Lecture 16 - The solar surface and atmosphere o Topics to be covered:
o Transition region
o Corona
The solar atmosphere
o Photosphere o T ~ 5,800 K o d ~ 100 km o Chromosphere o T ~ 105 K o d <2000 km. o Transition Region o T ~ 105.5 K o d ~2500 km o Corona o T >106 K o d >10,000 km The photosphere o T ~ 5,800 K
o r ~ RSun o Photosphere is the visible surface of the Sun. o At the photosphere, the density drops off abruptly, and gas becomes less opaque. o Energy can again be transported via radiation. Photons can escape from Sun. o Photosphere contains many features: PG 2nkT o Sunspots β = = 2 PB B /8π o Granules >>1 in photosphere € The photosphere (cont.) o Sunspots are dark areas in the photosphere. o Formed by the concentration of large magnetic fields (B>1000 G). o Sunspots appear dark because they are cooler (~4,300 K). o Granulation is a small scale pattern of convective cells o Results from temperature gradients close to the solar surface. Determining the photospheric temperature.
o The Sun emits a blackbody spectrum with peak ~ 5100 Å
peak
2.8978 × 10−3 o Using Wein’s Law: T = K λ peak and λ = 5100 × 10−10 m peak 2.8978 × 10−3 € T = sun 5100 × 10−10 ~ 5700 K
€ The solar constant o We know from Stephan-Boltzman Law that
L = A T4 W o A is area of Sun’s surface, T is temperature, and is Stephan-Boltzman constant (5.67 10-8 W m-2 K-4). o The flux reaching the Earth is therefore:
F = L / 4πd2 = 4πR2 T4 / 4πd2 Wm-2 [d = 1AU, R = solar radius]
= T4 (R/d)2 = 1396 W m-2 o This is relatively close to the measured value of 1366 W m-2.
The solar constant
o The “solar constant” actually has a tiny variation (~0.1%) with the solar cycle. o Represents the driver for Earth and planet climate modelling. The chromosphere o Above the photosphere is a layer of less dense but higher temperature gases called the chromosphere. o First observed at the edge of the Moon during solar eclipses. o Characterised by “spicules”, “plage”, “filaments”, etc. o Spicules extend upward from the photosphere into the chromosphere.
The chromosphere (cont.)
o Prominence and filaments are cool volumes of gas suspended above the c h r o m o s p h e r e b y magnetic fields. o Plage is hot plasma (relative to the chromosphere), usually located near sunspots. Model solar atmosphere
β >>1 β <<1
€ € P β ~ 1? β = G PB
€ € The corona
o Hot (T >1MK), low density Yohkoh X-ray image plasma (i.e. an ionized gas).
o There are currently two coronal heating theories: o Magnetic waves (AC). o Magnetic reconnection (DC).
o Coronal dynamics and properties are dominated by the solar magnetic field.
PG 2nkT β = = 2 <<1 PB B /8π
€ Static model of the corona
dP o Assuming hydrostatic equilibrium: = −gρ Eqn. 3 dr
where the plasma density is =n (me+mp) ≈ nmp (mp= proton mass) and both electrons and protons contribute€ to pressure: P = 2 nkT = 2 kT/mp
2kT dρ o Substituting into Eqn.3, = −gρ mp dr and integrating => $ mgr' ρ = ρ0 exp& − ) % kT ( € where 0 is the density at r ~ R. The scale height is H = kT / mg.
€ o OK in low coronae of Sun and solar-type stars (and planetary atmospheres). Static model of the corona
o Chapman (1957) attempted to model a static corona with thermal conduction. o Coronal heat flux is q = T
5/2 where thermal conductivity is = 0T ,
5/2 o In absence of heat sources/sinks, q = 0 => ( 0T T) = 0 o In spherical polar coordinates,
1 d # 2 5 / 2 dT & 2 % r κ 0T ( = 0 Eqn. 1 r dr $ dr '
€ Static model of the corona
dT o Eqn. 1 => r2κ T 5 / 2 = C 0 dr C dr o Separating variables and integrating: T 5 / 2dT ∫ = ∫ 2 κ 0 r € 2 C 1 => T 7 / 2 = − 7 κ 0 r C 7 o To ensure T = T at r = r and T ~ €0 as r ∞ set 7 / 2 0 0 r0T0 = − κ 0 2
€ 2 / 7 # r & ∴T = T % 0 ( Eqn. 2 0$ r ' € 6 5 o For T = 2 x 10 K at base of corona, ro = 1.05 R => T ~ 4 x 10 K at Earth (1AU = 214R). Close to measured value. € Static model of the corona
o Subing for T from Eqn. 2, and inserting for P into Eqn. 3 (i.e., including
conduction), 2 / 7 d # ρ # r & & GMρ 2 kT 0 % 0% ( ( = − 2 dr $ mp $ r ' ' r
1 dρ ρ GMmp ρ o Using multiplication rule, − 2/7 = − r2 / 7 dr r9 / 7 2kT r2 / 7 r2 € 0 0
ρ dρ r dr GMmp r dr 2/7 ∫ = ∫ − 2 / 7 ∫ 12 / 7 ρ 0 r0 r0 ρ r 2kT0r0 r € 7 GMm r5 / 7 ln(ρ /ρ ) = 2/7ln(r /r ) + p 0 0 0 5 2kT r r5 / 7 € 0 0 2 / 7 # r & # 7 GMm *# r & 5 / 7 -& (r) exp% p 0 1 ( ρ = ρ0% ( % ,% ( − /( Eqn. 4 $ r0 ' $ 5 2kT0r0 +$ r ' .' €
€ Static model of the corona
o Both electrons and protons contribute to pressure: P = 2 nkT = 2 kT/mp
" 7 GMm )" r % 5 / 7 ,% o Substituting into Eqn. 4 => P(r) P exp$ p 0 1 ' = 0 $ +$ ' − .' Eqn. 5 # 5 2kT0r0 *# r & -&
o As r ∞, Eqn.4 => € ∞ and Eqn. 5 => P const >> PISM.
-15 -4 o PISM ~ 10 P0. Eqn. 5 => P ~ 10 P0
=> There must be something wrong with the static model.