1 Introduction

Stock 2 is an open cluster situated in the Orion spiral arm almost in front of the double cluster h & $\chi$ Persei. The nominal cluster centre as given by Lynga ([1987]) is $\alpha\left(1950\right)=2^{\mbox{h}}11.4^{\mbox{m}}$, $\delta\left(1950\right)=59^{\circ}2'$ (or $l=133.4^{\circ}$, $b=-1.9^{\circ}$). It was discovered by Stock ([1956]) from a study of photographic plates taken at the Warner and Swasey Observatory, who originally estimated the distance of the cluster to be $\sim 300$ pc, corresponding to a distance modulus of m-M=7.5. Results from UBV photoelectric photometry by Krzeminski & Serkowski ([1967]) agreed with this distance, and they found a mean reddening of E_B-V=0.375. More recently, Piskunov ([1980]), using existing photometry, redetermined the ages and distances of 68 open clusters. For Stock 2, he found the age to be 100 Myr, and the distance modulus to be m-M=7.4. In a study of the integrated parameters of open clusters, Pandey et al. ([1989]) also lists details of Stock 2, viz. a distance of m-M=8.36 and a reddening of E_B-V=0.30, using the age as determined by Piskunov. The large differences in distance moduli are due to a mixture of apparent and true distance modulus. In the most recent study on Stock 2, Robichon et al. ([1997] and [1999]) derived cluster membership of 5 stars using Hipparchos data, and concluded a cluster age of 170 Myr. We have chosen to adopt the closer cluster distance (m-M=7.4). The faintest cluster member detected by these studies has a magnitude of $V\sim 12$. To date, there have been no studies of the lower mass cluster members.

This paper is the fourth in a series devoted to finding low mass cluster members in nearby (<400 pc) open clusters. Previous papers discussed the open clusters NGC 5460 (Barrado & Byrne [1995]), IC 2602 (Foster et al. [1997]) and IC 2391 (Rolleston & Byrne [1997]). As a consequence of the proximity of these open clusters, and the intrinsic faintness of late-type stars, it is difficult to separate cluster members from the field dwarfs and giants. To date, we have found member candidates by comparing CCD colour magnitude diagrams with theoretical isochrones. Radial velocities and spectral classification cannot be used as a first approach because of the large number of contaminating objects. X-ray studies have been used to identify cluster members (see Randich et al. [1995]; Prosser et al. [1995]). However, this method introduces a bias towards active stars (Jeffries & Tolley [1998]). In this paper, we demonstrate the effectiveness of combining proper motion data with CCD photometry to select cluster members. An established list of cluster members at the faint end of the main sequence is essential for studies of luminosity functions, the evolution of lithium abundance (e.g. Jeffries [1997]), and the evolution of angular momentum (e.g. Stauffer et al. [1997]).

Section 2 describes the CCD photometry and Sect. 3 the proper motion data and reduction. The method used for identifying cluster members is described in Sect. 4.