Post on 24-Apr-2020
Molecular Spectral Lines
Han UitenbroekNational Solar Observatory/Sacramento Peak
Sunspot, USA
Hale COLLAGE, Boulder, Feb 23, 2016
Han Uitenbroek/NSO Molecular Spectral Lines
Molecular Spectral Lines in the Solar Spectrum
Molecules are abundant in the solar atmosphere, in particularin cooler areas like Sunspot umbrae.
The G band is one of the most used pass bands in solar highresolution imaging. Its major source of opacity is a band oflines of the CH molecule.
CO lines are important temperature diagnostics for the solaratmosphere.
Molecules are sensitive to the Zeeman effect, and have muchmore diverse sensitivity than atomic lines. This can be used toadvantage.
In some cases molecular lines can be used for abundancedeterminations when spectral lines of one of the constituentsare not readily observable (Fluorine).
Han Uitenbroek/NSO Molecular Spectral Lines
CO Lines in the Solar Spectrum
2142.0 2142.5 2143.0 2143.5Wave number [cm−1]
4.0•10−9
4.5•10−9
5.0•10−9
5.5•10−9
6.0•10−9
Inte
nsity
[J s
−1 m
−2 H
z−1 s
r−1 ]
4668 4667 4666 4665Wavelength [nm]
4500
5000
5500
6000
Brig
htne
ss T
empe
ratu
re [K
]
6−
5 R
46
7−
6 R
106
2−
1 R
21
[13]
2−
1 R
6
3−
2 R
14
7−
6 R
67
6−
5 R
126
4−
3 R
23
3−
2 R
31
[13]
7−
6 R
105
5−
4 R
120
[13]
5−
4 R
59
[13]
4−
3 R
43
[13]
5−
4 R
139
7−
6 R
68
4−
3 R
136
[13]
6−
5 R
47
Han Uitenbroek/NSO Molecular Spectral Lines
Water Lines in Umbral Spectrum
Han Uitenbroek/NSO Molecular Spectral Lines
Degrees of Freedom and Energy Levels Diatomic Molecule
Energy Levels:
Translational energy:
Etrans =1
2mv2 =
p2
2m
Rotational energy:
Erot = L2/2I
= J(J + 1)~2/µr20
Vibrational energy:
Evibr =
(v +
1
2
)~ω
Han Uitenbroek/NSO Molecular Spectral Lines
Electronic States in Diatomic Molecule
Han Uitenbroek/NSO Molecular Spectral Lines
Electronic States in Diatomic Molecule
Han Uitenbroek/NSO Molecular Spectral Lines
Energy Levels of the ground State (X) of the CO Molecule
0 1 2 3 4 5 6 7 8 900Vibrational level
0
1
2
3
4
5E
nerg
y [e
V]
Han Uitenbroek/NSO Molecular Spectral Lines
Vibration-Rotation Transitions in CO ground State
0 1 2 3Vibration number
2.2
2.4
2.6
2.8
3.0
3.2
3.4E
[eV
]P branchR branch
110 109 108 107 106 105 104 103 102 101
Han Uitenbroek/NSO Molecular Spectral Lines
Molecular Lines are grouped in Bands
4000 4500 5000 5500 6000 6500 7000Wavelength [nm]
10−8
10−7
10−6
10−5
10−4
10−3
Line
str
engt
h
1 − 0 transitions3 − 2
Bandheads T = 4000 K
R branch
P branch
2400 2200 2000 1800 1600Wavenumber [cm−1]
Han Uitenbroek/NSO Molecular Spectral Lines
Example: CN band head at 388.3 nm
387.0 387.5 388.0 388.5 389.0Wavelength [nm]
0.0
0.2
0.4
0.6
0.8
1.0R
ela
tive Inte
nsity
CenterLimb [λ=0.2]
Han Uitenbroek/NSO Molecular Spectral Lines
Abundance of Molecules:
Abundance of atomic Species:
ntotA = AAnH
Chemical equilibrium:
nAnBnAB
=
(2πmABkT
h2
)3/2
e−D/kT(UA(T )UB(T )
QAB(T )
