial value problem for the same simple model using both analytical methods and numerical time evolutions. We derive a necessary and sufficient condition for dynamical shear instability. We discuss the dynamical behaviour of the continuous spectrum in response to an initial perturbation, and show that certain singular solutions within the continuous spectrum appear physically indistinguishable from the discrete modes outside the continuous spectrum.
Andersson Nils.
Watts Anna L.
Williams Liliya L. R.
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