Heat transfer in penumbral magnetic flux tubes
Origin of dark-cored penumbral filaments
Basilio Ruiz Cobo† & Luis R. Bellot Rubio‡
†Instituto
Astrofísica de Canarias
‡Kiepenheuer Institut für Sonnenphysik
Penumbral dark cores
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•
•
•
Scharmer et al (2002) Nature
Penumbral grains
Dark cores in bright filaments
Sütterlin et al (2004)
New Swedish 1m Solar Telecope
12/05/2005
Ruiz Cobo & Bellot Rubio
Penumbral dark cores
•
•
•
•
Scharmer et al (2002) Nature
Penumbral grains
Dark cores in bright filaments
Sütterlin et al (2004)
New Swedish 1m Solar Telecope
12/05/2005
Ruiz Cobo & Bellot Rubio
160 km
Penumbral dark cores
•
•
•
•
Scharmer et al (2002) Nature
Penumbral grains
Dark cores in bright filaments
Sütterlin et al (2004)
New Swedish 1m Solar Telecope
12/05/2005
Ruiz Cobo & Bellot Rubio
The model: magnetic field
• Cylindrical tube, radius R, in a stratified background atmosphere
• Magnetohidrostatic eq.
• Stationary diffusion eq.
Bb γ b
Bt γ t
• Schlichenmaier et al (1998) simulation of emerging bright tubes with small
and more horizonal magnetic field embedded in a stronger and more vertical one
12/05/2005
Ruiz Cobo & Bellot Rubio
The stationary diffusion equation
∇[− k r ∇T − Λkc (∇T − (dT dz )ad )] = S
Radiative flux
Convective flux
S = j2 σ
Kopecký & Kuklin
σ = σ long
(1969)
2D: No dependence with Y direction (along the tube)
Known: Pg(x,z)=Pg(x=0,z) Hydrostatic equilibrium
B(x,z)
+ Horizontal balance total pressure
Free: T(x,z)
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Straight tube
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 85º
Rt = 80km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
12/05/2005
Ruiz Cobo & Bellot Rubio
Evershed flow
• Material flow (speed 6 km/s) flowing along our
horizontal tubes.
• Evershed flow produces flux of energy (from entropy eq)
r
r
FE = ρ cVVE ⋅ [∇T − (dT dz )ad uz ]
• This flux is introduced as a source in the diffusion
equation
∇[− k r ∇T − Λkc (∇T − (dT dz )ad )] = j 2 σ + FE
12/05/2005
Ruiz Cobo & Bellot Rubio
Evershed flow
axis at –150 km
axis at –50 km
axis at 0 km
axis at +75 km
12/05/2005
Ruiz Cobo & Bellot Rubio
Evershed flow
Bb = 2000 − 1400G
γ b = 30º −60º
Bt = 1000G
γ t = 40º −90º
Rt = 80km
δ = 2km
σ = 0.01σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Evershed flow
Bb = 2000G
γ b = 30º
Bt = 500G
γ t = 40º −90º
Rt = 15km
δ = 2km
σ = 0.1σ long
12/05/2005
Ruiz Cobo & Bellot Rubio
Conclusions
• Horizontal weak tubes block thermal flux
• Dark-cored penumbral filaments: τ=1 cuts heated layers
at the walls & shadow regions on the top of filaments
• Evershed flow heats penumbral filaments, increasing
brightness of dark cores. It also generates penumbral grains
• Radius of around 80 km are required in order to explain
observations with this model
12/05/2005
Ruiz Cobo & Bellot Rubio
Muchas gracias