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So there has been talk in the news of a star named Methuselah that is "older than the universe". Moreover, this star happens to belong to our very own Milky Way.

The article mentions that Methuselah is consistent with universe age estimates if we consider the margin of error, but this would seem to imply (statistically-speaking) that this method of age estimation is biased towards overestimation. The article also mentions that other studies have put Methuselah's birth at pre-Big-Bang. This seems to indicate that many methods are overestimating its age. To me this seems to indicate a fundamental theoretical misunderstanding or some consistent problem in the measurement phase of the estimation.

I must admit that I only have a modicum of familiarity with stellar evolution, and so these incredible headlines have left me strapped with questions:

  1. How reliable is this research?
  2. What method do they use to measure the age of such a star as Methuselah?
  3. Which is more likely to be wrong, the age of Methuselah or the current estimate of the age of the universe?
  4. Could relativistic effects account for some of the age?
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I would guess this is much ado about very little actually. From the article: "The uncertainty Bond refers to is plus or minus 800 million years, which means the star could actually be 13.7 billion years old — younger than the universe as it's currently understood, though just barely." They don't actually say what that error bar means ($1\ \sigma,\ 2\sigma,\ 95\%$ etc.) but it is unlikely that cosmology needs revision in light of this. Indeed the scholarly paper says that the star is fully compatible with the age of the universe. –  Michael Brown Aug 12 '13 at 4:34
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A skim of the paper confirms that the error bar is indeed $1\ \sigma$. I wouldn't lose any sleep over this. –  Michael Brown Aug 12 '13 at 4:37
    
That's definitely reassuring. However, I'm still puzzled as to why multiple studies have been overestimating its age (assuming the age of the universe is correct). Unless there are an equal number of underestimating estimates, it seems that the methods of age estimation have some sort positive bias. –  Christian Bueno Aug 12 '13 at 4:52
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"The article mentions that Methuselah is consistent with universe age estimates if we consider the margin of error, but this would nevertheless mean that (statistically-speaking) this method of age estimation is biased towards overestimation." Err...no it doesn't. It means that you have one outlier, which doesn't tell you much of anything (even taking a Bayesian approach; go frequentist and you learn exactly nothing). Now if you had several like this you could start to worry. –  dmckee Aug 12 '13 at 7:08
    
We pretty much have the age of the universe as well as we could like, but this is a great question from a historical perspective. Back before we knew the age of the universe well and before we had sophisticated stellar models, this same issue arose in a much stronger version, given various astronomers' work on stars in globular clusters, which seemed to be very old. –  Chris White Aug 29 '13 at 20:35

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up vote 15 down vote accepted

I work with stellar models, so I thought I'd chip in here. My instant reaction is that you shouldn't worry too much: determining the age of a star is difficult and different models will disagree (sometimes significantly!) on that age.

How reliable is this research?

I can't see an obvious reason to doubt the conclusion.

What method do they use to measure the age of such a star as Methuselah?

Basically, one tries to measure as many properties about the star as accurately as possible, and then find the best fitting stellar model. These models are solutions to a set of differential equations (in time and one spatial dimension) that tries to capture all the relevant physics that determines how stars evolve. The bulk physics is a fairly well-defined problem but there are several potentially important components that are lacking in these models. (I'll expand on this if desired...)

The usual difficulty here is breaking down the degeneracy between brightness and distance. That is, a distant object is fainter, so it's hard to know whether a certain object is intrinsically faint or just further away. The principal result in this paper is the Hubble-based parallax measurement, which makes a big improvement on that distance measurement and, therefore, the brightness of the star. The other things they use are proxies for the surface composition and the effective temperature of the star, as far as I can see.

Incidentally, this is where I would suspect the tension can be resolved. If you look at Fig. 1 of the paper, they show the evolution of different stars for different compositions. What you're looking for, roughly speaking, is lines that go through the observed points. That figure shows that if the oxygen content is underestimated, then the best fit is actually about 13.3 Gyr, which is no longer at odds with the age of the Universe.

Take note of Table 1, where the sources of error (at 1$\sigma$) are listed. It's interesting that, not only is the star's oxygen content the largest source of error, but even the uncertainty of the oxygen content of the Sun is a contributor!

Which is more likely to be wrong, the age of Methuselah or the current estimate of the age of the universe?

The age of Methuselah, definitely. I would describe our estimates of the age of the Universe as in some way "converegent": different methods point to consistent numbers. Sure, Planck shifted the goalpost by 80 Myr or so, but it'd be a real shock to see that number change by, say, half a billion years.

Could relativistic effects account for some of the age?

I have no idea and haven't really thought about it. Since I'm pretty sure this isn't a big problem, I don't think relativistic effects are necessary to explain the discrepancy.

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Re: the relativistic effects. These come in two categories: (a) time dilation due to peculiar velocity and gravitational redshift, and (b) effects of relativistic dynamics on the stellar evolution itself. (a) is completely negligible for anything (barring black holes) in the Milky Way to the sort of accuracy of these measurements. (b) I don't really know about. I would imagine that relativity would only have a small effect here as well, since it's generally only important for neutron stars, though I'll leave that to the astrophysicist. :) –  Michael Brown Aug 12 '13 at 13:48
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@MichaelBrown, I can answer (b): basically nil. This is a small star, probably less massive than the Sun. There are two calculations that tell you what the relativistic effects are. First, from $E=mc^2$, is the energy density at all comparable to the mass density? Second, are there any fluid flows (e.g. convection or rotation) that have relativistic speeds? On both counts the answer is definitely no. –  Warrick Aug 13 '13 at 7:04

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