Chapter 6: Symbols, Nebular Lines and electronic configurations

Chapter 6: Symbols, Nebular Lines and electronic configurations#

Symbols#

  • α Recombination coefficient (\(\alpha_{B}\) is for Case B)

  • ε emissivity

  • θ angle (spatial resolution or grating)

  • \(\kappa_{\nu}\) Absorption coefficient

  • λ Wavelength

  • μ Reduced mass

  • ν Frequency

  • \(\rho_{\nu}\) Radiation field energy density

  • \(\sigma_{\nu}\) Absorption cross section

  • τ Radiative lifetime

  • \(\tau_{\lambda}\) Optical depth

  • Υ Effective collision strength

  • \(\chi_{\rm ion}\) ionization energy

  • Ω Collisional strength

  • \(a_{0}\) Bohr radius

  • \(A_{\lambda}\) Dust extinction at wavelength λ

  • \(A_{ul}\) Einstein A (spontaneous) coefficient

  • \(B_{lu}\) Einstein B (stimulated) coefficient

  • \(B_{\nu}\) Planck formula

  • \(c\) Speed of light

  • \(c_{H\beta}\) Extinction coefficient (for nebulae)

  • \(C_{lu}\) Collisional excitation rate

  • \(d\) distance (to source) or separation (between slits)

  • \(D\) diameter of telescope

  • \(E\) Energy (above ground state)

  • \(E_{\rm B-V}\) colour excess

  • \(f_{ul}\) Oscillator strength

  • \(F\) line flux or total angular momentum of atom

  • \(F_{\rm cam}\) Focal length of camera

  • \(g\) Statistical weights (or degeneracies)

  • \(\mathcal{G}\) energy input rate

  • \(h\) Planck’s constant

  • \(H_{0}\) Hubble constant

  • \(I\) intensity or nuclear spin quantum number

  • \(j\) total angular momentum of electron (\(J\) sum in outer shell)

  • \(J\) number of stellar photons

  • \(k\) Boltzmann constant

  • \(l\) Electron orbital angular momentum (\(L\) sum in outer shell)

  • \(L\) luminosity

  • \(\mathcal{L}\) Energy loss rate

  • \(m_{e}\) Electron mass

  • \(m_{p}\) Proton mass

  • \(M\) magnification of telescope

  • \(n\) Diffraction grating order or principal quantum number

  • \(n_{c}\) Critical density

  • \(n_{e}\) Electron density

  • \(n_{H}\) Hydrogen density

  • \(N(H)\) column density of hydrogen atoms

  • \(N\) number of lines in grating

  • \(N2\) Ratio of nebular lines (for abundance estimates)

  • \(N_{\rm O7V}\) Number of O7V stars

  • \(O3N2\) Ratio of nebular lines (for abundance estimates)

  • \(p\) Parity

  • \(Q_{0}\) Number of hydrogen ionizing photons

  • \(Q_{1}\) Number of singly ionizing photons of He

  • \(Q_{2}\) Number of doubly ionizing photons of He

  • \(Q_{\rm ext}\) Efficiency factor of extinction

  • \(R\) resolving power

  • \(R_{23}\) Ratio of strong nebular lines (for abundance estimates)

  • \(R_{V}\) ratio of visual extinction to colour excess

  • \(R_{\infty}\) Rydberg energy

  • \(\mathcal{R}_{s}\) Strömgren radius

  • \(s\) Spin angular momentum (\(S\) sum in outer shell)

  • \(T\) temperature (\(T_{e}\) electron, \(T_{\ast}\) stellar)

  • \(v_{\rm r}\) radial velocity (\(v_{\rm turb}\) turbulent velocity)

  • \(W\) grating width

  • \(W_{\lambda}\) Equivalent width

  • \(x_{\lambda}\) coefficient of extinction at wavelength λ vs V-band

  • \(z\) redshift or zenith distance

Common nebular lines#

Table 11 Selected nebular emission lines in H  ii regions and Planetary Nebulae in the UV and optical,#

λ

(Å)

Ion

Transition

1032,1038

O  vi

\(2s ^{2}\) S - \(2p ^{2}\) P °

1238,1242

N  v

\(2s ^{2}\) S - \(2p ^{2}\) P °

1486

N  iv]

\(2s^{2} \hspace{1mm} ^{1}\) S - \(2p ^{3}\) P °

1548,1551

C  iv

\(2s ^{2}\) S - \(2p ^{2}\) P °

1640

He  ii

3–2

1663

O  iii]

\(2p^{2} \hspace{1mm} ^{3}\) P - \(2p^{3} \hspace{1mm} ^{5}\) P °

1747,1754

N  iii]

\(2p^{2} \hspace{1mm} ^{4}\) P - \(2p \hspace{1mm} ^{2}\) P °

1907,1909

C  iii]

\(2s^{2} \hspace{1mm} ^{1}\) S - \(2p ^{3}\) P °

2297

C  iii

\(2p ^{1}\) P \(^{\circ} - 2p^{2} \hspace{1mm} ^{1}\) D

2323,2328

C  ii]

\(2p^{2} \hspace{1mm} ^{4}\) P - \(2p \hspace{1mm} ^{2}\) P °

2796,2803

Mg  ii

\(3p ^{2}\) P \(^{\circ} - 3s ^{2}\) S

3726,3729

[O  ii]

2 D - S \(_{3/2}\)

3868,3967

[Ne  iii]

