2021AJ....161..101S

We present an investigation of NGC 2158 using Gaia DR2 data. We identified 800 most likely cluster members with membership probability higher than 90%. The mean proper motions of this object are determined as (µ_x = -0.203 ± 0.003, µ_y = -1.99 ± 0.004) mas yr^–1. The limiting radius, log(age), and distance of the cluster are obtained as 23.5 arcmin, 9.38 ± 0.04 Gyr, and 4.69 ± 0.22 kpc, respectively. The overall mass function slope (0.93 ± 0.14) is flatter than the Salpeter value (1.35) within the mass range of 1.17-1.44 M_☉. This cluster also shows the mass-segregation effect and our study demonstrates that NGC 2158 is a dynamically relaxed open cluster. Using the apex diagram (AD), the apex coordinates of the cluster are obtained in different ways and are examined using the (µ_U,µ_T) diagram. The best value of the apex coordinates is determined as A = 87.°24 ± 1.°60, D = -36.°61 ± 5.°30. We also determined the orbit of the cluster and found that NGC 2158 moves almost in the solar antapex direction. The resulting spatial velocity of NGC 2158 is 51 km s^–1. A significant oscillation along the Z-coordinate up to 529 pc is detected. Various scenarios regarding the origin of this cluster are also discussed.