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?

  • $\begingroup$ Are you talking about spatially unresolved observations? $\endgroup$
    – ProfRob
    Apr 21 '20 at 19:04
  • $\begingroup$ @RobJeffries Yes - we were assuming a high-redshift object that would be no more than a point source. $\endgroup$
    – HDE 226868
    Apr 21 '20 at 20:05

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