<p>Forbidden lines are caused by a quantum mechanical effect that makes a <em>radiative</em> transmission between two quantum states very unlikely.</p>
<p>Above some density threshold, transitions between these two states will occur by collisions. Below the threshold, radiative transitions, even though unlikely, will dominate and a &quot;forbidden line&quot; will be observed.</p>
<p>The density thresholds will vary from transition to transition and with temperature. Indeed the ratios of forbidden line strengths or their appearance at all can be used as both density and temperature diagnostics.</p>
<p>Thus, you can't generalise. At some temperatures there will be groups of forbidden lines that will tend to occur below similar threshold densities. If you increase the density, some, but probably not all-but-one, of those lines will disappear (or be &quot;quenched&quot;). At other temperatures you will see completely different lines because the excitation conditions are different. For instance O VII lines (oxygen with 6 electrons knocked off) will only be seen in very hot plasmas. These are lines at X-ray wavelengths. On the other hand the O III lines of doubly ionised oxygen at 436, 493, and 501 nm are formed at lower temperatures.</p>

CC BY-SA 4.0
2023-10-08T07:14:11.447Z
2023-10-08T07:14:11.447Z
ProfRob
<p>My question is: <em>Can a star have one forbidden line, or does it have to have multiple?</em></p>
<h1>Some Examples</h1>
<p>I'll be using the O ᴠɪɪ line as an example.</p>
<p>ζ Puppis is a well studied O4Ief star with the O ᴠɪɪ forbidden line and I found <a href="https://works.swarthmore.edu/cgi/viewcontent.cgi?referer=&amp;httpsredir=1&amp;article=1014&amp;context=fac-physics" rel="nofollow noreferrer">this paper</a> that says the star has the lines S xv, Si xɪɪɪ, Mg xɪ, Ne ɪx, and O ᴠɪɪ.</p>
<p>Another star, β Crucis, this time with the spectral type B0.5 III, also has the O ᴠɪɪ line. Using <a href="https://academic.oup.com/mnras/article/386/4/1855/1456919" rel="nofollow noreferrer">this other paper</a>, I found that the star has many forbidden lines including O ᴠɪɪ, Ne ɪx, Si xɪɪɪ, Mg xɪ, N ᴠɪɪ, and Fe xᴠɪɪ.</p>
<p>I see that both stars share (besides the O ᴠɪɪ line) the Ne ɪx, Si xɪɪɪ, and Mg xɪ lines, so I'm leaning towards a star with one forbidden line, provided it has a high enough concentration of the various elements (in this case, neon, magnesium, and silicon), should have multiple lines.</p>
<p>Thank you for reading this question.</p>

<star><astrophysics>
Can a star have one forbidden line or does it have to have many?
Neil Iyer
# Can a star have one forbidden line or does it have to have many?

(Asked by: username_0 on 2023-10-08)

My question is: *Can a star have one forbidden line, or does it have to have multiple?*

# Some Examples

I'll be using the O ᴠɪɪ line as an example.

ζ Puppis is a well studied O4Ief star with the O ᴠɪɪ forbidden line and I found [this paper](https://works.swarthmore.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=1014&context=fac-physics) that says the star has the lines S xv, Si xɪɪɪ, Mg xɪ, Ne ɪx, and O ᴠɪɪ.

Another star, β Crucis, this time with the spectral type B0.5 III, also has the O ᴠɪɪ line. Using [this other paper](https://academic.oup.com/mnras/article/386/4/1855/1456919), I found that the star has many forbidden lines including O ᴠɪɪ, Ne ɪx, Si xɪɪɪ, Mg xɪ, N ᴠɪɪ, and Fe xᴠɪɪ.

I see that both stars share (besides the O ᴠɪɪ line) the Ne ɪx, Si xɪɪɪ, and Mg xɪ lines, so I'm leaning towards a star with one forbidden line, provided it has a high enough concentration of the various elements (in this case, neon, magnesium, and silicon), should have multiple lines.

Thank you for reading this question.

**Tags:** star, astrophysics

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## 1 answers

### Answer by username_1 on 2023-10-08. Score: 3 | Accepted answer

Forbidden lines are caused by a quantum mechanical effect that makes a *radiative* transmission between two quantum states very unlikely.

Above some density threshold, transitions between these two states will occur by collisions. Below the threshold, radiative transitions, even though unlikely, will dominate and a "forbidden line" will be observed.

The density thresholds will vary from transition to transition and with temperature. Indeed the ratios of forbidden line strengths or their appearance at all can be used as both density and temperature diagnostics.

Thus, you can't generalise. At some temperatures there will be groups of forbidden lines that will tend to occur below similar threshold densities. If you increase the density, some, but probably not all-but-one, of those lines will disappear (or be "quenched"). At other temperatures you will see completely different lines because the excitation conditions are different. For instance O VII lines (oxygen with 6 electrons knocked off) will only be seen in very hot plasmas. These are lines at X-ray wavelengths. On the other hand the O III lines of doubly ionised oxygen at 436, 493, and 501 nm are formed at lower temperatures.


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