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Astron. Astrophys. 359, 1124-1138 (2000)

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5. Discussion

Self-similar solutions have been derived in Sect. 3 for a converging and cooling MHD flow. A magnetic transverse component, as expected, reduces and possibly stops the condensation, but a sufficient longitudinal component is able to force the alignment of the velocity and magnetic fields, hence reducing the magnetic pressure without stopping the condensation process. The numerical results of Sect. 4, obtained for interstellar thermally bistable gas, confirm this behaviour. The dynamically induced thermal condensation, described in Paper I, is possible when the angle between the initial magnetic and velocity fields [FORMULA] is smaller than a maximum value, [FORMULA], which depends on the magnetic field intensity and flow parameters. This maximum angle lies in the range 20 to [FORMULA] for ISM conditions. Except for this important restriction, the mechanism presented in Paper I remains almost unchanged. If the initial value of the maximum velocity reaches a critical value, thermal condensation occurs, with a fast dynamical growth phase and a slow conductive phase. If the mean thermal pressure is above the equilibrium pressure (value of the pressure at which the fronts do not propagate), the cloud further grows during the conductive phase, while it evaporates in the opposite case.

During the fast dynamical phase, the value of the transverse magnetic field starts to increase, then decreases possibly below the mean large scale value and finally slowly reincreases during the subsequent slow evolution until it reaches the mean large scale value. As a consequence in a non-gravitational thermally bistable flow, there is no correlation between the density of the gas and the magnetic field. The magnetic intensity is moderately affected by the evolution of the density, as long as violent compressions are considered (shocks, cloud collisions), and relaxes to the original value in both phases. Indeed, in a medium with an approximate equipartition between thermal and magnetic pressure, like the neutral ISM, a correlation between field intensity and density would prevent the cloud formation. This result agrees with the observational conclusions of Troland & Heiles (1986), who find no increase of magnetic field for densities between [FORMULA] and [FORMULA] (0.1 to [FORMULA]).

The typical column density of the clouds created by dynamically induced thermal condensation is in the range [FORMULA]-[FORMULA] ([FORMULA]-[FORMULA]), which are typical column densities for observed HI clouds (Kulkarni & Heiles 1987, Dickey & Lockman 1990) or filaments of interstellar cirrus (Joncas et al. 1992). This double agreement with observational data favours the proposed mechanism as actively participating to the formation of interstellar cirrus.

Passot et al. (1995) find that the magnetic field is more intense on average (small values are found also) and more turbulent in the dense regions than in the diffuse ones (see also Ballesteros et al. 1999). But we believe that the physical situations they consider are not directly comparable to ours. Their flows are continuously thermally stable between 102 and 104 K and consequently the denser parts (the clouds) have necessarily a higher thermal pressure at thermal equilibrium than the gas of low density (the intercloud medium). The structures are transient and the distinction between the diffuse phase and the dense phase is not clear-cut. The structures are dynamically formed and dynamically maintained and cannot relax into a stationary regime. On the contrary, as we showed in the previous section, the bistable behavior allows the formation of long lived structures and has deep consequences on the evolution of the velocity and magnetic fields. However we did not consider here a problem as general as the situation described by Passot et al. Our simulation is one dimensional only and we focused on the formation of one single cloud. In a more general higher dimensional situation with a MHD turbulent flow and with several clouds formed in the gas, it could be possible that the clouds never reach mechanical equilibrium and that highly dynamical effects like cloud collisions often occur and dominate the dynamics.

In their simulation, Passot et al. note that the stellar formation rate (which follows the rate of condensation) starts to decrease when the value of the magnetic field increases, then increases and finally decreases again. We believe, that the first decrease and subsequent enhancement of stellar formation with the magnetic field are likely, at least in part to be, due to the mechanism pointed out here. Condensations are easier when [FORMULA] is greater than the equipartition value. We did not find the saturation that they have identified at large intensities. A reason of this may be the absence of gravity in our simulation. Gravity can produce contraction of the gas even perpendicularly to the field lines. But, if the magnetic field is strong these contractions are not possible, and the rate of strong condensation is reduced.

Apart from the magnetic field, all the limitations listed in the discussion of Paper I still apply. Not least, in the case of the neutral interstellar medium, the chemistry of [FORMULA] will play a significant role and should be included. In spite of these limitations, we believe that the dynamically induced thermal condensation is a key in the description of thermally bistable flows like the neutral ISM. The magnetic field introduces, as expected, a strong anisotropy in the medium, but it does not prevent thermal condensation. In a trans-sonic flow, stable clouds with the same mean magnetic field as the intercloud medium can be easely formed.

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© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000