6. Critique of the basic assumptions
One of the fundamental assumptions in the present analysis is the assumption of LTE. However, this assumption may not be valid for optically thin discs. A crucial feature of the above analysis and consequences is the fact that the cooling fails to overcome the heating. From thermodynamics we can generally claim that NLTE cooling will be less powerful than LTE cooling, as indeed found by DCKL that the LTE overestimates the actual cooling. Thus, we expect that NLTE will aggravate the instability and enhance the heating.
A similar argument holds for very cool discs when the actual opacity decreases. Again we encounter a situation where the cooling decreases while the heating prevails.
We assumed the existence of a thermal balance. Clearly, as soon as the balance is violated the gas starts to expand and the momentum equation in the vertical direction contains two additional terms, namely and . Strictly speaking the 1D approximation is not valid anymore. Thus the entire considerations developed here must be reconfirmed using 2D approach.
The actual calculations and figures were carried out for free-free opacity and naturally the question arise what happens under other conditions. The situation does not change in an essential way when the opacity law changes (at least as long as ). The reason is the appearance of J in the energy balance. If we write then obviously, as the temperature decreases towards the pressure rises almost irrespective of n leading to a situation where T increases as P decreases. The fact that P does not increases, namely that a given P does not have two solutions for T implies that P continues to decrease while T increases preserving the hydrostatic equilibrium. In this case there is always hydrostatic equilibrium though the temperature rises as the pressure decreases. Hence no breakdown of the hydrostatic solution and no wind. However, here we recall the model of Meyer & Meyer-Hoffmeister (1994) in which electron conduction from a hot corona into the photosphere leads to evaporation of the disc. In a more general case in which the opacity changes along the radial distance, there can be a wind in one zone and no wind in the others.
© European Southern Observatory (ESO) 1999
Online publication: March 18, 1999