Carbon dioxide is the main culprit in causing our climate to change, but it is only recently that a key property of CO2 has been elucidated. This is linked to a surprising interaction between the molecular vibrations of carbon dioxide: the various modes of vibration of the molecules resonate with each other in a manner that enhances them as absorbers of radiation.
As a result, CO2 traps far more infrared radiation than a simple analysis would indicate. Surprisingly, global warming is tied to an apparent coincidence involving two of the principal ways in which CO2 can vibrate.
Greenhouse effect
The atmosphere insulates Earth, trapping heat and maintaining the temperature at a moderate level. Earth radiates heat in the form of infrared light. Some of that light hits molecules in the atmosphere, notably water vapour and CO2. A molecule absorbs the light, and then re-emits it, either upwards or downwards.
Some of the energy is lost to space while some is returned to Earth. NOAA’s Global Monitoring Laboratory reported in January that the concentration of CO2 in the atmosphere has risen by 50 per cent from its pre-industrial level of 280 parts per million to 420 parts per million — triggering a warming of about 1 degree.
About 1860, Irish-born physicist John Tyndall was the first person to measure the absorption of infrared light by water vapour, carbon dioxide and other atmospheric gases. Tyndall’s work demonstrated how Earth’s surface would be warmed by this process, the phenomenon we now call the greenhouse effect. In 1896, Svante Arrhenius, a Swedish physicist and chemist, used scientific principles to estimate the increase in the Earth’s surface temperature due to rising levels of CO2. His work was the beginning of modern climate science.
[ How Joseph Fourier discovered the greenhouse effectOpens in new window ]
Another Swedish physicist, Knut Ångström, argued that CO2 molecules only absorb a specific wavelength of 15 microns (15 millionths of a metre). Since there was already enough of the gas in the atmosphere to trap all the 15-micron light emitted by Earth, the addition of more CO2 would have no effect. However, this “carbon saturation argument” is erroneous, because CO2 can absorb energy over a broad band of wavelengths, as we shall see.
Molecular vibrations of carbon dioxide
The schematic diagram shows what a CO2 molecule looks like and how it vibrates. On top, we see the triatomic molecule made up of one carbon atom (black) and two oxygen atoms (red) linked by chemical bonds depicted as springs. The bonds linking the atoms are not rigid but can stretch and bend. The panels in the central part of the diagram show two of the primary modes of vibration, a stretching mode (centre left) in which the oxygen atoms move symmetrically towards and away from the carbon, squeezing and stretching the bonds, and a bending mode (centre right) in which the angle between the bonds oscillates.
It seems a fluke of nature that the frequency of the stretching vibrations is almost exactly twice the frequency of the bending modes. The bending mode vibrates 20 trillion times per second (20 THz) and the stretching mode at about double this rate. Because of this two-to-one frequency ratio, these two types of oscillation are coupled: if a photon hits the CO2 molecule causing it to bend, this energy can transfer easily to the stretching motion. This interaction is called Fermi resonance.
Swinging Spring
The complete explanation for how CO2 behaves lies in quantum mechanics, but we can explain the essence of the phenomenon by means of a simple mechanical analogue, the elastic pendulum or “Swinging Spring” (lower left panel of diagram). If a heavy mass or bob is suspended from a spring or elastic cord, two kinds of behaviour are found.
The bob may oscillate up and down if pulled away vertically from its equilibrium position (red arrows). If the bob is moved slightly sideways, it will swing back and forth like a clock pendulum (green arrows). Normally, these two kinds of behaviour — swinging and springing modes — do not interact strongly.
However, if the bob is of just the right mass to stretch the spring by one-third of its natural length, something remarkable happens: the swinging and springing motions are then strongly coupled and energy flows back and forth between them. This non-linear interaction is called resonance. In resonant conditions, the bob is observed to bounce up and down for a time but then change to a sideways motion, swinging back and forth. A little later, the energy flows back to the springing mode and the motion is vertical again. This behaviour is similar to Fermi resonance. It is fascinating to watch a resonant swinging spring exchanging energy periodically.
Fermi Resonance
The phenomenon of Fermi resonance was discovered by Italian-American physicist Enrico Fermi, who derived it in 1931. Fermi is remembered for building the first artificial nuclear reactor in Chicago and for his involvement in the Manhattan Project. In addition to nuclear physics, he made substantial contributions to statistical mechanics, quantum theory and particle physics. A family of subatomic particles – fermions – are named in his honour. In 1938, Fermi was awarded a Nobel Prize in Physics.
Fermi resonance might appear to be somewhat arcane, but it is relevant for water waves, Rossby triad interactions in the atmosphere, phonons (sound waves) in crystals, resonance in plasmas and non-linear optics. Moreover, the research described below shows that it has big implications for the future of our climate.
The climate link was made only last year by Prof Keith Shine of the University of Reading and his student Georgina Perry. They studied the climate effects of CO2 with and without Fermi resonance. The two graphs (lower right panel of diagram) show the radiative forcing for a doubling of CO2. In simple terms, this measures the warming effect of carbon dioxide without Fermi resonance (blue graph) and with Fermi resonance (red graph). The inclusion of Fermi resonance broadens the spectrum of CO2 absorption, contributing approximately half the total warming due to increased carbon dioxide levels in the atmosphere.
Quantum Mechanics and Climate
This year, in The Planetary Science Journal, Robin Wordsworth, Jacob Seeley and Keith Shine reported the results of a quantum mechanical study of “CO2 radiative forcing”. Their results show how directly the basic physical principles of quantum mechanics are relevant to large-scale climate change: their analysis shows why CO2 is such a powerful greenhouse gas and why increasing it further will continue to change the climate.
Every time the CO2 concentration in the atmosphere doubles, Earth’s temperature rises by about 3 degrees (best estimate). This “logarithmic scaling” means the Earth’s temperature increases by the same amount in response to any doubling of CO2. The physical reason for this remained a mystery until, in 2022, a team at the University of California, Berkeley, led by climate physicist David Romps, showed the logarithmic scaling comes from the shape of the CO2 spectrum – the way in which the energy absorption depends on wavelength or frequency.
It was found that absorption falls off on either side of the peak at just the right rate to give rise to the logarithmic scaling. Most gases absorb energy in a narrow range of wavelengths. The spectrum of carbon dioxide is unusually broad, with a distinct triangular shape. Why does it have this shape? The comprehensive quantum analysis of Wordsworth et al supplies the answer.
Fermi resonance has profound consequences for the climate. Without it, CO2 would absorb radiation only in severely restricted bands of wavelengths around 15 microns (20 THz), and the warming due to it would be less than half the observed value. With Fermi resonance, the absorption band is broadened so that energy over a greater range of wavelengths is possible. As a result, additional CO2 will continue to force the temperature to ever greater heights.
Peter Lynch is emeritus professor at the School of Mathematics & Statistics, University College Dublin. He blogs at thatsmaths.com
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