The age of the universe is 13.798±0.037 billion years, yet the age of HD 140283 is 14.46±0.8 billion years, how this can be the case?
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It's down the fact that different properties are used to calculate the ages and if you look at the margin of error in the calculations they're not incompatible.
The lower limit for the age of HD140283 is:
14.46 - 0.8 = 13.68 billion years
which is within the range for the age of the universe.
Once better measurements of HD140283 are made it's age will probably be revised to a more "sensible" figure that matches more closely the age of the universe.
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$\begingroup$ Still how a star could form exactly after formation of the universe and remain shining today (arent all early stars consist of only hydrogen)? $\endgroup$– AnixxCommented Dec 21, 2013 at 14:36
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$\begingroup$ @Anixx - If the star is 13 billion years old it probably isn't still shining "today". Don't forget we're seeing it as it was when it's light left it. If HD140283 is an appreciable distance from us then it has probably long since died. $\endgroup$– ChrisFCommented Dec 21, 2013 at 14:38
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2$\begingroup$ Very low mass stars are expected to have lifespans longer than the current age of the universe. The rate of fusion in the core of low mass stars is exponential in temperature, so it proceeds much more slowly in small, dim, cool stars than is a smallish, not-very-bright, tepid star like our sun, and our sun has a projected lifespan a bit over 10 Gyrs in total. $\endgroup$ Commented Dec 21, 2013 at 15:21