Convective overshoot mixing in old open clusters

THE ASTROPHYSICAL JOURNAL, 193: 109-111, 1974 October 1 © 1974. The American Astronomical Society. All rights reserved. Printed in USA. CONVECTIVE OVERSHOOT MIXING IN OLD OPEN CLUSTERS M. J. PRATHER* AND P. DEMARQUE Yale University Observatory Received 1974 April 4 ABSTRACT A simpliﬁed form of overshoot mixing of convective cores in intermediate-mass stars (0.90—1.40 9139) is investigated in order to explain the anomalous gap structure of M67. The amount of overshooting is assumed to be proportional to the pressure scale height at the convective core boundary, and the entire region is com- pletely mixed. Evolutionary tracks are computed for both standard and overshoot models, and isochrones are constructed. In the presence of overshoot mixing, the isochrones show (1) a higher gap, (2) a lower stellar number density immediately above the gap, and (3) the persistence of the gap to greater ages. Subject headings: convection -— interiors, stellar —— open clusters — stellar evolution Attempts to ﬁt open clusters with theoretical iso- chrones (Sandage and Eggen 1969; McClure, For- rester, and Gibson 1974) have been moderately successful with the notable exception of M67 (Racine 1971; Demarque 1973). Torres-Peimbert (1971) has examined M67 with respect to standard models and has found that (i) the gap in M67 is much too high relative to the most luminous K subgiants in the cluster and (ii) the density of stars immediately above the gap is much lower than expected. Since M67 is the only well-observed representative of its age group, we shall assume that these properties are typical of an old open cluster that shows a well-deﬁned gap. We must look for an effect which is maximal for masses characteristic of the stars near the M67 turnoff, but which is negligible for more massive or less massive stars. This paper examines the result of a convective over- shoot mixing proportional to the pressure scale height at the edge of the convective core as postulated by Roxburgh (1965). Although Saslaw and Schwarz- schild (1965) have shown that energy transport by convective overshooting in the deep interiors is negli- * Summer Research Assistant, Kitt Peak National Observa- tory, operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation. gible, recent work by Shaviv and Salpeter (1973) demonstrates that the time-average amount of such overshooting may be signiﬁcant. We shall ignore any energy transport by the overshooting elements, but shall be concerned only with the mixing beyond the core boundary which is affected by it. This overshoot mixing should be thought of as random overshooting elements which mix hydrogen-rich material into the hydrogen-depleted core. This type of mixing, as is pointed out by Shaviv and Salpeter (1973), is effectively realized only over a time scale much longer than the convective time scale of the core. The greatest amount of such mixing will occur in stars with convective cores with low masses which have longer nuclear time scales. Higher-mass stars will be affected less for two reasons. (i) The shorter main-sequence lifetimes will reduce the total number of overshooting elements and thus the amount of mixing. (ii) The total amount of material within a pressure scale height above the convective boundary is roughly constant. Hence, an overshoot mixing pro- portional to the pressure scale height will have a pro- portionally lesser effect on stars with larger convective cores. The lower-mass stars with no convective cores will not be affected. The stellar models were calculated with the Yale evolution code which was revised in order to calculate I I I I I I I SYIODIO lﬂﬂ. M bol | I PIRIIX I 0.15 3.3 '°9 Teff FIG. 1. —Evolutionary tracks in the (Mm, log Tm)-plane. The standard sequence of tracks for masses 0.90-1.40 9R9 is on the left; the overshoot-mixed models with Pm“, = 0.15 for masses 1.05-1.40 9220, on the right. 109 © American Astronomical Society - Provided by the NASA Astrophysics Data System