# How significant is the effect of galactic rotation on line broadening of carbon monoxide?

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?

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