CO ladder

The CO ladder (aka CO rotational ladder or CO J ladder) is a carbon monoxide (CO) series of rotational spectral lines, i.e., stemming from the steps in CO's possible rotational energy (CO transitions), modeled by:

       J(J+1)ℏ²
Erot = ————————
          2I

where E_rot is the energy level, I is the moment of inertia of a CO molecule, ℏ is the reduced Planck constant, and J is 0, 1, 2, etc. The frequencies of lines produced by stepping up or down these energy levels are multiples of an increment near 115 GHz. The lines are typically identified by this form: CO(number-number), with the two numbers indicating two successive values of J. Lines of interest include:

These can be detected in distant galaxies (e.g., z=1) within the millimeter/submillimeter range (e.g., submillimeter galaxies), and suggest gas clouds, i.e., indicating starburst galaxies and possibly mergers. CO lines, such CO(1-0) are useful for determining redshifts. CO(6-5) is used for observing protoplanetary disks and very distant (z>6) molecular clouds. Observations of multiple such lines (yielding their spectral line energy distribution (SLED)), can yield qualities of the gas, in particular, its temperature.