1 D \(_{2} - ^{3}\) P

3970

H  i

7–2

4101

H  i

6–2

4340

H  i

5–2

4363

[O  iii]

1 S \(_{0} - ^{1}\) D 2

4471

He  i

\(4d \hspace{1mm}^{3}\) D - \(2p \hspace{1mm} ^{3}\) P

4686

He  ii

4–3

4861

H  i

4–2

4959,5007

[O  iii]

1 D \(_{2} - ^{3}\) P

5755

[N  ii]

1 S \(_{0} - ^{1}\) D 2

5876

He  i

\(3d \hspace{1mm} ^{3}\) D - \(2p \hspace{1mm} ^{3}\) P °

6300,6364

[O  i]

1 D \(_{2} - ^{3}\) P

6548

[N  ii]

1 D \(_{2} - ^{3}\) P 1

6563

H  i

3–2

6584

[N  ii]

1 D \(_{2} - ^{3}\) P 2

6678

He  i

\(3d \hspace{1mm} ^{1}\) D - \(2p \hspace{1mm} ^{1}\) P °

6716,6731

[S  ii]

2 D \(^{\circ} - ^{4}\) S \(_{3/2}^{\circ}\)

7065

He  i

\(3s \hspace{1mm} ^{3}\) S - \(2p \hspace{1mm} ^{3}\) P °

7135

[Ar  iii]

1 D \(_{2} - ^{3}\) P

7319-7330

[O  ii]

2 P \(^{\circ} - ^{2}\) D °

9069,9531

[S  iii]

1 D 2 - 3 P
Table 12 Selected nebular emission lines in H  ii regions and Planetary Nebulae in the IR.#

\(\lambda (\mu\) m)

Ion

Transition

1.012

He  ii

5-4

1.083

He  i

\(2p \hspace{1mm} ^{3}\) P \(^{\circ} - 2s \hspace{1mm} ^{3}\) S

1.282

H  i

5-3

1.875

H  i

4-3

2.058

He  i

\(2p \hspace{1mm} ^{1}\) P \(^{\circ} - 2s \hspace{1mm} ^{1}\) S

2.626

H  i

6-4

3.09

He  ii

7-6

4.05

H  i

5-4

4.65

H  i

7-5

5.61

[Mg  v]

3 P \(_{1} - ^{3}\) P 2

7.46

H  i

6-5

7.50

H  i

8-6

7.65

[Ne  vi]

2 P \(_{3/2}^{\circ} - ^{2}\) P \(_{1/2}^{\circ}\)

7.90

[Ar  v]

3 P \(_{1} - ^{3}\) P 2

8.99

[Ar  iii]

3 P \(_{1} - ^{3}\) P 2

10.51

[S  iv]

2 P \(_{3/2}^{\circ} - ^{2}\) P \(_{1/2}^{\circ}\)

11.31

H  i

9-7

12.37

H  i

7-6

12.81

[Ne  ii]

2 P \(_{1/2} - ^{2}\) P \(_{3/2}\)

14.32

[Ne  v]

3 P \(_{2} - ^{3}\) P 1

15.55

[Ne  iii]

3 P \(_{1} - ^{3}\) P 2

18.71

[S  iii]

3 P \(_{2} - ^{3}\) P 1

19.06

H  i

8-7

24.32

[Ne  v]

3 P \(_{1} - ^{3}\) P 0

25.89

[O  iv]

2 P \(_{3/2}^{\circ} - ^{2}\) P \(_{1/2}^{\circ}\)

27.80

H  i

9-8

33.48

[S  iii]

3 P \(_{1} - ^{3}\) P 0

36.01

[Ne  iii]

3 P \(_{0} - ^{3}\) P 1

37.87

H  i

10-9

51.81

[O  iii]

3 P \(_{2} - ^{3}\) P 1

57.32

[N  iii]

2 P \(_{3/2} - ^{2}\) P \(_{1/2}\)

88.36

[O  iii]

3 P \(_{1} - ^{3}\) P 0

121.9

[N  ii]

3 P \(_{2} - ^{3}\) P 1

157.7

[C  ii]

2 P \(_{3/2} - ^{2}\) P \(_{1/2}\)

205.2

[N  ii]

3 P \(_{1} - ^{3}\) P 0

Electronic configurations#

Table 13 Electronic configuration of the first 20 elements. The inner K shell \((n=1)\) is full for helium, L shell (\(n=2)\) is full for neon, whereas the M shell (\(n\)=3) is incomplete for potassium and calcium (missing \(3d\)) despite the N shell (\(n=4\)) becoming populated.#

Element

Z

Electronic configuration

H

1

\(1 s\)

He

2

\(1 s^{2}\)

Li

3

\(1 s^{2} \hspace{2mm} 2 s\)

Be

4

\(1 s^{2} \hspace{2mm}2 s^{2}\)

B

5

\(1 s^{2} \hspace{2mm}2 s^{2} 2 p\)

C

6

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{2}\)

N

7

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{3}\)

O

8

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{4}\)

F

9

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{5}\)

Ne

10

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6}\)

Na

11

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s\)

Mg

12

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2}\)

Al

13

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p\)

Si

14

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{2}\)

P

15

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{3}\)

S

16

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{4}\)

Cl

17

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{5}\)

Ar

18

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6}\)

K

19

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6} \hspace{2mm} 4s\)

Ca

20

\(1 s^{2} \hspace{2mm}2 s^{2} 2p^{6} \hspace{2mm}3 s^{2} 3p^{6} \hspace{2mm} 4s^{2}\)
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