Artistic Licence
The scientific press has been trumpeting this press release from ESO, announcing the discovery of three 'super-Earth' planets orbiting the star HD 40307. It's accompanied by this rather nice artist's impression, showing a trio of worlds at least two of which are cloud-streaked and Earthlike.
(ESO press release image, used for purposes of reportage and commentary.)
But I rather doubt that this is the case.
According to this diagram, the three planets orbit about 0.05 AU, 0.09 AU and 0.14 AU from HD 40307 - in other words, well inside what would be the orbit of Mercury in our solar system. But HD 40307 is described as being somewhat dimmer than the Sun, so is it dim enough to counteract this?
This page describes HD 40307 as having a visual magnitude of 7.17 at a distance of 12.8 parsecs. Star brightness is described in terms of 'absolute magnitude', which is how bright a star would appear from 10 parsecs. At this distance, HD 40307's brightness would be:
7.17 - 2.512*log((12.8/10)^2) = 6.63
The Sun's absolute magnitude is 4.83, so the relative difference in luminosity is:
10^((4.83-6.63)/2.512) = 0.192
In other words, HD 40307 is about 19% the luminosity of the Sun. What does this mean for its planets?
Well, the outermost planet is 0.14 AU from it, so the insolation relative to 1 AU is:
(1/0.14)^2 = 51
Whew! But we have to multiply that by 0.19 to account for HD 40307 being only 19% as bright as the Sun, which gives us 9.7 times more heat falling on this planet than falls on Earth.
What does this do to its temperature? Well, if it is in thermal equilibrium it will be radiating as much heat as it receives. So, it must radiate 9.7 times as much heat as Earth does. How much hotter than Earth does it need to be to do this? The Stefan-Boltzmann law says that an object radiates in proportion to the fourth power of its absolute temperature, so inverting this tells us that an object's absolute temperature is proportional to the fourth root of its radiated energy. The fourth root of 9.7 is 1.76, so this planet should be, in absolute temperature terms, 1.76 times hotter than Earth.
'How hot is Earth' is of course a complex question, as it is enormously affected by the atmosphere and climate. However, Earth is around about 270K (say freezing - bits are hotter, bits are colder) so our planet's average temperature will be 476K - about 200 degrees Celsius. There won't be any oceans on it, because they'll have long since boiled away unless the atmosphere is so crushingly dense (20 bar or more) that it raises the boiling point far enough. And where would such a thick atmosphere come from? CO2 baked out of carbonate rock, as on Venus, leading to a runaway greenhouse effect and even higher temperatures.
Things are even worse for the inner planets. Following the same reasoning, for the middle and inner planets I calculate average temperatures of 320 degrees C and 525 degrees C respectively. We aren't talking about super-Earths here - more like super-duper Mercuries, or as noted above, super-Venuses.
So, I suspect that the artist took the description of 'super-Earths', meaning planets more massive than the terrestrial planets in our solar system, but much smaller than any of the gas giants, and interpreted it rather literally. But would a picture of one world shrouded in thick white clouds and the other two as scorched, arid wastes looked as pretty?
(ESO press release image, used for purposes of reportage and commentary.)
But I rather doubt that this is the case.
According to this diagram, the three planets orbit about 0.05 AU, 0.09 AU and 0.14 AU from HD 40307 - in other words, well inside what would be the orbit of Mercury in our solar system. But HD 40307 is described as being somewhat dimmer than the Sun, so is it dim enough to counteract this?
This page describes HD 40307 as having a visual magnitude of 7.17 at a distance of 12.8 parsecs. Star brightness is described in terms of 'absolute magnitude', which is how bright a star would appear from 10 parsecs. At this distance, HD 40307's brightness would be:
7.17 - 2.512*log((12.8/10)^2) = 6.63
The Sun's absolute magnitude is 4.83, so the relative difference in luminosity is:
10^((4.83-6.63)/2.512) = 0.192
In other words, HD 40307 is about 19% the luminosity of the Sun. What does this mean for its planets?
Well, the outermost planet is 0.14 AU from it, so the insolation relative to 1 AU is:
(1/0.14)^2 = 51
Whew! But we have to multiply that by 0.19 to account for HD 40307 being only 19% as bright as the Sun, which gives us 9.7 times more heat falling on this planet than falls on Earth.
What does this do to its temperature? Well, if it is in thermal equilibrium it will be radiating as much heat as it receives. So, it must radiate 9.7 times as much heat as Earth does. How much hotter than Earth does it need to be to do this? The Stefan-Boltzmann law says that an object radiates in proportion to the fourth power of its absolute temperature, so inverting this tells us that an object's absolute temperature is proportional to the fourth root of its radiated energy. The fourth root of 9.7 is 1.76, so this planet should be, in absolute temperature terms, 1.76 times hotter than Earth.
'How hot is Earth' is of course a complex question, as it is enormously affected by the atmosphere and climate. However, Earth is around about 270K (say freezing - bits are hotter, bits are colder) so our planet's average temperature will be 476K - about 200 degrees Celsius. There won't be any oceans on it, because they'll have long since boiled away unless the atmosphere is so crushingly dense (20 bar or more) that it raises the boiling point far enough. And where would such a thick atmosphere come from? CO2 baked out of carbonate rock, as on Venus, leading to a runaway greenhouse effect and even higher temperatures.
Things are even worse for the inner planets. Following the same reasoning, for the middle and inner planets I calculate average temperatures of 320 degrees C and 525 degrees C respectively. We aren't talking about super-Earths here - more like super-duper Mercuries, or as noted above, super-Venuses.
So, I suspect that the artist took the description of 'super-Earths', meaning planets more massive than the terrestrial planets in our solar system, but much smaller than any of the gas giants, and interpreted it rather literally. But would a picture of one world shrouded in thick white clouds and the other two as scorched, arid wastes looked as pretty?