© 2009: Instituto de Astronomía, UNAM - Magnetic Fields in the Universe II: From Laboratory and Stars to the Primordial Universe Ed. A. Esquivel, J. Franco, G. García-Segura, E. M. de Gouveia Dal Pino, A. Lazarian, S. Lizano, & A. Raga RevMexAA (Serie de Conferencias), 36, 149–154 (2009) MAGNETIZED DISKS AROUND YOUNG STARS S. Lizano, 1 F. H. Shu, 2 D. Galli, 3 and A. Glassgold 4 RESUMEN Discutimos la estructura y evoluci´ on de discos magnetizados en torno a estrellas j´ ovenes que han arrastrado su campo magn´ etico en el proceso de colapso gravitacional. El disco evoluciona debido a dos procesos difusivos: estreses viscosos que redistribuyen la masa y el momento angular, y la difusi´ on resistiva de masa a trav´ es de l´ ıneas de campo magn´ etico debido a la conducci´ on imperfecta. En estado estacionario existe un modelo anal´ ıtico de la estructura de estos discos magnetizados. Discutimos la aplicaci´ on de este modelo a discos alrededor de estrellas j´ ovenes de alta y baja masa y resultados recientes de modelos dependientes del tiempo. ABSTRACT We discuss the structure and evolution of a magnetized accretion disks around young stars that have dragged their magnetic field in the process of gravitational collapse. The disk evolves due to two diffusive processes: viscous stresses that redistribute mass and angular momentum, and the resistive diffusion of mass across magnetic field lines due to imperfect conduction. In steady-state there is an analytic model of the structure of these magnetized disks. We discuss the application of this model to disks around low and high mass young stars and recent results of time dependent models. Key Words: accretion, accretion disks — ISM: magnetic fields — stars: formation — stars: pre-main sequence 1. GENERAL Stars are formed in molecular clouds which have magnetic fields strong enough to affect their dynam- ics and evolution. During the phase of gravitational collapse, the magnetic field is dragged by the accre- tion flow. The dragged field can become so strong that it can produce a catastrophic magnetic braking of the infalling gas. Thus, the loss of some magnetic flux by dissipative effects in the inner regions of the cloud core is a necessary condition for the forma- tion of protoplanetary disks (see review of Galli et al. 2009). Then, a disk of gas and dust is formed around the central star because the infalling gas has angular momentum and reaches a centrifugal bar- rier. As a result of the gravitational collapse of the central parts of such a magnetized core, one expects a poloidal field to be dragged into the accretion disk. The hourglass shape of the magnetic field lines pre- dicted by the collapse of magnetized clouds has been recently observed by dust polarized emission with the SMA by Girart et al. (2006). Polarization vec- 1 Centro de Radioastronom´ ıa y Astrof´ ısica, Universidad Nacional Aut´ onoma de M´ exico, Apdo. Postal 3-72, 58090, Morelia, Michoac´ an, Mexico (s.lizano@crya.unam.mx). 2 Department of Physics, University of California, San Diego, CA 92093, USA (fshu@physics.ucsd.edu). 3 Osservatorio Astrofisico di Arcetri, Large E. Fermi 5, 50125 Firenze, Italy (galli@arcetri.astro.it). 4 University of California at Berkeley, Astronomy Depart- ment, Berkeley, CA 94270, USA (glassgold@berekely.edu). tors in the upper panel of Figure 1 are expected to be perpendicular to the magnetic field direction shown in the lower panel. Gon¸ calves, Galli, & Girart (2008) have recently modeled these observations. Due to ohmic dissipation and ambipolar diffu- sion, some magnetic flux is lost from the inner re- gions of a cloud core such that the expected dimen- sionless disk mass-to-flux ratio is (Galli et al. 2006) λ 0 = 2πG 1/2 (M ∗ + M d ) (Φ ∗ +Φ d ) ∼ 4 , (1) where M ∗ and Φ ∗ are the mass and magnetic flux of the star, and M d and Φ d are the mass and magnetic flux of the disk. As a result of viscous and resistive evolution, the mass of the disk becomes much smaller than the mass of the central star, M d ≪ M ∗ , and the angular momentum and the magnetic flux end up in the disk. Thus, accretion disks must be strongly magnetized. Here we review the evolution of such magnetized accretion disks that evolve by viscous torques that cause the redistribution of mass and angular mo- mentum, and by resistive diffusion of mass across the poloidal field that threads the disk (Shu et al. 2007a, hereafter S07). We consider the situation af- ter the main accretion phase over the 4π steradians has passed, giving the geometry depicted by Figure 2 where mass accretion onto the star occurs mainly through the disk. 149