COLLAGE 2019
37
COLLAGE 2019 Magnetic Field Structures over a Solar Cycle Xudong Sun (UH/IfA) Apr 04 2019
Transcript of COLLAGE 2019
COLLAGE 2019
Magnetic Field Structures over a Solar Cycle
Xudong Sun (UH/IfA)
Apr 04 2019
Outline
• PFSS Model for coronal field
• Solar cycle
• Babcock-Leighton mechanism & surface flux transport
PFSS Model for Coronal Field
PFSS Model
• Assuming lower corona is current free,
B can be expressed as a scaler potential
• B vector in spherical coord
• Coronal field governed by Laplace eq.
B = − ∇Ψ
∇2Ψ = 0
Br = −∂Ψ
∂r
Bθ = −1
r
∂Ψ
∂θ
Bϕ = −1
r sin θ
∂Ψ
∂ϕ
Sun (2012)
PFSS Model
• Inner boundary: photosphere radial field
• Outer boundary: source surface where
field becomes radial and open
• General solution of Laplace equation:
−∂Ψ
∂rr=R⊙
= Br(obs)
Ψr=Rs
= 0
Rs = 2.5R⊙
Ψ =
∞
∑l=0
r−(l+1)
l
∑m=−l
almYml
(θ, ϕ) +
∞
∑l=0
rll
∑m=−l
blmYml
(θ, ϕ)
NSO/GONG
PFSS Model Solution
• Matching outer boundary
• Matching inner boundary
• Use normalization properties of spherical harmonics
• Surface integral of observed field
∞
∑l=0
R−(l+1)s
l
∑m=−l
almYml
(θ, ϕ) +
∞
∑l=0
Rls
l
∑m=−l
blmYml
(θ, ϕ) = 0, or, alm = − R2l+1s blm
∞
∑l=0
(l + 1)R−(l+2)⊙
l
∑m=−l
almYml
(θ, ϕ) −
∞
∑l=0
lRl−1⊙
l
∑m=−l
blmYml
(θ, ϕ) = Br(R⊙, θ, ϕ)
∮ dΩ Yml
(θ, ϕ)Ym′ �
l′ �(θ, ϕ) = δll′ �δmm′ �
(l + 1)R−(l+2)⊙
alm − lRl−1⊙ blm = ∮ dΩBr(R⊙, θ, ϕ)Ym
l(θ, ϕ)
http
://wso
.stanfo
rd.e
du/w
ord
s/pfss.p
df
Utility of PFSS Model
Sun (2012)
Mapping Solar Wind: WSA Model
v ∝ f −1 =Br(Rs)R
2s
Br(R⊙)R2⊙
Topology Analysis for Sympathetic Flares
Titov et al. (2012)
Solar Cycle
Butterfly Diagram
Hathaway (2015)
Defining cycle minimum/maximum
Total Solar IrradianceC
ourte
sy G. K
op
p
Variability?
Spectral Irradiance Variability
Do
min
go
et a
l. (2009)
What features determine the variability in different wavelengths?
X-Ray View Over a Cycle
Credit: Yohkoh/ISAS/LMSAL/NAOJ/U. Tokyo/NASA
Cycle Parameters
Hathaway (2015)
Period Gnevyshev Gap
Waldmeier EffectAmplitude
Spörer’s, Hale’s, & Joy’s Law
Hath
away (2
015)
Spörer’s Law
Joy’s Law
Hale’s Law
Courtesy S. Solanki
Evolution of Magnetic Field
Hathaway (2015)
Magnetic Butterfly Diagram
Hathaway (2015)
Spörer’s Law; N/S asymmetry; polarity reversal
Minimum Phase
SoHO/MDI, EIT 19.5 nm
Ascending Phase
SDO/HMI, AIA 19.3 nm
Maximum Phase
SDO/HMI, AIA 19.3 nm
Declining Phase
SDO/HMI, AIA 19.3 nm
Magnetic TopologyN
SO
/GONG
Total Solar Eclipse Imageshttp
://ww
w.zam
.fme.vu
tbr.cz/~
dru
ck/Eclip
se/
Solar Wind Over a Cycle
McComas et al. (2008)
tan θ ∼ |k11 | / |k10 |
Babcock-Leighton Mechanism &
Surface Flux Transport
Babcock-Leighton Mechanism
α-effect
Sanchez et al. (2014)
B-L mechanism
Surface Flux Transport
• Br evolution within a thin spherical shell near surface
• Induction equation with source & diffusion
or,
• Surface flow: differential rotation & meridional flow; measurable
• Diffusion: supergranular dispersion, etc.; empirically determined
• Source: flux emergence; measurable
∂Br
∂t= ∇ × (v × B)r + κ∇2Br + S(θ, ϕ, t)
∂Br
∂t= − ω(θ)
∂Br
∂ϕ−
1
R⊙ sin θ
∂
∂θ[sin θv(θ)Br] +
κ
R2⊙
[1
sin θ
∂
∂θ (sin θ∂Br
∂θ ) +1
sin2 θ
∂2Br
∂ϕ2 ] + S(θ, ϕ, t)
Surface Flux Transport
• Toroidal field (sunspot) conversion to poloidal field (dipole)
• Essential ingredient: Hale’s law, Joy’s law, & cross equatorial cancellation
Charb
onneau
(2014)
Active Region Flux Dispersal
HMI CR 2102-2104
Active Region Flux Dispersal
SFT Model of Dipole Contribution
Jiang et al. (2019)
Polar FieldTsu
neta
et a
l. (2008)
Hinode/S
P
Polar Field Reversal
https://github.com/mbobra/plotting-polar-field
X. S
un &
M. B
ob
ra
Application on Active Stars
Emergence rate 10 x + rotation period 6 d = polar field 30 x
Schrijver & Title (2001)Courtesy S. Solanki
Cycle Prediction Based on B-L
Muñoz-Jaramillo et al. (2013) Upton & Hathaway (2014)
Poloidal field (polar field at min) of Cycle N ➢ Toroidal Field (SSN) of Cycle N+1
Constructing Better Synoptic Maps
Near-Real-Time Data Assimilation + Surface Flux Transport
Courtesy M. DeRosa
