Dynamical model of Praesepe and its tidal tails

¹ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstraße 12-14, 69120 Heidelberg, Germany
² Nicolaus Copernicus Astronomical Centre Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland
³ Fesenkov Astrophysical Institute, Observatory 23, 050020 Almaty, Kazakhstan
⁴ Main Astronomical Observatory, National Academy of Sciences of Ukraine, 27 Akademika Zabolotnoho St., 03143 Kyiv, Ukraine
⁵ Physics Department, Nazarbayev University, 53 Kabanbay Batyr Ave. 010000 Astana, Kazakhstan
⁶ Heriot-Watt International Faculty, K. Zhubanov Aktobe Regional University, 263 Zhubanov Brothers str., 030000 Aktobe, Kazakhstan
⁷ Energetic Cosmos Laboratory, Nazarbayev University, 53 Kabanbay Batyr Ave. 010000 Astana, Kazakhstan

^★ Corresponding author: just@ari.uni-heidelberg.de

Received: 25 July 2024
Accepted: 3 September 2025

Abstract

Context. The dynamical evolution of open clusters in the tidal field of the Milky Way and the feeding of the disc field star population depend strongly on the initial conditions at the time of gas removal. Detailed dynamical models tailored to individual clusters help us understand the role of open clusters in the Galactic disc evolution.

Aims. We present a detailed dynamical model of Praesepe, which reproduces the mass profile, the stellar mass function, and the mass segregation observed with the help of Gaia EDR3 data. Based on this model, we investigate the kinematic properties of the tidal tail stars in detail.

Methods. We used direct N-body simulations along the eccentric orbit of Praesepe in the tidal field of the Milky Way, where each particle represents one star. The initial mass and size of the cluster, the dynamical state, and the initial mass function were adapted to reach the best-fitting model. Based on this model and a comparison model on a circular orbit, we analysed the stars in the tidal tails in terms of density, angular momentum, and orbit shapes.

Results. Praesepe can be well reproduced by a cluster model with concentrated star formation in a supervirial state after instantaneous gas expulsion, adopting a global star formation efficiency of 17%. However, the mass distribution inside the cluster is highly sensitive to the random initialisation. About 75% of the initially 7500 M_⊙ are lost in the violent relaxation phase, and the observed mass segregation can be understood by two-body relaxation. The tidal tails have a length of about 1 kpc and show a vertical oscillation along the cluster centre’s orbit, which leads to temporal asymmetries in the tidal tails vertical thickness. As a major result, we find that the self-gravity of the tail stars is the dominant force altering the angular momentum of the tail stars. For a typical star, the total change after escaping is about 1.6 kpc km s⁻¹. This corresponds to an offset in guiding radius of 7 pc, where tail stars contribute up to 70% to the alteration. Additionally, the epicyclic motion leads to an increasing width of the tidal tails. The total radial shift of the orbit of the cluster in the Galactic plane can exceed 50 pc. This effect is not a result of the eccentricity of the orbit.