A&A 436, 127-143 (2005)

DOI: 10.1051/0004-6361:20042185

## Determination of stellar ages from isochrones: Bayesian estimation versus isochrone fitting

**B. R. Jørgensen and L. Lindegren**

Lund Observatory, Lund University, Box 43, 221 00 Lund, Sweden

e-mail: [bjarne;lennart]@astro.lu.se

(Received 15 October 2004 / Accepted 19 February 2005)

** Abstract **

We present a new method, using Bayesian estimation, to determine stellar
ages and their uncertainties from observational data and theoretical
isochrones. The result for an individual star is obtained as the relative
posterior probability density as function of the age ("*G* function"). From
this can be derived the most probable age and confidence intervals.
The convoluted morphology of isochrones and strong non-linearities make
the age determination by any method difficult and susceptible to
statistical biases, and as a result age uncertainties havee
often been underestimated in the literature. From simulations we find
that the *G* functions provide a general, robust and reliable way to quantify
age information. Resulting age estimates are at least as accurate as those
obtained with conventional isochrone fitting methods, and in some cases much
better, especially when the observational uncertainties are large. We also
find that undetected binaries, on the whole, have a surprisingly small effect
on the age determinations. For a stellar sample, the individual *G* functions
can be combined to derive the star formation history of the population;
this will be developed in a forthcoming paper. For a
coeval population the combination simplifies to computing the product of
the individual *G* functions, and we apply that method to estimate the
ages of the two open clusters IC 4651 and M 67, using Padova isochrones
and photometric data from the literature. For IC 4651 we find an estimated
age of
Gyr, assuming a true distance modulus of 9.80.
For M 67 we find
Gyr for true distance modulus 9.48. The
small formal errors of these age estimates do not include the (much larger)
uncertainties from calibration and model errors, but illustrate the
statistical power of combining *G* functions. Our statistical approach
to the age determination problem is well suited for the mass treatment
of data resulting from large-scale surveys such as the Gaia mission.

**Key words:**stars: fundamental parameters

**--**stars: evolution

**--**solar neighbourhood

**--**methods: data analysis

**--**methods: statistical

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*ESO 2005*