PY4A01 - Solar System Science Lecture 17 - The solar surface and atmosphere oTopics to be covered:...

PY4A01 - Solar System Science

Lecture 17 - The solar surface and atmosphere Lecture 17 - The solar surface and atmosphere

o Topics to be covered:

o Photosphere

o Chromosphere

o Transition region

o Corona

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The solar atmosphereThe solar atmosphere

o Photosphere o T ~ 5,800 K o d ~ 100 km

o Chromosphereo T ~ 105 K o d <2000 km.

o Transition Regiono T ~ 105.5 Ko d ~2500 km

o Coronao T >106 K o d >10,000 km




The photosphere 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:o Sunspotso Granules

€

β =PG

PB

=2nkT

B2 /8π

β >>1 in photosphere


The photosphere The photosphere (cont.)(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.




Photospheric granulationPhotospheric granulation

o Assume mass element in photosphere moves slowly and adiabatically (no energy exchange)

o Ambient density and pressure decrease: a

o Mass element expands and i and T Ti

o If i > a => cell falls back (stable)o If i < a => cell rises (unstable)

o Now replace internal parameters with adiabatic:

i ad, Ti Tad and a rad

, T

i, Tia, Ta

, T

x


Photospheric granulationPhotospheric granulation

o Now, pressure inside cell must balance with outside pressure:

Prad = Pad

=> radTrad = adTad

o Stable if |ad| < |rad| or over x if

or equivalently if

o From equation of hydrostatic equilibrium (dP/dx =- g) and the ideal gas law:

o Therefore, stable if

, T

i, Tia, Ta

, T

x

€

dρ

dx ad

<dρ

dx rad

€

dT

dx ad

>dT

dx rad

€

dT

dx=

dT

dP

dP

dx=

dT

dPρg ~

dT

dP

P

T=

d lnT

d lnP

€

d lnT

d ln P ad

>d lnT

d lnP radSchwartzchild criterion


Determining the photospheric temperature.Determining the photospheric temperature.

o The Sun emits a blackbody spectrum with peak ~ 5100 Å

o Using Wein’s Law:

and

€

T =2.8978× 10−3

λ peakK

peak

€

peak = 5100 × 10−10 m

Tsun =2.8978 × 10−3

5100 × 10−10

~ 5700 K


The solar constantThe solar constant

o We know from Stephan-Boltzman Law that

L = AT4 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 = 4πR2T4 / 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 constantThe solar constant

o The “solar constant” actually has a tiny variation (<1%) with the solar cycle.

o Represents the driver for Earth and planet climate modelling.


The chromosphereThe 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.)The chromosphere (cont.)

o Prominence and filaments are cool volumes of gas suspended above the chromosphere by magnetic fields.

o Plage is hot plasma (relative to the chromosphere), usually located near sunspots.


€

β ~ 1?

€

β >>1

€

β <<1

€

β =PG

PB

Model solar atmosphereModel solar atmosphere


The coronaThe corona

o Hot (T >1MK), low density 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.

Yohkoh X-ray image

€

β =PG

PB

=2nkT

B2 /8π<<1


Static model of the coronaStatic model of the corona

o Assuming hydrostatic equilibrium:

where the plasma density is =n (me+mp) ≈ nmp (mp= proton mass) and both electrons and protons contribute to pressure: P = 2 nkT = 2kT/mp

o Substituting into Eqn.3,

and integrating =>

where 0 is the density at r ~ R.

o OK in low coronae of Sun and solar-type stars (and planetary atmospheres).

€

dP

dr= −gρ Eqn. 3

€

2kT

mp

dρ

dr= −gρ

€

=0 exp −mgr

kT

⎛

⎝ ⎜

⎞

⎠ ⎟



o Chapman (1957) attempted to model a static corona with thermal conduction.

o Coronal heat flux is q = T

where thermal conductivity is = 0T5/2,

o In absence of heat sources/sinks, q = 0 => (0T5/2T) = 0

o In spherical polar coordinates,

€

1

r2

d

drr2κ 0T

5 / 2 dT

dr

⎛

⎝ ⎜

⎞

⎠ ⎟= 0 Eqn. 1



o Eqn. 1 =>

o Separating variables and integrating:

o To ensure T = T0 at r = r0 and T ~ 0 as r ∞ set

o For T = 2 x 106 K at base of corona, ro = 1.05 R => T ~ 4 x 105 K at Earth (1AU = 214R). Close to measured value.

€

r2κ 0T5 / 2 dT

dr= C

€

T 5 / 2dT∫ =C

κ 0

dr

r2∫

€

=>2

7T 7 / 2 = −

C

κ 0

1

r

€

∴T = T0

r0

r

⎛

⎝ ⎜

⎞

⎠ ⎟2 / 7

€

r0T07 / 2 = −

C

κ 0

7

2

Eqn. 2



o Subing for T from Eqn. 2, and inserting for P into Eqn. 3 (i.e., including conduction),

o Using multiplication rule,€

d

dr2

ρ

mp

kT0

r0

r

⎛

⎝ ⎜

⎞

⎠ ⎟2 / 7 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟= −

GMρ

r2

€

1

r2 / 7

dρ

dr− 2 /7

ρ

r9 / 7= −

GMmp

2kT0r02 / 7

ρ

r2

€

dρ

ρρ 0

ρ

∫ = 2 /7dr

rr0

r

∫ −GMmp

2kT0r02 / 7

dr

r12 / 7r0

r

∫

€

ln(ρ /ρ 0) = 2 /7ln(r /r0) +7

5

GMmp

2kT0r0

r05 / 7

r5 / 7

€

(r) = ρ 0

r

r0

⎛

⎝ ⎜

⎞

⎠ ⎟

2 / 7

exp7

5

GMmp

2kT0r0

r0

r

⎛

⎝ ⎜

⎞

⎠ ⎟5 / 7

−1 ⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ Eqn. 4



o Both electrons and protons contribute to pressure: P = 2 nkT = 2kT/mp

o Substituting into Eqn. 4 =>

€

P(r) = P0 exp7

5

GMmp

2kT0r0

r0

r

⎛

⎝ ⎜

⎞

⎠ ⎟5 / 7

−1 ⎡

⎣ ⎢

⎤

⎦ ⎥

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟ Eqn. 5

o As r ∞, Eqn.4 => ∞ and Eqn. 5 => P const >> PISM.

o PISM ~ 10-15 P0. Eqn. 5 => P ~ 10-4 P0

=> There must be something wrong with the static model.

PY4A01 - Solar System Science Lecture 17 - The solar surface and atmosphere oTopics to be covered:...

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