Download PDF presentation on the Sun

The Sun
Our Star
What we know about the Sun
•Angular Diameter θ = 32 arcmin (from observations)
•Solar Constant f = 1.4 x 106 erg/sec/cm2 (from observations)
•Distance d = 1.5 x 108 km (1 AU).
(from Kepler's Third Law and the trigonometric parallax of Venus)
•Luminosity L = 4 x 1033 erg/s.
(from the inverse-square law: L = 4 d2 f)
•Radius R = 7 x 105 km. (from geometry: R =  d)
•Mass M = 2 x 1033 gm. (from Newton's version of Kepler's Third Law,
M = (42/G) d3/P2)
•Temperature T = 5800 K. (from the black body law: L = 4πR2  T4)
•Composition about 74% Hydrogen, 24% Helium, and 2% everything
else (by mass). (from spectroscopy)
The Solar Surface
The photosphere. The visible light disk.
Galileo observed sunspots (earlier noted by Chinese observers)
• Sunspots are regions of intense magnetic fields
• Sunspots appear dark because they are cooler than the
photosphere
• A large sunspot is brighter than the full moon.
Solar Photosphere
Photosphere
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In radiative equilibrium
Convection dominates
J()=S(T) (mean intensity = source function)
Photosphere: where  = 2/3; T~5760K
Top of convective zone
Solar Granulation
Real time: 20 minutes
Magnetic Field
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Produced by a cyclic dynamo
Probably the - dynamo
Seed field at tachocline
Field is stretched by differential rotation ( effect)
Generates and amplifies poloidal fields
Convection twists field ( effect)
Field is buoyant because of magnetic pressure
Field emerges at the surface in Sunspots
- Dynamo
Photospheric Magnetic Fields
Zeeman Effect: = 4.7 x 10-13 g2B Å2 G
g: Landé g factor
g= 1+ [J(J+1)+S(S+1)-L(L+1)]/[2J(J+1)]
Sunspots
Bs2/8 + 3/2 nskTs =
3/2 npkTp
Bs ~ 2kG
Sunspots
Solar Irradiance
Temperature Profile
Solar Atmospheric Structure
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Photosphere: 5760K; 0 km
Temperature minimum: ~4000K, 500 km
Chromosphere: 8000-20000K, 500-2000 km
Transition Region: .02 - 1 MK, 2000 km
Corona: >106 K, >2000 km
Wind: >106 K, >2000 km
• Note heights are mean, and density-dependent
The Chromosphere
•First noticed in total solar eclipses.
•Name from the red color (from an emission line of Hydrogen)
•Hot (8000-20,000K) gas heated by magnetic fields.
•Bright regions known as plage.
H-alpha image
Ca II K Profile
Line profile traces source function when optically thick
Skumanich et al. 1984 ApJ, 282, 776
Chromosphere
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Densities are low
Optical depth  is low
Not in LTE
Cooling is radiative, not collisional
Chromospheric Heating
• P = kT/mH (isothermal atmosphere)
• dP/dz = -g (hydrostatic equilibrium)
• (z)=0 e(-z/H) (H = kT/mHg, the pressure scale height)
Acoustic Waves:
• Launched at z=0 (photosphere)
• Equal energy in kinetic motion, density fluctuations
• (v)2 = ()2/ cs2 [cs = sound speed, (P/) =5/3]
• Absent damping, (v)2 is constant as  decreases
• As v exceeds cs shock forms and wave dissipates
• Available energy ∝ v8; flux ∝ v8/ cs5
Chromospheric Heating II
Shocks dissipate as they propagate, heating the gas
• Heating rate Qshock = TS/(2) (S is entropy gain)
• Qshock ~  due to shock dissipation
Shock heating is balanced by radiative losses
• Qrad = nenH(T)
•  ~ 2(T)
(T) ~ -1 ~ e(z/H)
 Temperature must increase with height
Chromospheric Heating III
In the presence of magnetic fields, pressure waves are
Magnetohydrodynamic (MHD) waves, or Alfven waves.
Damping scale  ~ 1500 km
Mechanical flux: Fm = Fm,0 e-(z/ )
Note: dF/dz < 0 even though dT/dz > 0
Energy Balance
 Fm= Frad + Fcond
Fcond=-T5/2dT/dh (generally negligable)
Radiative cooling described by emission measure EM = ∫ne2dh
Frad = EM P(T)
P: power emitted in a line
 P(T) = (T) ~ 10-22 (T/30,000K) (empirical) ~2 in chromosphere
Ne = Pg/2kt electrons supply half gas pressure
Frad = ne2 P(T) = Pg2/(2kt)2 P(T) ~ ne2T 
For Fm ~ constant, ne decreases with height so T must increase
In the Transition Region T>105K and <0.
Radiation is an ineffective coolant.
Large dT/dh  large Fcond
Radiative Cooling Curve
The Corona
The diffuse outer atmospheres of the Sun.
The X-ray corona
The white-light corona
Also, the K corona - sunlight scattered from interplanetary dust
The Corona
Coronal Heating
Acoustic heating - Alfven waves
• Conductive cooling
• QA ~ v3/l (l = turbulent Eddy scale)
• Conductive heating: Fc = -T5/2 dT/dz
• T(z)=[T7/2 +(7Q/4K) (z-R)2]2/7
Joule heating
Twisting of B field drives a current
• Static loops: 1/c (JB) - + = 0 ( = GM/r)
• 1D approximation: Tmax = 1400 (L)1/3 K
Radiative Cooling
Corona is low density and not in LTE
• Radiative Recombination
A+j +e- A+j-1 +h
• Dielectronic Recombination
2S atom + e-  2P* + electron capture +h
• Charge Transfer
A+j +B A+j-1 +B+
Flares
The
Magnetic
Cycle
Spot cycle ~11 years
Magnetic cycle ~22 yrs
The Magnetic Cycle
The Butterfly Diagram
Coronal Cycle
Stellar Winds
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dP/dz = -GM/z2 (hydrostatic equilibrium)
N=/mp; P=2nekT (ionized gas)
d(2nekT)/dz = -GMnemp/z2
d(ne)/n = -GMmp/2kT (dz/z2)
Let the gas be isothermal
• ne(z) = n0e-(1-z0/z) ; = GMmp/2kTz0 and n=n0 at z=z0
• P = P0e-(1-z0/z) This does not go to 0 as z .
Residual pressure drives a stellar wind.
This is the Parker mechanism
Solar wind emanates from coronal holes, Tw ~ 2x106 K
Coronal Mass Ejections
Coronal Mass Ejections
Coronal Mass Ejections
Helioseismology
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p modes: non-radial pressure oscillations
pnlm
n: number of radial nodes
l: number of nodal lines
m: -l < m < l
|m|: number of nodes passing through poles
l-|m|: number of nodes parallel to equator
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Related to spherical harmonics Ylm(,)
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g modes: internal gravity waves
f modes: surface gravity waves
Non-radial Oscillations
l=6,m=0
l=6,m=3
Solar p modes
l=20, m=16, n=14
More Pictures and References
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Solar Data Analysis Center (SDAC): http://umbra.nascom.nasa.gov/
includes links to SOHO, SDO, HINODE, and YOHKOH
Other Solar Missions:
– STEREO:
http://www.nasa.gov/mission_pages/stereo/main/index.html
– TRACE: http://trace.lmsal.com/