All Figures

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f01.eps}\end{figure}$ Figure 1: HR diagram showing the location of two hypothetical observations at $(\log T_{\rm eff},M_V)=(3.825,~3.0)$ and (3.800, 3.0), with nominal uncertainties as in Sect. 2.5 (error bars show ${\pm } 1\sigma$ ). The zero-age main sequence (ZAMS) and selected isochrones for $\log(Z/Z_\odot)=-0.2$ ( ${\simeq} \mbox{[Me/H]}$ ) are also shown. The symbols along the isochrones show where the initial mass is a multiple of $0.01~{\cal M}_\odot$ . See text for further explanation.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f02.eps}\end{figure}$ Figure 2: Plot of the relative posterior probability density, $G(\tau )$ , for the observed data point ( $\mbox{[Me/H]}=-0.2$ , $\log T_{\rm eff}=3.800$ , M_V=3.0). The three curves are for the nominal uncertainties (thick solid line), half the nominal values (dashed) and twice the nominal (dotted); see Sect. 2.5. The vertical bars indicate the ages for the three isochrones in Fig. 1 that go though the observed data point.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f03.eps}\end{figure}$ Figure 3: Representative locations in the HR diagram used in the Monte Carlo experiments (Sect. 3.6) to test the validity of the approximation (14). The isochrones are for $\zeta =-0.2$ and $\tau =0$ , 1, 2, $\dots~$ , 8, 10, 12 and 15 Gyr. The points at the centres of the error ellipses indicate the true observational data, to which independent Gaussian errors are added with nominal errors. Note the behavior of the points marked A, B, C and D in Fig. 4.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f04.eps}\end{figure}$ Figure 4: Results of the Monte Carlo experiments described in Sect. 3.6. Each circle represents the statistics from 1000 experiments. The ordinate is the fraction of experiments in which the true age falls within the confidence interval defined by $G_{\rm lim}$ . The solid curve is the relation expected if $-2\ln G$ follows the chi-square distribution with 1 d.o.f., Eq. (14). The experiments follow the theoretical relation rather well except those for the points marked A, B, C and D in Fig. 3.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f05.eps}\end{figure}$ Figure 5: HR diagram for the synthetic sample of 2968 stars generated as described in the text. The assumed observational uncertainties in $\log T_{\rm eff}$ and M_V are indicated in the lower-left corner (in addition there is a $\pm$ 0.1 dex uncertainty in metallicity). The isochrones are for 0, 1, 2, ..., 8, 10, 12 and 15 Gyr.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f06.eps}\end{figure}$ Figure 6: Same as Fig. 5 but showing only the data for the 937 stars with well-defined ages according to the criterion in Sect. 3.6. Large dots show the subset having a relative precision ( $\epsilon$ ) in age better than 20%.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f07.eps}\end{figure}$ Figure 7: Estimated ages for the synthetic sample of 2968 single stars (same as in Fig. 5) compared with the true values. From left to right, the mean, median or mode of the G function was taken as an estimate of the stellar age.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f08.eps}\end{figure}$ Figure 8: Estimated ages (using the mode of G) for the synthetic sample of 937 stars with well-defined ages, compared with the true ages. The left panel is for single stars (same sample as in Fig. 6); for the middle and right panels secondary components have been added with two different mass-ratio distributions (see Sect. 3.8 for details).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f09.eps}\end{figure}$ Figure 9: Same as Fig. 8 but for the subsample with relative uncertainty $\epsilon \le 0.2$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2185f10.eps}\end{figure}$ Figure 10: Histogram of the age error for binary systems, when their ages are determined from the integrated photometry as for single stars. The full line is for a decreasing mass-ratio distribution (see text), the dotted for equal-mass binaries. The bin size is 0.25 Gyr.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f11.eps}\end{figure}$ Figure 11: A comparison of our age estimates and confidence intervals with those of Lachaume et al. (1999) for a sample of nearby stars. Only the stars with well-defined ages from both sources have been included.