**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Influence of the magnetic field on the thermal condensation 1 2 P. Hennebelle and T. Passot 1 Laboratoire de radioastronomie millim´etrique, UMR 8112 du CNRS, 7 E´cole normale sup´erieure et Observatoire de Paris, 24 rue Lhomond, 0 75231 Paris cedex 05, France 0 2 CNRS, Observatoire de la Coˆte d’Azur, B.P. 4229, 06304, Nice Cedex 2 4, France n a J Abstract. The neutral atomic interstellar medium (HI) is well known to be 4 stronglymagnetized. SinceHIisa2-phasemediumthequestionsariseofwhatis 2 the effect of the magnetic field on a 2-phase medium, how magnetic field affects thermalinstability ? Herewesummarizeanalyticalandnumericalresultswhich 1 have been obtained previously to investigate this question. v 6 8 1. Introduction 6 1 0 Measurements of magnetic intensity in the interstellar atomic hydrogen reveal 7 that the magnetic intensity is about 6µG (Troland & Heiles 1986, Heiles 1987, 0 Heiles & Troland 2005). This indicates that the magnetic energy overcomes the / h thermalenergy by afactor of afew. Sincethe density in HI varies over at least 2 p orders of magnitude, the question arises of how thegas can condense so strongly - o in spite of a strong magnetic field without the help of gravity which is negligible r in HI. Moreover, the magnetic intensity is observed to be nearly independent t s of the gas density. More generally knowing the effect of the magnetic field on a the development of the thermal instability is of great relevance for HI. Here we : v presentsomeresultsobtainedeither analytically orbythemeanof 1Dnumerical i X simulationstoanswerthesequestions. Inthesecondsection,weconsiderthecase of an initially uniform magnetic field and identify precisely a mechanism which r a permits naturally the condensation to proceed along the field lines. In section 3, we investigate the effects of circularly polarized Alfv´en waves on thermal instability. Section 4 concludes the paper. 2. Effect of an initially uniform magnetic field Dynamical motions such as shocks (Koyama & Inutsuka 2000) or converging flows (hennebelle & P´erault 1999) have been proposed to be an efficient way of triggering thermal instability. Here we study how an initially uniform magnetic field making an angle ω with the initial velocity field affects the condensation process. Figure 1 shows the results of a 1D numerical simulation. The config- uration being symmetrical with respect to y-axis, only half of the solution is displayed. The arrows display the velocity field whereas the thick solid line is the magnetic field line at the current time step. The thin solid line is the ini- tial magnetic field line. Three timesteps are displayed. First panel shows that 1 2 Hennebelle & Passot Figure 1. Velocity (arrows) and magnetic field lines (thick solid lines) at 3 time steps. Only half of the solution is displayedsince it is symmetrical with respect to the y-axis. the converging flow has bended the field lines therefore increasing the magnetic pressure. This has the effect to slow down the gas and tends to stop the conden- sation. However in the same way, magnetic tension has generated a transverse flow. Second panel reveals that the transverse flow has significantly unbended the magnetic field lines and therefore decreases the magnetic pressure. As a Influence of the magnetic field on the thermal condensation 3 Figure 2. Condensation threshold as a function of magnetic intensity and of the initial angle between velocity and magnetic field, ω. Figure 3. Left panel: CNM structure formed through the evolution of a density perturbation in thermally unstable gas. Right panels: Density field and magnetic field y-component when an Alfv´en wave is setup in initially. consequence the condensation can proceed along the field line as shown in third panel. Figure 2 shows the condensation threshold for various values of the angle ω and the magnetic intensity for 2 different values of the initial velocity field. When the magnetic intensity is small, ω decreases rapidly when B increases. This is a natural consequence of the magnetic pressure being stronger. However for intermediate values of B (≃ 3−5µG), ω does not decreases anymore when B increases and for strong values of B, ω increases with B. This behaviour is 4 Hennebelle & Passot a direct consequence of the magnetic tension which tends to unbend the field lines. Indeed when the field is strong so that the magnetic energy dominates the kinematic one, the gas is constraint to flow along the field lines. An important consequence of this mechanism is that no correlation be- tween the magnetic intensity and the density is expected in HI. This result first obtained in 1D by Hennebelle & P´erault (2000) (see also Passot & V´azquez- Semadeni 2003) has been confirmed in 3D simulations by de Avillez & Bre- itschwerdt (2005). 3. Effect the magnetic waves Since magnetic and kinematical energies are roughly comparable in the HI, one expects magnetic field fluctuations to be important. We have therefore explored analytically and numerically the influence of Alfv´en waves on thermal instabil- ity (Hennebelle & Passot 2006). In particular an exact stability analysis of a non-linear circularly polarized Alfv´en wave, of wavelength λ0, propagating in a thermally unstable medium has been worked out. The conclusions of this analysis are i) wavelengths larger than λ0 are generally stabilized against ther- mal instability by the Alfv´en wave, ii) wavelengths slightly smaller than λ0 are generally destabilized and even more prone to thermal instability. This is a consequence of the parametric instability studied by Goldstein (1978). iii) The wavelengths much smaller than λ0 are not affected by the Alfv´en wave. In order to confirm these results and to explore the non linear regime, we have performed 1D numerical simulations. We setup a density perturbation into a thermally unstable gas that we let evolve. Left panel of figure 3 shows that the perturbation has condensed and formed a CNM structure. When an Alfv´en wave is added, right panel of figure 3 shows that the evolution is drastically different. Instead of one, about 10 small structures of CNM have formed. This is because as shown by the analytical calculations, the waves have triggered the growth of smaller wavelengths. This mechanism together with turbulence (Au- dit & Hennebelle 2005) is likely to play an important roˆle in the formation of the small scale CNM structures recently observed by Braun & Kanekar (2005) and Stanimirovi´c & Heiles (2005) References Audit E., Hennebelle P., 2005,A&A 433, 1 Braun R., Kanekar N., 2005, A&A 436L, 53 de Avillez M., Breitschwerdt D., 2005, A&A, 436, 585 Goldstein M., 1978, ApJ, 219, 700 Heiles C., 1987, Interstellar processes, ed. Hollenbach D., Thronson H. (Reidel) Heiles C., Troland T., 2005, ApJ 624, 773 Hennebelle P., P´eraultM., 1999, A&A 351, 309 Hennebelle P., P´eraultM., 2000, A&A 359, 1124 Hennebelle P., PassotT., 2006, A&A 448, 1083 Koyama H., Inutsuka S., 2000, ApJ 532, 980 Passot T., Va´zquez-semadeni E., 2003,A&A 398, 845 Stanimirovi´c S., Heiles C., 2005, ApJ 631, 371 Troland T., Heiles C., 1986, ApJ 301, 339