• Corpus ID: 116205870

On the Minimum Energy Configuration of a Rotating Barotropic Fluid: A Response to Narayan & Pringle astro-ph/0208161

@article{Fromang2002OnTM,
  title={On the Minimum Energy Configuration of a Rotating Barotropic Fluid: A Response to Narayan \& Pringle astro-ph/0208161},
  author={S{\'e}bastien Fromang and Steven A. Balbus},
  journal={arXiv: Astrophysics},
  year={2002}
}

• S. Fromang, S. Balbus
• Published 1 September 2002
• Physics
• arXiv: Astrophysics

In a recent posting, Narayan & Pringle (2002, astro-ph/0208161) criticized a paper written by the current authors (Fromang & Balbus 2002, astro-ph/0207561 hereafter FB02). FB02 presented a second order variational calculation and concluded that supersonically rotating barotropic fluids had lower energy states neighboring that of equilibrium. (Note that this is not the same as claiming instability, a point noted explicitly in FB02.) Narayan & Pringle challenged this, presented a specific class of equilibrium solution, and claimed to prove that it represented a global energy minimum. They concluded that FB02 was incorrect. The calculation presented in FB02 is indeed incorrect. The difficulty is that the second order changes in the energy cannot be calculated directly from the energy itself, even when the variations are restricted to satisfy the constraints of mass and angular momentum conservation. Rather, the constraints themselves change the effective functional form of the energy, by forcing additional second order correlations that would otherwise be absent. Narayan & Pringle (2002) is therefore correct in stating that our second order variational calculation is in error. Nevertheless, we are compelled to respond to the critique of Narayan & Pringle (2002). Our reasons are twofold: (1) the critique unfairly misrepresents statements in FB02; and (2) the main discussion presented in the critique appears itself to have flaws. In particular, the conclusion of Narayan & Pringle that their chosen example is a global minimum with respect to arbitrary variations from equilibrium does not follow from the argument presented in their paper. We very briefly discuss these two points in turn.