Title: Fermi Resonance and the Quantum Mechanical Basis of Global Warming
Authors: R. Wordsworth, J. T. Seeley, K. P. Shine
First Author’s Institution: Harvard, Cambridge, MA, USA
Status: Published in The Planetary Science Journal [open access]
Climate change is so well-known at this point it’s not even worth arguing about. The average surface temperature of the Earth has increased by about 1 Kelvin (1° C, or 1.8° F) in the last 150 years, and the concentration of carbon dioxide (CO2) in the atmosphere has increased by a factor of nearly 150%. These facts, and the causal connection between them, are extremely well-established. However, more research on climate change is always useful, and it is surprisingly difficult to physically model exactly how the CO2 molecule absorbs heat, so today’s authors set out to rectify the issue.
One (1) wiggly boi
When light from the Sun reaches Earth, it interacts with air molecules in our atmosphere, which absorb light at particular frequencies depending on their structure and how their atoms interact with each other. The three atoms that make up CO2, in particular, can stretch or bend with respect to each other, as shown in Figure 1, or can rotate around the central axis. Each of these oscillation modes has a different characteristic frequency, and when a photon of exactly the right frequency hits the atom, it changes modes. This produces an absorption spectrum like the one shown on the left of Figure 2, where CO2 is more likely to absorb a photon at specific frequencies, with a complex oscillatory structure in between those frequencies.
This is all very well, but when we model those energy transitions, we run into problems. A simple molecular model might assume that the CO2 molecule is a perfect quantum simple harmonic oscillator, where the difference between each energy level is the same. But when we model CO2 using this assumption, we get an absorption spectrum like the one shown on the right in Figure 2, where the central frequency is well reproduced, but absorption at the side frequencies is completely neglected. This approach clearly misses a lot of information, so we have to do something to account for the missing lines.
One (1) even wigglier boi
The reason for the discrepancy between the simplest model and the reality is largely due to an effect called Fermi resonance. This can be understood by comparing to the classical double pendulum experiment, where two pendulums are suspended from a string as shown in Figure 3, and one is set in motion. This causes the string to move, and the other pendulum to swing, with the amplitudes of the two oscillating pendulums inversely correlated with each other. If there were only one pendulum, it would behave how we expect; it would swing the most when it was first set into motion, with the amplitude gradually decreasing until it eventually came to a stop. But because the two pendulums are coupled to each other, the motion of both is a lot more complex.
In the CO2 molecule, the frequency of oscillation for the stretch mode, labeled V1 in Figure 1, is coincidentally very close to twice the frequency of oscillation for the bending modes (V2 in Figure 1). This means that the two modes interact with each other in much the same way as the two pendulums. The frequency of absorbed photons for both modes is shifted, and the wave functions describing the vibration of the molecule blend together and interact, causing the absorption spectrum to spread out. When the authors modeled CO2 with Fermi resonance taken into account, they found that the absorption spectrum, shown on the right in Figure 4, mirrored the observations much more accurately.
Warming up
Heat that is absorbed by the CO2 molecule is not radiated out into space and instead stays in the Earth’s atmosphere, so the more CO2 in the atmosphere, the less energy escapes. The greenhouse effect is stronger, and the Earth gets hotter. The difference in the amount of energy escaping into space due to an increase in the concentration of CO2 is called the radiative forcing, and it’s directly proportional to the increase in surface temperature.
The model in Figure 4 allows today’s authors to predict the radiative forcing from the structure of the absorption spectrum, and therefore the change in surface temperature for a given increase in CO2 concentration. They find that if the amount of CO2 in the atmosphere doubles, we can expect an average surface temperature increase of 2.2 Kelvin (2.2° C, or about 4° F), which is reasonably close to the estimates produced by complicated numerical models while being significantly simpler and more physically motivated.
While the process of deriving this estimate involved quite a few simplifications, it still produced a reasonable result, and unlike with numerical models, the analysis presented by today’s authors was derived mostly from physical first principles. An intuitive understanding of the physics behind climate change is not only yet another argument for the validity of global warming as a phenomenon, but also a promising tool for analysing the atmospheres of other planets – after all, we aren’t the only planet with a greenhouse gas problem. By learning more about how climate change works, we gain the ability to mitigate it even more effectively. Global warming is very real–but so is the science that lets us work against it!
This article was written as a part of our Climate Change Series. We’d love to hear what you would like to see from this initiative – if you have ideas, please let us know in this google form.
Astrobite edited by: Samantha Wong
Featured image credit: NASA/GSFC
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