Isochrone-cloud fitting and asteroseismology of the Kepler open cluster NGC6866

Abstract

We investigate how isochrones computed with different input physics and initial conditions affect the age dating of the open cluster NGC 6866, and compare the results with asteroseismic ages derived from Kepler photometry. Using Gaia DR3 data, we identified 180 cluster members with a clustering algorithm. We then developed an isochrone-cloud fitting method that accounts for a range of free parameters in the input physics. Variable stars were subsequently identified among the cluster members. For 19 g-mode pulsators, we carried out modelling with a dedicated grid of rotating stellar models, constrained by spectroscopic and photometric parameters, the asymptotic gravity-mode period spacing, and the near-core rotation rate. We considered two cases: modelling each pulsator individually and modelling them under the assumption of a common cluster age. PARSEC and MIST isochrones yield discrepant ages of 690 and 467 Myr, respectively. The isochrone-cloud fit indicates an initial critical rotation distribution peaking at 0.6, about a factor of two higher than inferred from asteroseismology. The seismic modelling shows agreement between seismic and isochronal masses, but substantial differences in the derived ages due to differences in internal mixing. When the g-mode pulsators are modelled with a shared cluster age, we obtain 759 Myr, consistent with the PARSEC isochronal age. We conclude that age dating of open clusters is sensitive to the adopted input physics and initial conditions, highlighting the need for better calibrated stellar evolutionary models.

Figures (18)

• Figure 1: Clustering algorithm results for membership identification. The left and middle panels show the median and standard deviation of membership probabilities for all stars within the radius cut. The shaded region indicates the selected members with $p>0.8$. The right panel displays the colour-magnitude diagram (CMD) of NGC 6866, where the coloured markers represent the 180 identified member stars, and the grey markers correspond to field stars. The colour of each marker indicates the median membership probability. The grey vertical line represents the colour index cut for variability identification.
• Figure 2: Colour-magnitude diagrams illustrating the comparison process using a binned multiplicative sum. The grey dashed lines in both panels represent the binning grid used in our fitting. The left panel shows a synthetic CMD using the MIST isochrone grid. The input parameters are derived from the best-fitted MIST isochrone cloud. The colour code represents the initial critical rotation of the star. The markers in the right panel show the observational CMD. The grey markers represent photometric binaries and a blue straggler star, removed before the fitting. The red polygon highlights the removed stars near the eMSTO. The colour code on the right panel represents the weight of each box, equal to the product of the number of observed stars $N_\mathrm{obs}$ and the number of synthetic stars $N_\mathrm{synth}$.
• Figure 3: Best-fit isochrone cloud parameters for NGC 6866 using the PARSEC (left) and MIST (right) isochrone models. The upper panels display the corner plots of age and $A_0$, and the lower panels show the distribution of initial critical rotation.
• Figure 4: Synthetic CMDs based on the best-fit age, extinction ($A_0$), and initial rotation distributions. The left and right panels show the results for the PARSEC and MIST isochrone models, respectively. In each panel, the black markers represent the observed single stars in NGC 6866, while the coloured markers represent the synthetic stars. The colour of the synthetic stars indicates their initial rotation, the same as in Fig \ref{['binning']}. The grey dashed line marks the initial mass of the isochrone.
• Figure 5: The pulsating blue straggler star with g-mode pulsations KIC 8264293 in NGC 6866. Panel (a) shows its amplitude spectrum calculated from the Kepler light curve. Panel (b) is the zoomed-in period-amplitude diagram of its period spacing pattern. The blue dotted lines mark the fitted $l=1$ pulsation periods. Panel (c) displays the location of KIC 8264293 in the CMD of NGC 6866, marked by a red cross. The grey dots are the cluster members, with black crosses marking all the identified g-mode pulsators.