)mAB =
mAmB
mA + mB
Non-linear set of coupled equations:
nAB − nAnBΦAB(T ) = 0
nA + nAB = AAnH
nB + nAB = ABnH
Han Uitenbroek/NSO Molecular Spectral Lines
Molecular Concentrations in the Solar Atmosphere
FALC_82.atmos (Thu Apr 13 10:17:01 2000)
−500 0 500 1000 1500 2000 2500Height [km]
10−25
10−20
10−15
10−10
10−5
n mol
ecul
e / n
Htot
H2H2+C2N2O2CHCOCNNHNOOHH2OH−
Han Uitenbroek/NSO Molecular Spectral Lines
CO Concentration in Vertical Magneto-Comvection Slice
13
14
15
16
17
18
19
log(
n CO
/ m−
3 )
0
1 2 3 4 5 6x [Mm]
−0.2
0.0
0.2
0.4
0.6
z [M
m]
15.015
.0
15.0
16.016
.0
17.017.0
17.017.0
18.0
18.0
18.018.0
18.5
18.5 18.5
18.5
18.5
3−2 R14
7−6 R68
3.60
3.70
3.80
3.90
4.00
log(
Tem
pera
ture
/ K
)
−0.2
0.0
0.2
0.4
0.6z
[Mm
]
Han Uitenbroek/NSO Molecular Spectral Lines
CH Concentration in Magneto-Convection Slice
nCH / nH
0 2•10−8 4•10−8 6•10−8 8•10−8 1•10−7
−0.2
0.0
0.2
0.4
z [
Mm
]
0 1 2 3 4 5 6 7 8x [arcsec]
Han Uitenbroek/NSO Molecular Spectral Lines
G-band Intensity as Tracer of Small-scale Magnetic Field
Courtesy: LMSAL, SVT La Palma
Han Uitenbroek/NSO Molecular Spectral Lines
Filter Integrated Intensity
429.0 429.5 430.0 430.5 431.0 431.5 432.0wavelength [nm]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5In
tens
ity [1
0−8 J
m−
2 s−
1 Hz−
1 sr−
1 ]
Filter signal:
f =
∫ ∞0
Iλfλdλ
Han Uitenbroek/NSO Molecular Spectral Lines
Molecular Bands in the Blue
429.0 429.5 430.0 430.5 431.0 431.5 432.0Wavelength [nm]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Inte
nsity
[10−
8 J m
−2 s
−1 H
z−1 s
r−1 ]
387.0 387.5 388.0 388.5 389.0 389.5Wavelength [nm]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Inte
nsity
[10−
8 J m
−2 s
−1 H
z−1 s
r−1 ]
Han Uitenbroek/NSO Molecular Spectral Lines
Filtergrams in CH and CN Bands
G−band filter intensity
1.0 1.5 2.0 2.5
0
1
2
3
4
5
6
7
8
y [
arcs
ec]
0 1 2 3 4 5 6 7 8x [arcsec]
CN 388.3 filter intensity
0.5 1.0 1.5 2.0 2.5
0
1
2
3
4
5
6
7
8
y [
arcs
ec]
0 1 2 3 4 5 6 7 8x [arcsec]
Han Uitenbroek/NSO Molecular Spectral Lines
Filtergrams in CH and CN Bands
G−band filter intensity
1.0 1.5 2.0 2.5
0
1
2
3
4
5
6
7
8
y [
arcs
ec]
0 1 2 3 4 5 6 7 8x [arcsec]
CN 388.3 filter intensity
0.5 1.0 1.5 2.0 2.5
0
1
2
3
4
5
6
7
8
y [
arcs
ec]
0 1 2 3 4 5 6 7 8x [arcsec]
Han Uitenbroek/NSO Molecular Spectral Lines
Comparison of Observed and Calculated Spectra
387.0 387.5 388.0 388.5 389.0 389.5Wavelength [nm]
0.0
0.2
0.4
0.6
0.8
1.0
1.2R
elat
ive
inte
nsity
429.0 429.5 430.0 430.5 431.0 431.5 432.0Wavelength [nm]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Rel
ativ
e in
tens
ity
Han Uitenbroek/NSO Molecular Spectral Lines
Detailed Spectra of Granule and Bright Point
430.20 430.25 430.30 430.35 430.40wavelength [nm]
0
1
2
3
4
Inte
nsity
[10−8
J m
−2 s
−1 H
z−1 s
r−1]
388.15 388.20 388.25 388.30 388.35wavelength [nm]
0
1
2
3
Inte
nsity
[10−8
J m
−2 s
−1 H
z−1 s
r−1]
