The bleak scenario is proposed by astrobiologist Jack O'Malley-James of the University of St. Andrews, Edinburgh.
As the Sun ages over the next billion years, it will become more luminous, cranking up the thermostat on the Earth, O'Malley-James suggests in a computer model presented at a meeting of Britain's Royal Astronomical Society (RAS).
Increased evaporation rates and chemical reactions with rainwater will cause a dramatic fall in levels of atmospheric carbon dioxide (CO2), on which plants depend for photosynthesis. Animals, in turn, depend on plants.
"The far-future Earth will be very hostile to life by this point," O'Malley-James said in an RAS press release.
"All living things require liquid water, so any remaining life will be restricted to pockets of liquid water, perhaps at cooler, higher altitudes or in caves or underground."
But 2.8 billion years hence, even these hardy holdouts will have followed the dodo, according to his model.
The finding could help hunters of exoplanets who dream of finding an Earth-like planet in another solar system.
A dying planet would have a telltale nitrogen atmosphere where there would be only traces of methane pointing to residual bacterial life.
The five-day RAS annual meeting, gathering more than 600 astronomers and space scientists, runs at St. Andrews until Friday.
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