## Turbulent Convection in Stars

Kwing Lam Chan

Hong Kong University of Science and Technology

“A Birthday Celebration of the

Contribution of Bernard Jones to our Understanding of the Universe”

Relevance of Stellar Convection

Many unsolved problems and uncertainties in stellar astrophysics are related to convection.

e.g. massive star evolution, calibration of cluster age, …

The mixing length approach is still being heavily used.

Nature of Stellar Convection and Difficulties

• Strong Nonlinearity - Turbulence

• Deeply stratified - Large dynamical ranges

e.g. in the solar case:

depth of convection zone/ Kolmogorov micro scale ~ 10 ^{12}

thermal relaxation time/ eddy turnover time

~ 10 ^{6 }yr / 10min ~ 10 11 (limit the problem)

sound speed/ fluid velocity ~ 10 4 (implicit approach)

Two Types of Numerical Approaches

• Numerical Experiments - to study principles

relaxation enforced

(i) Direct Numerical Simulations

(ii) Large Eddy Simulations for Re>>1 relevance based on ‘similarity’

• Realistic Simulations

- to match observations

An Example of Numerical Experiments - Testing the Mixing Length Theory

An update (270x270x100 grids) of Chan & Sofia’s 1987 calculation (28x28x46 grids) Horizontal cuts at different depths of the vertical velocity field and the temperature

field for deep convection (8.5 pressure scale heights) in a 6x6x1 box

Bottom level Top level

V_{z}

T

Turbulence Spectrum and Comparison with MLT Formulas

-5/3 line (V/C_{S})^{2}

T”/T

An update (270x270x100 grids) of Chan & Sofia’s 1996 calculation (69x69x100 grids)

An Example of Realistic Simulations - Solar Granulation

Stein & Nordlund (1989)

An update

(6Mmx6Mmx2.2Mm, 174x174x86 grids)

of Kim & Chan’s 1998 calculation (1.2Mmx1.2Mmx1.5Mm,

58x58x60 grids)

< vertical cut of temperature field

< horizontal cut of temperature field

Elimination of Micro-turbulence in Spectral Line Formation

Extension to Other Stars

A simulation of Procyon’s granulation

by Robinson et al. 2005 29Mmx29Mmx16.3Mm 142x142x160 grids

A horizontal cut of the vertical velocity field

Current Interest

- Rotating Convection

A 6x6x1 box

(378x378x80 grids)
at 22.5^{o} latitude
Coriolis number

= ^{L/V ~ 9}

Longitude

Latitude

Faster Spinning

– Cyclones and Anticyclones

^{L/V ~ 18} ^{L/V ~ 36}

### AGAIN,

### HAPPY BIRTHDAY

### BERNARD

Simulation of Magnetic Loop Over an Active Region

A. Nordlund (2003)

- Convective wiggling creates million degree Corona