<p>In class the other day, we were discussing observations of rotational transitions of carbon monoxide, namely, the <span class="math-container">$J=1\to0$</span> and <span class="math-container">$J=2\to1$</span> lines. We originally had assumed that both lines would have essentially the same linewidth, but my professor then argued that the <span class="math-container">$1\to0$</span> transition would appear, in many cases, to be broader. His argument was this:</p>

<p>The <span class="math-container">$1\to0$</span> mode, at a rest of frequency <span class="math-container">$\nu=115\text{ GHz}$</span>, is only half as energetic as the <span class="math-container">$2\to1$</span> more at <span class="math-container">$\nu=230\text{ GHz}$</span>. As less energy is required to excite molecules from <span class="math-container">$J=0$</span> to <span class="math-container">$J=1$</span>, this transition could occur in many more environments throughout a galaxy, whereas exciting a CO molecule from <span class="math-container">$J=1$</span> to <span class="math-container">$J=2$</span> requires twice as much energy and would therefore be restricted to more energetic regions, perhaps more towards the center of the galaxy. As a galaxy's rotation curve is not flat, especially in the inner regions, the <span class="math-container">$1\to0$</span> transition should occur at a variety of radii and therefore  a variety of tangential speeds. If we observe the galaxy edge-on, we should then expect to see more broadening of the <span class="math-container">$1\to0$</span> line because of this wider velocity distribution.</p>

<p>We've been looking for some hard numbers on this but haven't been able to find any; the argument feels <em>slightly</em> hand-wavy, so it would be nice to quantify this. In reality, how much broadening does the rotation of an edge-on galaxy add to the <span class="math-container">$1\to0$</span> transition compared to the <span class="math-container">$2\to1$</span> transition of carbon monoxide? How significant is this to other CO line broadening mechanisms?</p>

CC BY-SA 4.0
2020-04-21T19:04:09.723Z
Are you talking about spatially unresolved observations?
ProfRob
CC BY-SA 4.0
2020-04-21T20:05:12.877Z
@RobJeffries Yes - we were assuming a high-redshift object that would be no more than a point source.
HDE 226868
<galaxy><radio-astronomy><spectroscopy><molecules>
How significant is the effect of galactic rotation on line broadening of carbon monoxide?
HDE 226868
# How significant is the effect of galactic rotation on line broadening of carbon monoxide?

(Asked by: username_0 on 2020-04-15)

In class the other day, we were discussing observations of rotational transitions of carbon monoxide, namely, the $J=1\to0$ and $J=2\to1$ lines. We originally had assumed that both lines would have essentially the same linewidth, but my professor then argued that the $1\to0$ transition would appear, in many cases, to be broader. His argument was this:

The $1\to0$ mode, at a rest of frequency $\nu=115\text{ GHz}$, is only half as energetic as the $2\to1$ more at $\nu=230\text{ GHz}$. As less energy is required to excite molecules from $J=0$ to $J=1$, this transition could occur in many more environments throughout a galaxy, whereas exciting a CO molecule from $J=1$ to $J=2$ requires twice as much energy and would therefore be restricted to more energetic regions, perhaps more towards the center of the galaxy. As a galaxy's rotation curve is not flat, especially in the inner regions, the $1\to0$ transition should occur at a variety of radii and therefore a variety of tangential speeds. If we observe the galaxy edge-on, we should then expect to see more broadening of the $1\to0$ line because of this wider velocity distribution.

We've been looking for some hard numbers on this but haven't been able to find any; the argument feels *slightly* hand-wavy, so it would be nice to quantify this. In reality, how much broadening does the rotation of an edge-on galaxy add to the $1\to0$ transition compared to the $2\to1$ transition of carbon monoxide? How significant is this to other CO line broadening mechanisms?

**Tags:** galaxy, radio-astronomy, spectroscopy, molecules

> **Comments:**
> **username_1**: Are you talking about spatially unresolved observations?  
> **username_0**: @RobJeffries Yes - we were assuming a high-redshift object that would be no more than a point source.  

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