New rotation periods in the open cluster NGC 1039 (M 34), and a derivation of its gyrochronology age ^*,**

¹ Hōkū Ke`a Observatory, Department of Physics & Astronomy, University of Hawai`i at Hilo, 200 West Kawili Street, Hilo, HI 96720, USA e-mail: david.james@hawaii.edu
² Department of Physics & Astronomy, Vanderbilt University, Box 1807 Station B, Nashville, TN 37235, USA
³ Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, USA
⁴ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
⁵ United States Naval Observatory, Flagstaff Station, 10391 West Naval Observatory Road, Flagstaff, AZ 86001-8521, USA
⁶ Astronomy Department, Indiana University, Swain Hall West 319, 727 East 3rd Street, Bloomington, IN 47405-7105, USA
⁷ Department of Physics & Astronomy, Johns-Hopkins University, Baltimore, MD 21218, USA
⁸ Department of Physics and Astronomy, 1 College Circle, SUNY Geneseo, Geneseo, NY 14454, USA

Received: 18 August 2009
Accepted: 16 March 2010

Abstract

Aims. Employing photometric rotation periods for solar-type stars in NGC 1039 [M 34], a young, nearby open cluster, we use its mass-dependent rotation period distribution to derive the cluster's age in a distance independent way, i.e., the so-called gyrochronology method.

Methods. We present an analysis of 55 new rotation periods, using light curves derived from differential photometry, for solar type stars in the open cluster NGC 1039 [M 34]. We also exploit the results of a recently-completed, standardized, homogeneous BVIc CCD survey of the cluster, performed by the Indiana Group of the WIYN open cluster survey, in order to establish photometric cluster membership and assign  colours to each photometric variable. We describe a methodology for establishing the gyrochronology age for an ensemble of solar-type stars. Empirical relations between rotation period, photometric colour and stellar age (gyrochronology) are used to determine the age of M 34. Based on its position in a colour-period diagram, each M 34 member is designated as being either a solid-body rotator (interface or I-star), a differentially rotating star (convective or C-star) or an object which is in some transitory state in between the two (gap or g-star). Fitting the period and photometric colour of each I-sequence star in the cluster, we derive the cluster's mean gyrochronology age.

Results. Of the photometric variable stars in the cluster field, for which we derive a period, 47 out of 55 of them lie along the loci of the cluster main sequence in and  space. We are further able to confirm kinematic membership of the cluster for half of the periodic variables [21/55], employing results from an on-going radial velocity survey of the cluster. For each cluster member identified as an I-sequence object in the colour-period diagram, we derive its individual gyrochronology age, where the mean gyro age of M 34 is found to be 193 ± 9 Myr.

Conclusions. Using differential photometry, members of a young open cluster can be easily identified in a colour–magnitude diagram from their periodic photometric variability alone. Such periodicity can be used to establish a period-colour distribution for the cluster, which for M 34, we have used to derive its gyrochronology age of 193 ± 9 Myr. Formally, our gyro age of M 34 is consistent (within the errors) with that derived using several distance-dependent, photometric isochrone methods (250 ± 67 Myr).