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f12.eps}\end{figure}$ Figure 12: HR diagram for 23 stars in IC 4651, together with isochrones at $\mbox{[Me/H]}=+0.1$ for the best-fitting age 1.56 Gyr (solid line), and for 1.3 and 1.9 Gyr (dashed). The symbols are: filled circles - well-defined ages with $\epsilon \le 0.2$ (as in panel c of Fig. 13); open circles - well-defined ages with $\epsilon >0.2$ (panel b); crosses - not well-defined ages (panel a).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f13.eps}\end{figure}$ Figure 13: Panels a)- c) show the G functions for the 23 stars in Fig. 12, subdivided according to the quality of the age estimates: a) - not well-defined; b) - well-defined with $\epsilon >0.2$ ; c) - well-defined with $\epsilon \le 0.2$ . Panel d) shows the product of all 23 G functions, normalized to G=1 at the mode. This combined G function gives an estimated cluster age of $1.56 \pm 0.03$ Gyr.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f14.eps}\end{figure}$ Figure 14: HR diagram for 412 stars in the M 67 region, together with isochrones at $\mbox{[Me/H]}=0.02$ for 4.05 Gyr (solid line), 3.4 and 4.9 Gyr (dashed line). The symbols are: filled circles - well-defined ages with $\epsilon \le 0.2$ (as in panel c of Fig. 15); open circles - well-defined ages with $\epsilon >0.2$ (panel b); crosses - not well-defined ages (panel a); small dots - no solution by Eq. (12).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f15.eps}\end{figure}$ Figure 15: A random selection of some 50 G functions for the M 67 data, subdivided according to the quality of the age estimates as in Fig. 13. The combined G function in panel (d) gives an estimated cluster age of $4.05 \pm 0.05$ Gyr.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f05.eps}\end{figure}$	Figure 5: HR diagram for the synthetic sample of 2968 stars generated as described in the text. The assumed observational uncertainties in $\log T_{\rm eff}$ and M_V are indicated in the lower-left corner (in addition there is a $\pm$ 0.1 dex uncertainty in metallicity). The isochrones are for 0, 1, 2, ..., 8, 10, 12 and 15 Gyr.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f06.eps}\end{figure}$	Figure 6: Same as Fig. 5 but showing only the data for the 937 stars with well-defined ages according to the criterion in Sect. 3.6. Large dots show the subset having a relative precision ( $\epsilon$ ) in age better than 20%.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f07.eps}\end{figure}$	Figure 7: Estimated ages for the synthetic sample of 2968 single stars (same as in Fig. 5) compared with the true values. From left to right, the mean, median or mode of the G function was taken as an estimate of the stellar age.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f08.eps}\end{figure}$	Figure 8: Estimated ages (using the mode of G) for the synthetic sample of 937 stars with well-defined ages, compared with the true ages. The left panel is for single stars (same sample as in Fig. 6); for the middle and right panels secondary components have been added with two different mass-ratio distributions (see Sect. 3.8 for details).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{2185f09.eps}\end{figure}$	Figure 9: Same as Fig. 8 but for the subsample with relative uncertainty $\epsilon \le 0.2$ .
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2185f10.eps}\end{figure}$	Figure 10: Histogram of the age error for binary systems, when their ages are determined from the integrated photometry as for single stars. The full line is for a decreasing mass-ratio distribution (see text), the dotted for equal-mass binaries. The bin size is 0.25 Gyr.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f11.eps}\end{figure}$	Figure 11: A comparison of our age estimates and confidence intervals with those of Lachaume et al. (1999) for a sample of nearby stars. Only the stars with well-defined ages from both sources have been included.
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=-90,width=8.6cm,clip]{2185f12.eps}\end{figure}$	Figure 12: HR diagram for 23 stars in IC 4651, together with isochrones at $\mbox{[Me/H]}=+0.1$ for the best-fitting age 1.56 Gyr (solid line), and for 1.3 and 1.9 Gyr (dashed). The symbols are: filled circles - well-defined ages with $\epsilon \le 0.2$ (as in panel c of Fig. 13); open circles - well-defined ages with $\epsilon >0.2$ (panel b); crosses - not well-defined ages (panel a).
Open with DEXTER

$\begin{figure} \par\includegraphics[angle=-90,width=8.7cm,clip]{2185f15.eps}\end{figure}$	Figure 15: A random selection of some 50 G functions for the M 67 data, subdivided according to the quality of the age estimates as in Fig. 13. The combined G function in panel (d) gives an estimated cluster age of $4.05 \pm 0.05$ Gyr.
Open with DEXTER