Why Hart Found Narrow Ecospheres — A Minor Science Mystery Solved

In searching for habitable exoplanets, knowing where to look is an important issue.  At least for humans there is a continuously habitable zone (CHZ), a region where life as we know it could appear and persist. This is also important for our understanding the young Earth.  Escape from Snowball Earth is still an area of investigation, how the Earth managed the great escape.

As in any field, there is secret sauce, magic ingredients that appear in the literature and no one quite knows where that came from.  Barton Paul Levenson has tracked down the source of one of those, an early estimate of the outer limit of the CHZ.  This will appear in Astrobiology, but, alas there is a rather high paywall.  Barton has sent Eli a summary of the paper.

There are some interesting hints in this and connections to current issues, the attitude of Elsasser to global warming for example.  So with no further introduction

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In 1953, Hubertus Strughold coined the word "ecosphere" (from Greek οικος, house) for the distance range where a star can have habitable planets. Too close in, the planet will be too hot.  Too far out, too cold. Rampino and Caldeira (1994) called this "[t]he Goldilocks Problem."

Early estimates of the Sun's ecosphere were optimistic. It might reach from 0.7 to 1.5 AUs, 1 AU being the Earth-Sun distance. Venus and Mars might both be habitable, at least for some forms of life.

By the early '60s we knew Venus was too hot and Mars too cold and airless. Dole (1964) found temperatures of 273-303 K were limits for human habitability, then used a static climate model to estimate a 0.86-1.24 AU Solar ecosphere.

Then, Michael Hart at NASA (1978) noticed that since stars increase in luminosity across the main sequence, the "Habitable Zone" (HZ) moves outward with time. The region where things are clement for long periods is the narrower "Continuously Habitable Zone" (CHZ). A planet too close undergoes a runaway greenhouse and winds up like Venus. A planet too far ices over. Hart found the narrow range of 0.95-1.01 AU for the Solar CHZ, later (1979) revised to 0.958-1.004 AU.

His findings hit the ETI community like a bombshell.  Isaac Asimov (1980) said: "[I]f Hart's computer simulation of Earth's past history is accurate, then it is very likely that no planet at all will form within the ecosphere... all the planets near the star will be Venuslike or Marslike... The probability of a planet within the ecosphere would then be close to 0.0.

Actually, Asimov failed to do the math. Planet orbits are spaced roughly evenly on a log scale.  Given that, the spacing ratio difference between Dole's ecosphere (1.24 / 0.86) and Hart's (1.004 / 0.958), compared to a mean 1.73 in the Solar system, lowers the chance of a planet in the ecosphere from 67% to 8.6%, a factor of 7.8. Compared to Dole's estimate of 600 million habitable planets in the Milky Way galaxy, this would still leave 77 million such planets.

But the effect of Hart's articles was disproportionate. Climate scientists Schneider and Thompson (1980) felt compelled to respond that the scientific knowledge available was too uncertain for such estimates. Schneider wrote me in 1983 that Hart's conclusions were "completely unjustified."

In 1981, Walker et al. found a stabilizing feedback that prevented runaway glaciation at the outer boundary.  A more ice-covered Earth has less weathering of rock. Less carbon gets washed to the sea, and CO₂ from volcanoes builds up in the air, eventually melting the ice. James F. Kasting and his colleagues at Penn State used this information in 1992 to find a wider Solar CHZ, 0.95 to 1.15 AU.

Later discoveries about warming from high-altitude CO₂ ice clouds extended the outer HZ limit as far as 1.7-2.4 AU.  This puts glaciated Mars well inside the HZ! But because of its small size, Mars cooled off early, plate tectonics never started, and it has no active volcanoes to add CO₂ to the atmosphere. Walker's feedback doesn't exist for it. If Mars were Earth-sized, it might be habitable.

Most (not all) estimates for the inner CHZ boundary are still close to Hart's.  But his outer estimate puzzled everyone.  It was an advance to account for thermal runaways in a planet's history to find CHZ boundaries, as Hart did. It was another advance to include Walker et al.'s stabilizing feedback.  But a certain mystery still surrounded Hart's findings. Kasting wrote in 2010: "Exactly why [Hart's] model failed to recover from runaway glaciation is not clear. It was a highly simplified model, though, and its treatment of both radiation and convection left much to be desired..."

How Hart got it wrong puzzled me for years. I wrote an indignant, completely incompetent reply to his 1978 paper the same year, when I was a high school student, and of course it got rejected. Hart, oddly enough, phoned me from the Manned Space Center in Houston, Texas (I was living in Charlotte, NC at the time) to discuss it. He and I were ideologically opposed on many points, and not just in science, but I have never forgotten how kind he was to a geeky kid. Nonetheless, I recently decided to revisit his model, and this time I got an accepted paper out of it.

