# What does the ']' in the spectral line "CIII] 1909 Å" mean?

The above emission line, as I understand, is a useful probe of early star-forming galaxies.

However, I do not understand what the ']' to the right of the 'CIII' means.

I could not find any online reference that can help me decipher this and other spectral line names (for example what does the double lambda in 'O III] λλ1661' mean. Any good reference is appreciated.

Under conditions of very high temperature and very low pressure forbidden conditions can occur, they shift the color of the excitation radiation from the ultraviolet into the visible spectrum giving nebula their beautiful colors. These are represented using brackets.

See Wikipedia's Selection Rules, section Angular Momentum:

"Semi-forbidden transitions (resulting in so-called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated. This is a result of the failure of LS coupling.".

1. Element.

2. Ionization state.

3. Forbiddenness - superallowed, allowed, first forbidden, second forbidden, third forbidden, fourth forbidden, etc. Think of "forbidden" as meaning "likelihood". Represented with one or two brackets.

See note below: "In many-electrons systems transitions that violate rule 4 change the total spin (semi-forbidden transitions) and are called intercombination lines (e.g. CIII]). Transitions which violate the propensity rule 5 and/or 6 are strictly forbidden, and are labelled by two square brackets (e.g. [CIII]). Table 1 gives examples of the 3 types of transitions.

Do not confuse the use of two brackets around an element with their usage around abbreviations for massive hot blue emission stars. With massive Wolf-Rayet stars, their spectra groups are enclosed in square brackets: e.g. [WC]. Most of these show [WC] spectra, some [WO], and very rarely [WN].

4. The "double Lambda", in the example you provided, is a 'half doublet'. A doublet for that element would be OIII]λλ1661,1666 another example would be SiIII]λλ1882,1892. One paper where this is discussed is: "CIII] Emission in Star-forming Galaxies at z ~ 1" (Mar 4 2017), by Xinnan Du, Alice E. Shapley, Crystal L. Martin, and Alison L. Coil. A doublet is two distinct spectral lines formed independently but which are so close that previously inaccurate instruments and poorer understanding of these mechanisms led many to believe a single line at a particular location. See: "Performance Analysis of Standard Fourier-Transform Spectrometers" 2007 by Douglas Cohen.

5. The Å ($\unicode{x212B}$$\unicode{x212B}$ or $\unicode{x00C5}$$\unicode{x00C5}$, a Latin capital letter "A" with a ring above it) is a Swedish letter, the symbol for the ångström, a unit of length equal to 10$^{−10}$ m (one ten-billionth of a metre) or 0.1 nanometre.

Note:

From "Spectroscopy - IPAG Grenoble" (.PDF), page 2:

"2.3 Selection rules for Hydrogenic atoms

In general, there is always a non-zero probability for any transition between two states to occur. However, in some instances, the probability is exceedingly small. Under some approximations (e.g. L-S coupling, dipole approximation, ...) the matrix element might be strictly zero. However, higher-order terms generally lead to non-zero, yet small, probability. The cases in which probabilities vanish, under given approximations, are called selection rules.

The dipole transitions described above are called dipolar electric transitions. The detailed computation of the key term $\scriptsize \left| \overrightarrow \epsilon \cdot \overrightarrow \mu_{if} \right|^2$ allows to determine the cases for which a transition is allowed:

• $\scriptsize{\overrightarrow \mu}\!_{i f}$ does not vanish: dipolar electric transition between states $i$ and $f$ is allowed;

• $\scriptsize{\overrightarrow \mu}\!_{i f}$ vanishes but there exists non-zero higher-order terms in the development of $e^{i \overrightarrow k \cdot \overrightarrow r}\!\!$: dipolar electric transition is said to be semi-forbidden, but e.g. electric quadrupolar transition are allowed, though with much smaller rates;

• $\scriptsize{\overrightarrow \mu}\!_{i f}$ and all higher-order terms of the development also vanish: the transition between $i$ and $f$ is forbidden. Other higher-order terms may still allow the emission/absorption of photons.

