Why Does Uranus Emit Very Little Heat?

As we've been preparing white papers on science themes for ESA's future L class missions, I've learned  a lot from the conversations flying back and forth via emails in the community.  One was about the Voyager-era result that the self-luminosity of the ice giants, Uranus and Neptune, was so different (Neptune's internal energy emission was a factor of ten larger than the of Uranus, such that the ratio between emitted and absorbed energy is 1.06±0.08 for Uranus but 2.61±0.28 for Neptune) that some strange scenarios had to be invoked to explain the vast difference.  Planets are warm inside and cool down as they age.  Voyager measurements suggest that Uranus’ evolution produced a planet with negligible self-luminosity, smaller than any other planet in our Solar System (Pearl et al., 1990). Combined with the sluggish appearance of the atmosphere as viewed by Voyager, this suggested that the interior of Uranus was either (a) not fully convective or that (b) it suffered an early loss of internal heat. For Case (b), a catastrophic event such as a collision early in Uranus' history could have shocked the matter in the interior and led to a catastrophic loss of internal energy.  

The interiors of the giant planets from evolution modelling.
Credit: Lunar and Planetary Institute

However, two scenarios were described for case (a) in the Neptune and Triton book (Hubbard, Podolak and Stevenson, 1995), which implies that the interior of Neptune is colder than the adiabatic case.  One idea suggested that Uranus might be stable to convection in the inner 40-60% of its radius, so that we essentially only measured the cooling history of the outer part of the planet.  The interior would be warmer, but that immiscibility of certain consitiuents (e.g., helium and carbon) prevents the efficient transport of heat from the interior outwards.  The other suggestion was that Uranus started cold, so cold that the ices in its deep interior could have been of a crystalline form.  

Since that time there have been improved thermal evolution models and data on the equation of state of the interior composition, leading to different solutions for the internal convection permissible within Uranus.  Nadine Nettleman described new Uranus evolution models using an assumption of an adiabatic interior that can explain the low luminosity of Uranus.  Essentially, with the new models, Uranus can have a convective interior and still cool enough over the age of the solar system to be consistent with the upper limits on the measured luminosity from Voyager. The inferred size of a non-convective, stable internal region is extremely sensitive to the measured intrinsic heat flux value: a mostly stable interior is predicted if the heat flux is close to zero, but a fully convective interior remains possible, as for Neptune, should the upper limit of the Voyager heat flux value prove true.  

These inferences come from a single measurement from the Voyager flyby in 1986, at a single point in Uranus’ seasonal cycle, and with error bars so large that many different scenarios are consistent with the data.  The heat balance arguments put forward by Barney Conrath, John Pearl and colleagues come from integrating the spectral irradiance measured by Voyager/IRIS over as broad a wavelength range as possible to estimate a total emitted power in Watts ((5.60±0.11)e15 W for Uranus, (5.34±0.29)e15 W for Neptune), and then relating this to the temperature of the equivalent blackbody producing the same spectrally-integrated irradiance (59.1±0.3 K for Uranus and 59.3±0.8 K for Neptune).  The fact that they are so similar, despite Uranus absorbing more than twice as much solar energy as Neptune, is the source of this enduring mystery.  IRIS' spectral coverage was narrow for the ice giants (25-50 µm or so), but included the peak of the black body emission of these planets, so it remains one of the best estimates we have.  The energy balance measured by Voyager is simply the ratio of this integrated power to the absorbed power.  The latter depends on the albedo of the planet, which is also rather hard to estimate (you need to know precisely how the planet - i.e. the clouds - reflect light over a full range of phase angles) and is a source of uncertainty on the ratio.  If we could obtain more accurate measurements of the intrinsic heat flux, via a mission seeking to determine the balance between Uranus' emitted energy and that absorbed from the Sun, then we might be able to distinguish between these competing scenarios for the evolutionary history of one of the strangest planets in our solar system.