Modelling Sun-like Stars:
Cyclic convective dynamos
w/ Browning,
Brun, Miesch,
Toomre, Zweibel
Friday, September 16, 2011
SORCE meeting
September, 2011
Ben Brown
(CMSO & NSF AAPF)
Univ. Wisconsin Madison
1
Magnetic Activity in Other Suns
Magnetic Activity
(Pizzolato et al. 2003)
Rotation Rate
F-, G-, Kand M-type
Rotation Period
Friday, September 16, 2011
2
(Convective
Envelope)
Magnetic Activity
Magnetic Activity
in Solar-like Stars
(Pizzolato
et al. 2003)
CZ
Rotation Period
Radiative
Zone (RZ)
No RZ!
CZ
RZ
RZ
CZ
CZ
G-type star
1M
Convection
Zone (CZ)
A-type star
Friday, September 16, 2011
F-type star
1.5 M
☉
~5 L
☉
☉
1 L☉
M-type star
K-type star 0.3 M
☉
0.5 M
☉ ~0.001 L☉
0.04 L☉
F-M: all magnetically active
3
Inside the Sun
(Mike Thompson)
CONVECTION ZONE
VERY TURBULENT
(depth of 200 Mm)
Re ~ 1015
Stratified, Rotating
and Magnetic
Friday, September 16, 2011
4
Dynamo Modeling
(Hathaway June 2010)
2D: Mean-field models
• α-Ω type
• interface dynamos
• flux-transport and many variants
(e.g. Babcock-Leighton)
(Dikpati & Gilman 2006)
Computationally inexpensive: simulate many cycles, try many ideas
In a position to try solar predictions (but many problems)
3D: Convection, Rotation & Magnetism
• global-scale flows, magnetism,
coupling from first principles
• now achieving cyclic behavior
Computationally expensive
Solar parameters well out of reach
Friday, September 16, 2011
5
Anelastic Spherical Harmonic
(ASH) Simulations
• Capture 3-D MHD convection
Solar convection
(Miesch et al. 2008)
Friday, September 16, 2011
at high resolution on massivelyparallel supercomputers
(~1000 processors for ~1 year)
• Study turbulent convection
interacting with rotation in bulk of
solar CZ: 0.72 R - 0.97 R
• Realistic stellar structure
• Simplified physics: perfect gas,
radiative diffusivity, compressible,
subgrid transport, MHD
• Now can study similar stars too
• Comparable in scale to climate
calculations (here T170-T680)
6
(based on Miesch et al. 2008)
Radial Velocities in
a solar simulation
Case F
Sun’s rotating
reference frame
Downflows: fast, narrow
Upflows: slow, broad
Swirling, vortical
convection near
polar region
Sweeping cells
near equator
Shown near the
solar surface (2%)
-40
m/s
Friday, September 16, 2011
+20
m/s
(Period ~ 28d)
7
Differential Rotation in Other Stars
G1
J1
K1
Different masses,
same rotation rate
K-type star
0.5 M ☉
Rossby scaling
G/K-type star
0.8 M
☉
G-type star
1M
☉
All three stars rotating
at solar rate (P~28d)
Friday, September 16, 2011
8
5 Ω0
Pole-to-Equator
Temperature:
Thermal Wind
Temperature structures within case G5. Mean latitudi
Temperature
temperature are shown relative to their spherical average T̄ in (a) as cont
contrast
in
and latitude and (b) as cuts at fixed radii at the top (solid, 0.96R! ),
latitude
grows
0.84R
)
and
bottom (dotted, 0.72R! ) of the domain. (c) Temperatur
!
substantially
a snapshot
near top of domain (0.95R! ) relative to the mean structur
Figure 3.5 —
with fast rotation
(few K in the Sun,
few 100 K in some)
9
(Brown et al. 2008)
structures are long lived and appear to be a separate phenomena fr
Friday, September 16, 2011
9
Early 3-D Solar Dynamo:
CZ has little global-scale order
Volume rendering of
longitudinal field Bφ
(near equator only)
1 Ω☉ Ro~1
Friday, September 16, 2011
Magnetic fieldlines
colored by Bφ
(near equator only)
(based on Brun, Miesch, Toomre 2004)
10
Early 3-D Solar Dynamo:
CZ has little global-scale order
Magnetic fieldlines
colored by Bφ
(near equator only)
Friday, September 16, 2011
(full hemisphere, looking in)
(based on Brun, Miesch, Toomre 2004)
11
Strong DR Wreath-building Dynamo
3 Ω☉ Ro~0.4
(Brown et al. 2010)
Friday, September 16, 2011
12
Poloidal Regeneration region
Toroidal Regeneration region
Poloidal Regeneration region
Friday, September 16, 2011
13
More Turbulent Dynamos:
Magnetic Wreaths
and Global-scale Reversals
Shortly before
Friday, September 16, 2011
(Brown et al. 2011)
Long after
5 Ω0
14
Shortly
before
A Global-scale reversal
During
reversal
Long after
(Brown et al. 2011)
Friday, September 16, 2011
5 Ω0
15
5Ω
Time-latitude
map of Bφ
t1
+
Torroidal
field …
flips!
(shown here
at mid-CZ)
−
t5
−
+
(Brown et al. 2011)
Friday, September 16, 2011
16
Changes in Differential Rotation Ω
5Ω
Ω’ at mid-CZ
Polar branch
of torsional
oscillations?
Toroidal field
at mid-CZ
(Brown et al. 2011)
Friday, September 16, 2011
17
Cyclic Activity: Nearly Ubiquitous
Failed
Dynamos
Persistent
Cyclic
Strong DR
Feedback
Also see Ghizaru et al. 2010,
Racine et al. 2011
Friday, September 16, 2011
18
Rotation and
Turbulence
Persistent
higher−η
Cyclic
Persistent (?)
3Ω
11 yrs ~ 4000 days
Friday, September 16, 2011
lower−η
Cyclic
5Ω
19
Rotation and
Turbulence
Persistent
Cyclic
Hemispheric dynamo
Friday, September 16, 2011
10 Ω
20
Next Step: Sunspots and
Buoyant Magnetic Loops
The Astrophysical Journal Letters, 739:L38 (5pp), 2011 October 1
(Nelson et al. 2011, ApJL)
Nelson e
Figure 3. Analyzing a rising loop. (a) Two-dimensional cuts in longitude at successive times (tracking in longitude at the local rotation rate of the loop) sho
toroidal magnetic field over radius and latitude. The rising magnetic loop A is seen in the cross section starting at 0.81 R! at t = tb and rising to 0.91 R! after rou
Friday,
September
16, 2011
21
15 days.
Proto-loop
B is also seen rising starting at 8.6 days, but the top of loop B never rises above 0.88 R! . (b) Three-dimensional visualization of magnetic
Cyclic Activity: Nearly Ubiquitous
Failed
Dynamos
Persistent
Cyclic
Friday, September 16, 2011
Strong DR
Feedback
22