... thermodynamics

Recently, Fa & Pedron (2001) have proposed to describe elliptical galaxies by an extended King model using Tsallis entropy. They obtained a good fit for NGC 3379. However, we believe that this agreement is fortuitous. An even better fit has been obtained by Hjorth & Madsen (1993) with a different model justified by more convincing physical arguments. Their model has an isothermal (instead of a polytropic) inner region in agreement with Lynden-Bell's statistical mechanics of violent relaxation. The polytropic envelope is justified by incomplete relaxation (or equivalently by a lack of ergodicity) when we depart from the central mixing region. Their model differs from the Michie-King model because the system is collisionless and not subject to tidal forces (King's models, which can be derived rigorously from the Fokker-Planck equation, only apply to tidally truncated collisional stellar systems such as globular clusters). It is seen in Fig. 3 of Fa & Pedron (2001) that an isothermal distribution in the inner region provides a sensibly better fit to observations than a polytropic one (it can reproduce the oscillations). In addition, the model of Hjorth & Madsen (1993) has only one fitting parameter $\Phi_{0}$ (the central potential) instead of two $\Phi_{0}$ and q in Fa & Pedron's analysis. These remarks tend to show that generalized thermodynamics is not necessary to understand the structure of self-gravitating systems. A similar conclusion has been reached by Brands et al. (1999) in two-dimensional turbulence.

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