A complete N-body model of the old open cluster M67

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here, we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 36 000 stars (12 000 single stars and 12 000 binaries) and a total mass of nearly 19 000 M-circle dot placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced to 2000 M-circle dot as a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations, although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions (LFs) are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function (IMF) is lost, both from the current LF and from the current mass fraction in white dwarfs (WDs). The model contains 20 blue stragglers (BSs) at 4 Gyr, which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of BSs in M67. The evolution and properties of two-thirds of the BSs, including all found in binaries, have been altered by cluster dynamics and nearly half would not have formed at all outside the cluster environment. On the other hand, the cluster environment is also instrumental in destroying potential BSs from the primordial binary population, so that the total number is in fact slightly smaller than what would be expected from evolving the same binary stars in isolation.