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

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1. Introduction

The neutral interstellar medium is usually described as a thermally bistable medium with a warm and diffuse phase (warm neutral medium, WNM) and a cold and dense phase (cold neutral medium, CNM) in rough pressure equilibrium. Field et al. (1969), Bergeron & Souffrin (1971), Wolfire et al. (1995) have made theoretical studies and Kulkarni & Heiles (1987), Dickey & Lockman (1990), Joncas et al. (1992), Hartmann (1994) observational ones. Measurements of the magnetic interstellar field in the atomic gas (HI) at scales below [FORMULA] (Heiles 1987, Troland & Heiles 1986, Myers et al. 1995) give values around [FORMULA] with evidence for a small ordered component and a random one. They show that the magnetic intensity is on average independent of the density in the range 0.1 to [FORMULA], i.e. the WNM and the CNM roughly have the same magnetic field. In both cases, thermal and magnetic energies have comparable orders of magnitude. Troland & Heiles (1986) argue that the concept of "relatively quiescent streaming of low-density gas along the field lines" (Parker instability at the [FORMULA] 1 kpc scale), which would naturally account for relatively constant field strengths, contradicts the evidence for supersonic flows. A theory of the formation of small scale CNM structures must account for these facts. For higher densities [FORMULA], the gas is gravitationally bound and the mean value of the magnetic field [FORMULA] increases with density (Crutcher 1999). Mouschovias (1976 a, b) and Scott & Black (1980) derive a theoretical relation between B and [FORMULA], namely:


where k takes values between [FORMULA] and [FORMULA].

Various studies deal with magneto-thermal processes. Field (1965), Oran et al. (1982), and Loewenstein (1990) investigate the effects of magnetic field on thermal instability. Balbus (1986) and Steele & Ibáñez (1999) consider magneto-thermal fronts. David & Bregman (1989) study the thermal instability with magnetic fields in the non-linear regime and note that even magnetic fields as weak as [FORMULA] can prevent the condensation. Friaça & Jafelice (1999) argue that the magnetic field has to be dissipated and consider the problem of magnetic reconnection. Gammie & Ostriker (1996) demonstrate that non-linear magnetic waves lead to strong density contrasts. However, their isothermal assumption is not suited to the study of thermal condensation. Elmegreen (1997) avoids this restriction and introduces more realistic thermal processes. He shows that non-linear magnetic waves in a thermally bistable medium produce a bimodal structure with dense clouds embedded in a diffuse intercloud medium. However, he starts from a uniform, thermally unstable medium that is neither CNM nor WNM, and it is unclear whether the two phases can exchange matter and how. Large-scale simulations of turbulent magnetized flows, including thermal processes (without thermal instability between [FORMULA] and [FORMULA] K), galactic rotation, star formation and gravity, have been performed by Passot et al. (1995) (see also Gazol-Patiño & Passot 1999, Ballesteros-Paredes et al. 1999 and Korpi et al. 1999). They study the role of the magnetic field on cloud formation and conclude, in a very extensive article, that condensations still happen for large magnetic fields (see for example Run 61 of Passot et al. 1995). Very recently Vázquez et al. (2000) investigated the development and the effects of the thermal instability in their simulations of the turbulent galactic gas and Burkert & Lin (2000) considered the emergence of small scale perturbations in a thermally unstable cloud.

Recently, Kovalenko & Shchekinov (1999) considered linear perturbations in a thermally bistable gas, initially near the unstable point ([FORMULA]). They demonstrate that thermal condensation occurs and they numerically follow the non-linear evolution. Independently we studied (Hennebelle & Pérault (1999) hereafter Paper I) the case of finite-amplitude velocity perturbations in a thermally bistable flow initially at thermal equilibrium in the diffuse phase. The diffuse phase is linearly stable but non-linearly unstable; compression can drive parcels of gas into unstable conditions, where they strongly condense until they reach the other thermal equilibrium branch (CNM). We showed that a thermal condensation occurs if the typical scale of the perturbation is large enough and the peak of the initial velocity field reaches a given threshold. We concluded that the dynamical condensation is much more efficient than the conductive condensation: the structure growth is much faster during a compression than in a quasi-isobaric medium. In a thermally bistable flow, compression effects are very important and cannot be ignored.

In our previous study, we ignored the magnetic field and one can wonder whether the condensation process still happens in the presence of magnetic field. What are the consequences of a magnetic field for thermal condensation? Condensation is always possible along the field lines, but a perfect alignment between magnetic and velocity fields is very unlikely and even a small transverse component can strongly affect the non-linear regime.

In the present article, we analytically and numerically study the dynamical condensation of a magnetized, thermally bistable flow. We deliberately ignore other physical aspects, like gravity or galactic rotation, in order to concentrate on dynamical magneto-thermal processes and restrict ourselves to 1-D slab geometry. Our approach is similar in many ways to the situation considered by Elmegreen (1997). The main difference is that condensation from the stable warm phase is driven by a converging flow rather than by non-linear magnetic waves. Further, we focus on one single event (compression leading to the formation of one cloud) whereas Elmegreen considers a larger scale with several clouds. Our approach aims at a detailed analysis and understanding of the MHD condensation mechanism.

Sect. 2 presents the equations of the problem, the notations, the orders of magnitude, and gives a qualitative discussion of the problem. Sect. 3 is an analytical investigation of the condensation and focuses on magnetic aspects. We derive self-similar solutions which describe the magneto-thermal process and show how strong condensations are possible in a magnetized gas. Sect. 4 presents a one-dimensional numerical simulation of the thermal condensation in the thermally bistable interstellar gas. Discussion and conclusions are given in Sect. 5.

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Online publication: July 13, 2000