Mass loss and Alfvén waves in cool supergiant stars

Aline A. Vidotto & Vera Jatenco-Pereira

Universidade de São PauloInstituto de Astronomia, Geofísica e Ciências Atmosféricas

São Paulo - Brazil

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

v

u

M

Late-Type stars

In cool supergiant winds:

In general: 5.0~0ev

u

8020 u

M yr-158 1010~ M

km s-1

The physical mechanism that drives these winds is still uncertain.

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.

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.

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.

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)

Our model for a typical cool K5supergiant 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

r0 = 400 R

T0 = 3500 K

B0 = 10 G

A0 = 106 erg cm-2 s-1

Equations

const.u rA

dr

d

dr

dp

r

GM

dr

d 2

11uu

2

Mass:

Momentum:

Energy:

Heating due to Alfvén waves.

Radiative cooling.

RB PQdr

d

r

GM

m

Tk

dr

d

2

u

2

5

2

uu

2

ALQ vu

RP

2v Wave energy density.

S

O

O r

rrArA

)()(

A simplified coronal holes geometry

Super-radial at the base and radial after a distance, called transition radius (rt). 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

Results

Velocity profile

Consistent with observations.

At 300 r0:

68u km s-1

710M M yr-1

Results Temperature profile

0

4max

0.2at

K10

rr

T

We also applied the model to Betelgeuse with results consistent with observations.

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!

Bibliography

Cranmer, S. R. & van Ballegooijen, A. A. 2005, Ap&SS 156, 265Falceta-Gonçalves, D. & Jatenco-Pereira, V. 2002, ApJ 576, 976Hartmann, L., Edwards, S., & Avrett, E. 1982, ApJ 261, 279Jatenco-Pereira, V. & Opher, R. 1989, A&A 209, 327Kuin, N. P. M. & Hearn, A. G. 1982, AA 114, 303Parker, E. N. 1963, “Interplanetary Dynamical Processes", Wiley

New YorkParker, E. N. 1975, ApJ 198, 205Parker, E. N. 1991, ApJ 372, 719Pneuman, G. W., Solanki, S. K. & Stenflo, J. O. 1986, A&A 154, 231Priest, E. R. 1999, Ap&SS 264, 77