THE ROLE OF DUST-CYCLOTRON DAMPING OF ALFVÉN WAVES IN STAR FORMATION REGIONS

Transcription

1 THE ROLE OF DUST-CYCLOTRON DAMPING OF ALFVÉN WAVES IN STAR FORMATION REGIONS Diego Falceta-Gonçalves, Marcelo C. de Juli & Vera Jatenco-Pereira Instituto de Astronomia, Geofísica e C. Atmosféricas Universidade de São Paulo, Brazil diego@astro.iag.usp.br, juli@astro.iag.usp.br, jatenco@astro.iag.usp.br Abstract HI regions of the interstellar medium are, in general, magnetized and present both, compressive and uncompressive, perturbations due to the gas turbulence. The uncompressive motions allow the generation of Alfvén waves that propagate through the region along the magnetic field lines. The emitted power spectrum can be well described by a power law spectrum, as observed in the solar wind. These regions also present great amounts of dust particles, which may play a role in the wave propagation. Recent works show the importance of dust-cyclotron damping of Alfvén waves in dusty plasma. This process is more important than the well-known ion-cyclotron damping since it affects a broad band of frequency instead of a strict one. In this work we model the energy transfer from the waves to the gas and determine the changes in the stability conditions of the cloud, that inhibits the star formation process. We show that, considering the presence of charged dust particles, the wave flux is rapidly damped due to dust-cyclotron resonance. Then the wave pressure acts in a small length scale, and cannot explain the observable cloud sizes, but can explain the existence of small and dense cores. 1. Introduction The Interstellar Medium presents several molecular clouds, which are dense ( n H 10 4 cm 3 ), and cold ( T 10 20K) (Evans II 1999). Some of these have lengthscales of several parsecs and can live for more than 10 8 yrs. They are called as Dwarf Molecular Clouds (DMCs), and are known as the main sites of star formation regions. However, the 1

2 2 Jeans Mass, calculated by: M J = ( π G )3 2 ρ 1 2 c 3 s, (1) gives, for the assumed parameter, 3 solar masses. In the same way, the free-fall collapse time, given by: t ff = ( 3π 32ρG )1 2, (2) is 10 6 yrs. Both parameters, when compared to the DMC mass, and lifetime, show that these objects could never be in mechanical equilibrium only by thermal pressure. Several additional supporting mechanisms have been proposed, like magnetic fields (e.g. Chandrasekhar & Fermi 1953), rotation (Field 1978) and turbulence (Norman & Silk 1980; Bonazzola et al. 1987). Tipically, magnetic fields are of few gauss in these objects (Crutcher 1999), and the magnetic pressure could increase M J to the observable values, but only in the fields perpendicular direction. To the parallel direction, Alfvén waves, generated by turbulence decay, could propagate along the field direction, adding an extra pressure term in this direction. Martin et al. (1997) calculated the mechanical stability of a DMC, if an Alfvén wave flux is considered. An scheme of the situation is shown in Figure 1. Figure 1. In this scheme we show the propagation direction of the considered Alfvén waves, and the way as they increase the cloud support against gravity (Falceta- Gonçalves et al. 2003). In their calculations, Martin et al. (1997) showed that the considered Alfvén waves flux will be efficient in preventing collapse only if

3 Dust-Cyclotron Damping of Alfvén Waves in Dusty SFR 3 there is a weak wave damping. They considered only ion-neutral collisional damping, and non-linear damping, to show that the waves are not strongly damped. And, in this case, it could be supposed to be the responsible for the extra pressure against collapse in the field parallel direction. However, DMCs are dusty environments, which dust particles can be charged. Once charged, dust particles will suffer the influence of the magnetic field that gives rise to a cyclotron frequency and a resonance damping associated to it. On the other hand, differently of ion-cyclotron resonance, dust-cyclotron resonance damps the waves in large wavelenghts, and in a broad frequency band, since dust particles are of different sizes, resulting in different cyclotron frequencies. 2. Cloud Stability The temporal mean of the momentum equation for a cloud in mechanical equilibrium can be written by: P + ɛ ρ g = 0, (3) where P is the thermal gas pressure, ɛ = <δb2 > 8π is the magnetic energy density of the MHD waves propagating in the parallel direction, ρ is the gas density and g is the local gravity field. The wave energy density gradient can be obtained by the energy conservation equation, using a WKB aproximation, given by: ln(ɛ.v A ) = L 1 (4) where v A = B 4πρ is the Alfvén wave velocity and L is the wave damping length. The dispersion relation of the Alfvén waves propagating in a radius power-law spectrum dusty plasma is calculated by Cramer et al. (2002). Using their theory, the dust-cyclotron damping length can be obtained. To complish the equation system, we use the Poisson s equation:. g = 4πGρ. (5) The system of equations 3 5 was solved, and the results are showed in Figure 2.

4 4 Figure 2. Density profile obtained using different ratios for the wave energy density to thermal energy density (Λ = ɛ U int ) parameter Λ. We used Λ = 0 (dotted line), 0.05 (dashed line), 0.15 (dot-dashed line) and 0.25 (solid line) (Falceta-Gonçalves et al. 2003). 3. Conclusions Although most authors use Alfvén waves as a possible mechanism to act against gravity in DMCs collapse, we have shown that if the presence of charged dust particles is taken into account, the result is quite different. If we include the dust-cyclotron damping effects in the propagation of the Alfvén waves, they are suddenly damped, in regions smaller than 1 pc. In this case, the waves could be responsible for the formation of dense cores (which are also observed) but could not be efficient in the stability of the entire cloud. Acknowledgments The authors wish to thank the Brazilian agencies CNPq, Fapesp and FINEP for support. References Bonazzola, S. et al. 1987, A&A, 172, 293.

5 Dust-Cyclotron Damping of Alfvén Waves in Dusty SFR 5 Chandrasekhar, S. & Fermi, E. 1953, ApJ, 118, 116. Cramer, N., Verheest, F. & Vladimirov, S. 2002, Phys. Plasmas, 9, Crutcher, R. 1999, ApJ, 520, 706. Evans II, N. 1999, ARA&A, 37, 311. Falceta-Gonçalves, D., de Juli, M. C. & Jatenco-Pereira, V. 2003, submitted to ApJ. Field, G. 1978, in Protostars & Planets, University of Arizona Press, 243. Martin, C., Heyvaerts, J. & Priest, E. 1997, A&A, 326, Norman, C. & Silk, J. 1980, ApJ, 238, 158.