A faster rotating early-Earth may have compensated for reduced Sun output
Guest post submitted by Ian Schumacher
The ‘faint young sun’ paradox states that according to star models, billions of years ago the Sun would have only been about 70% as bright as it is today. Given the same environment as today this would result in most water on Earth being frozen making early life difficult to exist. However, geological history does not show such a frozen Earth period and early Earth is thought to have been quite warm.
Most solutions to this problem relying on an enhanced greenhouse effect or on cosmic rays and clouds. To me these solutions, while possible, ignore much the simpler explanation of a shorter Earth day.
The Stefan-Boltzman law/equation states that, at equilibrium, the outgoing radiation from a black-body equals incoming radiation (from an external source) and is proportional to the fourth power of the temperature of a black-body.
S=σT⁴
From our perspective, what is important here is that outgoing radiation increases quickly with temperature. The average temperature is highest when temperatures are evenly distributed. The average temperature is less than or equal to the fourth root of the average of the fourth power of temperature:
≤ ()1/4
The more uneven the temperature distribution, the lower the average temperature. For example, consider the set of numbers:
{2, 2, 2, 2, 2}
The average of this set is 2. The fourth root of the average of the fourth power of these numbers is 2. Now consider the set of numbers:
{1, 2, 4, 2, 1}
The average of this set is also 2. The fourth root of average of the fourth power of these numbers is 2.75. In order to have the same fourth power average we would need the set of numbers:
{0.72, 1.45, 2.90, 1.45, 0.72}
which only has an average of 1.45; significantly less than 2 from the more even distribution.
A fast spinning Earth distributes temperatures more evenly allowing for a significantly higher average temperature than a slow spinning Earth. The faster the Earth spins, the higher the average temperature.
Billions of years ago, the Earth was rotating up to twice the rate it is today (it has slowed over time due to tidal friction). All else being equal, this would have distributed temperatures on the Earth’s surface more evenly and resulted in a higher average temperature. Since the Sun was also weaker the two effect may have roughly canceled each other out.
The Earth is not a black-body, but reflects a significant amount of light. Reflected light is not available to heat up the Earth’s surface and therefore has a large effect on Earth’s temperature. The reflection coefficient is also known as albedo. Water in solid state (snow, ice) has a very high albedo compared to water in liquid state or soil. A small increase in temperature can cause some snow to melt, reducing albedo and causing temperatures to increase further. In this way water provides a strong positive feedback; amplifying small changes in temperature. It is this effect that likely drives the Earth into and out of ice-ages by amplifying an otherwise small external forcing factors such as changes in Earth’s orbit. Similarly this positive feedback mechanism could work to amplify the increased average Earth temperature due to faster Earth rotation of an early Earth.
More here: http://blog.vzv.ca/2012/10/a-simple-resolution-to-faint-young-sun.html
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Interesting. Water melting requires heat, latent heat, when this evapourates more latent heat is required which will cool the surface. This heat is released when clouds form to escape to space. So a negative feedback. But certainly earth did rotate faster back in geological time.
For water read ice. Sorry folks.
W/o reading the post, I thought the early faint sun was compensated by a considerably higher atmospheric pressure. Perhaps earth had a single Hadley-cell circulation like Venus, which is a very efficient heat-transfer mechanism.
Here is the current status of our knowledge about the paradox: http://www.leif.org/EOS/2011RG000375.pdf
where 
is the orbital radius, and for a given fixed orbital angular momentum 
that radius scales like 
, so it is inversely proportional to the mass of the sun 
. This means that insolation intensity would be proportional to 
(exclamation point!). If the mass of the sun were 20% greater during the Archean, that would compensate for the a solar power only 70% of today’s.
Interesting article, and a lot more persuasive than the top article here, although the top article does point out correctly that anything that reduces the variance of temperature distribution contributing to some global average temperature is net warming all things being equal, which sadly is almost never true in climate science.