Computer power was far less in 1978 than today. Hart's simulation was probably written in the procedural language Fortran IV, and either punched into cards to be read in batch mode by a mainframe computer like an IBM 360, or entered via teletype or CRT-screen to a minicomputer like the DEC PDP-11. Although radiative-convective models (RCMs) of Earth's atmosphere had existed since 1964, a geohistorical model like Hart's would have needed far too much computer time to repeatedly run one.  His simulation used a time step of 2.5 million years and an Earth age of 4.5 billion years, requiring 1,800 iterations of the main processing loop. A detailed temperature model would simply have cost too much.

So Hart substituted an iterative semigray model. He estimated the infrared optical thickness of Earth's atmosphere at τ = 2.49, which for Earth's effective temperature T_eff = 255 K, gives a surface temperature T_s = 332 K.  This would be true for a purely radiative situation, but conduction, convection and evapotranspiration cool Earth's surface at the expense of the atmosphere.  Thus he introduced a "convection factor" F_conv = 0.43:

T_s = T_eff + [(1 + 0.75 τ)^1/4 - 1]T_eff F_conv

Hart took water vapor and carbon dioxide as the only greenhouse gases for present-day Earth.  He added ammonia and methane for a primitive Earth assumed, in line with theory at the time, to have a reducing atmosphere.  For present Earth he found τ_H2O = 2.34 and τ_CO2 = 0.15, for relative contributions of 94% and 6% to Earth's greenhouse effect. By way of contrast, RCM studies show the clear-sky greenhouse effect to be 9-26% from carbon dioxide.

Consider Mars, where almost all the greenhouse is from CO₂ and very little from H₂O.  A temperature model that undervalues CO₂ will be more vulnerable to glaciation as sunlight lessens. I eventually concluded that Hart never realized he was treating CO₂ as too weak a greenhouse gas, and missed it because his results were in line with climatological thinking at the time.

It turns out narrow CHZ boundaries were actually found much earlier--but no one considered both limits together until Hart did. In 1969, Ingersoll used a gray model to explain how the runaway greenhouse effect might have taken place on Venus. A year later, Rasool and de Bergh (1970) estimated the inner boundary of the sun's CHZ at 0.93-0.96 AUs.

Also in 1969, Budyko found an outer CHZ boundary of 1.008 AUs, based on a one-dimensional (in latitude) energy-balance climate model. The same year, Sellers, without knowing of Budyko's work, estimated the outer boundary at 1.01-1.025 AUs, also based on an energy-balance model. These models were considered state-of-the-art back then.

So years before Hart, the literature already implied a CHZ stretching from 0.93-0.96 AU at the inner boundary to 1.008-1.025 at the outer, for a spacing ratio of 1.05-1.10. Hart's 1978 paper cites both Budyko's paper and Sellers's. His simulation only reinforced a conclusion already "out there."  In short, he had no reason to question his results. This "ice catastrophe" had been in the air in professional circles for many years; he got the answer he almost certainly expected.

The only remaining question is why he took CO₂ as too weak a greenhouse gas. Hart cites the seminal work of Elsasser and Culbertson (1960) in his references. I collected estimates for CO₂ absorption coefficients in the band most important for terrestrial planet temperatures, the 15-micron (μ) band. In SI units, the geometric mean of Elsasser and Culbertson's figures from 14 to 16 μ is 0.438 m² kg^-1. The mean figure for Hanel et al. (1963) is 0.07, while Gonima (1992) finds 20 and Evans (2001) reports a point measurement of 16.3. Clearly 1960s figures are very low compared to later ones.

Nowadays, a researcher who wants to create a band scheme for a planet's atmosphere uses "line-by-line" software on the Air Force HITRAN or HITEMP line data compilations.  From individual lines, one estimates a mean absorption coefficient in a given wavelength domain.

But HITRAN only came out in 1973. Elsasser and Culbertson based their work on laboratory test data on carbon dioxide in glass tubes, with nitrogen as a line-broadening agent. Either because of problems with their mathematical model, or problems with the lab procedure, they concluded that carbon dioxide was a much weaker greenhouse gas than it really is. Similar problems must have arisen for Hanel et al. By the time of Gonima's paper, both better models and better data were available.

So because of earlier work which showed Earth orbiting very near the outer edge of a narrow CHZ, in danger of runaway glaciation if sunlight fell by even a few percent, and because of mistakes about radiation transfer in the source material available to him, Hart's planet temperature model really did have serious problems, as Kasting proposed. A better semigray model might have provided different results, even without considering the stabilizing feedback of Walker