The selection rules that apply to one-electron systems are:

• energy level: ∆n any
• orbital angular momentum: ∆l = ±1
• parity must change between i and f
• magnetic quantum number: ∆m = 0,±1
• spin does not change: ∆s = 0 (always true for the H atom)
• total angular momentum: ∆j = 0,±1

In a multi-electron atom, these rules apply to the jumping electron. These rules completely determine the spectra of one-electron atoms, such as HI and HeII, and also the alkali metals. Diagrams which show the allowed transitions are called Grotrian diagrams.

2.4 Selection rules for many-electrons systems

We have thus far discussed the interaction of single-electron atoms with a radiation field. The results can be generalized to many-electron systems, by considering the total electric dipole moment, $\scriptsize\overrightarrow D = \sum{_i} −e\overrightarrow {r_i}$. For multi-electron atoms, the selection rules for dipolar electric transitions are:

1. total angular momentum: ∆J = 0,±1 but J = 0 → 0 is strictly forbidden
2. magnetic quantum number: ∆M$_J$ = 0,±1
3. parity must change between i and f
4. spin does not change: ∆S = 0
5. one electron jumps, ∆n any, ∆l = ±1
6. orbital angular momentum: ∆L = 0,±1, 0 − 0 forbidden

The first three rules are rigorous and must be satisfied by all dipolar electric transitions. The last three are not necessarily satisfied in complex atoms, and are called propensity rules. Transitions which fulfill rules 1–3 are allowed. Transitions that violate 4 change the total spin and are called intercombination lines (e.g.CIII]). Transitions which violate the propensity rule 5 and/or 6 are strictly forbidden, and are labelled by square brackets (e.g. [CIII]). Table 1 gives examples of the 3 types of transitions.

$$\begin{array}{ccccccrrr} \\ \text{Species} & f \qquad \leftarrow \qquad i & λ (\unicode{x00C5}) & A_{ul}(s^{−1}) & \Delta J & \text{Parity}^\dagger & \Delta S & \Delta l & \Delta L \\ \hline \,\text{NII} & 2{p ^{2}} \; {^{3}\!P} ^e_0 \leftarrow 2p3s \; {^{3}\!D} ^o_1 & 1084.0 & 2.18×10^8 & -1 & o \rightarrow e & 0 & -1 & -1 \\ \;\text{CIII]} & 2{s ^{2}} \; {^{1}\!S} ^e_0 \leftarrow 2s2p \; {^{3}\!P} ^o_1 & 1908.7 & 114 & +1 & o \rightarrow e & -1 & -1 & -1 \\ \text{[CIII]} & 2{s ^{2}} \; {^{1}\!S} ^e_0 \leftarrow 2s2p \; {^{3}\!P} ^o_2 & 1906.7 & 0.0052 & +2 & o \rightarrow e & -1 & -1 & -1 \\ \end{array}$$ $$\text{Table 1: Examples of allowed, semi-forbidden, and forbidden transitions."}$$

• This is an incredible answer! semi-forbitdden; who'd a thunk it!?
– uhoh
Aug 2 '18 at 4:01
• Thanks. Along with answering the question I wanted to explain how to read the notation and provide sources for further reading and proof; also so dupes will be easier to assign. I thought "superallowed" was more humorous.
– Rob
Aug 2 '18 at 4:25
• Very complete, so although both answers do address my question, I've 'accepted' this one. Aug 2 '18 at 20:05

"O III]" looks a lot like a typo for [O III], a notation which is widely used. A [a recent paper in ApJ] uses both "[O III]" and "O III]" and I don't see a pattern. I can't believe that journal standards have slipped that badly, though, so I'm not certain it's a typo.

I've never run across the "λλ" notation before, but in that recent paper in ApJ I notice that "λλ" always precedes a pair of wavelengths (usualy a doublet) while a single λ proceeds single wavelengths. It appears it is either a symbol for "doublet" or the plural of λ

• The double square brackets denotes a forbidden line, the single square bracket is a semi-forbidden line (although the square bracket is normally before the emission line e.g. [OII) oxfordreference.com/view/10.1093/oi/authority.20110803095827784 Jul 30 '18 at 18:50
• @astrosnapper Thank you! I'd never run across that notation before. Jul 30 '18 at 19:39
• Many thanks both! I should have mentioned in my original question that I thought double square brackets indicated a forbidden line, but I was really confused with the single square bracket. Thanks both for the clarification. Jul 30 '18 at 20:16