One thing discussed in the article that I found very interesting was the fact that the radius of the Earth’s orbit would have been smaller around the more massive young Sun (it loses mass steadily from “evaporation” into the solar wind). Indeed, the intensity of insolation scales like
A nonlinear effect on top of this is the coupling of rotationalangular momentum of Earth and Sun to orbital angular momentum via the solar tides, which would have been similarly enhanced by increased solar mass and decreased orbital radius. The Sun’s “day” and Earth’s “day” were much shorter (the top article is of course devoted to the latter as part of its basic hypothesis) and the Earth’s orbit would have been even closer than strict scaling suggests because the Earth’s orbital angular momentum has not been been constant over that period — it has coupled a fraction of both its own and the Sun’s rotational angular momentum into its orbital angular momentum, decreasing insolation intensity like the orbital angular momentum of the earth to the inverse fourth power. I don’t have a good feel for this — the moon is moving away from the Earth at a rate of a few centimeters a year (and was around half the distance it is today when the Earth/Moon system was young, which may also have had a significant effect on the climate). If the Earth is moving away from the Sun only a few centimeters a year, it is a nearly negligible change in Earth orbit as far as net insolation is concerned, but I don’t know what the numbers really are, centimeters or meters.
Finally, it isn’t just variation of the semi-major axis that counts, it is also eccentricity, which varies considerably over time due to orbital resonances. The entire solar system would have been more compact around a more massive Sun, and so all of the orbital resonances would have been much stronger.
A hard problem. But I like a more massive sun as a proximate cause and solution to the paradox, or more likely, a big part of that multifactorial solution.
rgb
So…??? Dump truckloads of AMP Energy drink down that hole to the core of Earth and mega-flora returns? Don’t put Monster down there, spin rate out of control!
Well, there is always the Iron Sun and Electric Universe ideas. Or is that sentence going to get me a time out?
[Reply: A “/sarc” tag would provide added protection.☺ — mod.]
OK, after reading the post, faster revolution will indeed cause less temp variations, so this adds to my above points.
Consider if it only took 1 hour for the earth to rotate on its axis. The difference between nighttime and daytime temps would be much smaller than with a 24 hr rotation. the same logic applies to a 12 hr rotation. There is a more even distribution of temps between daytime and nighttime, the faster the rotation of the planet.
For example, consider what it would be like if earth took 180 days to rotate on its axis, so that day and night lasted 6 months each. Max temps in the daytime would be much hotter than at present and max temps in the nighttime would be much cooler than at present. Quite possibly the tropics would freeze during the nighttime.
george e smith says:
October 16, 2012 at 11:10 pm
I should clarify one item above: “””””…..Any spot on earth will receive the exact same total insolation in a single rotation, regardless of rotation rate…….”””””
——————————————————————————-
Sorry George but you totally missed the physical fact that the highest average temperature is obtained when there’s the least deviation from the mean. A faster rotating planet will have less diurnal temperature variation and thus a higher average temperature. Schumaker is quite correct about that.
RGB: The total mass loss during the main sequence phase is negligible…not 20%. The Sun was never that much more massive.
A more massive Sun is also brighter…luminosity is a very strong function of mass. This would help the idea of a more massive Sun supplying a greater density of power in combination with the orbital thing…but, mass loss is actually negligible during the main sequence phase and so neither of these ever actually occurred.
It is very likely that the earth’s crust was thinner in the past, allowing for greater heat transport from the interior to the surface. As it is the crust in scale is today much thinner than the skin of an apple, and it is quite possible that there is more heat transfer from the interior to the surface than is currently believed.
The big question is how much water there is BELOW the bottom of the oceans. Most likely water extends down through the crust, until it reaches boiling point under pressure. It could well be that the crust mantle boundary is the point at which water boils under pressure. Below this point the solid crust ends.
At this point the dissolved limestone (CO2 captured long ago) is converted to hydrocarbons in the presence of iron and steam. Steam in the presence of iron releases hydrogen, which combined with carbon from limestone produces hydrocarbons. The excess oxygen is captured by the iron.
The resulting hydrocarbons, being lighter than water then float upwards and escape into the atmosphere to become part of the carbon cycle once again, unless captured by a sub-surface rock formation. Thus, hydrocarbons are fossil fuel, they are created from fossilized CO2 captured in limestone.
There is no shortage of iron. Iron is the stable byproduct of both fusion and fission. It forms the core of the earth, but this of course leads to the controversial question of the sun’s core.
The earth’s core is evidence that there was plenty of iron in the solar system formation, so where did the sun’s iron go? How did the sun eject its iron? Why would it not be concentrated at the heart of the solar system during its formation by rotational forces? What was the mechanism? Or, is the iron still at the core of the sun?