averagegranulebright point
Han Uitenbroek/NSO Molecular Spectral Lines
Concentration of CH Molecule and Magnetic Field
101110121013
101410151016
CH
co
nce
ntr
atio
n [m
−3]
−0.2
0.0
0.2
0.4H
eig
ht [M
m]
0.0
0.5
1.0
1.5
2.0
2.5
Fie
ld S
tre
ng
th [kG
]
0
2 4 6 8 10x [Mm]
−0.2
0.0
0.2
0.4
He
igh
t [M
m]
Han Uitenbroek/NSO Molecular Spectral Lines
Formation Height of CH band
T [103 K]
6 8 10
−0.2
0.0
0.2
0.4
y [
Mm
]
0 1 2 3 4 5x [Mm]
µ = 0.93
Han Uitenbroek/NSO Molecular Spectral Lines
The Zeeman effect in atoms
H
M
L
J S
MJ = −J,−J + 1, . . . , J − 1, J
Jz = MJ~E = E0 + gLMJµHH
gL =3
2+
S(S + 1)− L(L + 1)
2J(J + 1)
0+1
−10 0
+1+2
−1−2
MM
M
S P D011
J
JJ
11 2
Han Uitenbroek/NSO Molecular Spectral Lines
Splitting pattern for Fe i 630.25 nm and 630.15 nm
−2 0 2Wavelength shift [Larmor units]
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
Nor
mal
ized
str
engt
h
gLeff = 2.500
5D0 − 5P1
π − component
ρ+
ρ−
−3 −2 −1 0 1 2 3Wavelength shift [Larmor units]
−0.6
−0.4
−0.2
0.0
0.2
Nor
mal
ized
str
engt
h
gLeff = 1.667
5D2 − 5P2
π − component
ρ+
ρ−
Han Uitenbroek/NSO Molecular Spectral Lines
Zeeman effect in molecules: Hund’s Case (a) and (b)
J
H
M R
ΛΣ
Ω
Hund’s case (a)
J
S
RN
Λ
H
M
Hund’s case (b)
Han Uitenbroek/NSO Molecular Spectral Lines
Comparison of effective Lande factors
Interaction energy:
E = gLMJ (e~/2mec)B
Lande factor for atomic energy level:
gL =3
2+
S(S + 1)− L(L + 1)
2J(J + 1)
Lande factor for molecular energy level in Hund’s case (b):
gL =MJ
J(J + 1)
Λ2 [J(J + 1) + N(N + 1)− S(S + 1)]
2N(N + 1)+
[J(J + 1)− N(N + 1) + S(S + 1)]
Han Uitenbroek/NSO Molecular Spectral Lines
Splitting Patterns for Main Branch (∆N = ∆J) J ′′ = 3.5
−2 −1 0 1 2Shift [Larmor units]
−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15S
treng
th
gLeff = −0.363
Branch: P11
−1.0 −0.5 0.0 0.5 1.0Shift [Larmor units]
−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
Stre
ngth
gLeff = −0.494
Branch: P22
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5Shift [Larmor units]
−0.15
−0.10
−0.05
0.00
0.05
Stre
ngth
gLeff = 0.464
Branch: Q11
−0.5 0.0 0.5Shift [Larmor units]
−0.15
−0.10
−0.05
0.00
0.05
Stre
ngth
gLeff = −0.083
Branch: Q22
−0.5 0.0 0.5Shift [Larmor units]
−0.10
−0.05
0.00
0.05
0.10
Stre
ngth
gLeff = 0.475
Branch: R11
−0.6 −0.4 −0.2 0.0 0.2 0.4 0.6Shift [Larmor units]
−0.10
−0.05
0.00
0.05
0.10
Stre
ngth
gLeff = 0.192
Branch: R22
Jl = 3.5
Han Uitenbroek/NSO Molecular Spectral Lines
Splitting Patterns for Main Branch J ′′ = 15.5
−0.4 −0.2 0.0 0.2 0.4Shift [Larmor units]
−0.02
0.00
0.02
Stre
ngth
gLeff = −0.068
Branch: P11
−0.2 −0.1 0.0 0.1 0.2Shift [Larmor units]
−0.02
0.00
0.02
Stre
ngth
gLeff = −0.126
Branch: P22
−0.2 0.0 0.2Shift [Larmor units]
−0.05
−0.04
−0.03
−0.02
−0.01
0.00
0.01
Stre
ngth
gLeff = 0.075Branch: Q11
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3Shift [Larmor units]
−0.05
−0.04
−0.03
−0.02
