Dynamical model of Praesepe and its tidal tails

TL;DR

This work presents a tailored dynamical model for the Praesepe open cluster using direct N-body simulations on an eccentric Galactic orbit to reproduce Gaia EDR3-observed mass profile, stellar mass function, and mass segregation. The best-fitting model (BFSR) assumes an initial mass of $7500\,M_\odot$, global star formation efficiency $\mathrm{SFE}_{\mathrm{gl}}=17\%$, a concentrated, near-supervirial initial state, and a broken-power-law IMF with breaks at $0.5$ and $1.5\,M_\odot$, without primordial binaries. Tidal tails extending ~1 kpc show vertical orbital oscillations and asymmetric vertical thickness; crucially, tail self-gravity dominates the angular-momentum evolution of tail stars, leading to typical $\Delta L \approx 1.6$ kpc km s$^{-1}$ and a guiding-radius offset of ~7 pc, with up to 70% of angular-momentum change arising from tail interactions. The study also provides sky-prediction maps for tail stars, aiding Gaia DR3 identifications, and highlights the importance of tail self-gravity and epicyclic/vertical motions for interpreting open-cluster tidal features in the Galactic potential.

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%. About 75% of the initially 7500 MSol are lost in the violent relaxation phase, and the observed mass segregation can be understood by two-body relaxation. 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. This corresponds to an offset in guiding radius of 7 pc, where tail stars contribute up to 70% to the alteration. 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.

Figures (12)

• Figure 1: Mass functions of the BFSR (solid blue histogram) and the observed cluster (solid red histogram) together with a fitted three-part power law (dotted lines in blue and red). Further, the course of the Kroupa IMF Kroupa2001 (dashed green) and the used IMF for the BFSR (dashed orange) are shown with an arbitrary scaling for good visibility. The completeness limit is marked by the black line. We emphasise that unresolved binary systems in the real cluster have not been taken into account in the models. This can lead to a significant bias Kroupa1991Wirth2024.
• Figure 2: Top panel: Orbit of the simulated cluster in the $X$--$Y$-plane. The black cross marks observed position of today. Bottom panel: Motion of the cluster centre in the $Z$--$\phi$-plane.
• Figure 3: Evolution of Jacobi mass, M$_J$, and ratio of half-mass radius to Jacobi radius, $\lambda$, as a function of age. Top panel: M$_J$ for the BFSR (blue) and the COSR (red). Bottom panel: $\lambda$ for the BFSR (blue) and the COSR (red). The observed values at $708\, Myr$ are marked with a black cross. The data of the BFSR are shown until the cluster dissolves after 1.53 Gyr.
• Figure 4: Three panels depicting cumulative mass profiles of stars at $708 \, \mathrm{Myr}$ under different scenarios: BFSR (solid blue), observational data (solid black), and ensemble averages from multiple simulations with varied parameters (dashed red with $1\,\sigma$ uncertainty in grey). Top and centre panels: Stars above the completeness limit derived from a random realisation of the distribution of initial coordinates and velocities, as well as the IMF, respectively. Bottom panel: Extended to all stars, averaging all 15 simulations. It also shows the Jacobi mass, M$_\mathrm{J}$(r), as a function of the Jacobi radius (by inverting Eq. (\ref{['eq:jacobi_radius']}), dotted green).
• Figure 5: Mass segregation represented by the cumulative mean mass profile of stars above the completeness limit at $708 \, \mathrm{Myr}$: from the BFSR (solid blue), from the observation (solid black), the average of 15 different simulations with different random seeds for the coordinate and velocity distribution or IMF (dashed red), and their $1\,\sigma$ range (grey area). The lighter shades of grey represent the lower number (only $\sim$4 -- 5) of simulations, which had stars inside that radius from the cluster centre.