Why do solar scientists claim that the sun is 99% hydrogen by counting molecules instead of mass. The human body is 99% water molecules by the same methodology. What value is there in saying humans are 99% water by molecule count, unless you are trying to mislead your audience?
@rgbatduke
Current solar mass loss rate from e=mc^2 and solar wind would only reduce its mass by 0.05% over 4.5 billion years. It takes several percent greater mass to explain faint young sun paradox which is a mass-loss rate about 100 times greater than today on average which means it would have 1000 times greater in its earlier history to get the 100 times greater average than today.
This seems very unlikely and there’s no physical model to explain it. On the other hand Schumaker’s point about T4 relationship between temperature and power along with faster rotation rate is a physical fact that I trust even you won’t argue.
The idea that you get a more even distribution of temperatures with faster rotation is not well explained. More even distribution in what dimension?
For a given location, the insolation and total energy being absorbed is exactly the same, when averaged out. However, what will be different is the temperature swing between night and day. What it means is that any location will still come to the same temperature given the insolation, but the diurnal swing will be smaller. The average shouldn’t change at all.
But then you also have the problem of atmosphere. Obviously, a very long day in which you would expect much night-time cooling can easily be made nearly non-existent (the cooling) when you have enough atmosphere. Such as on Venus. So, given the very strong effect that atmosphere has, completely dominating the rotational issue, it is a more dense atmosphere which is the most likely candidate, and which should be explored.
As others have posted, there is good circumstantial evidence found in the biota of the period which indicate a denser atmosphere. The planet did rotate faster back then too, but this would likely be a second order effect on local average temperatures.
@rgbatduke
The idea of a more massive sun and major changes in planetary orbits is not a factor, as the period being discussed takes place millions of years apart and after the formation of the early solar system. And depending on how the earth and moon formed, whether the Earth and moon formed together or if they formed separately as two planetary bodies that collided to form the Earth and moon.
———————
John Doe says:
October 17, 2012 at 6:42 am
Sorry George but you totally missed the physical fact that the highest average temperature is obtained when there’s the least deviation from the mean. A faster rotating planet will have less diurnal temperature variation and thus a higher average temperature. Schumaker is quite correct about that.
———————–
That’s not true John Doe. Look at your words. Less deviation from the mean doesn’t mean the mean becomes higher. It simply means the standard deviation about the mean is smaller. This doesn’t equate to higher average temperature. Sorry I don’t mean to use so many means when talking about the meaning of the mean.
It would only correspond to a higher average temperature if the small-number side of the mean decreased its range.
But in fact, both the max and the min would decrease with faster rotation, and so the effect on the mean should be small, if not outright negligible as expected from a simple mathematical perspective.
You have to have fewer small numbers to increase the mean….not just a smaller deviation in general.
Don K says:
October 17, 2012 at 5:08 am
“Robertvdl says:
October 17, 2012 at 3:35 am
Didn’t God do this in 7 days ?
==================
One day., two at most. … If you believe Genesis.”
The Bible says somewhere “With God one day is a thousand years and a thousand years is one day.”.
And the Vedas say that one cosmic day and night of Brahma equals 8.64 billion years.
RGB: The total mass loss during the main sequence phase is negligible…not 20%. The Sun was never that much more massive.
Hi Joe,
I mostly agree — I was throwing out the break even point. The article Lief links puts an upper bound between 7 and 10%, but as you say the effect is multifactorial. One factor suggests that the luminosity was not, in fact, only 0.7 of todays (because the Sun was more massive). The other is that the orbital radius was smaller and hence insolation given the luminosity was also larger, proportional to mass squared. The main point is that these two factors very likely explain a fair fraction of the “missing insolation” — quite possibly more than half of it — even if the mass increase was only 5% or 7%. 1.07^2 = 1.14 so there’s half of it right there.
There are many ifs, of course. I tend to be pretty skeptical about statements concerning the state of the Sun and Earth orbit 4.5 Gya as they are based on a chain of inference that is quite long, hence quite vulnerable to Bayesian correction. Or if you prefer, they are weak examples of the Ludic fallacy, that we know enough about the random factors/unknowns in the early time evolution of the Sun to be able to make a meaningful statement about e.g. its mass today. The same fallacy is rampant in climate science, of course, so why not here as well…
rgb
John Marshall says:
October 17, 2012 at 5:57 am
But certainly earth did rotate faster back in geological time.
