Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mrao.cam.ac.uk/~kjbg1/lectures/lect7.pdf Дата изменения: Wed Oct 8 17:50:06 2003 Дата индексирования: Tue Oct 2 03:15:55 2012 Кодировка: Поисковые слова: molecules

Molecular Spectra
Par ticularly impor tant in interstellar regions.


Most molecular lines observed are lines in teh rotational spectrum. For linear molecules (e.g. OH, CO, H(C C CN ) the permitted energy levels are given by quantum mechanics of a rigid rotator
0' )' (' &" %$ " #" ! Ў ¦ ў ё § ё ¦ Ґ ¤ё ў A

In general polyatomic molecules are not linear. For symettrictop molecules (e.g. ) which have two equal principle moments of iner tia, the angular momentum along the axis of symmetry also appears in the energy level equation.
0" 0' )' ' " ¦ 7 ё @ ў 4 6 54 3 9 ё § ё ¦ Ґ

Asymettric-top molecules (e.g. ) have rotational motion which cannot be described with simple formulae. They have even richer spectra.
B B

7

A "centrifugal" distor tion introduces a term in both and into energy ­ spectrum is therefore more complicated.
DE ё " FE DC ё

7

7

1

The selection rule may be observed.



2

¦

© Ё

then predicts which transitions

8© Ё



Fine and Hyperfine Structure
Other mechanisms can give rise to lines.
P I H G R G G G

Inversion symmetry. e.g. Nitrogen can tunnel through plane defined by 3 H atoms degenerate rotational levels. Degeneracy split by interaction of nuclear and electronic motion. Transitions between these levels gives line at 1.25 cm.

N H H H N
doubling. Non-zero angular momentum along linear molecule axis splits rotation energy levels. e.g. in OH molecule gives rise to lines near 18 cm. Nuclear quadrupole moment. This will again split the (otherwise degenerate) rotational energy levels.

Q

H H H



Rotation ­ Vibration Lines
Molecules can also vibrate and have associated energy levels characterised by a quantum number . These different energy levels give rise to widely spaced infrared lines. At each state there is a set rotational levels ro-vib spectrum.
U T T S S S

4

P branch J = -1 R branch J = +1

v=1

3 2 1 0

J
4

v=0

3 2 P(4) P(3) P(2) P(1) R(0) R(1) R(2) R(3) 1 0

.

c

d

b b

a a

` `

dp

Y

e.g. . Has no dipole moment so are forbidden. Quadrupole lines with Strongest line is
Y a ` %Y ih g f c a e X W V

transitions are allowed.



Electronic Transitions
Radiation due to electron transitions between different energy levels in atoms and ions. The levels are decribed by
q r r r r r r
Spin Orbital angular momentum

Principle quantum number

n

2S+1

L

J

Total angular momentum

F x

Dipole transitions are classically "allowed" and generally have shor t occupancy times. Quadrupole transitions are classically "forbidden" and have long occupancy times. They are indicated by e.g. [OIII] Atomic hydrogen has a par ticularly impor tant spectrum. Energy of transition from level to given by Transitions are named according to the final level, . Lyman (L), Balmer (H), Paschen (P) .... correspond to .... respectively. The initial level is specified by .... corresponding to ..... e.g. H is the transition at nm Also get transitions from energy level to unbound. This gives a continuum spectrum. e.g. Lyman continuum is at nm. This leads to high opacity for nm if there is any atomic hydrogen present. This fact is used to find high redshift galaxies at ­ "Lyman break galaxies".
w i t t h ig 8d fe d t yx w v t s u m g k j t t s t s o t n l g t k j

.



H Recombination lines
Occurs in galactic HII regions, AGN planetary nebulae.
p p p p p

Emission following electron capture by proton. Electron falls through cascade.

Line ratios can be calculated by considering teh detailed balance of transitions into and out of all states, and including the Boltzmann equation and Saha equation (ionisation) ­ complicated. Line ratios also depend on whether the region is optically thick or optically thin.


1.0 L/M=0.998 0.8

1.0 i=30 0.8
o

Flux (arbitrary)

0.6

Flux (arbitrary)

0.6

0.4

0.4

0.2

0.2 D E 0.6 F 0.8 / 1.0 1.2 1.4 1.6

0.0 0.6

0.7

0.8

0.9 /

1.0

1.1

1.2

0.0 0.2

0.4

(a) Two wings
1.5 1.0 L/M=0.998 0.8 1.0

(b) Var ying rotation

Flux (arbitrary)

0.6

Flux (arbitrary) C B 1.0 / 1.2 1.4 A 1.6 0.4 0.6 0.8

0.5

0.4 0.0 0.2

0.0 0.2

-0.5 0.4

0.6

0.8 /

1.0

1.2

(c) Var ying inclination

(d) Data

Figure 1: Fe line from accretion disk round black hole. The line is distor ted by:­ (i) the bulk motion of the gas (both red and blue shifted, and relativistic beaming) ­ depends on inclination of disc (ii) by the gravity (only redshift) ­ depends on radius of last stable orbit which depends on rate of rotation.
s r q


Figure 2: Predicted shift in line spectrum for accetion disk round a rotating black hole ­ with thanks to Russell Goyder.