Transcript Document
Physics 681: Solar Physics and
Instrumentation – Lecture 10
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
The Atmosphere
Radiative Transfer – LTE
Equation of Transfer
Equlibria
Absorption Lines in LTE
Radiative Transfer – Statistical Equilibrium (SE)
Model Assumptions
Line Radiation and Einstein Coefficients
Continuum Radiation
Collisions
Source Function
Equations of Statistical Equilibrium
October 4, 2005
Center for Solar-Terrestrial Research
Equation of Transfer
Optical depth
d dr
Radiative transfer equation
dI
I S
d
Formal solution
I , I 0 , exp 0 /
1
0
S exp / d
Total emergent intensity
I 0,
S exp / d
1
0
How can we derive the source function from the
absolute intensity? Inversion!
October 4, 2005
Center for Solar-Terrestrial Research
Equilibria
Thermodynamic equilibrium
Local thermodynamic equilibrium (LTE)
A single temperature T describes the state of the atmosphere
everywhere
Maxwellian velocity distribution
Ionization and excitation according to the Saha and Boltzmann
equations
Homogeneous and isotropic black-body radiation field
No temperature gradient!
Locally, a single temperature T describes the atmosphere
Important simplification: Sν = Bν (T )
Thermalization length has to be shorter than the distance over which
the temperature changes
LTE might not apply to all species of particles
Good approximation for visible and IR continua, line wings, and
weak line profiles
Non-LTE (a single temperature T is insufficient)
Radiative interactions are too rare
Thermalization length is too long
October 4, 2005
Center for Solar-Terrestrial Research
Absorption Lines in LTE
Continuum and line absorption coefficients
d d C d l or d 1 d C
Intensity at disk center
I 0,1 1 B exp 1 d d
0
0
Doppler and collisional line broadening (Voigt profile)
y
D
,
D
exp / D2
2
2
0
2
d ,
with
/ 4
2
0
, and a
D
4 D
1
a
e y
H a, with H a,
dy
2
2
D
y a
October 4, 2005
2
Center for Solar-Terrestrial Research
Radiative Transfer – SE
Statistical Equlibrium (SE)
Electrons are still described by a Maxwell distribution (single electron
temperature Te)
However, population depends on radiative processes
Einstein coefficients
Spontaneous emission
nU AUL / 4
Induced emission
nU BUL I / 4
Absorption
nU BLU I / 4
October 4, 2005
Center for Solar-Terrestrial Research
Continuum Radiation and Collisions
n j j I / h
Photoionization
Radiative recombination nC
Collisional transitions between two bound states
CUL
I / h
j
j
gL
EU EL
exp
gU
kT
Collisional transition from and to the continuum
h
CCj
2 me kT
2
October 4, 2005
3/ 2
EC E j
exp
2uC
kT
ne g j
C jC
Center for Solar-Terrestrial Research