Download Can We Successfully Apply A Solar Thin-Flux

What Thin Flux Tube
Models Can Tell Us About
Star Spots
Thomas Granzer,
Vienna, 13.01.04
What is a sunspot?
How does the flux tube get there?
1) They are generated close to the
photosphere.
2) They are generated somewhere
else, but are than transported
to the photosphere.
Observations tend to possibility 2
The Model, outline:
Magnetic flux tubes are stored and amplified in the
overshoot layer (tachocline).
The star must have an outer convection zone and a
radiative core underneath.
Parker instability sets in as the magnetic field grows.
As the crests penetrate into the convection zone, the
superadiabatic stratification accelerates the growth of
the instability, a loop forms.
The summit of the loop emerges in the photosphere as
an active region.
Details of the simulation:
Initial field strength of flux tube from linear
stability analysis. For the solar case yields field
strength of 105 G.
 Total flux set to 1022 Mx.
 Semi-implicit numerical scheme for eq. of motion
of a thin, adiabatic flux tube.
 Study evolution until the thin-flux-tube
approximation breaks down (0.98 R*).
 Project the end-points to photosphere, defines
emergence latitude.
Buoyant rise of a flux tube:
Sun
Giant
Main forces:
The ratio between FB and FC determines the emerging latitude.
Results for our Sun:
1) Butterfly diagram
2) Proper motion of sunspots
3) Joy’s law
4) Hale-Nicholson’s law
Butterfly diagram:
No explanation, but at least not contradictory
Proper motion of sunspots:
At all latitudes, leading spots rotate
0.6% faster than followers.
Young groups expand rapidly, while old
groups contract slowly.
Joy’s law
Varies with latitude:
-) 6-7º at 30º,
-) 1-2º at the equator.
Hale-Nicholson rules
Preceding and following spots are of
different polarity.
The leader polarity is opposite in
opposite hemispheres.
The magnetic axes are inclined.
The leader polarity changes at the end
of the cycle.
Why not extend this model to other
stars?
Outer convection zone.
Radiative core/zone.
HRD
Stellar case:
Stellar model from spherical evolution.
 Spin up to different  (0.25, 1, 4, 10, 25,
63, rigid rot. profile).
Mainly PMS-stars, a few (sub)giants for
comparison.
 Initial field strength of flux tube from linear
stability analysis.
 Total flux set to 1022 Mx.
Which stellar models have been chosen?
Forces, extremely small cores
Axisymmetric modes rise to the pole while m >0 modes are driven to the equator.
Spot probabilities
1) We consider twelve flux tubes at latitudes 5 º
to 60 º.
2) The end-points are converted into a probability
of spot formation.
T-Tauri stars
 No significant change in spot pattern for  < 10 .
 At   10  an almost immediate transition to polar
spots occurs.
 For  higher than   25 : bimodal spot patterns:
polar spots and medium-latitude spots.
Young PMS stars
 Spots on the 0.6 M star are independent of .
 Spots on the 1.0 M star are higher than on the 1.7
M star.
 Spot latitude increases with .
PMS stars:
 Spot latitude increases with  and decreases with mass.
 Spot latitudes are higher than for our Sun, even for the
1 M, 1  model.
 At  > 25 , a saturation effect for the 0.6 M model
is visible.
ZAMS stars:
 Spot latitude increases with  and decreases with
mass.
 Spot latitudes are lower than for the PMS models.
 The 0.4 M-ZAMS model shows an almost identical
spot pattern as the 0.6 M-PMS model.
Spot latitude vs. core size
Spot probability vs. core size for fixed  = 10 .
 For anchored flux tubes the core size determines
the emerging latitude for fixed rotational rates.
 For fully detached flux tubes the instability mode
(m = 0 or m > 0) determines the emerging latitude.
PMS-stars vs. giants
PMS-stars, Rc/R*=0.4,  = 1 .
Giants, Rc/R*=0.4,  = 1 .
Decrease of spot latitude with mass.
Broader region of spot latitudes at giants.
Comparison to stars.
Four well-observed PMS stars:
V410 Tau
Par 1724
HDE 283572
AB Dor
V410 Tau
Doppler Image of V410 Tau, flux tube model a 1 M, 1 Myr,  = 14.1 
The high-latitude feature and the lowlatitude spot are well reproduced
Par 1724
Doppler Image of Par 1724, flux tube model for a 3 M, 0.2 Myr,  = 5.68 
The spot centered at 30° latitude is reproduced.
HDE 283572
Doppler Image of HDE 283572, flux tube model for a 1.8 M, 2.5 Myr,  = 17.0 
High latitude features found, but no polar spot.
AB Dor
Doppler Image of AB Dor, flux tube model for a 1 M, 15 Myr,  = 51.2 .
The polar spot is not reproduced.
Questions not addressed:
1) Flux storage for amplification.
2) High field strength necessary.
3) Flux tube coherence on rise.
4) Post-emergence evolution.
Thanks To P. Caligari, M. Schüssler