Never mind geological time the earth was rotating faster last week!
http://en.wikipedia.org/wiki/Coordinated_Universal_Time#Rationale
Hi Robert,
During the main sequence, which is well into when life started on the planet, mass-loss is negligible…as someone pointed out about, maybe 0.05%. I think it is even less than that. As you point out, though, it could help if we picked the right numbers, but, this is one of those “pull the numbers out of a magic hat which gives the right answer” kind of deals.
We know that the atmosphere has a huge effect simply because it is a large thermal mass…it doesn’t need to trap heat it simply holds on to the heat it has, and will do so longer because there’s more mass. Like on Venus.
Maybe they can start a new alarmism based on the increase of the mass of the atmosphere from increasing CO2. It will eventually get so massive it will crush us all!
This is assuming the Sun we see today is the same sun in the past.
The Saturn theory says Earth was in a polar configuration with Saturn that was a brown dwarf at the time before it entered the solar system.This explains why there were tropical forests at both poles.Earth only entered into this solar system about 12,000 years ago.
To all criticizing my brief post: just do your homework and actually calculate the result. There is great diversity of day/night temperature difference, greatest in tropics and zero on poles. I did not spend my time integrating over that but so didn’t the author or I’d expect to see his math in the article rather than that crude and misleading example.
But what I can do is a crude estimate to show how ridiculous it is:
If I assume whole earth has exactly its average temperature of about 14°C and it has diurnal temperature variation 80°C (i.e. nighttime temperature is -66°C and daytime is +94°C on the whole Earth surface; notice how stretched that example is) then the black body radiation would be just 12% more than if there was no difference between daytime and nighttime temperature at all (two times faster rotation can’t achieve that).
And we still have some 18% to go to meet that 30% lower sun output.
So sure, if the sun output was 70% of today’s in these historical times, then faster earth rotation probably played some role. But I’d call it negligible.
Well, the Earth was closer to the Sun. Now it is receding about 15 cm per year further away from the sun. At the same step it makes only about 0.1% of the Sun Earth distance in 1 billion years, but was the movement constant? Or more accelerated in an early Earth?
Second – how much of the Earth was covered by the oceans 1 billion+ years ago?
The true greenhouse happens in the oceans where the sun radiation is warming in depth but losing warm only at the surface.
This study says there was more water in the early Earth, the slow lose of water and increase distance to the Sun, slow lose of atmospheric pressure could compensate for slow radiation increase of the Sun:
http://sciencenordic.com/earth-has-lost-quarter-its-water
Joe Postma says:
October 17, 2012 at 7:11 am
The effect of higher mean temp on a faster rotating orb is because energy loss is greater when darkness begins at a higher temperature. The slower rotating orb gets warmer during the day and due to T4 relationship between power and temperature when the hotter dayside rotates into the night side it loses energy faster. The highest average day/night temperature is thus obtained when there’s the least diurnal temperature swing. If this weren’t correct Duke U physicist Rob Brown would have been quick to point it out.
The flaw Schumaker’s hypothesis is there isn’t a whole lot of diurnal temperature change over the global ocean and in fact the diurnal change in temperature over the ocean is so small that that you can basically ignore the T4 slope. If we were talking a diurnal swing of 300C over the entire orb (like the moon) then the average temperature change becomes significant.
http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/
http://wattsupwiththat.com/2012/01/06/what-we-dont-know-about-energy-flow/
Rob Brown and Willis talk about it in the links above if you’d like a more in depth explanation of how, why, and magnitude.
“It’s all fun & games until somebody pokes an eye out.”
Man, there’s a lot of handwaving in this thread. Eye protection is recommended.
In addition to my previous post above, is the “inside of the Earth” not warmed due to radioactive decay? And does this not lose power with the time? We now have certain energy coming from below:
http://www.heatflow.und.edu/maplinks.html
How much was it 1 billion + years ago?
There are several factors that contributed to the young Earth being warm that are forgotten and people try to find one factor that explains it all – and clearly the CO2-zelots point to CO2. The CO2 shows however no correlation between CO2 quantities and historic temperature.