−0.01
0.00
0.01
Stre
ngth
gLeff = −0.051Branch: Q22
−0.2 −0.1 0.0 0.1 0.2Shift [Larmor units]
−0.02
0.00
0.02
Stre
ngth
gLeff = 0.124
Branch: R11
−0.2 0.0 0.2Shift [Larmor units]
−0.02
0.00
0.02
Stre
ngth
gLeff = 0.058
Branch: R22
Jl = 15.5
Han Uitenbroek/NSO Molecular Spectral Lines
Effective Lande Factor of CH A2∆–X2Π System(Main Branches)
0
5 10 15 20 25 30J’’
−2
−1
0
1
2g e
ff
P11 P22
Q11
Q22
R11
R22
See also: Berdyugina & Solanki, 2002
Han Uitenbroek/NSO Molecular Spectral Lines
The G band Stokes V Spectrum with B = 103 G
431.00 431.10 431.20 431.30 431.40 431.50Wavelength [nm]
0
5.0•10−9
1.0•10−8
1.5•10−8
2.0•10−8
2.5•10−8
3.0•10−8
Inte
nsi
ty [J
m−
2 s
−1 H
z−1 s
r−1]
431.00 431.10 431.20 431.30 431.40 431.50Wavelength [nm]
−5•10−9
0
5•10−9
Sto
kes
V [J
m−
2 s
−1 H
z−1 s
r−1]
Han Uitenbroek/NSO Molecular Spectral Lines
Sunspot observations in the G band
2000
4000
6000
8000
Co
un
ts
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Re
lative
in
ten
sity
−1
0
1
Ve
locity [
km
]
Han Uitenbroek/NSO Molecular Spectral Lines
Observed Sokes V in the G band
430.2 430.4 430.6 430.8 431.0 431.2 431.4Wavelength [nm]
0.0
0.2
0.4
0.6
0.8
1.0
1.2S
tokes I / I
cont
430.2 430.4 430.6 430.8 431.0 431.2 431.4Wavelength [nm]
−0.2
−0.1
0.0
0.1
0.2
Sto
kes V
/ I
cont
Han Uitenbroek/NSO Molecular Spectral Lines
Magnetogram in CH line
−2000
−1000
0
1000
Ma
gn
etic f
ield
[G
au
ss]
Han Uitenbroek/NSO Molecular Spectral Lines
Determination of Fluorine (F) Abundance
Fluorine is an important element in tracing the mechanisms ofstellar nucleosynthesis and the chemical history of the Galaxy.
Having an almost full outer electron shell, the first excitedlevel from the ground state lies at 102,000 cm−1 (12.65 eV).Almost nothing in the photosphere can excite this, so higherlying levels are almost not populated, making associated linesvery weak.
The HF molecule has line in the 2.3 micron range, but HF hasa low dissociation energy (5.87 eV) and only exists in sunspotumbrae in the solar atmosphere.
Han Uitenbroek/NSO Molecular Spectral Lines
Determining the effective temperature of Sunspot atlasobservation
1564.6 1564.8 1565.0 1565.2 1565.4 1565.6wavelength [nm]
0.0
0.2
0.4
0.6
0.8
1.0
rela
tive inte
nsity
OH
15
65
.06
OH
15
65
.08
OH
15
65
.19
OH
15
65
.35
OH
15
65
.41
OH
15
65
.51
AO = 8.66
MACKKL
Teff 4250
Teff 4500
Maiorca, Uitenbroek, Uttenthaler, Randich, Busso, Magrini 2014,ApJ 788, 149
Han Uitenbroek/NSO Molecular Spectral Lines
Fitting of the Fluorine lines with AF = 4.40
Han Uitenbroek/NSO Molecular Spectral Lines
Partition Function of Discrete System
In a closed system with discrete states i = 1, . . . ,N, andcorresponding energy levels Ei and statistical weights gi , thepartition function Z (T ) is given by:
Z (T ) =N∑i=1
gie−Ei/kT
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Han Uitenbroek/NSO Molecular Spectral Lines