Absorption in Solar Atmosphere

A black body spectrum emitted from solar surface causes excitation processes on atoms in the solar atmosphere. This in turn causes absorption of characteristic wavelengths corresponding to those atoms that are the most abundant ones in the solar atmosphere – absorption spectroscopy.

Solar Emittance Spectrum

Spectrum is characterized by many atomic absorption lines,

primarily by H-Balmer series of highly abundant hydrogen.

infrared visible

ultraviolet

Wavenumber: 11

cm

ck

The Hydrogen Atom

E ZE

nE eV

E

Z Z

n 2 0

2 0

0

136.

is energy necessary to ionize atom

is charge of nucleus, = 1

n : main quantum number, n=0, 1, 2, ...

ℓ : orbital momentum quantum number, ℓ = 1, 2, 3, ...n-1

m: magnetic quantum number , 2ℓ+1 values from -ℓ, -ℓ+1 ...0... ℓ+1, ℓ

s = ½ spin quantum number, s=1/2, -1/2

http://www.walter-fendt.de/ph14e/bohrh.htm

http://www.falstad.com/qmatom/

n=1

ℓ=0

n=2

ℓ=0

n=2

ℓ=1

r n m

En

eV

n

n

2 9

2

0529 10

13606

. [ ]

.[ ]

Electron transition between orbits requires or releases energy:

Transition between Energy Orbitals

Possible emission or absorption of light with fixed wavelengths by transitions of electrons between orbits! Wavelength depends on energy difference between orbits!

Hydrogen emission spectrum

Balmer Series

n=1

n=2

En = -13.6/n2

N=3⇒2

Hα: =656.3nm

N=4, N shell

L transitions

N=2, L shell

N=3, L shell

N=1, K shell

Energy and Wavelength

of emitted or absorbed Photons

eVnnch

chhE

if

22

116.131

2 2

eVnn

EEEif

nn fi

22

116.13

. J s

. m s

6 626 10

2 987 10

34

8

h Planck Co nstant: ]

c Speed of L ight:

[

[ / ]

HR

mhc

eV

110097.1

6.13 7

Multi-Electron Atoms Z is the charge and determines the chemical characteristics of the element, e.g. Z=1(Hydrogen), Z=2 (Helium) Z=8 (Oxygen). Electron transitions and photon emission is more complex and depends on Z and the shielding Sn by inner electron shells.

1

2

2

2

2

2

2

1

2

2

2

2

116.131

1

6.131

6.131

6.131

6.13

EE

hc

E

hc

hc

nZE

Zn

ZEEE

nZ

nSZE

n

K

K

K

nK

nn

K-transitions

to n=1

Example: Calculate the K and L UV-Ray Lines for He

nmE

cheVeVE

neVZE

nmE

cheVeVE

nmE

cheVeVE

ZHe

neVZE

L

L

i

L

K

K

K

K

i

K

8.656889.19

1

4

16.131

1

2

16.131

6.10209.129

116.131

6.1212.104

116.131

2:

116.131

22

2

2

2

n=1

n=2

n=3

Kα

Kβ Lα

Kα and K transitions in the ultraviolet range! L α and other L and M transitions in visible range

Each element has its own characteristic transitions

depending on the orbit quantum numbers and the

charge Z (number of electrons, protons). These

transitions can be analyzed by spectroscopy of the

light to determine the elemental abundance!

Characteristic Spectrum of Elements

ultraviolet visible infrared

Solar Spectrum

Absorption in the Earth Atmosphere

Absorption and scattering of radiation in the atmosphere depends on the

chemical and physical composition of the atmospheric layers. This includes

dust and molecular composition, moisture, temperature as well as density. It

also depends on the nature of the interaction processes of the incoming (and

exiting) radiation (photons) with the atomic and molecular gas components!

Solar Radiation in Atmosphere

dxx

d

eFF

eII

),(

0

0

)()(

F() transmitted radiation

(,x) absorption coefficient

x: thickness of atmosphere layer

The absorption coefficient

includes absorption probabilities

by molecular rotational or

vibrational excitation processes,

and photon scattering, it depends

on the composition of the

atmosphere and its atomic and

molecular components: N2, O2,

O3, CO2, CH4, H2O

Absorption Probabilities

The particle density ni(x)

depends on the overall radial

density dependence and the

mass fractions of the gas

components in the different

atmospheric layers.

The cross section i is the interaction

probability of light (photons) with a

certain wavelength or energy E=h·

with various atmospheric gases and

dust particles (excitation and

scattering)

A

i

ii

i

ii

dxx

NA

xXxn

xnx

eF

F

)()(

),(

)(

)( ),(

0

ni(x): particle density (cm-3)

i(): cross section (cm2)

dxx

abs eF

F

F

F ),(

00

)(1)(

1)(

Transmission Absorption (heat production in absorbing material)

Atmospheric Composition

Physical and Chemical Characteristics

Large variation in ni(x) with altitude for different gaseous elements and

molecules I. Enrichment of H2O vapor in lower atmosphere, the

troposphere. CO2, O2, Ar fairly continuous, O3 break up in stratosphere!

mass fraction

Ar

Rayleigh Scattering

4

257.44)(

Volume polarizability: gas =1.7·10-24 cm3

Rayleigh scattering is the elastic scattering of light by particles of size d much

smaller than the wavelength of the light , such as molecules or dust particles.

Rayleigh scattering is a function of the electric polarizability of the particles.

Scattering cross section increases with lower

wavelengths, blue light gets more scattered than

red light. It gives the sky its typically blue color

(otherwise sky would have solar white spectrum

color). Looking at sunset, scatter has increased

because of increased thickness of atmospheric

layer, blue is removed from line of sight to sun.

blue red

nmdd 100

Example Calculate Rayleigh scattering cross section on air for blue

b=450 nm and red light r=650 nm; gas =1.7·10-24 cm3

224

3

227

227

4

44

4

25

101

22.2)(

1022.2)(

64.9)(

1064.9)(

10953.37.44)(

cmbarn

mbarn

cm

mbarn

cm

cm

r

b

b

A

i

ii

i

ii NA

xXxnxnx

)()(),(

110101.1),(

00

410100.9),(

0

1033.3)(

)(

1023.1)(

)(

56

2

55

eeeF

F

eeeF

F

ddxx

H

ddxx

air

xi αi Ai ni [cm-3] σi [cm2] i cm1

N2 0.78 1.77 28 1.6776E+22 4.67145E-27 7.8366E-05

O2 0.19 0.8 32 3.5756E+21 9.543E-28 3.4122E-06

Ar 0.01 1.66 38 1.5847E+20 4.10886E-27 6.5115E-07

H2O 0.01 1.48 18 3.3456E+20 3.26609E-27 1.0927E-06

CO2 0.003 2.63 44 4.1059E+19 1.03137E-26 4.2347E-07

SO4 0.001 4.34 98 6.1449E+18 2.80856E-26 1.7258E-07

Air 0.994 1.7 2.0891E+22 4.30926E-27 9.0026E-05

everything scattered

66% scattered

Wave length =550 nm, Density 1g/cm3, Thickness of atmosphere layer d10 km

Rayleigh Scattering

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

13000 15000 17000 19000 21000 23000 25000

Scattering cross section in barn

Transmission through

10 km air (vertically)

Transmission through

30 km air (horizontally)

blue red

ddxx

air

eeF

F

),(

0 )(

)(

4257.44)( kk

Wave number k=1/

σ(

) [b

arn

], T

()

769 666 588 526 476 435 400 [nm]

[cm-1]

0/ FF