1. Mass loss and Alfvén waves in cool supergiant stars Aline A. Vidotto & Vera Jatenco-Pereira Universidade de São Paulo Instituto de Astronomia, Geofísica e Ciências Atmosféricas São Paulo - Brazil

2. Introduction Stellar mass loss has been systematically derived from observations and is present in almost all regions of the HR diagram. In general, stars with the same spectral type and luminosity class show characteristic values of mass loss rate and terminal velocity

3. Late-Type stars In cool supergiant winds: In general: M  yr -1 km s -1 The physical mechanism that drives these winds is still uncertain.

4. Sun - Sun  benchmark for stellar astrophysics. - Solar wind  a necessary reference for the study of stellar winds. - Magnetic fields  play a significant role in determining the equilibrium state of the plasma in the solar atmosphere and solar wind (e.g. Parker 1975, 1991; Priest 1999). - The outflowing solar wind  guided by open mangetic flux tubes, and  many MHD processes have been proposed to deposit heat and momentum at locations ranging from: the extended corona to interplanetary space.

5. HAO/NCAR Coronal holes: origin of fast solar wind u  > 600 km s -1. Cranmer & Ballegooijen (2005) intergranular flux tube supergranular “funnels” The open magnetic field lines are expected to expand superradially near surface: i.e. into a larger volume than would be expected if the field were radial.

6. Alfvén waves We have direct evidence for Alfvén waves in the solar wind. So, they are used as the main mechanism for wind acceleration in many regions of HR diagram. Alfvén waves are observed as large perturbations in the magnetic field and negligible density perturbations. These waves propagate outward and the dissipation of their energy and the transfer of their momentum can accelerate the wind.

7. Late-Type stars winds Several models have been proposed using: the transference of momentum and energy from Alfvén waves to the gas. Models: - constant damping length (Hartmann, Edwards & Avrett 1982) - radial geometry of magnetic field (Hartmann, Edwards & Avrett 1982) - winds are isothermal (Jatenco-Pereira & Opher 1989) - winds with ad hoc temperature profile (Falceta-Gonçalves & Jatenco- Pereira 2002)

8. Our model for a typical cool K5 supergiant star: The Model We suggest a model where we assume: - a flux of Alfvén waves as the main acceleration mechanism. - temperature profile determined by solving the energy equation taking into account both the radiative losses and the wave heating. - ressonant damping mechanism for the Alfvén waves. M  = 16 M  r 0 = 400 R  T 0 = 3500 K B 0 = 10 G  A0 = 10 6 erg cm -2 s -1

9. Equations Mass: Momentum: Energy: Heating due to Alfvén waves. Radiative cooling. Wave energy density.

10. A simplified coronal holes geometry Super-radial at the base and radial after a distance, called transition radius (r t ). The cross section of the flux tube, showed in the figure, is given by Kuin and Hearn (1982) and Parker (1963) We assume: F=  t /  0 = 10 S = 5.0 not on scale

11. Results Velocity profile Consistent with observations. At 300 r 0 : km s -1 M  yr -1

12. Results Temperature profile We also applied the model to Betelgeuse with results consistent with observations.

13. Open question Generation of Alfvén waves: can involve turbulent motions in the convection zone below the photosphere. There are evidences for large convective cells in the extended Betelgeuse atmosphere, for example. If we can measure the change in flux due to this convective motion we can study the possibility of infer the turbulence level and the eventual wave generation assuming that the turbulence can be pictured as a hierarchy of eddies. Other ideas on this subject are welcome!

14. Bibliography Cranmer, S. R. & van Ballegooijen, A. A. 2005, Ap&SS 156, 265 Falceta-Gonçalves, D. & Jatenco-Pereira, V. 2002, ApJ 576, 976 Hartmann, L., Edwards, S., & Avrett, E. 1982, ApJ 261, 279 Jatenco-Pereira, V. & Opher, R. 1989, A&A 209, 327 Kuin, N. P. M. & Hearn, A. G. 1982, AA 114, 303 Parker, E. N. 1963, “Interplanetary Dynamical Processes", Wiley New York Parker, E. N. 1975, ApJ 198, 205 Parker, E. N. 1991, ApJ 372, 719 Pneuman, G. W., Solanki, S. K. & Stenflo, J. O. 1986, A&A 154, 231 Priest, E. R. 1999, Ap&SS 264, 77